Liquid‐Core Optical Fibers—A Dynamic Platform for Nonlinear Photonics

Softphotonics has emerged as a new discipline that utilizes soft matter (i.e., liquids, gels, bio‐materials) as waveguide materials with versatile functionalities. The flexible properties of soft matter show great potential for further exploiting nonlinear in‐fiber phenomena to gain more insights into their fundamental dynamics and to inspire a new generation of broadband optical light sources and signal processors that are adaptable, reconfigurable, and biocompatible. In particular, incorporating solvents with extraordinary temperature sensitivity, miscibility, and nonlinearity into optical fibers has spawned a series of inventions and fundamental scientific findings over the last decades. This review highlights the current state of development of nonlinear photonics in liquid‐filled fibers. The current state of knowledge in the linear and nonlinear material properties of the most prominent solvents (CS2, CCl4, C2Cl4, benzene and its derivatives) are revisited, and recent advances in nonlinear liquid‐core fiber optics, including a special highlight on phenomena that are unique to liquids, such as modified solitary states and local dispersion control are summarized. Finally, the leading scientific challenges for advancing the field, which highlights liquid‐core fibers as a rich platform for science and technology, are discussed.


DOI: 10.1002/lpor.202300126
waves. Yet, as we continue to exploit the entire spectrum of optical properties of those materials, we have reached the application boundaries of those platforms. Hence, the search is open for other material classes for advancing optical sciences and technologies. In this development, liquids-the natural hosts of life and chemistry-emerged as an innovative platform for fundamental and applied optics. In particular, the research field of nonlinear optics has progressed significantly with fundamental studies on the unique molecular properties and interaction dynamics liquids have to offer. [1][2][3] Since the 70s, pioneers of the fiber optics community have been interested in the application potential arising from incorporating liquids into optical fibers. Already in 1972, a series of publications reported on high-throughput optical transmission through carbon chlorides acting as core liquid infiltrated in glass and quartz capillaries [4][5][6][7][8] with recordlow losses down to 10 dB km −1 (i.e., for hexachlorobuta-1,3-diene at 1.05 μm operation wavelength. [4] ) In the following years, operation in the visible, ultraviolet, [9] and mid-infrared [10][11][12] spectral regimes was demonstrated, too, and first linear liquid-core devices were proposed. Some of the most notable demonstrations in the linear operation regime of the 2000s include all-fiber or microscopic dye lasers, [13][14][15][16] temperature controllable spatial and spectral filters, [17,18] dispersion compensation fibers, [19] in-fiber polarizers, [20] and highly sensitive absorption, [21,22] Raman, [23] temperature sensors, [24] refractive index sensors, [25][26][27][28] and in-fiber cytometers. [29] Meanwhile, a significant increase in available laser power also opened the nonlinear optical regimes for hybrid material fibers. Along with recent developments on gas-filled hollow-core fibers for high-power applications [30,31] and soft-glass fibers (i.e., fibers made from heavy-atom glass frameworks with low transition temperatures) for highly nonlinear applications, [32][33][34] liquid-core optical fibers (LCF) have gained substantial interest. To date, experimental work demonstrating broadband supercontinuum generation has been conducted across the whole landscape of known nonlinear operation regimes. [35] The most common nonlinear regimes are depicted in Figure 1a with pulse width and fiber dispersion being the key parameters. The markers indicate the operational regimes of a few examples of experimental work conducted in liquid-core optical fibers with the premise of generating broadband spectra. The achieved bandwidths for the se-Fiber types (marker shape) step-index fiber photonic crystal fiber hollow-core fiber  Fiber types (line style) step-index fiber photonic crystal fiber hollow-core fiber Figure 1. Selected nonlinear optical experiments in liquid-core fibers with a focus on broadband frequency generation. a) The experiments are ordered accordingly to the fiber dispersion at their respective pump wavelength and to the pump pulse width, which allows grouping them according to the dominant broadening processes. Each marker contains information about the core liquid (corresponds to marker color) and the fiber type (corresponds to marker style) used in the experiment, as specified in the legend above. b) An overview of the achieved spectral coverage in the experiments is mentioned in (a). Information about the core liquid and fiber type used in the experiment is encoded in the line style and the line color (see legend in (a)), respectively. Note that in both panels, an asterisk (*) marks the work which uses liquids in the fiber cladding rather than as core medium.
Laser Photonics Rev. 2023, 17,2300126 lected cases are shown in Figure 1b over power. Incorporating liquids as nonlinear core material generally has unique features for each regime, which we will outline in detail later in this review. This review provides the necessary literature and a comprehensive toolbox for entering the field of nonlinear liquid-core fiber optics that is, "nonlinear soft photonics." We start with an overview of the material systems and fiber designs most commonly used in current experimental demonstrations (Section 2). We then summarize the best practices in modeling nonlinear light propagation in liquid-core waveguides in Section 3. This is followed by the main chapter, where we outline the advances in nonlinear light generation in liquid-core fibers over the last 50 years (Section 4). This chapter is thoughtfully structured accordingly to the dominant nonlinear effects in specific operation domains (i.e., fiber dispersion and pulse width). Particular emphasis is put on the unique properties of the liquids, such as enhanced Raman scattering or high nonlinearity, which will be explained and discussed concerning their specific benefits for selected nonlinear processes like supercontinuum generation. Here, we also highlight the one-of-a-kind application potential of liquids by recalling recent observations of modified solitons, external control over nonlinear conversion dynamics, and core reconfigurability. The review finishes with a comprehensive conclusion and outlook in Section 5.
We like to emphasize that this review article covers mainly experimental demonstrations in nonlinear fiber optics. It is hence complementary to other reviews in the field of hybrid-material fiber that mainly cover the linear operation regimes in fibers [36][37][38][39] or that put a particular emphasis on photonic-crystal fibers. [40]

Typical Selection Criteria for Optical Liquids
Nonlinear optics in liquids is a broad field with a long history. The variety of liquids suitable for optics in the visible (VIS) to near-infrared (NIR) seems large. However, demands on chemical, physical, and optical properties already exclude a large part of liquid candidates. Most works focus on water or liquid carbonates, sometimes referred to as organic solvents, with simple molecular structures. From the perspective of liquid-core fibers, the following selection criteria should be considered for the design and implementation: i) Data availability: Studying nonlinear light generation requires extensive knowledge of the material's dispersion, absorption, and nonlinearity over a large bandwidth. There are many potentially transparent and nonlinear liquids (e.g., inorganic solvents such as Ge-/Si-Cl 4 ) for which, however, this data is not provided. ii) High transparency: Effective light propagation along centimeters of the optical fiber requires low losses (<1 dB cm −1 ), which is generally not given in complex organic molecules with numerous C−H, C−O, or O−H bonds. Thus, longchained alkanes, alcohols, aromatics, esters, and oils (such as the well-characterized Cargille oils [134]) might still well be suited for the visible domain but cannot be used in the near-infrared. Even some simple molecules, such as water, may inhibit optical operation in the infrared but might open a considerable window in the ultraviolet. [41] iii) Suitable refractive index for silica fibers: Liquids, such as short-chained alkanes, alcohols, liquid fluorides (e.g., perfluorohexane C 6 F 14 , hexafluorobenzene C 6 F 6 ), and some polar solvents (e.g., acetone, water) have a refractive index lower than silica, which prevents light guidance in silica capillarytype fibers, representing the mostly used type of LCF. More complex fiber structures, such as microstructured hollowcore fibers, are required to host those fluids, which might add to costs and handling difficulties. iv) Low toxicity: Health and safety concerns play an essential role in working with solvents, such as aromatics (i.e., benzene and benzene derivatives), which are considered genetically harmful and carcinogenic. Thus, potentially highly nonlinear and transparent but volatile solvents such as bromides (e.g., bromoform CHBr 3 ), iodides (e.g., methyl iodide CH 3 I), or arsenides (e.g., carbon diselenide CSe 2 , arsenic trichloride AsCl 3 ) are often not considered in optical sciences. However, optical fibers usually contain only nanoliters of filling volume, and experimental precautions (e.g., small dead volumes, sealed sample mounts etc.) can be taken to ensure the acceptable safety limits constituted by law (e.g., see Table 1). v) Other physical properties: Viscosity, boiling point, and vapor pressure impact the ease of handling a liquid and may considerably alter the filling properties into fiber compartments. Still, various liquids across a range of physical properties could be utilized in nonlinear optical experiments. The details of a few common candidates are listed in Table 1.

Attenuation
Classical optical devices are subject to efficiency and bandwidth limitations imposed by the attenuation of their incorporated  Attenuation spectra in the vis to NIR of a) carbon disulfide, b) tetrachloroethylene, c) carbon tetrachloride, d) chloroform (and its deuterated counterpart), e) toluene (and its deuterated counterpart), and f) nitrobenzene (and its deuterated counterpart). a,b) Reproduced with permission. [46] Copyright 2018, Optica Publishing Group. c) Reproduced with permission (while the crosshatched domain was not measured in the data source). [43] Copyright 2012, Optica Publishing Group. d-f) Reproduced with permission. [44] Copyright 2017, Optica Publishing Group.
materials. The need for integrated optical sources and waveguides operating in the NIR and mid-infrared (MIR) triggered substantial research in glass chemistry with a strong focus on fluoride (F) and chalcogenide (S, Se, Te) compound glasses. Those so-called soft glasses enabled low-loss operation up to 5 μm wavelength (e.g., for ZrF 4 -BaF 2 -LaF 3 -AlF 3 -NaF composition, also called ZBLAN glass, or for ZnTe glass) and even beyond in case of some special chalcogenide compounds (e.g., As 2 S 3 ). [42] Many materials of the same chemical classes are in the liquid phase and largely overlooked for advanced optical applications in the N/MIR, although they promise similar transmission as their amorphous partners. One main reason for such missing impact is a lack of quantitative models with dB m −1 accuracy for the individual liquid's absorption. Only a few works exist where transmission along centimeters of propagation through low-loss liquids was measured so that attenuation values in applicationready units (e.g., dB cm −1 ) could be given. [43][44][45] Moreover, most loss studies exclude the domain between 1.7 and 3 μm due to the sensitivity limits of the used spectrometers or spectrophotometers.
With the change in molecular structure, the loss characteristics of liquids are fundamentally different from amorphous solid materials. In particular, the electronic and molecular optical transitions of liquid molecules are narrower due to reduced inhomogeneous broadening. Thus, absorption lines in simple (i.e., short-chained) binary molecular liquids generally appear sparse and narrow, opening numerous optical operation regimes. For instance, a larger range of halides (i.e., binary compounds containing F, Cl, Br, I) is reported in the literature with expansive transmission windows from the VIS to the MIR. In the scope of this review, we would like to highlight the current state-ofthe-art in attenuation measurements of two main classes of liquids: a) low-loss chalcogenide and halide liquids (i.e., CS 2 , CCl 4 , C 2 Cl 4 , Cl 3 CH, and b) common benzene derivatives (i.e., C 7 H 8 , C 6 H 5 NO 2 ). Figures 2 and 3 summarize the available attenuation data for those liquids in the vis-NIR and the MIR domain, respectively.
The challenge in measuring liquids with such high transparency lies in finding an appropriate method that allows accurate, spectrally broadband referencing as well as light propagation through meter-long samples. Kedenburg et al. (and similar work [44][45][46] ) used cuvettes and long tubes (up to 1 m length) sealed with 1 mm thick silica windows. [43] The transmitted spectrum of the tube was measured using a broadband white-light source (e.g., Yokogawa AQ4305, or NKT SuperK) and a fiber-coupled spectrometer at the output. Stability of both optical source and sample, broadband beam collimation, and accurate data corrections (e.g., by accounting for wavelength-dependent reflection coefficients of the silica windows as well as for residual chromatic beam divergence) are essential and determine the sensitivity limit of the setup (note the discrepancy in the sensitivity limits of the CCl 4 measurement in Figure 2c, being at approximately 0.01 dB m −1 , [43] and of the C 2 Cl 4 /CS 2 measurements in Figure 2a,b, being at approximately 2 dB m −1 ). [46] As impurities of the liquid composition play a significant role in the maximally achievable transmission, all measurements used neat liquids with at least 99.9% purity.
Such setups revealed transmission properties of CS 2 and chlorides (see Figure 2) that outperform benzene derivatives in the NIR domain considerably while showing comparably low attenuation in the vis. Comparing the attenuation of CCl 4 and CHCl 3 , the deteriorating impact of CH bonds becomes apparent. [47] The overtones of the CH-stretching and the CH-deformation modes dominate the spectrum and drastically reduce the transmission properties of CHCl 3 in the NIR domain. The use of CHCl 3 for LCF design is therefore limited for applications in the NIR. . Attenuation spectra in the MIR of a) carbon disulfide, b) tetrachloroethylene, and c) carbon tetrachloride, and d) bromoform. Reproduced with permission. [45] Copyright 2022, Optica Publishing Group. However, the work by Plidschun et al. has shown that this limitation can be eased using the deuterated counterparts of the liquid. [44] Deuteration is the chemical process that replaces covalently bonded hydrogen atoms in a molecule with deuterium atoms (i.e., heavy hydrogen). The increase of the atom mass leads to a red-shift of the dominant molecular resonances, which significantly reduces the losses in the NIR domain. [47] This effect has been quantified for chloroform, toluene, and nitrobenzene (Figure 2d-f).
Noteworthy, the refractive index models of the non-deuterated compounds still serve as a good approximation since the change in refraction with deuteration is of the order 10 −3 or less (e.g., measured at 1064 nm [48] ). The impact of deuteration on the refractive index is, therefore, negligible for most fiber designs, where the cladding index is in the order of 10 −1 − 10 −2 lower than the core liquid.
Further advances in attenuation studies require: 1) solvents of even higher purity (beyond the commonly available ≥ 99.9%); 2) degassing techniques; [49] 3) novel, reliable measurement techniques, for example, using meter-long liquid-core fibers [22,50] or broadband cavity ring-down methods; [51,52] and 4) extending the scope of studies to other attractive candidates for highly transparent light guidance, such as Ge-/Si-Cl 4 or liquid chalcogenides. In particular, the safety of working with liquids of even higher toxicity might be well enabled through in-fiber techniques, which require tiny liquid amounts in the order of micro-to nanolitres.
requires precise knowledge of the refractive index (RI) dispersion of the liquids used. The RI dispersion of liquids was investigated over the past 80 years with a strong emphasis on carbon disulfide and organic solvents such as chloroform and benzene. [53][54][55] This research focus has provided a solid database that made these liquids the most important candidates for integrated nonlinear optofluidics today. In contrast, other promising candidates (e.g., C 2 Cl 4 [46] and CBrCl 3 [45] ) were disregarded. In particular, the seminal works by Samoc et al. [56] and Kedenburg et al. [43] have provided a solid basis for dispersion data that enabled a new generation of dispersion models for a variety of common, optics-friendly liquids. Those models have been either based on Cauchy's equation with the real refractive index n, and the expansion coefficients A n , or a Sellmeier equation [57]  In most previous works [43,56,58] the Cauchy model or a singleterm Sellmeier equation (i.e., Equation (2) with m = 1) was used. Both models do not account for the strong molecular absorption in the MIR wavelength domain and are often insufficient for a physically meaningful extrapolation of the RI beyond the NIR. As a consequence, these models provide an incomplete description of the spectral distribution of the group-velocity dispersion (GVD), which is particularly relevant in the context of nonlinear photonics with ultrashort pulses. For instance, in the case of CS 2 , both literature models deviate from the measured RI data beyond 2 μm in Figure 4a, with the consequence of a largely different zero-dispersion wavelength (ZDW) in Figure 4b. This is why larger sets of published RI data have been reanalyzed over the last years [46,59] to obtain new dispersion models for four selected, highly transparent solvents. A two-to threeterm Sellmeier equation (i.e., Equation (2) with m = 2, 3) was chosen as a model function to fit collected RI data from multiple sources (see Table A1, Appendix for model parameters). The overall good match between the data and the model fits in Figure 4, confirms how the new models account for the first strong molecular resonance in the MIR, for example, at 6.6 μm for CS 2 , or at 12.8 μm for C 2 Cl 4 . Moreover, the resonance frequency and amplitude of the first model term (i.e., UV term) differ only slightly from those reported by Kedenburg et al. for CS 2 , CCl 4 , and CHCl 3 . [43] The strong impact of the second Sellmeier term on the position of the ZDW makes the multi-term Sellmeier equations essential for accurate fiber design, as well as simulations of wavelength ranges across the entire NIR domain. However, it shall be noted that the multi-term fitting is only possible for liquids with high transparency and a significant amount of RI data. In the case of Benzene and derivatives, the multiple strong resonances in the NIR make a proper multi-term fitting extremely hard. Here, we still added the commonly used Cauchy models to Figure 4e,f for completeness and ease in comparison to the other solvents.
Liquid Mixtures: One clear advantage of liquids is their miscibility, which allows for adjusting the optical properties of the corresponding liquid mixture. The miscibility of two liquids compounds depends on multiple parameters but most prominently on their permanent dipole moment. One general mixing rule is that liquids with similar dipole moments mix well as soon as no other forces (e.g., hydrogen-bridge bonds) hinder them. [65] Assuming perfect miscibility, the RI of a multi-component mixture changes in response to the new composition of the molecular ensemble. There are multiple models to calculate the RI of the composition (a compact overview can be found in [65,66] ), which all work similarly well in the case of liquid compounds with similar molecular mass. The most general model is based on the assumption of a linear combination of individual molecular polarizabilities. This model is known as Lorentz-Lorenz model [67,68] with the volume of the individual liquids V k and the volume of the final mixture V. The Lorentz-Lorenz model generally remains valid for liquid compounds with entirely different molecular masses as well as all high-density media. The refractive index in Equation (3) might be assumed weakly imaginary so that the rule can be extended to include weak absorption as recently proposed. [69]

Thermodynamic Dispersion Model
The RI of all materials strongly depends on the electron configuration of the atoms and molecules of the material, which is again influenced by the thermodynamic environment (i.e., temperature and pressure). As a consequence, the RI depends on temperature and pressure, known as thermo-optic and piezo-optic effects. Liquids feature two to three orders of magnitude stronger temperature dependence of their RI than glasses. Also, against the common belief that liquids are incompressible, the RI depends on the local pressure (or molecular density), which can be controlled by the environment to a certain extent. Both dependencies can be described in first approximation with a simple linear perturbation term [62] n( , T, p) = n 0 ( ) + n T with n∕ p| T 0 ,p 0 as piezo-optic coefficient (POC) and n∕ T| T 0 ,p 0 as thermo-optic coefficient (TOC) at room temperature T 0 = 293 K and atmospheric pressure p 0 = 10 5 Pa.
The TOC and POC, if even known, are mostly treated wavelength independent and constant in first approximation. This Figure 5. Dispersion of the TOC for various liquids. Measured TOC data of CS 2 (various marks) from collaborative work with Pumpe et al., [75] various sources, [78][79][80][81][82] excluding two points in the VUV, along with the novel thermo-optical Sellmeier dispersion model (solid line). Adapted with permission. [76] Copyright 2018, Optica Publishing Group. For completeness, the plot includes the dispersive TOC estimates for methanol, CCl 4 , benzene, and toluene, marked with an asterisk (*), as shown in ref. [58]. Since the origin of those mathematical models is unknown, these data can only serve as a tentative estimate. treatment might cause significant inaccuracies in modeling broadband nonlinear effects as well as multi-spectral applications. In particular, ultrafast phase-matched processes depend on higher-order derivatives of the RI (e.g., group velocity or group velocity dispersion), which are not affected by constant offsets of the RI caused by the linear TOC and POC treatment in Equation (4). A change of RI with temperature (or pressure) is significantly stronger in the vicinity of an electronic resonance (i.e., absorption line) than far away from it. Thus, the change of the material dispersion with temperature and pressure must be assumed wavelength-dependent in general. For silica, it is known that such dependence can be expressed accurately via temperaturedependent Sellmeier coefficients. [70,71] Such models are yet missing for most optical liquids and solid materials, hampering advances in unveiling the true tuning potential of liquid-core nonlinear devices.
The spectral distribution of the TOC has only been determined for a few selected solvents. [58,[72][73][74] Still, the physical models assumed here do not justify an extension of the validity domain beyond the visible. To address this problem, Pumpe et al. investigated the wavelength dependence of TOC (and POC) for selected solvents based on broadband measurements. [75] In particular, the data of CS 2 , shown in Figure 5a allowed to construct a partial temperature-dependent Sellmeier model [76] n( , T) = The related temperature-dependent Sellmeier coefficients in Table 2 allow us to accurately describe the impact of temperature on the RI dispersion of CS 2 from ultraviolet to NIR wavelength. The data did not cover the entire MIR range, the impact of which is however significantly weaker (i.e., B 2 ≪ B 1 ). Figure 5 illustrates the wavelength dispersion of the TOC model alongside  the underlying TOC data of CS 2 and models of other groups of liquids. It shall be noted that the database for the other models is rather sparse, and thus predictions based on those models should be handled with care. In general, the POC has to be considered wavelengthdependent and potentially even nonlinear. [77] While the fit procedure used to retrieve temperature-dependent Sellmeier coefficients can, in principle, be applied to the POC, too, the POC of CS 2 is only known for three wavelengths. Hence, the current data basis is too sparse for a trustworthy fit and only allows using the standard linear approximation from Equation (4) in Equation (5) to date.
In conclusion, the extended database of the RI from UV to MIR for multiple temperatures and pressures makes CS 2 the most well-known solvent for nonlinear liquid photonics so far. Recent findings regarding broadband dispersion design of LCFs in combination with thermodynamic tunability (see Section 4.3.2) clearly demonstrate the scientific potential that follows from accurate material models and should motivate further research in material sciences to fill knowledge gaps for other promising liquid candidates for nonlinear softphotonics (e.g., C 2 D 5 OH, CCl 4 , CBrCl 3 , C 2 Cl 4 , CSe 2 , SiCl 4 ).

Nonlinear Refraction
Liquids feature a nonlinear optical response considerably more complex than glasses. In general, the transient nonlinear polarization of a material can be expressed in the form of the nonlinear refractive index (NRI) and the nonlinear optical response function (NRF) R( ). In rather static molecular networks, such as crystalline and amorphous solids, the nonlinear optical response originates mainly from the electrons, and only by small parts (<20%) from ultrafast molecular vibrational (i.e., Raman) modes. Moreover, in silica, the response time of the Raman response is about 32 fs, and can thus be assumed (quasi-)instantaneous for most applications of picosecond to nanosecond pulsed sources. [83,84] In liquids, the molecular motions are caused by induced dipole moments following the incident field polarization, leading to a relatively slow nonlinear response in the order of picoseconds. This response can be understood as an inelastic scattering process and is hence of dissipative nature. For more than four decades the nonlinear optical response of liquids has been studied in the light of their unique non-instantaneous response (e.g., refs. [85][86][87][88]). However, first in 2014, an accurate multi-term model for the NRF of CS 2 was presented by Reichert et al., [89] which enabled the calculation of the NRI in dependence of pulse width, field polarization, and wavelength. Follow-up work was published shortly after by Zhao et al. [90] and Miguez et al. [91] Their works have established a quantitative model to estimate the pulse-width dependent nonlinearity n 2,eff of selected liquids, which is of key importance for realistically simulating nonlinear optical pulse propagation through LCFs. Here, the NRI of liquids is calculated by where n 2,el is the electronic NRI, n 2,m is the NRI associated with the molecular nonlinearities, andR(t) is the natural (not normalized) NRF of the liquid response. Equation (6) incorporates the general molecular dynamics induced by an excitation pulse with intensity distribution I(t). It is paramount to emphasize that n 2,eff strongly depends on the pulse width and shape. Most numerical studies to date do not involve this important dependency, which causes, for example, an overestimation of the liquid's nonlinearity in the femtosecond pulse regime up to two orders of magnitude.
The NRF model, as introduced by Reichert et al. [89] considers the total nonlinear response as with the sum over k accounting for each of the molecular processes, that is, diffusive reorientation (d), collision (c), or libration (l). Each response term r k is normalized to ∫ r k (t)dt = 1 and weighted by a process-specific NRI n 2,k . The full nonlinear material response, including the instantaneous, electronic term, can thus be written R(t) = n 2,el (t) +R(t). Figure 6a shows all response terms and their superposition exemplary for CS 2 , as well as pictograms illustrating the physical origins of the underlying nonlinear mechanisms. It should be noted that Reichert's model does not include other sources of nonlinearity such as electro-or thermostriction, which feature timescales in the order of nanoseconds, or Raman scattering. For comparison, Raman is added here to the Reichert model terms in Figure 6, with an amplitude estimate based on linear Raman scattering measurements of selected solvents and silica (reference). As obvious from the optical response spectrum in the inset of Figure 6, the Raman line of CS 2 (i.e., at 19 THz, ≈660 cm −1 ) is relatively distant and is only relevant for pulses shorter than 60 fs. However, the situation can be substantially different in the case of other molecules with resonances closer to the pump, such as CCl 4 or all kinds of Benzene derivatives. Here, an extension of the Reichert model is required in future studies to accurately include these vibrational molecular motions.
Because of their different molecular shape, the dominating nonlinear processes and, thus, the individual nonlinear response may vary drastically for all liquids. Figure 7 shows the nonlinear response of selected solvents taken from refs. [90,91], and the resulting n 2,eff in dependence of the pulse width of a sechpulse. Also, the pulse-width dependence of the molecular fraction f m = n 2,m ∕n 2,eff is presented-an analog to the Raman fraction f R often used on literature, which describes the molecular contribution to the total NRI.
The decay times of the response functions in Figure 7b are characteristic of the molecular shapes of the liquids. For   Table A2 of the Appendix. c) The molecular fraction over the half-power pulse width. The legend in (a) applies to all curves in each panel. The dotted curves in (c) include the Raman terms for CCl 4 and C 2 Cl 4 in the NRF.
instance, CCl 4 features a quasi-isotropic molecular shape, and its nonlinearity is dominated by instantaneous electronic excitation with small contributions from intermolecular dipole-dipole interactions and intramolecular vibrational Raman oscillations. Its NRF does not feature reorientation or libration components (i.e., n 2,d = 0 and n 2,l = 0 [90] ), but shows a rather fast dynamic. The response of CCl 4 can therefore be seen as quasi-instantaneous due to its small molecular contribution (e.g., f m = 0.18, i.e., 18% for a pulse width of 300 fs). Consequently, the effective NRI of CCl 4 varies only weakly between pulses of different widths.
In contrast, C 2 Cl 4 , for example, is a prolate molecule such as CS 2 , which causes an intensity-dependent anisotropy based on molecular reorientation in a linearly polarized light field. The resulting response in Figure 7b shows that C 2 Cl 4 has a highly noninstantaneous temporal response (e.g., with a comparably large molecular contribution of f m = 67% in case of a 300 fs excitation  Step-index fiber for liquids with RI above silica. Reproduced with permission. [59] c,d) Selectively filled photonic crystal fiber for liquid with RI similar to silica. Reproduced with permission. [108] e,f) Hollow-core fiber for liquids with RI below silica. Reproduced with permission. [109] g) A typical setup for mounting LCFs, consisting of two sealed optofluidic mounts on a rail. Reproduced with permission. [110] a,b) Reproduced under terms of the CC-BY license. [59] Copyright 2017, The Authors, Published by Nature Publishing Group. c-g) Reproduced with permission. [108][109][110] Copyright 2010, 2012, 2020, Optica Publishing Group. pulse), that is slightly lower than highly noninstantaneous CS 2 . Thus, the effective NRI of C 2 Cl 4 increases drastically for increasing pulse width, as shown in Figure 7a.
Notably, most prolate-type molecules allow reaching large molecular fractions beyond 85% for picosecond pulse widths. Such high molecular contributions are unique for liquids and might allow enhanced nonlinear functionalities observed in other Raman-driven systems, such as pronounced Raman redshifts in gas-filled fibers. [94] To date, only a few studies investigated the special impact of the slow nonlinearities of liquids on in-fiber light propagation. Novel nonlinear dynamics have been identified, such as reduced spectral broadening with increasing molecular fraction, [95] the formation of unconventional, solitonlike optical features, [96,97] and lower noise vulnerability of soliton fission. [59] Those particular results are reviewed in Section 4.3.1.

Step-Index Fiber
Liquid-filled fiber-type glass capillaries-representing the simplest fiber designs-offer a great platform for initial studies on nonlinear light propagation. Their simplicity in waveguide geometry and fabrication allows for: i) accurate modeling of fiber designs, ii) straightforward sample fabrication, also in large batches, and, as a consequence, iii) good reproducibility of samples and experimental data.
The typical configuration is based on silica glass capillaries of core diameters between 2 and 10 μm filled with a high-index liquid as core medium (cf. Figure 8a,b). The fabrication of such capillaries is well-controllable and has been well-exploited for liquid-and gas-chromatographic purposes, hence leading to vast commercial accessibility. However, it should be noted that commercial capillaries for chemical use may incorporate glasses of minor optical quality. Hence, capillaries drawn in state-of-the-art fiber drawing facilities may become a prerequisite for reaching meters of propagation lengths, as they feature much higher transmission efficiencies.
Filling of capillaries is commonly realized using capillary force with filling times of minutes to hours [98] and, thus, is relatively effortless as soon as the capillary is appropriately mounted. Capillary mounting in a sealed, work-safe fashion has been demonstrated in several ways including, for example, optofluidic mounts [10] (cf. Figure 8g) and microfluidic platforms, [99] splicing techniques on fibers with side-wall openings, [100] or 3D-printed fiber-to-capillary interconnections. [101] In particular, (fusion or mechanical) splicing of the LCFs with single-mode glass fibers opens up the path to integrated, compact, and practical liquidbased light sources [13] and hosts a plethora of new opportunities to grow as new functional, easy-to-integrate fiber device for sensing, and signal processing applications. [102] Step-index fibers come with the benefit of accurate design and modeling capabilities at low computational costs. The liquid/glass interface is defined more accurately than for usual all-glass fibers, in which diffusion of dopants can wash out boundaries. The effective refractive index of the transverse optical modes of cylindrical fibers can be calculated semi-analytically from a transcendental dispersion relation (see relevant literature such as books by Snyder and Love, cf. chapter 12, or more recently by Yeh and Shimabukuro, cf. chapter 5). In general, the dispersion and the zero-dispersion wavelength (ZDW) of step-index fibers can be tuned remarkably by varying the core diameter. The allowed range of core diameters for a given wavelength is limited Laser Photonics Rev. 2023, 17,2300126 www.advancedsciencenews.com www.lpr-journal.org by the V-parameter V = k 0 R × NA, with the vacuum wave number k 0 , the core radius R and the numerical aperture of the fiber NA. The V-parameter should be chosen such that V c < V to avoid scattering and bending losses. The critical guiding limit V c must be found empirically and usually lies between 1 and 1.5. Also note that V ≤ 2.405 denotes the criterion for single-mode operation.
Another important design parameter for nonlinear fibers is the nonlinear parameter , which can also be calculated semianalytically for step-index fibers. [103] As the nonlinear parameter is intrinsically dependent on the effective mode field diameter, it varies as a function of the core diameter and coarsely follows the single-mode criterion. [103] With these numerical tools at hand, the ease of fabricating and modeling step-index LCFs has led to numerous experimental demonstrations over the last decade, that benefited considerably from the accurate match between experimental data and simulations.
On the downside, step-index LCFs only give limited access to anomalous dispersion (AD) or flat, near-zero all-normal dispersion regimes, which are both especially attractive for broadband supercontinuum generation and soliton studies. Bulk liquid solutions possess ZDWs well in the mid-infrared domains (i.e., 2 μm). In LCFs with neat CS 2 or C 2 Cl 2 as core liquids, ZDWs between 1.75 μm and above are achievable for the fundamental mode (i.e., HE 11 ) at reasonable core diameters of 2-10 μm. [46,59] Mixed core compositions allow further index suppression, reaching ZDWs below 1.5μm. [104,105] We also like to emphasize that some higherorder modes (e.g., TM 01 , TE 01 , or HE 21 ) also feature significantly lower ZDWs than the corresponding fundamental mode. [106,107]

Selectively Filled Photonic Crystal Fibers
Photonic crystal fibers (PCFs) are well known for their design flexibility by providing additional degrees of freedom, such as air-hole size and lattice pitch, granting extended control over the dispersion profile of fibers. Here, guidance is realized either through complex interference effects (e.g., photonic bandgap or anti-resonant effects) or a suppressed effective cladding index. Infiltration of certain liquids into the air holes allows for combining the excellent design flexibility of PCFs with the unique properties of liquids (such as MIR transparency, high nonlinearity, and high thermo-optical coefficient), providing an excellent platform for studying nonlinear light propagation in optical fibers. Liquidfilled PCFs allow access to the dispersion landscapes, which are inaccessible to step-index LCFs (e.g., access to the AD regime at 1550 nm). Moreover, liquid-filled PCF also provides control over the mode field diameter hence enabling accurate tuning of the fiber's nonlinearity.
However, while many advantages have been proposed theoretically in numerous publications, practical demonstrations in liquid-filled PCFs are still challenging due to the complexity of the sample preparation. Two main strategies were proposed: liquidcore waveguiding in PCFs selectively filled with high-index liquids and silica-core waveguiding in PCFs filled with low-index liquids.
Vieweg et al. has demonstrated nonlinear spectra broadening using a PCF selectively filled with high-index toluene or CCl 4 , [111] forming liquid-core fibers with suppressed cladding index. Twophoton direct laser writing was used to selectively block the holes of the PCF, which should remain empty. Complicated design patterns such as checker-board have been demonstrated, emphasizing the design flexibility of the proposed method. This principle also allows multi-core designs of PCF as experimentally demonstrated using CCl 4 . [108,112] One key advantage of liquid-filled PCFs is that they also allow utilizing low-index liquids to exploit their temperature tuning capabilities while guiding the light still in a silica core. Velazquez-Ibarra et al. demonstrated widely tunable four-wave mixing (FWM) exploiting ethanol-infiltrated PCF. [113] Note that ethanol has a lower refractive index than silica. The ethanolfilled holes hence act as temperature-tunable suppressed effective cladding.

Hollow-Core Fibers with Liquid-Core
Hollow-core fibers (HOFs) are a special class of microstructured fiber that usually features a very high fraction of air in the cladding and a core with a much larger diameter than the cladding holes. Guidance is often realized through complex interference effects such as the anti-resonant (Kagome-style or antiresonant reflecting optical waveguides) or photonic band gap effect. HOFs with liquid in the central core have attracted significant interest due to several advantages, such as control over dispersion design parameters and modal characteristics in combination with high transparency and nonlinearity. The air cladding even allows to host liquids with lower refractive index than silica, for example, water with a refractive index of 1.33 (at = 589 nm).
Several techniques have been proposed to isolate the cladding holes of HCFs from the core hole for capillary-effect-based filling. Similar to PCFs, two-photon direct laser writing can block the cladding holes to ensure the filling of the central hole only. This method is most flexible for utilizing different HCF structures but requires exact control across the fiber facet. [111] Another technique is the so-called injection-cleaving method which relies on exploiting different filling speeds of different hole sizes (i.e., larger channels fill faster). In this method, [114] UV-curable glue is filled in the HCF under UV radiations to block cladding holes allowing for filling the central hole with a liquid of choice. Note that this principle is only applicable when the size of the core hole is significantly different from the cladding holes due to the different collapsing rates. Moreover, this technique suffers from the lack of availability of suitable UV-curable glue with an appropriate refractive index (comparable or lower to silica) and mid-infrared spectral transparency. Wang et al. also proposed selective filling of HCF into any desired pattern using a focused ion beam to mill microchannels on the facet of the HCF, [115] which, however, remains to be very time and resource intensive.
Presumably, the most popular and straightforward technique is collapsing the cladding holes of the HCF using a controlled splicer arc. This technique is swift and versatile but requires significantly larger core sizes than the cladding holes due to the mentioned different collapsing rates of core and cladding holes. [109,[116][117][118] The simplicity of the splicer-collapse method made it the method of choice in multiple experimental demonstrations. Bozolan et al. exploited this technique for the first time for supercontinuum generation in water-filled HCFs. [116] Their HCF featured a core diameter of 10.7 μm and a cladding with 2.2 μm hole pitch and 1.9 μm hole diameter. Due to the high filling fraction in the cladding (about 70%), the effective refractive index of the cladding is sufficiently low to ensure light guiding through total internal reflection in the water core. The ZDW of this sample was upshifted to 1066 nm, where Q-switched and mode-locked lasers are commercially well available. A similar experiment has been conducted by Bethge et al. [109] with a different water-filled HCF (9.5 μm core diameter, 2.75 μm pitch, and 2.68 μm cladding hole diameter) featuring a ZDW at 985 nm.
Exploiting the same principle of sample preparation (i.e., hotsplice collapse), Hoang et al. demonstrated an all-normal dispersive HCF with a 12 μm large core infiltrated with toluene. [119] The absolute dispersion values varied between -150 and -5 ps/nm/km for the 1-2 μm spectral range. In a few other experiments, Hoang, Van Le et al. also presented several HCF designs infiltrated with CCl 4 showing flat normal dispersion in a broad spectral range (i.e., 0.8-1.7 μm [120] and all-normal up to 2.5 μm [121] ).
Notably, all above-mentioned experiments use large core sizes (9-12μm) filled with liquids of reasonable RI, for example, water, toluene, and CCl 4 . In order to exploit other liquids with higher refractive indices, such as CS 2 or nitrobenzene, lower core sizes are needed to ensure single (or few) mode guidance. Recently, Junaid et al. demonstrated an HCF with a core size of 3.2 μm infiltrated with CS 2 shifting the ZDW toward telecommunication wavelengths (i.e., 1500-1600 nm) while remaining single (or few) mode operation. [118]

Best Practice in Modeling Nonlinear Pulse Propagation
This section is dedicated to a brief discussion regarding the modeling of nonlinear pulse propagation through liquid-core waveguides. A large part of contributions to the current field of nonlinear liquid-core fiber optics is based on novel dispersion designs as well as simulations of the impact of such dispersion on the spectral broadening efficiency. Few of these works have led to fundamental insights into the novel nonlinear dynamics caused by the special optical response of liquids. [59,96,108,[122][123][124][125][126] Moreover, multiple dispersion studies promise spectral broadening into the MIR, watt-level supercontinua, ultra-flat all-normal dispersive broadening, and more, all based on the added functionality of the liquid.
However, a majority of those numerical studies are based on insufficient models, which will unlikely hold their predictions. Overall simplifications or overly exceeding extrapolations of the liquid absorption, dispersion, or nonlinearity lead to false conclusions and wrong impressions. What is missing is a common standard in the numerical modeling of liquid-core waveguides.
Hence, in what follows, we like to provide a step toward such a standard by outlining a state-of-the-art nonlinear Schrödinger equation that allows realistic, reliable predictions.
The main challenge in modeling liquid-core systems is the incorporation of all fiber parameters over a broad spectral range. Moreover, involving the precise nonlinear temporal response is essential to cover the full nonlinear dynamics when the system is excited with sub-picosecond to nanosecond pulses. The bandwidth demands of the problem can be covered by the general-ized nonlinear Schrödinger equation (GNSE) in the frequency domain (similar to ref. [127]) with the spectral field amplitude of a single spatial modeÃ (in units of √ W ), the broadband absorption coefficient , the propagation constant , the modified nonlinear gain parameter̄= k 0 n 2 ∕A 1∕4 eff , the convolution operator [ * ], and the inverse Fourier transform operator  −1 . In general, the effective mode area A eff ( ) must be considered to be frequency-dependent, too. The NRF R(t) = (1 − f m ) (t) + f mR (t) accounts for both the instantaneous electronic response and the molecular responseR(t) from Equation (7) (here normalized to ∫ dtR = 1) with the molecular fraction f m = n 2,m ∕n 2,eff . Note that, the presented definition of the dispersion operator i[ ( ) − 0 − 1 Δ ], does not necessitate a Taylor expansion as used in many other works. However, to account for the slowly varying envelope approximation in the co-moving time frame of the propagating pulse, the carrier phase constant 0 and the group velocity parameter 1 must be subtracted from the propagation constant . Also noteworthy, the normalization of the fieldÃ incorporates the frequencydependent (effective) mode area used in the temporal convolution since the temporal envelope is now defined as A(z; t) =  {Ã(z; )∕ 4 √ A eff }. This normalization is often forgotten in the recent literature but was explicitly proposed as correction, for example, by Laegsgaard. [128] While Equation (8) represents the most physical variant of the nonlinear Schrödinger equation, it just solves the propagation of a single spatial mode in linear polarization. Further extensions are required to involve higher order modes, as well as the degenerate (orthogonal) polarization of each mode. [129] In particular, the degenerate polarization of each mode might play a decisive role in nonlinear pulse propagation as the cross-polarization component of the third-order susceptibility (i.e., (3) xy ) is non-zero in highly noninstantaneous liquids. [89,130] This leaves room for future studies in order to show extraordinarily strong nonlinear polarization rotations in non-birefringent waveguides. A consistent treatment of polarization modes in modeling polarization maintaining LCFs has been recently presented by Wang et al. [131] Yet, further improvements of the GNSE model are required to include a cross-polarization nonlinear parameter (i.e., a separate related to (3) xy ) that is treated differently from the commonly used single-polarization nonlinear parameter̄.

Nonlinear Optics in Liquid-Core Fibers
The past decade has seen an increasing interest in nonlinear optics in LCFs. This section briefly summarizes the achievements in each nonlinear operation domain outlined in Figure 1 and finishes with a special section dedicated to novel phenomena which can be observed solely in liquid-core fibers to that extent. Rev. 2023, 17, 2300126 www.advancedsciencenews.com www.lpr-journal.org

Stimulated Brillouin Scattering
Stimulated Brillouin scattering (SBS) is a fundamental consequence of molecular electrostriction (i.e., the change of the electronic environment through the optically induced displacement of ions) and causes a highly material-specific nonlinear scattering effect (i.e., frequency red-shift) mediated by the coupling between optical and traveling acoustic waves. Liquids allow for alteration of the interaction of optical and acoustic waves, and hence the strength and spectral characteristics of the Brillouin gain, over a wider range owing to their thermodynamic properties. Most intriguingly, liquids, other than solids, do not feature internal strains or any mechanical coupling to their containment (e.g., the capillary or HCF). This limits the set of available acoustic modes and allows efficient high-finesse coupling to the remaining modes. [132] While SBS has been identified to be particularly pronounced in bulk liquids (e.g., water and benzene [133] already in the '60s, the effect has not been observed in LCFs for a long time. an SBS shift in large-core LCFs (100-300 μm core diameter) at 7.7 GHz and 2.5 μm threshold energy in a backscattering configuration with up to 90% reflectivity using a 532 nm, 10 ns pulse pump source. [134] Kieu et al. used an amplified continuous-wave pump-probe setup at 1550 nm and small-core LCFs (2 μm core diameter) to identify a Brillouin shift of 2.45 GHz with<KHz linewidth at 100 mW power threshold. [135] Recently, the group has also reported on an unprecedented forward Brillouin scattering gain (i.e., 5.8 W −1 m −1 ) located at a frequency as low as 827 MHz in a tightly confined CS 2 -filled LCFs (1.8 μm core diameter). [136] Today, our advanced understanding of the mechanisms involved with SBS allows us to enter peculiar thermodynamic regimes. In a most recent experimentally study, [102] the authors Geilen and Popp et al. utilized optoacoustic interactions in special fully-sealed CS 2 -filled LCFs to identify different thermodynamic regimes, including the uncommon regime of negative pressures, which was to date only observed in water. [137] Hence, SBS in LCFs appears to offer a vital framework to obtain new insights into the thermodynamic properties of liquids in exotic states, such as superfluidity. [138]

Stimulated Raman Scattering
As liquids intrinsically show much more narrowband but more pronounced Raman lines than amorphous glasses, the implications on in-fiber nonlinear effects related to stimulated Raman scattering are one of the most interesting aspects of liquidcore fiber. LCFs allow harvesting great Raman gain over meters of fiber lengths, only limited by modal attenuation of the used core liquid. In fact, the substantial Raman gain of CS 2 -filled LCFs has led to the very first demonstration of low-power Raman oscillators in the 1970s, [139] years before stimulated Raman scattering (SRS) was discovered in silica fibers. [83,140] This work was followed by demonstrations of Raman amplifiers made of C 2 Cl 4 and CCl 4 mixtures, [141] as well as the first demonstration of continuous-wave-pumped Raman amplification in Benzenefilled LCFs at a record-low power of 100 mW. [142] After a strong focus on fused silica systems, attention has turned back to liquid-core systems due to substantially higher nonlinearity. Kieu and Schneebeli demonstrated five to six very clean Raman orders (pumped at 1030 and 532 nm ns pulses, respectively) in CS 2 with record-low pump thresholds of 1 nJ for the first order. [143] Given the large spectral distance to the first Raman mode in CS 2 of about 660 cm −1 , they achieved a considerably broadened spectral output up to 632 and 1650 nm, respectively. Their experiments in CCl 4 resulted in lower, but still highly-narrowband Raman orders. The efficiency of their system largely benefited from efficient fiber-to-fiber coupling, through which they gained between 20% and 50% device transmission depending on the LCF core diameter used in their experiment (e.g. 2, 5, or 10 μm) (Figure 9a). SRS in LCFs is well known to be useful for efficient spectral broadening. Fanjoux et al., for example, demonstrated an impressive spectral range of eight Raman orders covering about 450 nm in a toluene-filled step-index fiber which has set the current bandwidth record in SRS-based supercontinuum generation in LCF to our knowledge (Figure 9b). [144] They used a 532 nm pulsed pump at an energy of 3 μJ (corresponds to 5 kW peak power). A few years later, the same authors improved the spectral coverage and flatness at much lower pulse energies of about 200 nJ from an 18 ps, 10 Hz pump at 532 nm. [145] Notably, the authors Bouhadida et al. follow another approach for implementing efficient Raman converters with liquids. Their approach builds on the conversion within an evanescent field from a tapered nanofiber emersed in the respective liquid. Highly efficient optical conversion of a sub-nanosecond pump at 532 nm to a yellow Raman signal at 630 nm with 60% photon efficiency has been demonstrated in ethanol. [146] This scheme compares very well with previous results of the group where they demonstrated 67% conversion efficiency in carefully designed photonic bandgap fiber filled with propanol. [147] Yet, the evanescent Raman conversion provides a higher level of reconfigurability as the Raman-active liquid can straight-forward be exchanged.

Four-Wave Mixing and Modulation Instabilities
Four-wave mixing (FWM) in nonlinear optical fibers is an upand-coming platform for tailored nonlinear light generation in a compact and robust format. FWM in optical fibers is a third-order nonlinear optical interaction that takes place among four waves. In a semi-classical picture, this process can be understood such that two photons of pump waves annihilate each other to create a pair of signal and idler photons provided that energy and phase are conserved (i.e., phase-matching condition is fulfilled). In case, no initial seed wave is provided, FWM in optical fibers is driven by noise photons in the input field. Those incoherent photons Figure 9. Stimulated Raman scattering observed from LCFs filled with a) CS 2 (2 μm core, 1 m length, pumped with 500 ps pulses at 532 nm at 1.5 kHz) [143] and b) toluene (8 μm core, 2 m length, pumped with 600 ps pulses at 532 nm at 42.5 Hz). [144] The inset above the left spectrum shows the output mode images behind a dispersive prism. Multiple Raman orders can be observed. In case of toluene, secondary Raman lines can fill up spectral gaps between the main orders, leading to a supercontinuum. a) Reproduced with permission. [143] Copyright 2012, Optica Publishing Group. b) Reproduced with permission. [144] Copyright 2014, Optica Publishing Group. experience nonlinear amplification within the phase-matched domains of the pump leading to ultrafast temporal modulations in the time domain-a process commonly referred to as modulation instability (MI). Yet, MI is mainly known for operating in the anomalous dispersion domain as the process delivers a seed for the disruptive formation of optical solitons (i.e., self-confining nonlinear optical states).
LCF offers a great platform for FWM/MI due to several aforementioned properties of liquids. Most importantly, flexibility in tuning the dispersion of LCFs offers a significant advantage in fulfilling the phase-matching conditions of FWM/MI. In the 1990s, Chen et al. demonstrated for the first time FWM and SRS from LCFs using a mixture of CS 2 and phenyl-ethanol as core liquid. [155] The mixing ratio of the liquids was chosen such that SRS for both liquids can simultaneously occur. The liquid was filled in a 30 m long silica HCF with an inner diameter of 70 μm and pumped with 10 ns pulses at 532 nm, leading to prominent SRS and FWM peaks.
In 2011, Frosz et al. [156] presented a susceptible refractive index sensor for liquids exploiting FWM in liquid-filled microstructured optical fiber (Figure 10c,d). A solid-core microstructured fiber with air-hole cladding, having a ZDW at 1030 nm, is used. The fiber was designed so that the ZDW is close to 1064 nm when filled with liquids, where pump lasers are readily available. Water and methanol were used as filling materials, shifting the ZDW to 1130 nm. Filling liquids changed the effective index of the cladding, leading to a modification of the phase matching condition and, hence, a change of the FWM signal/idler wavelengths. In detail, a shift of 28 nm for a refractive index change of 0.0032 is reported. This corresponds to a sensitivity of 8.8 × 10 −3 RIU nm −1 , which was a new record for fiber sensors at the time the work was published, which could reportedly further be improved to an order of 10 −6 RIU nm −1 .
The flexible tuning capabilities of LCF also allow tuning the FWM-based signal/idler between the Raman bands of liquids ensuring pure Raman-background free signal and idler photons generation. This offers an excellent advantage for entangled photon generation which is of great importance in the field of quantum information technology. [157] Barbier et al. exploited unique Raman properties of liquids that is extraordinarily narrow Raman lines for the generation of Raman-free photon-pair using FWM in liquid-core microstructured fiber. Deuterated acetone was used as a core with a diameter of 12 μm of the fiber with air holes in the cladding (pitch of 4 μm). The fiber was carefully designed so that it was possible to tune the FWM phase-matching such that the photons can be generated outside the thin Raman band of the liquid while pumping at 896 nm. This is not possible with silica fibers due to broad Raman bands of silica glass. The coincidentto-accidental ratio of 63 and pair generation efficiency of 10 −4 was demonstrated. [158] The tuning capabilities of LCFs offer a great advantage to adjust the dispersion and phase-matching for FWM in LCFs to tune signal/idler generation over a wide wavelength range. Wideband spectral-tuning of FWM-based signal/idler in liquidfilled fiber was demonstrated by Velazquez-Ibarra et al. [113] A solid-core microstructured fiber infiltrated with ethanol was used for the generation of FWM using a 1064 nm pump source. The large thermo-optical coefficient of ethanol was exploited to tune the dispersion and FWM phase-matching of the fiber, leading to widely spaced signal/idler generation. Spectral shifts of 175 nm for signal (i.e., 745-920 nm) and 500 nm of idler (i.e., >1750-1260 nm) are observed by changing temperature by 40 • C. These results host great technological potential in CARS microscopy, where the spectral spacing between two intense pump waves needs to be accurately matched to the Raman modes of interest.
Laser Photonics Rev. 2023, 17, 2300126 Figure 10. Examples of four-wave mixing/modulation instabilities in LCFs. a) Tuning of phase matching condition of modulation instability by varying concentration ratio of a binary liquid mixture defined as (V 1 ∕(V 1 + V 2 ) where V 1 and V 2 are the volumes of C 2 Cl 4 and CCl 4 , respectively. b) Experimental demonstration of modulation instability from LCFs filled with a mixture of C 2 Cl 4 and CCl 4 with a concentration ratio of 0.2. c) Phase matching condition of FWM in a solid-core photonic crystal fiber with a cladding filled with either air, water, or methanol. d) Simulation and measurement of FWM signal when using a 1.5 m-long fiber with water-filled cladding. a,b) Reproduced with permission. [105] Copyright 2020, Optica Publishing Group. c,d) Reproduced with permission. [156] Copyright 2011, Optica Publishing Group.
MI in the anomalous dispersion domain may lead to the formation of soliton bursts accompanied by broadband supercontinuum generation (SCG). Recently, Junaid et al. have presented MIbased SCG from step-index LCF using binary mixtures of C 2 Cl 4 and CCl 4 as a core material. By changing the concentration ratio of the mixture, the dispersion of the fiber sample was tuned allowing to probe of different dispersion regimes using a single pump source (e.g., 1555 nm and 900 fs pulse duration as used in ref. [118]). Moreover, remarkable control over FWM and MI is presented by varying the phase-matching as a function of the concentration ratio of the liquids (Figure 10a,b).

Self-Phase Modulation
Self-phase modulation (SPM) is a direct consequence of the nonlinear Kerr effect. As large optical intensities change the refractive index locally, the local optical field is varied in phase, causing self-induced shifts toward lower frequencies on rising pulse edges and toward higher frequencies on falling pulse edges. SPM in liquids, and in particular LCFs, has largely been exploited for spectral broadening due to their large nonlinearity that leads to an enhancement of the effect. Remarkable hundreds of nanometer bandwidths have been demonstrated by Kedenburg et al. and Churin et al. in step-index LCFs with 2-10 μm core size filled with CS 2 . [100,159] The direct dependency between the SPM bandwidth and the nonlinear coefficient has also been utilized to determine the total nonlinear refractive index of liquids, as shown by Phan Huy et al. for acetone and acetone-D6 using microstructured hollow-core LCFs [160] or by Kedenburg et al. for toluene, nitrobenzene, and CS 2 using step-index LCFs. [101] However, it is important to note, that the nonlinear refractive indices retrieved by this method are slightly overestimated when using femtosecond pulses, even though the electronic contribution has been extracted. The long propagation in the highly dispersive LCFs lead to a considerable broadening of the pulse, effectively increasing the impact of the long-lasting molecular orientational contribution to the nonlinearity. Kedenburg was able to partially compensate for this effect by retrieving the molecular fraction f m from carefully matching simulations and experimental data, which allowed to separate the electronic from the molecular contribution. [101] The dissipative nature of the molecular nonlinearity may lead to a further effect that is very characteristic of elongated molecular liquids. The strong noninstantaneous response of such  All pump configurations feature an extraordinarily large molecular nonlinear contribution of f m ≥ 0.7. The spectral bandwidth is drastically enhanced by the strong noninstantaneous nonlinearity of the liquid that leads to pronounced red-shifting soliton-like features driving a strong asymmetric broadening. Those features have not been made explicit in the original papers, yet they share the same distinct spectral characteristics as the states introduced by Karasawa et al. [96] a-c) Adapted with permission. [159] Copyright 2015, Optica Publishing Group. d,e) Adapted with permission. [100] Copyright 2013, Optica Publishing Group.
liquids causes a significant shift of the SPM spectrum toward shorter frequencies. In extreme cases, this enhanced red-shift may further evolve to characteristic temporal spiking events, which are currently subjects of further studies under terms like soliton-like states [96] or concurrent shock-collapse singularities [161] (see also Section 4.3.1). Such nonlinear events may have been the dominant, yet unrecognized cause for the efficient SPM-based supercontinuum generation in CS 2 -filled LCFs observed earlier by Kedenburg et al. [159] and Churin et al., [100] since their measured broadening characteristics (cf. Figure 11a,d) is governed by a very distinct, red-shifted peak.
However, such effects only occur in fibers filled with elongated liquid molecules. Isotropic molecular liquids, such as CCl 4 , instead allow the creation of nonlinear devices with all-normal dispersion characteristics and the familiar broadening behavior that is well-known for glass fibers. For instance, Huang and Van Le et al. have demonstrated efficient broadband selfphase modulation in a widely normal and all-normal dispersion domain, respectively (i.e., from 0.93-2.5 μW at sub-nJ pulse energies). [120,121,162]

Supercontinuum Generation via Soliton Fission
Solitons are analytic solutions of the nonlinear Schrüdinger equation that neither includes Raman nor higher-order dispersion terms. When pumping an optical fiber in a low anomalous dispersion at high powers, the formation of an Nth-order soliton can be perturbed by third-order dispersion and Raman scattering, leading to a break-up of the initial pulse into a series of N fundamental solitons, usually accompanied by dispersive wave radiation to the ND domain. This process is known as soliton fission and is one of the primary broadening mechanisms in soliton-mediated supercontinuum generation pumped by femtosecond pulses. Note that anomalous dispersion is especially hard to achieve in liquids, which commonly are normal dispersive up to the mid-infrared.
Bozolan et al. demonstrated soliton-mediated continuum generation in liquids for the first time in a water-core PCF. Water was chosen as it features comparably large nonlinearity (only 10× lower than CS 2 ), low volatility, and a ZDW around 1066 nm. With a 980 nm pump laser at 60 fs pulse duration, the authors Laser Photonics Rev. 2023, 17, 2300126 Figure 12. Examples for soliton-fission driven supercontinuum generation in various fiber types and core liquids. a,b) High (peak) power soliton fission in water-filled hollow core fibers. Reproduced with permission. [109,116] Optica Publishing Group. The 5-7 cm long structures were pumped at 970 and 800 nm wavelength with 60 and 45 fs pulse width, respectively. c) Soliton fission in a 26 cm long photonic crystal fiber with one cladding air hole being selectively filled with CCl 4 . The fiber was pumped at 1030 nm with 210 fs pulses. Reproduced with permission. [111] Copyright 2010, Optica Publishing Group. d,e) High (average) power supercontinuum generation in a 15 cm long CS 2 -core step-index fiber pumped at 1.95 μm with 110 fs pulses. The inset shows a typical mode profile at the pump wavelength. The long-term stability of the long-wavelength (soliton) side of the spectrum, pumped with 526 mW average power) has been monitored over 24 h in (f) without any significant fluctuation. In the same work, [164] the authors report on a 70 h stable exposure of a CS 2 with up to 1.6 W average power, when a larger core diameter was used (i.e., 20 μm instead of 4.6 μm as in panels (d-f)). Adapted with permission. [164] Copyright 2019, Optica Publishing Group.
demonstrated spectral broadening of about 500 nm at 940 kW of peak power, limited by the strong water absorption beyond 1300 nm. [116] Despite the pump initially operating in the ND, the close proximity to the ZDW led to a combination of rapid SPM and FWM beyond the ZDW, causing soliton fission with clearly distinguishable dispersive wave generation at around 700 nm as indicators of the unnoticed process. In a similar experiment in 2010, Bethge et al. verified soliton fission when they demonstrated two-octave spanning SCG using a water-filled PCF with a ZDW at 985 nm. [109] A pump source at 1200 nm wavelength and 40 fs pulse duration was used, leading to fission-based spectral broadening from 410-1640 nm spectral range. Notably, even though the system was operated significantly beyond the coherence condition (i.e., soliton number N < 15, [163] here N = 29), the average first-order degree of coherence of the supercontinuum output was calculated to be close to ideal (i.e., g (1) = 0.97). Yet, in both experiments, the optical solitons beyond 1300 nm were not clearly distinguishable in the spectrum (Figure 12a,b).
In 2017, Chemnitz et al. presented a detailed study on the impact of the noninstantaneous response of CS 2 on soliton fission and consequently on the noise characteristics of the generated SC spectra. In this work, a CS 2 -filled step-index fiber with ZDW 1.83 μm was pumped in the anomalous dispersive region using a Tm-doped fiber laser with 1.95 μm wavelength and 450 fs pulse duration. Fission-based spectral broadening from 1.0-2.7 μm has been experimentally demonstrated with soliton numbers approaching N = 150. A detailed theoretical study has been performed, demonstrating the impact of non-instantaneous response on the noise characteristics of generated SC spectra and its dependence on the input pulse duration. The authors found that a strong noninstantaneous contribution improves the spectral pulse-to-pulse stability, that is, the first-order coherence, which is lacking in conventional soliton fission in solidcore fibers due to the drastic amplification of input noise for N > 15. [163] This improvement in LCFs has been attributed in the work to the formation of so-called hybrid solitary states, which appear to undergo a fission process known from conventional Kerr solitons, yet feature a notably different spectro-temporal and noise characteristic similar to the one of previously predicted noninstantaneous solitons. [122] Additional theoretical and experimental work is required to reveal the full nature of those hybrid solitary states and a potential link to the theory of shock-collapse singularities. [161] Further studies, however, necessitate better accessibility to the AD domain www.advancedsciencenews.com www.lpr-journal.org for a wider range of laser sources in order to mitigate the equipment constraints (and costs) of Thulium-doped fiber lasers and respective diagnostics. Three approaches were currently demonstrated to grant this access to more cost-effective Erbium-doped fiber laser technologies: 1) In a work from 2010, Vieweg et al. succeeded to excite soliton fission with spectrally clearly distinguishable dispersive waves and solitons in a PCF selectively filled with carbon tetrachloride. [111] Indeed, light guidance in low-refractive carbon tetrachloride is challenging in step-index fiber, especially when the core size is meant to be kept small to maximize the nonlinear parameter. Suppression of the cladding index by the microstructure of PCFs has allowed Vieweg et al. to still achieve effective light guidance in 2.5 μm-wide liquid cores and to observe soliton-mediated spectral broadening by pumping the anomalous dispersion domain with a 210 fs pulses at 1030 nm wavelength ( Figure 12c). 2) Robust guidance in anomalous dispersion of a fundamental mode around 1560 nm has been achieved by carefully lowering the refractive index of the core medium by optimizing the concentration of two liquids in a composite-core fiber. [46,105] In all those works, well-distinguishable soliton fission could be demonstrated using a 30 fs pulse. The method comes with the benefit of utilizing a large variety of liquid admixtures, such as health-friendly, highly transparent tetrachloroethylene, highly nonlinear toluene-d8, and nitrobenzene-d5, as demonstrated in the individual works. Nonetheless, the high amount of lowrefractive, low-nonlinear buffer solution (here carbon tetrachloride), as well as the larger core sizes reduces the nonlinear performance of the hybrid fibers.

3) Recently, Scheibinger, Qi et al. demonstrated soliton-
mediated SCG in CS 2 -core LCF by exploiting higher-order mode excitation (i.e., TM 01 , TE 01 , HE 21 ). Those modes feature an altered dispersion compared to the fundamental fiber mode with significant shifts of the ZDW toward wavelengths lower than the Erbium-doped laser bands at 1550 nm. [106] This approach benefits from the great design flexibility that comes with using different liquids as core media, which allows tailoring the dispersion landscape to a level where up to two ZDWs become relevant. Such dispersion configurations are of high interest in chip-integrated platforms, [165,166] since they are typically very hard to achieve in fibers. Double-ZDW dispersion profiles especially promise the generation of two dispersive waves with octave-spacing spectral spacing that can be used for on-chip optical self-referencing of laser sources. The work by Scheibinger et al. has shown that efficient, double-band dispersive wave generation (at 1.0-1.2 μm and 2.5-3.5 μm) can be achieved readily in cm-long LCFs, too, by using a broadband, mode-converted, 30 fs fiber laser at 1.56 μm center as a pump source. In follow-up work, Qi et al. used the same excitation scheme for higher-order modes to adjust the bandwidth and spectral shape over a wide range within 1.0 to 2.5 μm wavelengths by axial modulation of the core size in multiply spliced heterostructures. [167] Another group recently proposed a similar approach using the fundamental mode and a cascaded sequence of single-mode fibers and LCF tapers within one monolithic fiber device, achieving similar wavelength coverage. [168] All examples above highlight the inherent flexibility in designing liquid-core fiber devices, which host much potential for applications that critically rely on dynamically reconfigurable systems. Notably, the work by Schaarschmidt et al. has proven long-term stability over days and watt-level operation of supercontinua generated in CS 2 -core fibers [164] and has hence strengthened a realistic perspective toward practical, dynamically tunable supercontinuum sources (Figure 12d-f).

Nonlinear coupling and spatial soliton formation
Their ease of handling and their high nonlinearity make liquids good candidates for reconfigurable multi-core experiments. This has been greatly demonstrated in two works by Vieweg et al. The authors used selectively filling commercial photonic crystal fibers to investigate nonlinear waveguide coupling, [112] and spatial soliton formation, in a 1D waveguide array. [108] In the first work, they infiltrated two adjacent holes of the microstructured cladding of a 3.6 cm fiber sample with CCl 4 . Despite the moderate nonlinearity of CCl 4 , the team achieved nonlinearly activated coupling from one core to the other at 24 kW peak power using a 180 fs pulse. Moreover, they found that the linear coupling coefficient can be tuned over a full coupling period by changing the temperature by just 6 K, which eventually allowed nearly linear tuning of the coupling coefficient with powers from 0 to 70 kW. The results are unprecedented since no other multi-waveguide platform allows this level of tuning in order to optimize the nonlinear device performance posterior fabrication.
In their second work in 2012, Vieweg et al. utilized their flexible platform in order to demonstrate the formation of spatial solitons in an array consisting of five neighboring waveguides. Once again, the authors used a 180 fs laser and a 3 cm PCF sample with five neighboring cladding holes being filled with CCl 4 (cf. Figure 13a,b). First, the authors showed linear diffraction of a beam coupled to the central core at low power, that is, the output power was distributed between all five waveguides at the output. Finally, at high peak power (i.e., >45 kW), they found tight mode confinement to the central waveguide at the output, which they attributed to the formation of a spatial soliton with the help of simulations. [169,170]

Third-Harmonic Generation
The efficient generation of the third-harmonic of an optical field remains a particular challenge in fiber optics due to the simultaneous need for phase matching (i.e., 3 FM = TH ), group velocity matching, and spatial mode matching over a spectral distance of two octaves (i.e., spectral spacing between fundamental mode FM and third-harmonic mode TH , ( TH − FM )∕ FM = (3 0 − 0 )∕ 0 ). Tackling these challenges for fundamental mode conversion is barely feasible and requires complex hybrid photoniccrystal fibers. [171] More feasible is the third-harming generation Laser Photonics Rev. 2023, 17, 2300126 Figure 13. Spatial solitons and third-harmonic generation. a) Experimental realization of a coupled waveguide array by selectively filling a photonic crystal fiber cladding with CCl 4 . b) The measured and simulated intensity distribution of the fiber output reveals a characteristic self-focusing to the central waveguide for increasing peak power, being indicative of the formation of a spatial waveguide soliton. c) Principle of phase-matched thirdharmonic generation from a fundamental fiber mode (i.e., HE 11 , see red mode in inset) to a low-order higher-order mode (i.e., HE 13 , see green mode in inset). d) Third-harmonic spectrum for increasing pump power of an 850 fs excitation. The inset shows the measured mode intensity. e) Measured third-harmonic energy for increasing pulse energy of the fundamental mode for various pulse durations (lines are respective cubic fits to the data). a,b) Reproduced with permission. [108] Copyright 2012, Optica Publishing Group. c-e) Reproduced with permission. [110] Copyright 2020, Optica Publishing Group.
(THG) from the fundamental to a higher-order mode, yet it still requires careful dispersion design and high field confinements in sub-nanometers fiber cores. [172] In 2020, Schaarschmidt et al. have demonstrated, that SIFs with C 2 Cl 4 core medium allow for higher-order mode THG, too. Compared to their silica predecessor, those LCFs benefit from moderate core sizes (i.e., 3.2-3.4 μm) that enable efficient coupling and hence a higher source-to-detector conversion efficacy. [110,173] Moreover, the authors took advantage of the straight-forward dispersion design enabled by the LCFs in order to phase-match a spatial fundamental mode around 1550 nm with a set of third-harmonic higher-order modes around 515 nm. The broad bandwidth of the femtosecond laser sources provided phase matching to 2-3 higher-order modes simultaneously. Modal degeneracies that cause HOMs with mixed polarization properties from coupling to both orthogonal representatives of the same mode set (e.g., HE 31 mode in 0 • and 90 • orientation) could successfully be lifted by using elliptical cores. [110] Noteworthy, elliptical core geometries are the only way, to date, to induce polarization maintenance in LCFs, since liquids are free of any intrinsic material tension. Additionally, maintaining the polarization may boost nonlinear interactions as the pump power is not distributed between orthogonal modes. Hence, the pump will suffer less from nonlinear polarization rotation, which reduces energy conversion efficiency. Elliptical-core LCFs may therefore provide a great platform for other nonlinear applications in the future.

Soliton-Like Features and Hybrid Soliton Dynamics
A major feature of liquids compared to other material classes is the unusual noninstantaneous nonlinear response originating from light-induced molecular motions. This type of nonlinearity is particularly strong in a liquid composed of elongated molecules. As outlined in Section 2.3, the noninstantaneous contribution to the total nonlinearity can become higher than 90% (e.g., in CS 2 for >1 ps excitation or C 2 Cl 4 for >4 ps excitation), which is much larger than the Raman contribution of any medium. Not much is known about the impact of this type of nonlinearity on the common nonlinear broadening processes. Yet, a few studies gave some insights and extended our common understanding, which is discussed in the following.
Nonlocal effects were first proposed as means to understand the propagation of self-trapped beams [174,175] with fundamental implications for stabilization of beam collapse, [176] steering of spatial beam dynamics and modulation instabilities, [177,178] and for the existence of propagation-invariant optical states in photorefractive media and Bose-Einstein condensates. [175,179] Similar effects can be expected in the time domain as outlined in the initial theoretical work by Conti et al. in 2010. [122] The authors predicted the existence of noninstantaneous solitons as a solution of the generalized nonlinear Schüdinger equation, underlying the Figure 14. Soliton-like states in noninstantaneous media. a) Spectro-temporal intensity distribution of a GNSE supercontinuum simulation from 50 cm realistic CS 2 -core fiber (pump parameters: 450 fs pulse width, 1950 nm center wavelength, 10 kW peak power). The inset highlights a hybrid solitary state that features an unusual asymmetry at the trailing edge of the pulse. Reproduced under the terms of the CC-BY license. [59] Copyright 2017, The Authors, Nature Publishing Group. b-e) Simulated shape and spectrum (linear scale (b,d), logarithmic scale (c,e)) of a 50 fs input pulse after propagating through a hypothetical, normal dispersive LCF with a pulse-width independent, high molecular fraction (f m = 0.95). The pulse shape features nearly constant peak power and a similar spectro-temporal asymmetry as in (a). Reproduced with permission. [96] Copyright 2018, Optica Publishing Group. f) Numerical simulation based on the Vlasov equation in the strongly nonlinear regime. The results show the collapsing dynamics of a pulse propagating through a highly noninstantaneous medium (anomalous dispersion, normalized response time: 300, while LCFs usually feature 0.1-10). Beyond the collapse of the waveform, the temporal characteristics feature a similar asymmetry as shown in the other works (i.e., (a-e)). Reproduced under terms of the CC-BY license. [161] Copyright 2018, The Authors, MDPI.
approximation of exponential response functions with response times much larger than the optical pulse duration. Their theoretical approach identified two measurable properties of such states: 1) temporal oscillations of the state within the optically induced nonlinear potential and 2) a gradual decrease of the soliton-self frequency shift with decreasing pulse width from the picosecond to the femtosecond regime (opposite to the dynamics in silica fibers).
This first theoretical concept was supported by the empirical numerical study by Pricking et al. [95] Here, the authors investigated the influence of the slow nonlinear response of liquids to soliton-mediated supercontinuum generation using simulations based on the generalized nonlinear Schrödinger equation. The authors showed that the fission length (i.e., the onset of the spectral broadening) drastically increases if the response time of the noninstantaneous contribution approaches the input pulse duration. The authors derived an approximation for calculating the altered fission length. Moreover, their findings support Conti's hypothesis that the soliton self-frequency shift reduces with increasing response time.
In 2017, Chemnitz et al. gave the first experimental evidence on altered soliton fission dynamics. [59] The authors correlated carefully conducted numerical studies with their spectral measurements to deduce a significant modification in both the soliton fission dynamics and the propagation of fundamental solitons due to the dominant nonlinear noninstantaneous contribution. Indications for the altered dynamics have been found indirectly by carefully comparing simulated and measured supercontinua (1.2-2.7 μm) at the output of a CS 2 -filled step-index LCF. The fiber was pumped in the anomalous dispersion domain with a 450 fs pulse from a Thulium fiber laser operating at 1.95 μm pump wavelength. The authors could identify four indicators of the modified fission dynamics and the involvement of so-called hybrid solitary waves. Relative to a conventional instantaneous Kerr system with equal parameters, those indicators are: 1) an altered phase-matching condition for dispersive wave emission; 2) a reduced spectral bandwidth; 3) an extended fission length; and 4) an increased temporal coherence among the output pulses. The authors speculated the occurrence of solitonlike wave packets (i.e., hybrid solitary waves) with a dissipative spectral-temporal characteristic (cf. Figure 14a) as a result of the broadening dynamics in the LCF. Measurements to confirm the potentially improved coherence or even the existence of hybrid soliton states are pending.
It is a striking curiosity that similar soliton-like pulse formations have also been predicted recently in the normal dispersion domain of CS 2 -core fibers. [96] Karasawa et al. have shown per simulation that input pulses of widths between 25 to 200 fs undergo specific dynamics leading to propagation-invariant pulses with 60 to 70 fs widths after the first 5 cm of propagation (cf. Figure 14b,c). The emerging states feature a characteristic pulse duration dependence of the output peak power following the relation P p ∝ 1∕T 3.5 p . A similar relation holds for solitons in the anomalous regime (i.e., P p ∝ 1∕T 3.5 p [180] ). Moreover, those peculiar states experience a continuous frequency redshift with propagation alongside an increasing acceleration (cf. Figure 14d,e)-characteristic features usually intrinsic to soliton states. However, it should be mentioned that the author's model does not incorporate the pulse width dependence of the nonlinear response of CS 2 , hence overestimating the molecular fraction with f m = 0.95 in the lower femtosecond pulse domain (compared to f m = 0.3 at 50 fs, cf. Figure 7c). Finally, the authors observed the typical spectral shape of such soliton-like pulses experimentally from the output of a 5 μm-core CS 2 /silica step-index fiber pumped with 50 fs pulses centered at 785 nm.
A unique, potentially unifying theory to explain those phenomena without using the common soliton terminology has been proposed by Xu et al. [161] Following a hydrodynamic model, the authors showcased that noninstantaneous nonlinear media can exhibit so-called concurrent shock-collapse singularities independent of the sign of the system dispersion. Indeed, their temporal and spectral characteristics (cf. Figure 14f)  Reproduced with permission. [113] Copyright 2016, Optica Publishing Group. b) Measured output spectra from a dispersion-tailored step-index fiber filled with CS 2 and pumped in the TM 01 mode at 1560 nm (see measured output mode in the inset). The higher-order mode undergoes soliton fission in an anomalous dispersion (AD) domain restricted by two zero-dispersion wavelengths (ZDW), leading to a double-emission of a dispersive wave. With increasing temperature, the AD domain becomes more confined, leading to a shift and an intensity increase of both dispersive waves. Reproduced under the terms of the CC-BY license. [107] Copyright 2023, The Authors, Published by Wiley.
exploiting nonlinear dynamics in liquid-core waveguides in future studies.

Local Dispersion Control via Thermal Tuning
The strong susceptibility of the optical properties to temperature changes is one of the most often praised properties of liquids, promising a new class of dynamically tunable light sources. Yet, only a few works have experimentally demonstrated the capabilities of thermal tuning for nonlinear applications.
As mentioned earlier, one of the most impressive demonstrations has been shown for phase-matched four-wave mixing in an ethanol-filled photonic crystal fiber by Velazquez-Ibarra et al. [113] Tuning the temperature in the domain 20-60 • C allowed us to experimentally shift the signal band from 750 nm up to 900 nm and the idler band from beyond 1750 nm down to 1250 nm (cf. Figure 15a).
In 2018, the authors Chemnitz et al. demonstrated the impact of local temperature tuning in step-index LCFs on the soliton fission process and the dispersion-critical dispersive wave generation. Using an LCF with a dispersion tailored for high thermal sensitivity, frequency shifts of the dispersive wave of 3.5 nm K −1 could be measured, adding up to an overall shift of >100 nm over 30 K temperature change. [76] In a later work, Scheibinger et al. highlight the use of temperature tuning in a more sophisticated dispersion landscape featuring multiple zero-dispersion wavelengths of selected low-order waveguide modes. [107] Here, the spectral locations of several dispersive waves can be shifted simultaneously with up to 33 nm K −1 sensitivity on the long wavelength side (cf. Figure 15b). Most strikingly, the proposed scheme allows to accurately trap an optical soliton in a confined anomalous dispersion domain, which can be further narrowed down with temperature and even go over to all-normal dispersion.
Among two-color applications in biophotonics, such tunability allows to adjust the conversion process accurately to match an f-2f phase-locking scheme to gain control over the carrier-envelope phase. Hence, the impact of temperature soliton fission and supercontinuum generation is prominent but becomes especially eminent under very special design considerations.

Global Reconfigurability via Core Composition
A further only partially explored potential of liquids as a core material is the flexibility in managing loss, gain, dispersion, and nonlinearity through combining two or more liquids into a mixture. In two initial works, the dispersion-and loss-tuning capabilities of binary mixtures have been highlighted. [46,104] The authors demonstrated that adding a controlled concentration (e.g. 20 vol%) of C 2 Cl 4 to CCl 4 decreases the ZDW to 1510 nm, ultimately opening the soliton fission operation regime to the cost-effective Erbium laser domain (1500-1600 nm). The authors also demonstrated accurate control over the spectral location and gain of the dispersive emission of optical solitons in LCFs by varying the concentrations of toluene (16-24 vol%) or deuterated nitrobenzene (12 vol%) in CCl 4 . In particular, in the latter case, the authors illustrate that a careful trade-off between loss and nonlinearity enables an efficiency boost impossible to achieve in neat core liquids. In particular, soliton fission could be observed at femtosecond pulse energies as low as 50 pJ, and a maximum soliton self-frequency shift of 200 nm was achieved at 220 pJ pulse energy, limited by the pump power. In follow-up work, the group also demonstrated the use of tailored fluids to accurately adjust the waveguide dispersion at the edge of a bandgap of microstructured fibers to enhance nonlinear light conversion. [181] Solid substituents, such as molecules with large hyperpolarizability, represent another interesting option for future research. For example, a recent work by Keyser et al. [182] reports on functionalizing LCFs on the molecular level by doping the liquid core with hydrogen-free charge-transfer molecules. Dynamic poling of those molecules through an externally applied electric field Laser Photonics Rev. 2023, 17,2300126 grating can enable in-fiber quasi-phase-matching for difference frequency generation. Here, the use of highly asymmetric molecules such as Disperse Red 1 (DR1) [183] may result in the integration of a strong (2) material into fiber. This would take nonlinear fiber photonics to a new level because the lack of anisotropy in glassy materials implies that efficient exploitation of second-order nonlinear processes in fibers is impossible with current fiber devices.
Hence, liquid mixtures provide high-level flexibility in fiber design and might open pathways towards single-mode waveguiding up to the MIR, or can be employed for incorporating nonlinear or active dopants such as nanoparticles, or asymmetric nonlinear molecules with large hyperpolarizability.

Conclusion and Outlook
Liquid-based nonlinear fiber optics represents a cutting-edge and multifaceted research field at the interface between various disciplines including materials science, fundamental nonlinear optics, engineering, and integrated photonics. Due to the unique properties of liquids, liquid-core optical fibers enable uncovering of fundamental effects such as light-molecule interactions, propagation-invariant states of light, and noise-reduction in nonlinear dynamics. Nonlinear effects, which are well understood in glass-and gas-based fiber and waveguides systems, can be studied from new points of view.
Here, LCFs offer a straightforward and cost-effective platform for investigations with unprecedented control over key parameters such as absorption, gain, dispersion, and temporal nonlinearity. LCFs also provide unique features compared to solidstate systems, such as unprecedented thermo-optic sensitivity or a dominant non-instantaneous response of the molecular ensemble. This response enables studying the interaction of lightinduced molecular susceptibilities and ultrafast optical pulses across long distances. Also, the unique spectral shape of the Raman response has been used in a series of experiments to redshift defined amounts of electromagnetic radiation at extraordinarily high levels of efficiency. In addition, the dispersion flexibility of the fluids obtained by mixing or thermo-optic tuning allows for the realization of partially reconfigurable dispersion scenarios beyond the capabilities of glass-or gas-filled fibers. Therefore, the findings of the community reviewed in this article show a clear path for LCFs to emerge as key tools for creating tunable multiwavelength light sources, low-power nonlinear signal processors, and even low-noise photon pair sources.
Yet, the field requires a closer community with open communication and collaboration to identify the technological opportunities and pitfalls as well as the open scientific questions of nonlinear softphotonics to advance the field significantly. The benefits of liquid-core systems are more subtle than gas-or soft-glass systems, which share the market with high-power applications on the one side and low-power applications on the other. In this development, liquid-core systems have long been overlooked due to hasty assumptions on missing power scalability, long-term stability, and practicability of such systems, which have been refuted in several papers over the last decade. These recent demonstrations give new momentum to the research field with potential for scientific explorations and out-of-the-lab applications over the following years.
As shown in several works, the performance of LCFs in terms of losses, electronic nonlinearity, and damage thresholds lies within the range of established soft glass fibers, with liquids offering additional features. Due to low optical losses, inorganic liquids such as C 2 Cl 4 and CCl 4 are currently considered the most practical candidates, allowing for realizing meter-long fibers. Furthermore, high refractive index liquids, such as CS 2 , combined with mid-IR transparent glasses as cladding forming material, also provide an alternative fiber platform for addressing spectroscopic applications in the mid-infrared range. In principle, this opens up a wide range of studies and applications for wavelengths >2 μm, which are not addressable with fused silica systems due to very high optical losses.
To some extent, liquid-core fibers may fill up an important niche between soft-glass fibers (considering their highly nonlinear and partial mid-IR transparency) and gas-filled hollow-core fibers (considering their unique tuning properties and physicsrich molecular interactions). Notably, the thermal tuning in LCFs can be performed locally, which is hard to realize in any other fiber system, ultimately hosting unique application potential for adaptive fiber devices.
Crucial to the use of LCFs is the precise knowledge of the optical parameters, especially in the infrared range. Here, further advances in measurement accuracy (down to the dB/km level) and research into the broadband optical properties of novel ultratransparent liquids are required to improve the attractiveness of LCFs. Examples of candidate materials that have been little explored include CSe 2 , CBrCl 3 , CDBr 3 (i.e., deuterated CHBr 3 ), AsCl 3 , and fluorides (e.g., C 6 F 6 ). Here, the molecular structure promises high transparency and nonlinearity, but broadband measurements on the refractive index, absorption, and nonlinear response are incomplete or not existing. Existing hurdles, e.g. in workspace safety and handling, can be overcome by performing in-fiber measurements, which allows to reduce the sample's dead volume down to nanoliter amounts. Further, fiber implementation via high-purity fluids or degassing to reduce dissolved oxygen, nitrogen, and CO 2 content may be critical to improving performance. [49] The results reviewed in this work clearly demonstrate the scientific potential arising from the use of accurate material models and should motivate further research in materials science to fill knowledge gaps for other promising fluid candidates.
The unique properties of LCFs motivate the exploration of little or previously untouched areas of fundamental science. For example, additional theoretical and experimental work is needed to reveal the full nature of the observed hybrid solitary states and their possible connection to the theory of shock-collapse singularities. Such work could reveal new coherent nonlinear operation regimes, such as noise-robust supercontinuum generation beyond 150 fs pulse widths, or coherent pulse compression of picosecond pulses. [46] While those phenomena can be traced back to dominant noninstantaneous nonlinearities, further questions remain on the impact of the fifth-order nonlinearity (i.e., nonlinear effects related with the (5) susceptibility) which is non-negligible in highly nonlinear liquids, such as CS 2 . For instance, (5) has been shown experimentally to lead to robust spatial soliton formation [184] and, in modeling, to have an impact on promoting or inhibiting modulation instabilities. [185] Laser Photonics Rev. 2023, 17, 2300126 www.advancedsciencenews.com www.lpr-journal.org Another approach that has been little pursued is doping the liquids with nonlinear or active materials such as molecules, nanoparticles, or salts (i.e., ionic liquids). For example, strongly asymmetric molecules with strong hyperpolarizability have been used in polymer films for a second harmonic generation. This approach can in principle be transferred to LCFs, allowing for the integration of a strong (2) -response into fiber and leading to applications such as sum-/difference-frequency generation, [182] electro-optic switching, [186][187][188][189] or optical parametric oscillation. [190] Those approaches are particularly exciting when combined with in-fiber electrodes [191] to provide the external electric fields to break the centrosymmetry of the molecular ensemble. Furthermore, the high nonlinearity of nanoparticles, molecules, or ions can be incorporated to increase the nonlinear response of the fiber system, in general. [192,193] For instance, the incorporation of fluorophores has realized an in-fiber autocorrelator based on two-photon absorption. [194] Similar advantages can be expected from nanocrystals dissolved in LCFs. [195] Another aspect is the narrow-band Raman resonances of the liquids, which allows for anticipating interesting potential applications in fields such as quantum technologies or ultrafast molecular spectroscopy. For example, LCFs can be designed such that four-wave mixing processes occur outside the Raman bands of the liquid, which in principle, allows the generation of photon pairs with reduced noise compared to glass systems. [157,158] With regard to ultrafast applications, the use of long picosecond pulses offers the possibility to effectively exploit the noninstantaneous response as it increases with pulse duration. This combined with long fibers, can be used to realize effective Raman shifters with very strong redshifts using self-phase modulation or to significantly increase the parameter range for coherent pulse compression Another challenge in the context of LCFs is their integration into fiber circuitry to achieve monolithic, fully spliced device packaging. Here, initial steps have been achieved using a combination of cooling facilitating liquid contraction and splicing, [102] although much more research is needed to optimize the postprocessed fibers to demonstrate their application potential. It shall also be noted that the further exploration of liquid-liquid microfluidic waveguides [196] may allow transferring of multiple concepts from LCFs to an even more compact and flexible onchip platform in the future.
Finally, dispersion tunability by means of thermo-optics or liquid mixing opens up new fields of application. One particular appealing approach relies on the possibility of local control of dispersion by means of an applied temperature distribution, which opens up completely new fields of application, such as reconfigurable optical fibers for application-specific frequency generation [197] or on-demand dispersion compensation. Here, unique opportunities arise with respect to the use of artificial intelligence and optimization algorithms to generate tailored output spectra by realizing non-intuitive dispersion profiles.
With their wide variety of operating modes, liquid-filled fibers provide a highly reconfigurable platform with unique opportunities for advancing technologies, such as low-power nonlinear devices, fiber-based photon sources, and adaptive broadband light sources, while holding a wealth of new scientific explorations to be discovered in the future. Table A1 shows the best-fit parameter of the multi-parameter Sellmeier fit applied to the RI data of various sources (cf. citations in the caption). The fits were based on the nonlinear least squares method and the inbuilt Trust-Region algorithm of Mathwork's programming environment MATLAB. The goodness of the fit is expressed by means of the R-squared value R 2 in the same table. All R 2 values are very close to 1 confirming a high quality of the fits.

A.1.2. Review of the Nonlinear Response Model by Reichert et al.
The nonlinear response function of liquids in Equation (7) can be composed of three individual molecular responses r k (t) that have their origin in molecular reorientation, libration, and dipole-dipole interactions. The temporal response of molecular reorientation and dipole-dipole interaction can be modeled through the model of an overdamped oscillator r re (t) = C re (1 − e −t∕ r )e −t∕ d,re Θ(t) ( A 1 ) which accounts for the rise times r and decay times d,X of the respective process and the respective normalization constants C X . The Heaviside function Θ(t) ensures causality. The rise time r is usually approximated with 100 fs since the temporal resolution of common pump-probe setups is limited to 50-100 fs. However, it shall be noted that this rise time significantly influences the impact of the molecular nonlinearities caused by an ultrafast laser pulse with pulse durations of 100 fs and below. The temporal response of the libration process can be expressed by the model of an underdamped oscillator r l (t) = C l e −t∕ d,l Θ(t) ∫ ∞ 0 sin( t) g( ) d (A3) with decay time d,l and normalization constant C l . As suggested by Reichert et al. the spectral resonance of this process can be fit by an anti-symmetric Gaussian distribution g( ) = exp (−( − Ω) 2 ∕(2 2 )) − exp (−( + Ω) 2 ∕(2 2 )) (central frequency Ω, spectral width ). The resulting spectral distribution is clearly visible in the response spectrumR( ),  as exemplarily shown for CS 2 in the inset of Figure 6, and, thus becomes also visible in Raman spectra. The model above can be widely applied to other liquids. [90,91] However, it misses the impact of coherently excited vibrational modes (i.e., Raman modes) because of the lack of temporal resolution of pump-probe experiments. For some liquids with Raman bands beyond 10 THz (e.g., CS 2 ), neglecting the Raman response is a reasonable assumption. Nevertheless, other liquids, such as CCl 4 , have strong Raman lines around 10 THz and below, and Raman can become reasonably strong for pulse widths of 100 fs or below. Therefore, for illustration in Figure 6, this work attempts to extend the model by Reichert et al. by the vibrational Raman response r v due to its relevance for femtosecond pulse dynamics in LCFs. This was done by straightforwardly extending Equation (7)  where C v is chosen such that ∫ r v (t)dt = 1. The specific nonlinear refractive index n 2,v in Table A2 were estimated from the linear Raman spectra of each liquid normalized to a silica reference and may serve as an estimate. Table A2 lists the model parameters for six prominent liquids, accordingly to ref. [90].