Electric Control of Thermal Contributions to the Nonlinear Optical Properties of Nitrobenzene

Thermal effects are inevitable when an absorptive nonlinear optical material interacts with long pulse duration or high repetition rate laser pulses. It results in inaccurate characterization and reduction in efficiency of the nonlinear materials for device applications. In this article, the study investigates the influence of an external electric field on the thermal contribution to the nonlinear optical response of nitrobenzene (NB). Z‐scan measurements are performed on NB using 330 ps laser pulses at a wavelength of 532 nm with variable (10 Hz to 1 kHz) repetition rates. At low repetition rates, NB shows a positive nonlinear refractive index (+ n2), which leads to self‐focusing of the laser beam due to the optical Kerr effect. Cumulative thermal effects occur above a repetition rate of 200 Hz. At high repetition rates (>750 Hz), the sign of n2 becomes negative, implying a self‐defocusing behavior of the sample arising from the thermal‐induced nonlinear refractive index. By applying an external DC field to the NB, a reduction of the thermal contribution can be observed. At a sufficiently high electric field strength, the thermal contribution is suppressed and the inherent Kerr nonlinearity can be observed despite the high repetition rate of the pump laser.


Introduction
[5][6][7][8][9] The effect of OKE is described DOI: 10.1002/apxr.202300053 by a third-order nonlinear refractive index (n 2 ) and it can be measured by using the Z-scan technique. [10,11]The Z-scan technique is very sensitive to spatial distortion (both amplitude and phase) of a laser beam transmitted through the sample.The closed aperture (CA) Z scan provides the sign and quantitative values of n 2 .The characteristics of pump sources, such as wavelength, pulse width, and repetition rate, play an important role in measuring the intrinsic nonlinear optical (NLO) properties of photonic materials.In general, excitation with wider pulse widths or high repetition rate pulses results in predominantly thermal-induced nonlinear effects. [12,13]The inherent Kerr optical nonlinearity can be obtained with short pulses (ps to fs pulse duration) at low repetition rates.
Typically, OKE is an ultrafast process that is on the order of the fs to ps time scale, while thermal effects are slower, ranging from microseconds to several milliseconds.Depending on the pump pulse width, various mechanisms can be responsible for the OKE include electronic distortion (≈0.1-10 fs), molecular libration, molecular redistribution (≈0.1 ps), and molecular reorientation motion (>10 ps). [3,14,15][20] Absorption is the prime component for generating local heat under intense laser irradiation, which results in a temperature-induced refractive index gradient (thermal lens) inside the sample.Under the excitation with high repetition rate or long-duration laser pulses, thermal effects in liquids usually cause a negative nonlinear refractive index as the refractive index decreases during thermal expansion.It leads to a self-defocusing behavior detectable in Zscan measurements. [12,21]The inherent electronic (Kerr) nonlinear optical response remains constant, especially with the repetition rate, while thermally induced effects alter drastically.Therefore, thermal effects present in the system can cause an inaccurate estimation of NLO coefficients and reduce the efficiency of nonlinear photonic devices.
[24] Among transparent materials, the OKE is particularly prominent in many liquids, including nitrobenzene (NB) or carbon disulfide (CS 2 ), which also support wide bandgap operation and a high degree of homogeneity.][30] However, the existence of linear and strong twophoton absorption (2PA) in NB deteriorates the efficiency of Kerr nonlinearity in some cases due to the dominant thermal effect. [12,13,31,32]The suppression or reduction of the thermal contribution is an important factor in the case of simultaneous existence of both Kerr and thermal nonlinearity.[35][36][37] Sandeep et al., and Wickremasinghe et al., have shown the role of pulse repetition rate on suppression of thermal effects in a nonlinear medium. [13,33]Abdullah et al., have extracted the pure nonlinear optical coefficients under high repetition rate excitation by using a theoretical approximation. [38]Sirohi et al have experimentally demonstrated a reduction in thermally induced NLO response by pumping with Laguerre-Gaussian vortex (LGV) beams compared to Gaussian beam excitation. [37]Singhal et al. found that by creating a substantial flow inside a liquid sample, they were able to eliminate the thermal impact that was observed in CS 2 under high repetition laser illumination. [39]In this article, we demonstrate a method to control and suppress the thermal nonlinearity in NB.In the literature it is reported that polar liquids show macroscopic movement under the influence of an external DC field. [40]In our experiments, we also observe such macroscopic movement of the NB inside a glass cuvette, when applying a voltage to the electrodes.Here, we term this movement an electrical stirring of the liquid (see Video S1, Supporting Information).For the first time, to the best of our knowledge, this electrical stirring is used to control thermal induced nonlinear optical effects.

Results and Discussion
To examine the thermal induced nonlinear optical effect in NB, we have performed closed aperture (CA) and open aperture (OA) Z-scan measurements (Figure S1, Supporting Information) under ps pumping at 532 nm wavelength with varying repetition rate of the pump laser.The optical path length of the sample cell is 1.36 mm.The beam waist radius ( 0 ) is 21.1 μm and the Rayleigh range is 2.62 mm.In all cases, the energy per pulse was kept constant at 2.5 μJ. Figure 1 shows the CA/OA Z scan profiles and the deduced values for the effective (both thermal and Kerr) nonlinear refractive indices of NB upon pumping with various repetition rates (10, 50, 100, 300, 500, 750, and 1k Hz).In OA scans (see Figure S2, Supporting Information), NB exhibits a dip at the Z 0 position corresponding to two-photon absorption. [31]The curves were fitted with the OA Z scan equation, and the deduced two photon absorption coefficient ( 2PA ) is 0.36 cm GW −1 . [13,41]The empty cell was also scanned at similar experimental conditions in both CA and OA Z scan measurements.It was confirmed that the empty glass cell does not show nonlinear optical behavior.
Further, the effective nonlinear refraction of NB was extracted by normalizing the CA scans to the corresponding OA scans obtained under identical experimental conditions.NB exhibits three different types of curves at repetition rates ranging from 10 Hz to 1 kHz (see Figure 1a).At low repetition rates (≤600 Hz), the Z-scan curve shows a valley followed by a peak, which indicates the existence of self-focusing nonlinear refraction (NLR) due to the optical Kerr effect (inherent electronic nonlinearity). [42,43]A constant magnitude of Z-scan curves was observed at repetition rates below 200 Hz, and thus reveals the absence of a cumulative thermal effect.Above 200 Hz, the valley-peak magnitude gradually reduces and flattens at ≈750 Hz attributed to the accumulation of thermal effects generated by the strong pump pulse.The Kerr nonlinear optical response of NB exhibits self-focusing behavior in the CA Z-scan, while thermal induced effects show a self-defocusing nature.At higher repetition rate (800 Hz and above), the NLR curves switch to the peak-valley characteristic and show a dominant contribution of thermal induced NLR. [21,44]The time scale on which thermal effects become significant can be estimated by the thermal conduction time ( tc ) of NB using the following equation.
Here,  0 is the beam waist radius, , C p , and K are the density, specific heat capacity and thermal conductivity of the medium, respectively.The corresponding values for NB are  = 1206 Kg m −3 , C p = 1509 J kg −1 K −1 , and K = 0.149 W m −1 K −1 . [45,46]he estimated time constant  tc for NB is  tc = 1.35 ms.For measurements performed at repetition rates between 10 and 200 Hz, the temporal inter-pulse distance is above 5 ms, and thus much longer than tc .At higher repetition rates (above 200 Hz), the pulse separation is comparable to  tc and hence thermal lens effects can be expected.This behavior is consistent with our experimental results shown in Figure 3.
By considering a Gaussian beam excitation under low irradiance limit, the normalized transmittance due to nonlinear refraction can be expressed as [47] T Where Δ∅ = kn 2 I 0 L eff is the on-axis phase shift due to a refractive nonlinearity, k is the wave number, n 2 is the order nonlinear refractive index, I 0 is the pump irradiance, and L eff = 1− exp( −  0 L)/ 0 is the effective path length.x is the ratio of the scan length (z) to that of the Rayleigh range (z 0 ).The Z-scan curves were fitted with Equation ( 2) and the deduced effective nonlinear refractive indices (n 2eff ), which include both Kerr and thermalinduced nonlinearities, are shown in Figure 1b.The values of the effective nonlinear refractive indices are positive and identical up to 200 Hz pulse repetition rate, which corresponds to the optical Kerr effect.The obtained Kerr nonlinear refractive index and cubic nonlinear optical susceptibility of NB at lower repetition rates (≤200 Hz) are 2.28 × 10 −18 m 2 W −1 and 1.97 × 10 −20 m 2 V −2 , respectively.These values are in the same order of magnitude reported elsewhere under comparable excitation conditions. [14,43]ith a further increasing repetition rate, the value forn 2 gradually reduces and eventually becomes negative as thermal-induced NLR dominates at high repetition rates.
For studying the effect of an external DC field on the optical and thermal induced nonlinear optical responses of NB, we have fabricated a separate glass cell containing two stainless steel electrodes.The optical path length of the cell is 7 mm and the electrode separation is 10 mm.The sample cell was kept on the Z-scan stage in such a way that the excitation beam (horizontally polarized) propagates in the center between the electrodes.Figure 2 shows the normalized CA/OA Z-scan profiles of NB in absence and presence of various DC fields at a low (50 Hz) and high (1 kHz) repetition rate of the laser pulses.For all the measurements, the experimental conditions are identical except for the variation of the applied DC field.At 50 Hz repetition rate (see Figure 2a), without a DC field, NB exhibits the valley-peak profile corresponding to the Kerr nonlinear optical response.In presence of an external DC field, varying from 1 × 10 5 to 7 × 10 5 V m −1 , the Z-scan profiles of NB remains unchanged.Similar results were also observed with vertical and elliptical polarized light under identical experimental conditions, indicating that there is no effect of the external DC field on the Kerr nonlinear optical response.
The normalized CA/OA Z-scan profiles of NB at 1 kHz repetition rate in absence and presence of various external DC field (a and k = 8.5 × 10 5 V m −1 ) are shown in Figure 2b.In contrast to Figure 2a, it shows the drastic variation in magnitude and switching in the valley-peak positions.In absence of a DC field, the CA Z scan curve-a (black line) shows the peak-valley behavior corresponding to the dominant thermal induced nonlinear refraction rather than Kerr nonlinearity.When a small DC field strength of 0.1 × 10 5 V m −1 is applied, the curve-b (red) exhibits a reduction in the peak-valley magnitude, suggesting the suppression of thermally induced nonlinear optical refraction.With further increasing DC field strength, the peak-valley magnitude decreases gradually and becomes nearly flat at ≈0.5 × 10 5 V m −1 .It demonstrates that at this DC field strength, the nonlinear refraction due to thermal and Kerr nonlinearity has the same magnitude and the two contributing effects cancel each other.However, as external DC fields increase even further, the curve-f (0.7 × 10 5 V m −1 ) changes from a peak-valley to a valley-peak characteristic, indicating the dominating Kerr effect.With further increase of the external DC field strength, the valley-peak magnitude gradually increases and reaches a saturation level above a DC field of 5 × 10 5 V m −1 .It indicates that the external DC field reduces the thermal effects and leads to the retention in the Kerr nonlinear optical response.The peak-valley distance along the Z-axis as a function of the repetition rate of the laser and of the external DC field is provided in Figure S3 (Supporting Information).While at low repetition rates, the peak-valley distance remains constant, it slightly varies at higher high repetition rates, so with increasing thermal impact.These observations are consistent with previous reports. [48,39]As expected, this change is quite small, due to the nonlinear absorption properties of NB, (see Supporting Information).For high DC field strengths, we obtain the same peak-valley distance compared to a measurement at low repetition rates without applying a DC-field, which also indicated the suppression of the thermal impact.The characteristics of electric current flow and temperature variations of NB in relation to applied fields are given in Table 1.To compare the amount of suppression of thermal contribution by applying the DC field, the CA Z-scan profiles of NB at 1 kHz with 0 and 7 × 10 5 V m −1 DC field are plotted along with the CA Z-scan profile of 50 Hz pulses in Figure 2c.One clearly sees that the nonlinear refraction profile at 1 kHz with 7 × 10 5 V m −1 DC field exactly matches with the profile obtained for 50 Hz pulses, and thus it is evident that the thermal contribution is completely suppressed.
When an external DC field is applied to the solvent NB, a robust solvent stirring is noticed within the sample cell.Such rapid electrical stirring is highly efficient in annihilating the thermal load caused by solvent absorption under high-intensity laser pumping.To estimate the flow velocity of the NB, we measured the motion speed of particles inside the NB using a high framerate camera and various applied DC fields (see Supporting Information).The estimated motion speeds are 44, 59, 98, and 135 μm ms −1 for the DC field of 2 × 10 5 , 3 × 10 5 , 5 × 10 5 , and 7×10 5 V m −1 , respectively.The flow velocity of the liquid is expected to be at least as high as the motion speed of the particles.At a field strength of 5 × 10 5 V m −1 , the flow velocity is 98 μm ms −1 .That means that for a laser beam diameter of 42 μm in our Zscan measurements and an inter-pulse distance of 1 ms, the flow speed is sufficient for heated material to leave the illumination  region before interacting with the subsequent laser pulse.This is consistent with the results from the Z-scan measurements, where we have observed the genuine Kerr nonlinearity (positive nonlinear refraction) for DC fields above 5 × 10 5 V m −1 .
Further, to explore the accumulation of the thermal contribution with respect to the pulse repetition rate, we have carried out the detailed Z-scan measurements on NB with various repetition rates of laser pulses in absence and presence of the DC field.An external DC field of 7 × 10 5 V m −1 was applied and the pulse energy is 2.5 μJ for all measurements.Figure 3 shows the CA/OA Z-scan profiles of NB without (black curve) and with the DC field (red curves) over a pulse repetition rate of 10 Hz to 1 kHz.In all CA Z-scan measurements, the red curves at a DC field of 7 × 10 5 V m −1 are identical and indicate the Kerr nonlinear optical response, which we consider as the reference curve for comparing the measurements with no DC field.It can be seen, that the magnitudes and the positions of valley-peak profiles remain the same with and without a DC field below the repetition rate of 200 Hz (a−d), which confirms the absence of cumulative thermal effects.On increasing the pulse repetition rate beyond 200 Hz the magnitude of the black curve reduces remarkably, indicating the accumulation of cumulative thermal effects.On further increase in repetition rate, the magnitude of the black curve reduces and switches the valley-peak behavior to peak-valley above 750 Hz.In all cases, the Kerr nonlinear optical response was retained entirely in the presence of a DC field.We have also performed OA measurements at identical conditions provided in Figure S5 (Supporting Information).At a high repetition rate above 750 Hz, we found that there is remarkable reduction of two-photon absorption.This indicates that thermal effects even reduce the efficiency of 2PA of NB.Interestingly, the restoration of an intrinsic 2PA coefficient was also observed in presence of the external DC field.The measurements were well reproducible under similar experimental conditions (Figure S6, Supporting Information).
The deduced effective nonlinear optical refractive indices of NB in absence (■) and presence (•) of the DC field as a function of repetition rate are shown in Figure 4a.When an external DC field of 7 × 10 5 V m −1 is applied, the nonlinear refractive indices of NB are identical over a pulse repetition rate from 10 Hz to 1 kHz instead of alteration in n 2 (curve •).This indicates that the pure Kerr nonlinear optical response that was masked by a dominant thermal-induced nonlinear optical response was retrieved completely with the help of an external DC field.This method can provide the intrinsic nonlinear optical coefficients of the organic liquids while interacting with long-duration or high repetition rate laser pulses.
To validate the mechanism and efficiency of electrical stirring for reducing the thermal nonlinearity, we have performed Z scan measurements on NB under mechanical stirring with otherwise identical experimental conditions.The experimental layout for the mechanical stirring is given in Figure S7 (Supporting Information).The applied voltage and current for the mechanical stirring experiments are 7.5 V and 0.65 A, respectively, so the corresponding electric power is 4.87 W. In case of electrical stirring, the estimated electric power levels range from ≈10.5 to 550 mW, only.Figure 4b shows the CA/OA Z-scan profiles of NB a) without stirring, b) using mechanical stirring and c) electrical stirring.Compared with the case of mechanical stirring, the electrical stirring is found to be more efficient for suppressing the thermal nonlinearity.Using electrical stirring, an electric power of 0.145 W is already sufficient to suppress the thermal effect, entirely.For mechanical stirring, however, even one order of magnitude more power does not lead to a full suppression of the thermal effect.An additional drawback of mechanical stirring is that mechanically moving parts have to be placed in close proximity to the focal spot of the laser, which can disturb the wave fronts of the beam and hamper precise measurements.Moreover, it is challenging to incorporate mechanically moving parts into miniaturized photonic devices. [26]n the last step, we have measured the temperature change of the NB while applying the DC field.Around 3 min after each DC field strength has been applied, the NB has reached a constant temperature.These steady-state temperatures have been recorded for every DC field strength (see Table 1).Afterward, we have performed Z-scan measurements at all steady-state temperatures of the NB, both in presence and absence of the DC field.This way, we could confirm, that the suppression of the thermal nonlinearity is caused by the electric stirring and the suppression mechanism does not depend on the absolute temperature of the NB.

Conclusion
We have shown that an external DC field enables to control the thermal contribution to the nonlinear optical response of NB.At sufficiently high field strengths, the thermal nonlinearity can be completely suppressed, and the pure Kerr effect can be measured via Z-scan despite high repetition rates of the pump laser pulses.This suppression is caused by a permanent material exchange through electrical stirring.The rapid material exchange ensures that heated material leaves the illumination region quickly, allowing subsequent laser pulses to interact with unheated material.Comparative Z-scan measurements with mechanical stirring confirm that our electrical stirring approach allows to suppress the thermal nonlinearity more efficiently.In addition, electrical stirring has the advantage of contactless operation without mechanically moving parts, which also enables application in miniaturized systems.Since the concept of electrical stirring is not restricted to NB, we believe that our findings can support material scientists with the precise measurement of Kerr nonlinearities in novel liquid material systems in the future and it can also be utilized to enhance the stability of nonlinear photonic systems with low tolerance for thermal effects.

Experimental Section
For the experiments, the AR grade solvent nitrobenzene (Roth, 99%) was used.For the nonlinear optical measurements of NB, a glass cell of 1.3 mm was used.A separate glass cell with stainless steel electrodes was fabricated for DC field controlled thermal-induced nonlinear optical measurements.The optical path length of the cell is 7 mm and the electrode separation is 10 mm.
The experimental layout for the open and closed aperture Z-scan setup is shown in the Figure S1 (Supporting Information).The samples were excited with a Gaussian ps pump pulse at 532 nm (330 ps and 10 Hz to 1 kHz, PNG-M020101×0, Teem Photonics).The initial pump beam of 1 mm diameter passed through a beam expander (BE, x5).The pump intensity was controlled precisely by the variable intensity filter (VF) and it is the combination of a /2 plate and a linear polarizer.Further the pump beam was split into two beams with the help of a beam splitter (B.S), known as reference and signal beams.The signal beam was focused by lens L 2 and the beam waist radius of the pump beam was controlled by the initial iris (I 1 ).The transmitted light from the samples was collected at far field by using a large aperture lens (L 3 ) and detected by the signal detector (D 2 ).The signal and reference measurements were carried out while moving the sample in the focal plane of lens L 2 with the help of a Lab-VIEW controlled high precession stepper motor.The ratio of signal to reference measurements provides the nonlinear transmittance profile of the sample as a function of Z.The open and closed aperture scans were performed by controlling the linear transmittance of the final iris, I 2 .S = 1 for the open aperture measurements and S = 0.4 for all the CA scans.Power detectors were used for measuring the signal and reference beams.A /2 plate and a linear polarizer were used for changing the pump polarization.

Figure 1 .
Figure 1.a) Closed aperture Z-scan profiles of NB with various pulse repetition rates at constant peak power; b)The effective nonlinear refractive index as a function of the repetition rate of the laser.

Figure 2 .
Figure 2. Normalized CA/OA Z-scan profiles of NB in presence of various electric field strengths at a repetition rate of the laser of a) 50 Hz and b) 1 kHz; c) Comparison of the CA/OA Z-scan profiles of NB under 1 kHz (with 0 and 7 × 10 5 V m −1 ) and 50 Hz repetition rate pumping.

Figure 3 .
Figure 3. CA/OA Z-scan profiles of NB with various repetition rates of the laser in absence and presence of a DC field at a laser pulse energy of 2.5 μJ.

Figure 4 .
Figure 4. a) Change in the nonlinear refractive index of NB in absence and presence of a DC field as a function of the repetition rate of the laser; b) CA Z-scan profiles of NB without stirring (a), with mechanical stirring (b) and with electrical stirring (applied DC field) (c).

Table 1 .
Electrical parameters used for the DC field-induced stirring experiments.