Semiconductor optical waveguide amplifiers deliver high gain per unit length (up to ∼1000 dBcm−1),1, 2 enabling light amplification over short distances in photonic integrated circuits.3 In contrast, rare-earth ions are regarded as impurities providing low gain (up to ∼10 dBcm−1),4–7 because electronic transitions within their 4f subshell are parity forbidden, dictating low transition probabilities and cross-sections. Nevertheless, devices such as fiber amplifiers and solid-state lasers profit from accordingly long excited-state lifetimes–hence increased excitation densities–in rare-earth-ion-doped materials, combined with large device lengths. Here we exploit the extreme inversion densities attainable in rare-earth-ion-doped microstructures in a host material, potassium double tungstate,8 that provides enhanced transition cross-sections and dopant concentrations,9, 10 thereby demonstrating a gain of 935 dBcm−1 in channel-waveguide and 1028 dBcm−1 in thin-film geometry, comparable to the best values reported for semiconductor waveguide amplifiers. Further improvement seems feasible with larger dopant concentrations. This gain is sufficient to compensate propagation losses in plasmonic nanostructures,11, 12 making specific rare-earth-ion-doped materials highly interesting for future nanophotonic devices.
Amplification of optical signals is required whenever the optical losses per unit length times the total distance (e.g., in long-haul optical communication or plasmonic waveguides) or the losses per unit device element times the number of device elements (e.g., in very-large-scale-integrated optical circuits), requires periodic recovery of the signal strength.
Among the available amplifier types, fiber amplifiers doped with trivalent rare-earth ions (specifically Er3+) are a standard in optical communication systems due to their low insertion loss, low noise, negligible non-linearities, superior characteristics at high-speed amplification, and high overall gain (30–50 dB). However, this high gain comes at the expense of employing several meters of fiber length, making this solution unsuitable for on-chip integration. The amplifier length can be shortened to typically a few centimeters by increasing the dopant concentration of rare-earth ions accordingly, but this approach is ultimately limited by the solubility of rare-earth ions in the chosen host material as well as the scattering losses and spectroscopic quenching processes induced by these high dopant concentrations. The typical gain per unit length reported for rare-earth-ion-doped integrated waveguides has hardly exceeded a few dB cm−1.4–7
Semiconductor optical amplifiers (SOAs), including organic semiconductors,13, 14 and III–V semiconductors,15–19 with different gain structures, such as quantum wells (QW),15, 16 multiple quantum wells (MWQ),17 and quantum dots (QD),18 deliver high gain over short distances, which in combination with heterogeneous integration techniques, make SOAs suitable for providing on-chip gain. However, due to the short carrier lifetime in these materials and significant refractive-index changes accompanied with the excitation of electron-hole pairs, temporal and spatial gain patterning effects limit their performance. Also dye-doped optical amplifiers (DOAs) can deliver high gain per unit length.
The enormous difference in gain per unit length provided by these materials originates in their physical properties, as exemplified in Table1. The relevant performance parameter, their modal gain (dBcm−1),
|Material||λ [μm]||σem [cm2]||N2 [cm−3]||Nt or N1 [cm−3]||Γ||gmat [dBcm−1]||gmod [dBcm−1]|
|Semiconductors||InGaAsP bulk||1.50 – 1.55||1.2 – 2.5 × 10−1620||3.25 × 10181||1 × 101820||0.31,a)||34401,b)||10321|
|1.2–2.5 × 10−1620||–||1 × 101820||–||–||775–11922|
|AlInGaAs/InP MQW||1.28||–||–||2 × 101817||–||–||22017|
|GaAs/AlGaAs QW||0.83||6 × 10−1620||14.6 – 19.6 × 101816a,c)||2 × 101820||0.013316,a)||2255616a,d)||30016|
|Strained InGaAs/AlGaAs QW||0.98||7 – 22 × 10−1615||8.4 – 11.1 × 101816a,c)||0.5 – 1 × 101820||0.017416,a)||1530016a,d)||26616|
|Organic semi-conductors||F8BT/Dow Red-F||0.66||2 × 10−1614||–||–||–||–||77514|
|MEH-PPV||0.63||4 × 10−1713||–||–||–||–||29013|
|Laser Dyes||OC1C10PPV||0.60||1 – 5.3 × 10−1721a)||4 × 101721a)||–||121||4421||4421|
|Poly (9,9-dioctyfluorene) PFO||0.466||0.3–4 × 10−1620||0.1–10 × 101820||–||122||31822||31822|
|PM650 in PMMA||0.616||3.7 × 10−1622||0.24 × 1018 cm−322||–||122||38522||38522|
|Rare earths||Er (8 wt%)-Yb (12 wt%) codoped phosphate glass||1.534||2 × 10−214a,e)||7.5 × 10204||–||14||13.64||13.64|
|Nd-complex-doped polymer||1.064||3.78 ×10−206||4.1 × 10196||–||0.836||6.96||5.76|
|KGd0.447Lu0.078Yb0.475(WO4)2||0.9806||σem = 1.155 × 10−19 σabs = 0.945 × 10−19 [this work]||2.53 × 1021 [this work]||N1 = 0.47 × 1021 [this work]||0.88 [this work]||up to 1062 [this work]||935 [this work]|
is given by the fractional overlap (or mode-confinement factor) Γ of the signal beam at wavelength λS with the gain structure exhibiting a material gain gmat (dBcm−1) that derives as the product of stimulated-emission cross-section σem (cm2) at λS times the inversion density Ninv (cm−3); this approximation is valid for . In semiconductor waveguide amplifiers, Ninv = N2–Nt represents the number of carriers N2 above the transparency excitation Nt, while in rare-earth-ion-doped materials, Ninv = N2–N1 is the difference between the population densities of excited state and ground state. These different notations represent the same underlying physics. The net modal gain (dBcm−1) is gnet = gmod–L; the propagation losses L are usually small compared to the modal gain and can be neglected.
A material gain of several × 103 dB cm−1 is achieved in the recombination region of III–V semiconductors due to the large stimulated-emission cross-sections of the excited carriers of several × 10−16 cm2, while Ninv is in the range of a few × 1018 cm−3.1, 15, 16 However, in QW and MQW SOA waveguides, the usually μm-sized signal mode exhibits a poor overlap Γ with the few-nm-thin active gain region, reducing accordingly the modal gain of QW and MQW SOA waveguides to several × 102 dBcm−1.15–19 Dyes can provide similarly high stimulated-emission cross-sections. However, their inversion density is an order of magnitude lower, resulting in values of the material gain up to a few × 102 dBcm−1; due to an excellent overlap Γ, DOAs can, nevertheless, provide a modal gain of a few × 102 dB cm−1. Rare-earth ions doped into amorphous materials, such as Al2O3, silica, and phosphate glass or polymers, suffer from stimulated-emission cross-sections whose values are typically four to five orders of magnitude smaller than in semiconductors, namely several × 10−21 cm2. The larger density of excited ions of several × 1020 cm−3, combined with an excellent overlap Γ, cannot compensate this disadvantage, resulting in the modal gain hardly exceeding 10 dB cm−1, which is two orders of magnitude lower than the best values reported in SOA waveguides.
In this work, we show that by appropriate design of host material, dopant concentration, and geometry one can enhance the modal gain of rare-earth-ion-doped waveguide amplifiers to values at which they can easily compete with SOAs and DOAs, while simultaneously providing the desirable gain characteristics present in rare-earth-ion-doped fibers, holding promise for a new generation of highly efficient optical gain materials. Our approach utilizes the family of monoclinic potassium double tungstates KY(WO4)2, KGd(WO4)2, and KLu(WO4)2.8 The transition cross-sections of rare-earth ions, specifically Yb3+, doped into these materials are among the largest observed in rare-earth-ion-doped hosts,9, 23, 24 exceeding by more than an order of magnitude the cross-sections observed in amorphous materials (Table 1). Furthermore, the active ions are incorporated in lattice sites with large ion separation, permitting larger dopant concentrations without introducing significant spectroscopic quenching effects.25 Very large dopant concentrations, reaching the stoichiometric composition KYb(WO4)2,10 can be incorporated in these materials. Combination with a long excited-state lifetime, tight pump and signal light confinement, and excellent pump-mode overlap with the active region allows us to achieve extremely large excitation densities. By improving all three relevant parameters in Equation (1), Γ, σem, and Ninv, we demonstrate a modal gain of 935 dBcm−1 in waveguide geometry, thereby increasing the small-signal gain achieved in rare-earth-ion-doped microstructures by two orders of magnitude.4–7 When passing tightly focused pump and signal light perpendicularly through a thin film, 1028 dB cm−1 gain is obtained.
We grow Yb3+-doped thin layers onto undoped KY(WO4)2 substrates by liquid phase epitaxy,26 resulting in planar waveguides (see Experimental Section).27 Co-doping the layers with appropriate percentages of optically inert Gd3+ and Lu3+ (or Yb3+) ions,28 which change the lattice constant in opposite directions, enables lattice matching of highly doped KGd0.447Lu0.078Yb0.475(WO4)2 layers with the undoped KY(WO4)2 substrate. Besides, we obtain an enhanced refractive-index difference between layer and substrate of ∼2 × 10−2, thereby enabling thinner active layers. Microstructuring of these layers by Ar+ beam etching results in channel waveguides with tight pump and signal light confinement,29 ensuring enhanced pump intensity and modal overlap of pump and signal beam with the active waveguide region.
With room-temperature Boltzmann factors b11 (0.605) and b23 (0.065) of the Stark levels (assuming the electronic structure of KY(WO4)2) involved when pumping at 932 nm, the maximum inversion, which is obtained at transparency for the pump photons, is given by:
The maximum pump intensity available in our experiment allows us to excite a fraction β of ∼84.3% of the active ions, resulting in an inversion of Ninv of ∼68.6% of the dopant concentration. With emission and absorption cross-sections σem of 1.155 × 10−19 cm2 and σabs of 0.945 × 10−19 cm2, respectively, at the signal wavelength λS (980.6 nm), derived for our co-doped samples (Figure1) as weighted averages of the cross-sections measured in KGd(WO4)2, KLu(WO4)2, and KYb(WO4)2,23, 24, 10 and a dopant concentration of Nd of 3.0 × 1021 cm−3 (= 47.5 at.%), a material gain gmat of 1075 dBcm−1 can be achieved according to Equation (1).
We perform two gain experiments (see Experimental Section). In the first approach, we tightly focus pump and signal light perpendicularly through a planar active layer of thickness (25 μm). Without pumping, the absorption cross-section σabs of 0.945 × 10−19 cm2 at λS leads to a signal-light absorption 4.34 σabs Nd of 3.08 dB. Under pumping, we measure 5.65 dB enhancement of the transmitted signal light. The net gain of 2.57 dB over the layer thickness results in a modal gain of 1028 dBcm−1. Despite complete overlap of the signal light with the pumped region (Γ = 1), the achieved gain is slightly smaller than the calculated material gain of 1075 dBcm−1, because the propagating pump and signal beams diverge and the wings of the signal-beam profile coincide with the wings of the pump-beam profile, where the inversion is negative and signal light is absorbed.
In the second experiment, we focus pump and signal light in-plane into a channel waveguide. Wing absorption is greatly diminished, because the wings of pump and signal beam partially propagate outside the doped region. Moreover, the tight pump and signal foci are maintained over the whole waveguide length (180 μm). By use of mode-solver software, we estimate the overlap (Γ) of the signal mode with the active medium to be 88%, resulting in an expected modal gain of 946 dBcm−1 at the highest available pump power (Figure2, solid curve). In excellent agreement with this expectation, we measure a modal gain of 935 dBcm−1 in this waveguide (Figure 2, circles).
A stoichiometric KYb(WO4)2 waveguide (Nd = 6.3 × 1021 cm−3),10 pumped to transparency, would potentially provide a modal gain gmod of 1987 dBcm−1. Although excited-state absorption, energy-transfer upconversion, or cross-relaxation do not occur in Yb3+, because this ion has its 4f subshell occupied with 13 electrons, hence only one excited state, at such high dopant concentrations lifetime quenching in Yb3+ can arise due to cooperative upconversion between neighboring Yb3+ ions or energy transfer to impurities such as Tm3+ and Er3+. However, the large ion separation in monoclinic double tungstates25 and the choice of ultra-pure Yb3+ raw material diminish these quenching processes.
The long excited-state lifetimes of rare-earth ions provide temporal and spatial stability to the optical gain. This is essential for achieving crucial performance parameters, such as high-bit-rate transmission of wavelength-division-multiplexed signals through optical amplifiers without cross-channel patterning effects or ultra-narrow-linewidth lasers without the linewidth-broadening effect of spatial gain modulation.30, 31 The extraordinarily high gain values reported here make rare-earth-ion-doped materials interesting candidates for providing gain in nanophotonic devices, such as nanoamplifiers and nanolasers, and may enable loss-less propagation in plasmonic nanostructures.