# Low threshold mid-infrared supercontinuum generation in GaAs 0.51 Sb 0.49 /InP waveguides

Edoardo de Toma, Victor Turpaud, Kevin Zhang, Yijun Yang, Laurent Vivien, Gerhard Böhm, Anna Köninger, Delphine Marris-Morini, Mikhail A Belkin

► To cite this version:

Edoardo de Toma, Victor Turpaud, Kevin Zhang, Yijun Yang, Laurent Vivien, et al., Low threshold mid-infrared supercontinuum generation in GaAs 0.51 Sb 0.49 /InP waveguides. Optica, 2025, 12 (3), pp.399. 10.1364/OPTICA.540702. hal-05471775

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# Low threshold mid-infrared supercontinuum generation in GaAs<sub>0.51</sub>Sb<sub>0.49</sub>/InP waveguides

EDOARDO DE TOMA,<sup>1,3</sup> VICTOR TURPAUD,<sup>2</sup> KEVIN ZHANG,<sup>1</sup> YIJUN YANG,<sup>2</sup>

LAURENT VIVIEN,<sup>2</sup> GERHARD BÖHM,<sup>1</sup> ANNA KÖNINGER,<sup>1</sup> DELPHINE MARRIS-MORINI,<sup>2</sup>

AND MIKHAIL A. BELKIN<sup>1,*</sup>

Received 28 August 2024; revised 9 January 2025; accepted 22 January 2025; published 13 March 2025

Chip-scale broadband light sources in the mid-infrared spectral range are highly desirable for the development of compact spectroscopy and sensing instrumentation in the molecular fingerprint region. Recently, generation of subpicosecond pulses with over 5 W of peak optical power was demonstrated from mode-locked mid-infrared quantum cascade lasers. Monolithic integration of these lasers with a waveguide for supercontinuum generation may dramatically broaden the emission spectrum of these devices. Here we report mid-infrared supercontinuum generation in GaAs<sub>0.51</sub>Sb<sub>0.49</sub>/InP dielectric waveguides with, to our knowledge, a record-low peak pump power of only approximately 6 W for a pump wavelength of 5 µm, which is required to double the spectral bandwidth of the pump pulse. This pump power level is more than an order of magnitude lower than the current state of the art. Our results pave the way towards the development of an electrically pumped chip-scale mid-infrared supercontinuum source based on a monolithic integration of a quantum cascade laser pump with passive waveguides on an InP platform. © 2025 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

https://doi.org/10.1364/OPTICA.540702

## 1. INTRODUCTION

The mid-infrared “molecular fingerprint” region (mid-IR, $\lambda \approx 3–15$ µm or $1/\lambda \approx 3300–600$ cm<sup>-1</sup>) is one of the most important spectral bands for molecular spectroscopy and sensing. It is widely used in physics, chemistry, materials science, biology, and many other fields of science and technology to determine the chemical composition of materials based on their molecular vibrational absorption fingerprint [1]. Traditional mid-IR spectroscopy systems, such as Fourier-transform infrared spectrometers (FTIRs), employ thermal “globar” lamps [1]. However, their brightness is limited by Planck’s law.

Mass-producible electrically pumped semiconductor sources of bright and broadband mid-IR radiation may enable the development of compact and relatively inexpensive mid-IR spectroscopy and microscopy instruments with performance exceeding that of spectroscopic systems based on thermal sources [2]. To that end, mid-IR frequency-comb (FC) emission was demonstrated in quantum cascade lasers (QCLs) [3,4] and interband cascade lasers (ICLs) [5]. However, due to the gain-bandwidth constrains and the difficulties in maintaining broadband low GVD in electrically pumped devices, the bandwidth of the best FC QCLs is still smaller than ~120 cm<sup>-1</sup>, which is only about 5% of the entire mid-IR spectral band [6,7].

It is now well-known that the bandwidth of short-pulse laser sources can be drastically increased using supercontinuum generation (SCG) in optical waveguides with high Kerr nonlinearity ($n_2$) and low group velocity dispersion (GVD) [8,9]. In the mid-IR spectral range, SCG sources covering most of or even the entire mid-IR spectral range were demonstrated recently based on Kerr nonlinearity SCG in optical fibers (see, e.g., Refs. [10–12]) and in on-chip dielectric waveguides (see, e.g., Refs. [13–21]) pumped by short-pulsed table-top mid-IR lasers.

Recently, it was experimentally demonstrated that the emission of FC QCLs can be compressed into a train of short optical pulses with a pulse duration of ~0.5 ps and peak powers of ~5 W [22]. Given that pulse compression can, in principle, be done on a chip (see, e.g., Refs. [23,24]), one may consider monolithic integration of a short-pulse mid-IR laser pump with passive waveguides for SCG on the same semiconductor chip. However, all chip-scale supercontinuum sources demonstrated so far required pump peak powers above 100 W to produce SCG [13–21] and, at the present state of QCL technology, these values would be unrealistic to achieve with FC QCLs.

In this work, we report on-chip mid-IR SCG with record-low pump peak power. Peak power of only approximately 6 W of a pump pulse at 5 µm wavelength is sufficient for broadening of the –20 dB spectral bandwidth of the pump pulse by a factor of two. An output pulse bandwidth of 3500–6500 nm at –20 dB

<footnote n="1"><sup>1</sup>Walter Schottky Institute, Technical University of Munich, Garching 85748, Germany</footnote>

<footnote n="2"><sup>2</sup>Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, Palaiseau, 91120, France</footnote>

<footnote n="3"><sup>3</sup>edoardo detoma@wsi.tum.de</footnote>

<footnote>*mikhail.belkin@wsi.tum.de</footnote>
intensity is achieved after soliton fission at 44 W of input peak power at the same pump wavelength. The measured values for the required peak pump power for the pulse bandwidth doubling and for soliton fission are further confirmed by mathematical estimates and numerical simulation results (Section 3) and are more than one order of magnitude lower than the ones reported in the current state of the art for all chip-scale SCG sources [13–21]. A low SCG threshold is achieved by employing the highly nonlinear GaAs<sub>0.51</sub>Sb<sub>0.49</sub>/InP dielectric waveguide platform. We have recently reported near-zero GVD and very large mid-IR Kerr nonlinearity in GaAs<sub>0.51</sub>Sb<sub>0.49</sub>/InP waveguides [25]. We further note that GaAs<sub>0.51</sub>Sb<sub>0.49</sub> material is grown epitaxially lattice-matched to InP, and the latter is also the native substrate for the highest-performing FC QCLs. InP-based waveguiding systems allow for monolithic integration of high-performance QCL pumps with the passive waveguides, as demonstrated recently [26,27].

## 2. DESIGN AND FABRICATION

In order to enable SCG in dielectric waveguides at low pump powers, the waveguide should provide low optical losses, low and slightly anomalous group velocity dispersion (GVD) over a broad spectral range, and a high modal nonlinear coefficient $\gamma = \omega_0 n_2 / c A_{\text{eff}}$, where $\omega_0$ is the pump frequency, $n_2$ is the Kerr nonlinearity, c is the speed of light in vacuum, and $A_{\text{eff}}$ is the effective waveguide cross-section area [9]. We have recently measured the values of $n_2$ of GaAs<sub>0.51</sub>Sb<sub>0.49</sub> to be $8.5 \cdot 10^{-17} \text{ m}^2/\text{W}$ at $5.2 \text{ µm}$ [25], more than 10 times higher than that reported in Ge waveguides [15]. This value is expected to remain nearly constant in the $3–15 \text{ µm}$ range, given the broad mid-IR transparency of GaAs<sub>0.51</sub>Sb<sub>0.49</sub> material. A relatively high index contrast of ~0.6 between GaAs<sub>0.51</sub>Sb<sub>0.49</sub>

and InP [25] allows for a tight mode confinement in the waveguide core. Finally, both GaAs<sub>0.51</sub>Sb<sub>0.49</sub> and InP offer low GVD values in the mid-IR spectral range, which is far away from both spectral regions that correspond to interband and optical phonon absorption in these semiconductor compounds. Further optimization of the modal GVD in the GaAs<sub>0.51</sub>Sb<sub>0.49</sub>/InP waveguides can be performed adjusting the waveguide structure.

Figure 1 shows the structure as well as the computed GVD and modal nonlinear coefficient of the waveguides used in this paper. The waveguide is processed from a semiconductor heterostructure grown on an InP substrate n-doped to $2.5 \cdot 10^{18} \text{ cm}^{-3}$. The heterostructure is made of a 4.5-µm-thick iron-doped semi-insulating (SI) InP lower cladding layer followed by a nominally undoped 2-µm-thick GaAs<sub>0.51</sub>Sb<sub>0.49</sub> waveguide core layer that is capped by a 2-µm-thick SI InP upper cladding layer. The background doping of the nominally undoped GaAs<sub>0.51</sub>Sb<sub>0.49</sub> material was found to be $n = 2.0 \cdot 10^{15} \text{ cm}^{-3}$ by Hall measurements. The waveguides were processed into 5.5- and 6.5-µm-wide ridge waveguides as shown in Fig. 1(a). The waveguide layer structure and the ridge widths were chosen to provide tight mode confinement with a small effective area for the fundamental TE and TM modes while providing a low and slightly anomalous GVD in the 4–12 µm spectral range. Figures 1(a) and 1(b) show the waveguide mode profiles for TE<sub>00</sub> mode in a 5.5-µm-wide waveguide at $\lambda = 5 \text{ µm}$ and $\lambda = 11 \text{ µm}$, respectively. The TE<sub>00</sub> mode intensity confinement in the waveguide core varies from 98% at $\lambda = 5 \text{ µm}$ to 87% at $\lambda = 11 \text{ µm}$ to 84% at $\lambda = 12 \text{ µm}$. The TM<sub>00</sub> waveguide mode is more loosely bound with the intensity confinement factor varying from 97% at $\lambda = 5 \text{ µm}$ to 61% at $\lambda = 12 \text{ µm}$. The GVD parameters $D_{\lambda} = -\frac{\lambda}{c} \frac{d^2n}{d\lambda^2}$ computed to TE<sub>00</sub> and TM<sub>00</sub> modes for two different ridge widths using Lumerical eigenmode solver

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Waveguide design. (a) Cross section of the waveguide profile and the intensity distribution for the fundamental TE mode at 5 µm. (b) Cross section of the waveguide profile and intensity distribution for the fundamental TE mode at 11 µm. (c) GVD parameter ($D_{\lambda}$) spectrum for the TE<sub>00</sub> and TM<sub>00</sub> modes for different waveguide widths for the waveguide structure shown in (a). (d) Mode effective area and nonlinear coefficient $\gamma$ for the TE<sub>00</sub> and TM<sub>00</sub> modes as a function of wavelength. The results are shown for TE<sub>00</sub> (solid lines) and TM<sub>00</sub> (dashed lines) modes for a 5.5-µm-wide ridge waveguide shown in (a).</figcaption></figure>
are shown in Fig. 1(c). Figure 1(d) plots the computed effective area of the optical mode and the modal nonlinear coefficient $\gamma$ for TE$_{00}$ waveguide mode in a 5.5-µm-wide ridge waveguide as a function of wavelength. It should be noticed that the modal nonlinear coefficient decreases as the wavelength is increased, both due to the increased mode effective area at longer wavelengths [see Figs. 1(a) and 1(b)] and due to its functional dependence on the wavelength, ($\gamma = \frac{\omega_0 n_2}{c A_{eff}}$). We have previously confirmed a good agreement of our computed GVD values with that measured experimentally in GaAs$_{0.51}$Sb$_{0.49}$/InP waveguides [25]. Figure 1(c) predicts the GVD parameter for the TM$_{00}$ mode to be near-zero and become normal ($D_{\lambda} < 0$) for wavelengths below approximately 5 µm, which would prevent the occurrence of soliton fission. Furthermore, from Fig. 1(d) it is shown that, while high values of the nonlinear coefficient $\gamma$ can be achieved for the TM$_{00}$ mode, this parameter is higher for the TE$_{00}$ mode, making TE polarization overall more suitable for achieving self-phase modulation (SPM) broadening and soliton fission at the lowest possible pump threshold. We further note that the definition of $\gamma$ of Ref. [9] used in this work assumes the same values of $n_2$ for both the waveguide core and the waveguide cladding materials. In our case, the larger-bandgap cladding layer material (InP) is expected to have a significantly lower value of $n_2$, compared to that of the GaAs$_{0.51}$Sb$_{0.49}$ waveguide core. Thus, we expect that the value of $\gamma$ shown in Fig. 1(d) is an overestimate. While this overestimate is expected to be no more than 10% across the 4–12 µm wavelength range for the TE$_{00}$ mode that has high (>84%) intensity confinement in the waveguide core at all of these wavelengths, the overestimate is higher for the TM$_{00}$ mode, particularly at longer wavelengths.

The ridge waveguides were etched using Cl/Ar/H$_2$ inductively coupled reactive ion etching. A 1-µm-thick layer of Si$_x$N$_y$ patterned with an e-beam lithography was used as a hard mask. Figure 2(a) shows the scanning electron microscope (SEM) image of the entire waveguide structure. Figure 2(b) shows a scanning electron microscope (SEM) of the waveguide facet.

For the SCG measurements, waveguides of different lengths with a double S-bend were fabricated as shown in Fig. 2(a). The geometry choice was dictated by the positions of the input and output objectives in the SCG measurement setup. The bending radius was kept at 600 µm, which is expected to result in a bending loss of less than 0.04 dB/half turn, which provides a negligible addition to the total propagation losses discussed further below. Additionally, in order to characterize optical losses in the waveguides used for the SCG measurements, waveguides with a 90 deg bend with a bending radius of 600 µm and the same width and etch depth as the SCG waveguides were fabricated and characterized using a

Fabry–Perot (FP) fringe contrast setup similar to that used for loss measurements in In$_{0.53}$Ga$_{0.47}$As/InP waveguides in Ref. [28].

### 3. LOSS CHARACTERIZATION AND SCG THRESHOLD ESTIMATE

The waveguide loss measurements were performed using the setup depicted in Fig. 3(a). Light from a broadly tunable external-cavity single-mode continuous-wave QCL source (MIRcat, Daylight Solutions, Inc), providing a tuning range $\lambda \approx 5.2–6$ µm and 7.5–11 µm was coupled to the input facet of the 90-deg-bent waveguide using a high numerical aperture (NA = 0.85) lens. The laser radiation exiting from the output facet was collected and directed toward a mercury-cadmium-telluride (MCT) detector using a lens pair. A half-waveplate and a polarizer were used to rotate the polarization of the light to explore losses for both TM- and TE-polarized modes. Propagation losses are then calculated from FP oscillations of the transmitted wave power. For simplicity, we chose to observe FP oscillations by keeping the laser wavelength fixed and tuning the waveguide effective refractive index by changing the temperature of the sample as shown in Fig. 3(b). Waveguide propagation losses $\alpha$ are then computed using the following equation [28,29]:

$$ \alpha = 4.34 \times \frac{1}{L} \ln \left( \frac{1 - \sqrt{(1 - \gamma^2)}}{\gamma R} \right), \quad (1) $$

where $\alpha$ is in dB/cm, L is the waveguide length in cm, R is the facet power reflectivity (assuming equal reflectivity of both facets), and $\gamma = (P_{max} - P_{min})/(P_{max} + P_{min})$ is the FP fringe contrast, with $P_{max}$ and $P_{min}$ being the maximum and minimum power of the transmitted signal, respectively. The waveguide facet reflectivity is computed by Ansys Lumerical for our waveguide geometry to be $R = 0.43$ and 0.36 for TE$_{00}$ and TM$_{00}$ waveguide modes, respectively. The waveguide propagation losses obtained with this analysis are shown in Fig. 3(c) as a function of wavelength. It can be noted that the waveguide system is characterized by moderately low losses of 2 dB/cm that stay approximately constant across 5–9 µm range for both TE- and TM-polarized waves.

While pulse propagation simulations, discussed further below, must be used for the detailed analysis of the pulse spectrum evolution, we can use simple analytical expressions to estimate the pump power requirements to observe significant pulse broadening. For the waveguides with near-zero GVD, the effect of self-phase-modulation (SPM) becomes significant when the nonlinear interaction length $L_{NL} = (\gamma P_0)^{-1}$ becomes comparable with the effective propagation length $L_{eff} = \frac{1-\exp(-\alpha L)}{\alpha}$, where $P_0$ is the peak pump power and L is the waveguide length [30,31]. Taking

<figure><img src="image_4.png" /><figcaption>Fig. 2. SEM images of the fabricated waveguides. (a) SCG sample. Waveguides of different lengths are fabricated with a double S-band and a 200 µm lateral shift between input and output. (b) An image of a typical waveguide.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 3. Measurement of waveguide losses. (a) Schematics of the experimental setup used for the loss measurements. (b) Normalized power transmission through an 18-mm-long 5.5-µm-wide ridge waveguide at $\lambda \approx 5.8$ µm as a function of the sample temperature. (c) Computed optical losses for the fundamental TE and TM modes as a function of wavelength. Dashed lines connect the two wavelength ranges accessible by our QCL system.</figcaption></figure>

$L_{eff} = L_{NL}$ and assuming $L \approx 1/\alpha$ as in the case of our waveguides, we obtain the value of the required pump power $P_0 \approx \alpha/\gamma$. Taking $\gamma \approx 0.14 \text{ cm}^{-1} \text{ W}^{-1}$ from Fig. 1(c) and $\alpha \approx 0.55 \text{ cm}^{-1}$ from Fig. 3(c) (after conversion from dB/cm to cm$^{-1}$) at pump wavelength of 5 µm, we obtain $P_{th,SPM} \approx 4$ W, much lower than that reported to date in any on-chip mid-IR SCG system and well within the range of pump powers achievable with FC QCLs [6,22].

Mode detailed analysis of SCG in our waveguides is performed by numerical modelling. The modeling consists of numerically solving the generalized nonlinear Schrödinger equation (GNLSE) [32,33] with a fourth-order Runge-Kutta algorithm [34]. We assumed the temporal profile of the input pulse to be a hyperbolic secant:

$$P(t) = P_0 \text{sech}^2 \left( \frac{t}{\tau_0} \right), \quad (2)$$

where $P(t)$ is the pump pulse instantaneous power, $P_0$ is the pump peak power, $t$ is time, and $\tau_0 = 125$ fs, which corresponds to the pulse length of 220 fs full width at half maximum. The value for the nonlinear Kerr refractive index $n_2$ is assumed to be equal to

$8.5 \cdot 10^{-17} \text{ m}^2/\text{W}$ at all mid-IR wavelengths [25], and the values of GVD are taken to be that shown in Fig. 1(c). The theoretical model neglects Raman contribution as it is expected to be low in the wavelength range of interest. Additionally, as the tuning range of the QCL source used for the propagation loss measurement is limited to $\lambda = 5.2-6$ µm and $7.5-11$ µm, as described earlier, losses of 2 dB/cm were assumed for both TE$_{00}$ and TM$_{00}$ modes in the range 6-7.5 µm and below 5.2 µm, cf. Fig. 3(c).

Figure 4(a) shows the spectral evolution of the propagating pulse in 5.5-µm-wide ridge waveguides assuming the temporal pulse given by Eq. (2) with peak power $P_0 = 50$ W. The data confirms a very low SPM threshold and shows that the pulse spectrum stabilizes after approximately 12 mm of propagation. To find the optimal pump wavelengths we performed simulations of SCG spectra at different pump powers and different pump wavelengths for 20-mm-long 5.5-µm-wide ridge waveguides. The results are shown in Figs. 4(b)-4(d). We only show the results for TE$_{00}$ pump modes as simulations of TM$_{00}$-pumping result in a higher required pump threshold for the reason discussed earlier. Simulations indicate that the lowest parametric threshold is expected to be attained

<figure><img src="image_6.png" /><figcaption>Fig. 4. SCG simulation results. (a) Spectral evolution of an optical pulse with an input peak power $P_0 = 50$ W and a center wavelength of 5 µm propagating in 5.5-µm-wide GaAs$_{0.51}$Sb$_{0.49}$/InP ridge waveguides. (b), (c) Normalized pulse spectra at the exit of a 20-mm-long 5.5-µm-wide GaAs$_{0.51}$Sb$_{0.49}$/InP ridge waveguide for different input peak powers and pumps. Pump pulse spectrum is also shown for comparison.</figcaption></figure>
at pump wavelength centered at around $\lambda \approx 5$ µm. This result can be understood by considering the spectral dependence of the non-linear coefficient $\gamma$ in our waveguides in Figs. 1(c) and 1(d) as well as the waveguide losses shown in Fig. 3(c). While the waveguide losses stay relatively constant in the 5–9 µm range, the value of the nonlinear coefficient $\gamma$ is maximized at shorter wavelengths. Simulation results indicate that the pump wavelength of 5 µm results in the lowest peak pump power requirements to broaden the spectrum of the pulse through SPM and to achieve soliton fission. We attribute these results to a lower value of the GVD and higher value of the modal nonlinear coefficient in our waveguides for the 5 µm pump wavelength compared to other pump wavelengths.

Considering the simulation results for the $\lambda = 5$ µm pump in Fig. 4(b), one can observe that doubling of the pulse spectral bandwidth at the –20-dB level is achieved at peak pump power of $P_0 \approx 6$ W. Furthermore, the onset of soliton fission and subsequent dispersive wave (DW) generation can be seen at a pump peak power of $P_0 \approx 50$ W. This value is also in a general agreement with an analytical estimate using $L_{\text{eff}} = L_{\text{fiss}}$, where $L_{\text{fiss}} = \tau_0/(\beta_2\gamma P_0)^{0.5}$ is the soliton fission length [9,35], where $\beta_2 = -\frac{\lambda^2}{2\pi c} D_\lambda$. Using $\tau_0 = 125$ fs, $L_{\text{eff}} \approx 1.1$ cm, $\gamma \approx 0.14 \text{ W}^{-1} \text{ cm}^{-1}$, $\lambda = 5$ µm and taking $D_\lambda = 10$ ps/(nm·km) [cf. Fig. 1(c)], we obtain
$$P_0 = \frac{2\pi c \tau_0^2}{\lambda^2 D_\lambda \gamma L_{\text{eff}}^2} \approx 70 \text{ W}.$$

## 4. SUPERCONTINUUM GENERATION

To confirm theoretical predictions, we used a tunable mid-IR short-pulse optical parametric amplifier (OPA) system to study SCG in $GaAs_{0.51}Sb_{0.49}/InP$ waveguides. The experimental setup is identical to that used to study SCG in $SiGe$ waveguides [13,21] and is shown in Fig. 5. The Yb-doped-fiber-laser-pumped tunable OPG-OPA system (Opera HP, Coherent, Inc.) provides tunable mid-IR pulses, assumed to have a hyperbolic secant temporal profile [see Eq. (2)], at a repetition rate of 1 MHz with the pulse duration of approximately 220 fs [full width at half maximum, which corresponds to $\tau_0 = 125$ fs in Eq. (2)]. Laser pulses were focused onto the waveguide facet with a 0.6 NA ZnSe lens. The light coming from the output waveguide facet was collimated with another 0.6 NA ZnSe lens and sent to a grating monochromator equipped with an MCT detector to record the output spectra. Mid-IR optical attenuators were used to control the input pump power.

In order to measure the power coupling efficiency of the impinging pump laser beam into the waveguide, a large-area ($\sim 1$ cm$^2$) thermopile power meter was used to measure the average pump power right before the input of the waveguide. The power meter was then placed next to the output facet of the waveguide and average power output from the waveguide was measured. The measured average power output was then corrected by the collection efficiency of the setup (0.77) obtained by comparing the simulated TE$_{00}$ mode diffraction out of the waveguide facet with the numerical aperture of the power meter sensor element. The pump power coupled into the waveguide through the input facet was then deduced from the output power from the waveguide by considering the computed output facet reflectivity (0.43) and the measured waveguide propagation losses. Coupling efficiency of approximately 0.03 ± 10% was obtained in this analysis at both 5 µm and 7.5 µm pump wavelength and the value of 0.03 was used to obtain the pump power coupled to the waveguide from the input pump power. The measurements were repeated at different pump

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Experimental setup used for the SCG measurements.</figcaption></figure>

power levels and the results were consistent. Unlike measurements with continuous-wave QCLs (Fig. 3), no Fabry–Perot oscillation of the power transmission was observed due to broadband spectrum of the pulse.

Based on the results of simulations, we tested SCG in 20-mm-long 5.5-µm-wide ridge waveguides described in Fig. 1(a) using TE-polarized pumping. The spectra of the output signal from the waveguides at different pump powers are plotted in Fig. 6(a) for the pump center wavelength of 5.0 µm and in Fig. 6(b) for the pump center wavelength of 7.5 µm.

The spectra of the pulses coming from the waveguide output facet for the pump center wavelength of 5 µm [Fig. 6(a)] show that, due to the low value of GVD at the pump wavelength [Fig. 1(c)], at low pump peak powers, the broadening of the pulse is symmetrical and dominated by SPM. The parametric threshold behavior is evidently shown by the increase in the spectral bandwidth occurring around 5.5 W of peak input pulse power. Additionally, a dispersive wave (DW) was observed at approximately 3.7 µm wavelength for a pump peak power of 44.6 W. This value is in good agreement with the simulation results shown in Fig. 4(b), meaning that as soon as the broadband higher-order soliton breaks down, energy is promptly and efficiently transferred to the dispersive wave. This behavior is also confirmed by the measured output pulse spectrum at 400 W of the input peak power, in which it may be noticed that no more energy is transferred to the DW.

The output pulse spectra obtained with the pump center wavelength at 7.5 µm show a less efficient example of pulse broadening via dispersive wave generation. In fact, due to the higher value of GVD [Fig. 1(c)] and the lower value of the modal nonlinear coefficient $\gamma$ [Fig. 1(d)] at the pump wavelength of 7.5 µm, numerical calculations show that the threshold power for parametric generation and soliton fission should occur at around 15 W of the input peak power. This situation results in low SPM broadening of the injected soliton before its breakdown. Consequently, the overlap of its bandwidth with the dispersive wave resonance in the normal dispersion regime is reduced, and the energy transfer to the dispersive wave is significantly less efficient, becoming measurable at –30 dB only at a pump peak power of 91 W. Increasing the pump power further results in a gradual, but limited broadening of the SC spectrum in the vicinity of the injected pulse, as predicted by the simulations in Fig. 4(d) and confirmed with the experimental results in Fig. 6(b).
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Experimental results. Measured output relative power for different input pump peak powers and pump wavelengths of 5 µm (a) and 7.5 µm (b). For clarity purposes, each trace has been shifted by 15 dB.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 7.** The spectral bandwidth of SCG measured at –20 dB of the maximum as a function of pump power for the pump center wavelength of 5 µm and 7.5 µm. The dashed lines indicate the –20 dB bandwidth of the original pump pulse at 5 µm (black) and 7.5 µm (red) center wavelength.</figcaption></figure>

In order to visualize the experimental dependence of the spectral bandwidth of the output pulse on the pump peak power, Fig. 7 plots the spectral bandwidths of the output pulses measured at –20 dB of the maximum as a function of the input pump power for the pump center wavelength of 5 µm and of 7.5 µm. The original pulse bandwidth doubles at a pump peak power of approximately 6 W in agreement with simulations. If we keep increasing the pump power further, the spectral broadening of the injected pulse increases further due to SPM and ultimately reaches its maximum value of 3 µm at 44 W of input peak power, spanning approximately 0.9 octave (3500–6500 nm) bandwidth at –20 dB intensity.

In contrast to pumping at 5 µm center frequency, the relatively high value of the anomalous dispersion limits the increase in bandwidth due to the SPM of the injected pulse at the center wavelength of 7.5 µm, thus leading to an inefficient energy transfer to the dispersive wave after its fission. We note, however, that the spectrum of the waveguide GVD is highly dependent on the waveguide structure and the GVD minimum can also be engineered at other mid-IR wavelengths, including 7.5 µm. Overall, the experimental results for both pump wavelengths show good agreement with the simulations, and this confirms the predictive power of our theoretical model. We expect that, through further optimization of the GVD profile of our GaAs<sub>0.51</sub>Sb<sub>0.49</sub>/InP waveguides via variations

of the waveguide structure (core thickness, waveguide width, etch depth, etc.) and with the reduction of optical losses, particularly at longer wavelengths, through waveguide growth, processing, and postprocessing steps optimization (similar to that done, e.g., for In<sub>0.53</sub>Ga<sub>0.47</sub>As/InP waveguides recently [28]), pump power requirements could be further reduced and the spectral bandwidth of the SCG in GaAs<sub>0.51</sub>Sb<sub>0.49</sub>/InP waveguides could reach the best results obtained with SiGe waveguides, e.g., 3–13 µm as reported in Ref. [13].

## 5. CONCLUSIONS

In conclusion, we have demonstrated mid-IR SCG with a record-low pump threshold in dielectric waveguides fabricated from GaAs<sub>0.51</sub>Sb<sub>0.49</sub>/InP epitaxial layers grown on an InP substrate. The doubling of spectral bandwidth was observed at pump peak powers as low as 6 W and nearly one octave of spectral broadening (3500–6500 nm) was achieved at pump peak power of 44 W. These values are more than an order of magnitude lower than that reported in other mid-IR dielectric waveguiding platforms [13–21] and they are within the capabilities of short-pulse FC QCLs [22]. A very low pump threshold was achieved due to exceptionally large mid-IR Kerr nonlinearity of GaAs<sub>0.51</sub>Sb<sub>0.49</sub> material [25] combined with low GVD and relatively low optical losses of GaAs<sub>0.51</sub>Sb<sub>0.49</sub>/InP ridge waveguides in mid-IR. We note that, while our results are attained for TE<sub>00</sub> polarization and QCLs provide TM-polarized output, on-chip polarization rotators with nearly 100% efficiency have already been demonstrated on the InP platform [36]. Furthermore, monolithic integration of QCLs with passive waveguides has already been demonstrated [26,27]. We expect that further improvements in processing and post-processing of GaAs<sub>0.51</sub>Sb<sub>0.49</sub>/InP waveguides will lead to a further decrease in optical losses similar to the situation with InGaAs/InP waveguides [28] and this will lead to a further reduction in the SCG pump threshold.

**Funding.** H2020 Industrial Leadership (101016956); Deutsche Forschungsgemeinschaft (463411319).

**Acknowledgment.** This work was supported in part by the H2020 Industrial Leadership (IL) PASSEPARTOUT project and by the German Research Foundation (DFG).

**Disclosures.** The authors declare no conflicts of interest.

**Data availability.** Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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