Broadband Mid-Infrared Frequency Comb in Integrated Chalcogenide Microresonator

Abstract

Mid-infrared (MIR) frequency combs based on integrated photonic microresonators (micro combs) have attracted increasing attention in chip-scale spectroscopy due to their high spectral resolution and broadband wavelength coverage. However, up to date, there are no perfect solutions for the effective generation of MIR micro combs because of the lack of proper MIR materials as the core and cladding of the integrated microresonators, thereby hindering accurate and flexible dispersion engineering. Here, we have firstly demonstrated a MIR micro comb generation covering from 6.94 μm to 12.04 μm based on a sandwich-integrated all-ChG microresonator composed of GeAsTeSe and GeSbSe as the core and GeSbS as cladding. The novel sandwich microresonator is proposed to achieve a symmetrically uniform distribution of the mode field in the microresonator core, precise dispersion engineering, and low optical loss, which features a wide transmission window, high Kerr nonlinearity, and hybrid-fabrication flexibility on a silicon wafer. A MIR Kerr frequency comb with a 5.1 μm bandwidth has been numerically demonstrated, assisted by dispersive waves. Additionally, a feasible fabrication scheme is proposed to realize the on-demand ChG microresonators. These demonstrations characterize the advantages of integrated ChG photonic devices in MIR nonlinear photonics and their potential applications in MIR spectroscopy.

1. Introduction

Mid-infrared (MIR) spectroscopy has been attracting significant attention in the past decade, especially in the region from 7 to 12 μm, including the distinctive spectral fingerprints of most biomolecules. It has been successfully demonstrated in multicomponent molecular detection, quick environmental and industrial monitoring, and non-destructive medical diagnosis [1,2,3,4]. Leveraging high spectral coherence and broadband wavelength coverage, optical frequency combs revolutionize a wide range of applications in frequency synthesizers, ultrafast ranging, coherent communications, molecular or atomic spectroscopy, etc. [5,6,7,8,9,10]. With the uninterrupted drive of the semiconductor fabrication technologies, chip-scale Kerr optical frequency combs achieve remarkable advancement in terms of high compactness, large-scale integration, and low power consumption [11].

Generally, the double balance of nonlinearity and dispersion, as well as dissipation and gains, plays a critical role in the formation of integrated micro combs [12]. In comparison to the well-established optical frequency comb generators operated in the visible and near-infrared regions in recent years, MIR Kerr frequency combs have been less investigated [13,14]. Although several material platforms, including silicon, germanium, silicon nitride, and crystalline fluorides, have been developed for MIR photonics, very few demonstrations have successfully extended the frequency range of micro combs into the MIR. The main challenges of MIR micro comb generation are the lack of high-quality integrated MIR microresonators with low optical loss and precise dispersion engineering. The typical optical materials as the cladding of the integrated microresonator, such as SiO₂, have strong absorption in the MIR region, hindering realizing high-quality(Q)-factors of the MIR microresonators [15]. Additionally, for MIR photonic waveguides, a relatively thick film is preferable to reduce the surface scattering loss and implement the flexibility of dispersion engineering. Moreover, based on the current film-deposition approach, most of the materials mentioned above are hard to achieve high-quality thick film with precise thicknesses and without cracks. It is a long-term target to develop ideal MIR nonlinear optical materials for integrated MIR nonlinear photonics. Alternatively, chalcogenide glasses (ChGs) feature high Kerr nonlinearity, extremely low absorption loss and no multiphoton absorption effect in the long-wavelength range, low thermo-optic coefficient, and flexibility of hybrid fabrication on the silicon wafer [16,17,18,19]. Moreover, the optical properties of ChGs can be optimized by adjusting the composition. Most recently, a new ChG (Ge₂₅Sb₁₀S6₅)-integrated microresonator with a high Q factor of 2 × 10⁶ and precisely engineering dispersion by complementary metal–oxide–semiconductor (CMOS)-compatible nano-fabrication has witnessed the generation of the soliton frequency comb with low pump power in the telecommunication bands.

In this work, a highly nonlinear hybrid-integrated microresonator with all-ChGs as the core (GeAsTeSe and GeSbSe) and the cladding (GeSbS) is proposed for MIR frequency comb generation. Moreover, to achieve precise dispersion engineering and low optical loss, a novel sandwich structure of the ChG microresonator featuring insensitive dispersion to the core height changes of the microresonator is proposed for the robust generation of MIR frequency combs. As a result, a MIR Kerr frequency comb with 5.1 μm spectral spanning from 6.94 μm to 12.04 μm assisted by dispersive waves has been numerically demonstrated. In addition, a feasible fabrication scheme to realize the designed microresonators is proposed and discussed. The advanced structure is also suitable for other material platforms, providing more flexibility for further optimization of MIR-integrated photonic devices. Our results pave the way for integrated ChG photonic devices in MIR nonlinear photonics and potential applications in MIR spectroscopy.

2. Design Principle

First, we design an all-ChG microresonator with a novel sandwich waveguide structure comprised of a medium-index material sandwiched between two high-index materials, which have high transmission in the infrared wavelength region, see Figure 1. By optimizing the effective refractive index of the microresonator, a majority of the mode field can be confined to the medium-index material. Here, the chalcogenide microresonator with a radius of 200 μm is designed with a sandwich microresonator structure, in which a GeSbSe layer with a 6 μm thickness is sandwiched between two GeAsTeSe layers with a 0.5 μm thickness and the width of the waveguide is 6.3 μm, see Figure 1. The waveguide is covered with a more than 10 μm thick GeSbS cladding to avoid the absorption of the light field by the substrate [20,21]. The waveguides can realize a unique mode field distribution [22] and feature thickness-insensitive dispersion, significantly different from the slot waveguide structure [23]. Thus, it enables us to engineer the dispersion by tailoring the sandwich microresonator’s structure and realizing a broadband generation of MIR micro comb.

The mode field distribution profile in the sandwich microresonator depends on the mode effective indices of different layers; see the insets of Figure 1. Typically, a large cross-section of the MIR waveguide is expected for confining IR light in the waveguide to reduce surface scatterings of the top and sidewall. However, in multilayer-hybrid waveguide cases, the light tends to be guided into the upper or lower thin layers with a higher refractive index because of the total internal reflection (TIR). We should carefully tailor the multi-layers geometric parameters (i.e., H1) to break the TIR conditions, which enables the mode field to leak into the medium-index layer from the high layer and also leads to a symmetrically uniform distribution of the mode field in the whole waveguide. Therefore, this enables us to demonstrate flexible dispersion engineering for broadband MIR micro comb generations that are insensitive to the middle layer thickness.

We achieve the mode effective refractive index matching condition at H1 = 0.5 μm, in which the mode field can leak into the medium-index layer from the high-index layer, see Figure 2a. Compared to the common microresonator (CM) with a core consisting of a single layer, the mode effective refractive index of the sandwich microresonator at the wavelength of 9 μm is insensitive to the middle layer thickness. Taking into account micro/nano-fabrication tolerance, we also simulate the mode effective refractive index in H1 = 0.35 μm and H1 = 0.65 μm, respectively. As a result, the variation of the mode effective index is negligible even if the H2 thickness changes up to 5 μm, see Figure 2a. Additionally, the radius of the sandwich microresonator is also carefully explored to reduce the radiation loss in the MIR [24]. However, as the radius increases, its large effective modal volume will result in a higher frequency comb generation threshold due to the cavity’s weak light–matter interaction. We simulated the propagation power loss (PPL) in COMSOL software using the following equation [20]:

$$\mathsf{\alpha }=\raisebox{1ex}{$4\mathsf{\pi }\mathrm{k}$}\!\left/ \!\raisebox{-1ex}{$\mathsf{\lambda }$}\right.$$

(1)

where k is the imaginary component of the simulated mode effective refractive index; the PPL decreases as the radius increases. For example, the PPL of the microresonator with a radius between 100 μm and 150 μm exceeds 0.1 dB/cm, even more than 1 dB/cm in the 100 μm one at the wavelength of 12 μm, see Figure 2b. As a result, we choose the microresonator with a radius of 200 μm and PPL of 0.1 dB/cm at the wavelength of 12 μm.

3. Results and Discussion

3.1. Dispersion Engineering

The integrated dispersion represents the role of the higher-order dispersion in the integrated microresonators, which is given by [25,26].

$$D_{int}={\omega }_{\mu }-{\omega }_0-D_1\mu =\frac{D_2}{2!}{\mu }^2+\frac{D_3}{3!}{\mu }^3+\cdots$$

(2)

where $\mu$ is the mode number relative to pump mode, ${\omega }_{\mu }$ is the resonance frequency of the cavity, ${\omega }_0$ means the pump frequency, $D_1=\frac{\partial {\omega }_{\mu }}{\partial \mu }{|}_{\mu =0}=\Delta {\omega }_{FSR}$ means the free spectral range (FSR) of the cavity, and $D_2=\frac{{\partial }^2{\omega }_{\mu }}{{\partial \mu }^2}{|}_{\mu =0}$ represents the second-order dispersion composed of material dispersion and waveguide dispersion. The high-order dispersion profile allows the reshaping of the spectra of the frequency comb and is critical for generating dispersive waves (DWs). The integrated dispersion can be tailored by finely tuning geometric structures, which renders the phase-matching condition of DWs and contributes to the bandwidth extension of the frequency comb. The phase-matching condition of DWs is given by [27],

$$\beta \left({\omega }_d\right)-\beta \left({\omega }_0\right)=v_g^{-1}\left({\omega }_d-{\omega }_s\right)+\frac{\gamma P}{2}$$

(3)

where $\beta$ is the mode propagation constant and ${\omega }_d$ and ${\omega }_s$ are the angular frequencies of DWs and the soliton central angular frequency, respectively. The $v_g$, $P$, and $\gamma$ are group velocity, pump power, and nonlinear coefficient, respectively [28]. The phase-matching condition of DWs can be simplified to D_int(μ) = 0 in the microresonator model [29]. Hence, we design a geometry profile with two zero dispersion wavelengths (ZDWs) to obtain a broadband MIR frequency comb.

By comparing the sandwich microresonator and CM microresonators, the influence of the geometric parameters on second-order dispersion and the integrated dispersion is negligible in our sandwich microresonator, see Figure 3a. Two ZDWs can be obtained, and the right ZDW is moving to a longer wavelength as H2 increases from 6.1 μm to 6.5 μm. Moreover, as the core thickness H2 sweeps in a 200 nm step, the integrated dispersion curve represents a small variation in the sandwich microresonator than that in CM, see Figure 3b. Therefore, our sandwich microresonator is promising for an overall flat and thickness-insensitive dispersion profile.

3.2. Generation of MIR Micro comb

In order to obtain a MIR frequency comb with a bandwidth coverage from 7 μm to 12 μm, the integrated dispersion curves with two DWs have been demonstrated by pumping at 9 μm. The pump wavelength can be obtained through QCL lasers with output powers larger than 1 W and the narrow linewidth in the kHz-MHz [30,31,32,33,34,35]. Since the actual third-order nonlinearity of these ChGs has not been measured in the mid-infrared wavelengths, we use the measured refractive index to calculate the nonlinear coefficient in the MIR region by the following equation [36]:

$$n_2=4.27\times {10}^{-16}\frac{{(n_0^2-1)}^4}{n_0^2}{\mathrm{c}\mathrm{m}}^2/\mathrm{W}$$

(4)

where $n_0$ is the linear refractive index. For a more accurate result, n₂ is multiplied by a correction (0.3) according to Ref. [21]. We get the linear refractive index n₀ = 2.5943 and calculated third-order nonlinearity n₂ = 2.05 × 10⁻¹⁸ ${\mathrm{m}}^2/\mathrm{W}$ at the wavelength of 9 μm.

Our numerical simulations on the nonlinear dynamics of comb generation are carried out using the Lugiato–Lefever equation [37,38,39,40],

$$\frac{\partial {\tilde{A}}_{\mu }\left(t\right)}{\partial t}=\left(-\frac{\kappa }{2}+i\left(2\pi {\delta }_0\right)+i{D}_{int}(\mu )\right){\tilde{A}}_{\mu }-ig\mathcal{F}{[{\left|A\right|}^{2}A]}_{\mu }+\sqrt{{\kappa }_{ex}}{S}_{in}$$

(5)

where ${\tilde{A}}_{\mu }$ is spectral envelopes of the light field in microresonators, and $A$ is the Fourier transform of ${\tilde{A}}_{\mu }$. $\kappa$ is the cavity total decay rate in which $\kappa ={\kappa }_0+{\kappa }_{ex}=\frac{\omega }{Q_0}+\frac{\omega }{Q_{ex}}$ composed of the intrinsic decay rate ${\kappa }_0$ and the external coupling rate ${\kappa }_{ex}$. ${\delta }_0$ is the pump detuning. $g=\frac{\hslash {\omega }^{2}c{n}_2}{n_g^2{\mathrm{V}}_{\mathrm{e}\mathrm{f}\mathrm{f}}}$ represents the Kerr gain coefficient, $V_{eff}=\frac{{\left(\iiint {\left|\overrightarrow{E}(\overrightarrow{r},t)\right|}^{2}dV\right)}^2}{\iiint {\left|\overrightarrow{E}(\overrightarrow{r},t)\right|}^{4}dV}$ means the effective mode volume, ${\left|S_{in}\right|}^2$ means the pump power and $D_{int}\left(\mu \right)$ represents the integrated dispersion of $\mu$th frequency component, respectively. In our simulation, high-order dispersion and self-steepening are included. We set the microresonator as assumed critical coupling, which means ${\kappa }_0={\kappa }_{ex}$. The integrated dispersion is composed of six components, $\frac{D_2}{2\pi }=$0.778 MHz, $\frac{D_3}{2\pi }=$−2.606 KHz, $\frac{D_4}{2\pi }=$−0.832 KHz, $\frac{D_5}{2\pi }=$15.973 Hz, $\frac{D_6}{2\pi }=$−0.395 Hz in the geometry parameters with W = 6.3 μm, H2 = 5.25 μm, H1 = 0.35 μm, R = 200 μm, and pump power is 405 mW. Additional numerical simulation parameters used in our simulation are listed in

Table 1. Numerical simulation parameters for generation of MIR Kerr frequency comb.

LLE Simulation Parameters
Pump frequency $v_{\mathrm{p}}$(THz)	33.31
Nonlinear refractive index n2 (m2/W)	2.05 × 10−18
Intrinsic quality factor Qi	2 × 106
External coupling factor Qc	2 × 106
Effective mode volume Veff (μm3)	5.05 × 104
Input pump power Pin (mW)	405
Free spectral range FSR (GHz)	87.97
Group refractive index ng	2.7

. We chose a reasonable Q factor according to the reported MIR microresonator [41]. As a result, a soliton step can be observed, which indicates the Kerr frequency comb could be generated in the ChGs microresonator [42], see Figure 4a. The MIR Kerr frequency comb is dynamically evaluated from the Turing state (i), chaos state (ii), and to single-soliton state (iii), see Figure 4b.

We further investigate the effect of microresonator widths on the micro comb bandwidth to compensate for microresonator dimensional changes caused by nano-fabrication tolerances, see Figure 5. Because the width of the waveguide can be tailored by lithography, we set the width of 6 μm and increase it with a step of 100 nm or 200 nm, and H2 is at the typical size of 5.25 μm. As a result, a tunable microcomb bandwidth can be realized, specifically, by extending the longer-wavelength region from 11.32 μm to 12.03 μm when the width (W) increases from 6.1 μm to 6.5 μm, see Figure 5b. It should be noted that the generation of frequency combs is dependent on the integrated dispersion profiles. For example, a Kerr soliton comb cannot be obtained in our simulation when W is 6.0 μm, probably because the modulation instability gain and stability of solitons is dramatically deteriorated by high-order dispersions in the near-to-zero group velocity dispersion microresonators [43].

In general, the influence of effective volume (V_eff) on the frequency comb in the telecommunication band is considered negligible. However, the influence of V_eff should be considered due to the broad MIR wavelength range. Particularly, to achieve a broadband mid-infrared frequency comb, the change of V_eff will seriously affect the shape of the frequency comb. In this work, we have added the V_eff effect in the LLE simulation (see Figure 6a) to analyze its influence on the total shape of the mid-infrared frequency comb. Figure 6b shows that the frequency-dependent V_eff does not play a significant role in the formation of a broadband soliton micro comb. It does have a slight impact on the spectral profile due to the variations in comb power at different wavelengths, leading to slight changes in the positions of dispersive waves.

3.3. Schematic of Fabrication Procedures

We propose a feasible nano-fabrication procedure for our sandwich microresonators depending on our previous experiment results [44,45,46], see Figure 7. Firstly, an 8 μm thick GeSbS lower cladding, a 0.5 μm thick GeAsTeSe layer, a 6 μm thick GeSbSe layer, and another 0.5 μm thick GeAsTeSe layer are deposited successively by thermal evaporation on a silicon substrate with a 3 μm thick thermal oxidation layer [16]. Then, the photoresist itself is spin-coated onto the wafer, and the waveguide pattern is transferred using an i-line contact mask aligner. After that, ultraviolet lithography and inductively coupled plasma etching (ICP-RIE) are used to fabricate the waveguide, and then the residual photoresist of the chip is removed [21]. The upper core selenide layers are etched in an ICP reactive ion etcher with CHF₃ gas. Finally, a 10 μm thick GeSbS upper cladding is thermally deposited onto the patterned wafer, and the all-ChG sandwich microresonator is observed.

4. Conclusions

In this work, a novel sandwich-integrated ChG microresonator is proposed to achieve precise and thickness-insensitive dispersion engineering for MIR micro comb generation. A broad bandwidth of 5.1 μm of the MIR Kerr frequency comb assisted by dispersive waves has been numerically demonstrated. The geometrical parameters of the sandwich all-ChG microresonators have been discussed in detail, paving the way for a robust dispersion engineering approach of the multilayer-hybrid integrated waveguides. Moreover, our MIR micro combs results propose the potential of integrated photonic devices based on all-ChGs for MIR nonlinear photonics and spectroscopy.