Theoretical Investigation of Broadband Frequency Conversion Bridging the Mid-Infrared and Telecom Band Through a Chalcogenide/Sio2 Hybrid Waveguide

Capturing the distinctive spectral fingerprints of molecules in the infrared (IR) region is of vital importance in gas detection. However, it is still limited by the resolution, sensitivity and signal to noise ratio of IR detectors. Here, a broadband frequency conversion scheme from the middle IR band (MIR) to the telecom band based on four-wave mixing process is proposed and theoretically investigated, combining the advantages of well-established detectors in the telecom band and unique molecular vibrations in the MIR band. A flat and low dispersion profile is generated in an asymmetric Ge-As-Se/SiO2 hybrid waveguide, which exhibits four zero-dispersion wavelengths and a dispersion variation of sub-20 ps/nm/km. Furthermore, taking advantage of the high order phase-matching, an ultra-broad 3-dB continuous wavelength conversion bandwidth covering 1454–4521 nm is achieved, which to the best of our knowledge is the widest frequency conversion bandwidth in the chip-scale devices. In addition, a fabrication scheme is proposed for the precise manipulation of dispersion. It holds great potential for practical applications in photonic integrated gas sensing, biomedical diagnostics.


Introduction
Highly sensitive and accurate identification of molecules is in great demand in national security, biomedical and industrial engineering applications [1]- [3]. Infrared (IR) spectroscopy is considered the gold standard for molecular structures identification by detecting the distinctive spectral fingerprints of molecules in middle infrared (MIR) region. For example, several trace gases such as CH 4 , CO, NO, N 2 O, and NO 2 have weak absorption in the near-IR region (NIR, 0.8-1.6 μm) and 100 times stronger absorption peaks in the MIR region (e.g., the stretching frequencies of the molecules containing C-H bonds in the 3-3.7μm region) [4]. Nevertheless, the detectivity is still challenged by low resolution and signal-to-noise ratio of available MIR detectors. Furthermore, MIR spectral systems generally require a low-temperature environment or multi-stage thermoelectric cooling system to suppress dark current noise, which severely impairs their versatility [5], [6].
The frequency conversion scheme based on four-wave mixing process (FWM) has been successfully demonstrated in fibers or on-chip waveguide systems in a wide variety of platforms [6]- [13]. Especially, chip-scale waveguide devices have advantages of small size, low cost, and low power consumption. Such a broadband conversion provides an alternative method for implementing photonic integration of molecular detection. Infrared laser signal carrying the spectral fingerprints of molecule in the MIR band is converted to the telecom band by FWM and detected by the uncooled, high-performance integrated detector in telecom band. The schematic is illustrated in Fig. 1, where the unique combination of the advantages of high-performance devices in the telecom band and the distinctive molecular fingerprints in the MIR band realized in a chip-scale waveguide. However, to achieve a broadband and efficient frequency conversion based on the FWM process in a chip-scale waveguide, it is still challenging to ensure the phase-matching over a large wavelength range.
An ideal integrated nonlinear platform for our target would have both a high optical nonlinearity and a large transparent bandwidth. Chalcogenide glasses (ChGs), which are well-known for their wide transparency window ranging from visible to long-wave IR, high Kerr nonlinearity, low twophoton absorption and ultrafast nonlinearity response, are particularly promising material platforms for photonic integrated nonlinear devices [14], [15].
Among them, Ge 11.5 As 24 Se 64.5 shows excellent film-forming property and negligible refractive index change under intense illumination, which have been verified as a photostable nonlinear candidate in planar waveguides [16]- [19]. Moreover, recent advances in fabrication technology including atomic layer deposition and nano-lithography have realized precise film thickness control and low optical loss. On the other hand, the phase-matching over a large bandwidth is still a problem. Multilayer waveguides structures have been proposed to flatten waveguide dispersion with multiple zero dispersion wavelengths (ZDWs), which provides flexible material and structure choices [20]- [27]. In AlGaAs waveguide, ultra-high conversion efficiency of −4 dB is realized but the conversion bandwidth is only ∼700 nm [28]. Later, the authors showed in simulation that the conversion bandwidth can be improved to an octave (1.1-2.5 μm) [29]. In silicon nanowaveguide, conversion bandwidth over two-thirds of an octave from 1241 nm to 2078 nm is realized [13]. In As 2 S 3 -SiO 2 double-slot waveguide, a simulated conversion bandwidth of about 1200 nm is realized [30]. However, to date, the conversion bandwidth is still not enough for our target application.
In this work, an asymmetric Ge 11.5 As 24 Se 64.5 /SiO 2 hybrid waveguide is proposed and designed to obtain a flat and low dispersion over a large wavelength range. The frequency conversion performance is optimized through utilizing the high-order phase matching and carefully selecting the pump wavelength, as well as waveguide length. A 3 dB continuous frequency conversion covering a 3067 nm or 140 THz bandwidth from MIR to telecom band is achieved in a compact waveguide on chip. In addition, a fabrication process of the hybrid waveguide is proposed to ensure the dispersion tolerance caused by fabrication errors. The proposed scheme might facilitate the on-chip trace gas sensing, biomedical diagnostics, scientific exploration of early diagnosis of cancer.

Principle of Dispersion Flattening Based on ChG/SiO 2 Hybrid Waveguide
Achieving phase-matching over a large wavelength bandwidth is of vital importance in realizing our target. Here, a multilayer waveguide structure is proposed to flatten dispersion, whose cross section is demonstrated in Fig. 2(a). We carefully choose Ge 11.5 As 24 Se 64.5 and SiO 2 as the constituents of the hybrid waveguide here. Besides Ge 11.5 As 24 Se 64.5 having high transmittance from visible to MIR [18], the SiO 2 film with a thickness of sub-500 nm also shows good transmission performance in the range of 1.5-5 μm [31], as shown in Fig. 2(b). A high RI contrast between SiO 2 and Ge 11.5 As 24 Se 64.5 shown in Fig. 2(c) provides strong light confinement for enhancing the optical nonlinearity. These attributes are essential for broadband efficient frequency conversion. What's more, considering the aging problem of ChGs when exposed in air, we add a 5-nm layer of Al 2 O 3 on the surface as a protective layer [32], [33]. In the following section, we will discuss how to optimize the waveguide parameters to achieve a broadband flattened dispersion profile.

Design and Optimization of Waveguide Structures
Firstly, the effects of each structural parameter on dispersion are systematically investigated. As shown in Fig 2(a), the structural parameters W, Hu, Hs, and Hl stand for the waveguide width, the upper strip height, the slot height, and the lower strip height, respectively. The chromatic dispersion profile of the quasi-TM mode can be calculated through the equation D = −(λ/c) · (d 2 n eff /dλ 2 ), where n eff is the effective refractive index. Taking into account material dispersions of Ge 11.5 As 24 Se 64.5 , SiO 2 and Al 2 O 3 [31], the dispersion value as a function of wavelength is obtained using finite element method. As is shown in Fig. 3(a), when increasing the lower strip height Hl, the overall dispersion profile is moved from normal to anomalous regime gradually. In contrast, the dispersion is moved from anomalous to normal regime as the Hu increases, as shown in Fig. 3(b). The profile flips with respect to around 2.1 μm, reflecting more sensitivity to Hs at long wavelengths than that at short ones, shown in Fig 3(c). At the same time, the dispersion profile flips with respect to around 2.5 μm when W increases, as indicated in Fig. 3(d). Following the trend of the shape and bandwidth of dispersion profile on these parameters, a low and flat dispersion profile can be finely tailored by adjusting these structural parameters.

Dispersion Profile and Nonlinear Characteristics of the Optimized Waveguide
From above, a flat and low dispersion profile with saddle-shape of the hybrid waveguide can be achieved by setting the structural parameters as W = 1400 nm, Hu = 305 nm, Hl = 710 nm, Hs = 110 nm. The four ZDWs are located at 1720 nm, 2170 nm, 2690 nm and 3200 nm, as shown in Fig. 4(a). The quasi-transverse-magnetic (quasi-TM) mode distributions at the wavelengths of 1600, 2200, 2800 and 3400 nm are also demonstrated in Fig 4(a). It shows that a great part of the optical field for the quasi-TM modes gradually shifts from the lower Ge 11.5 As 24 Se 64.5 layer to the SiO 2 layer as the wavelength increases. At shorter wavelength, most part of the fundamental quasi-TM mode is confined in lower Ge 11.5 As 24 Se 64.5 layer, thus, the total dispersion is mainly determined by material dispersion in this wavelength range. In the middle wavelength range, optical power enters the slot layer (mode transition), which provides additional normal dispersion and results in four ZDWs, generating a saddle-shaped dispersion profile [20]. At longer wavelengths, the total dispersion is dominated by waveguide dispersion and only a small portion of power enters the substrate and cladding layer. This effect could load the low and flat dispersion by tailoring structural parameters.
Besides, the waveguide structure is quite small so that it only supports two higher-order modes at the TM polarization, i.e., TM 10 and TM 20 modes. Fig. 4(b) shows the effective refractive indices of higher-order modes and fundamental quasi-TM mode. The cut-off wavelengths of higher-order modes are below 3200 nm.
Moreover, the effective mode area and nonlinear coefficient play a vital role in frequency conversion based on FWM. The effective mode area (A eff ) and the real part of nonlinear coefficient (γ ) of the waveguide are [35], [36]: where e and h is the electric field vector and magnetic field vector respectively, n 2 is the Kerr index of materials (in this study, we take n 2 = 9 × 10 −18 m 2 /W for Ge 11.5 As 24 Se 64.5 [18]), and λ is wavelength. The A eff and γ of the optimized waveguide as a function of wavelength are depicted in Fig. 4(c). The A eff is increased as wavelength increases, which is less than 1.4 μm 2 in the wavelength range from 1.5 μm to 3.5 μm. On the other hand, the γ is gradually decreased as wavelength increases. The maximum γ is as large as 59 W −1 m −1 at 1.5 μm, which is about 2.8 × 10 4 times higher than that of the single-mode silica fiber [35].

High-Order Phase-Matching Enabled Broadband Frequency Conversion
In order to obtain higher frequency conversion efficiency, the effects of dispersion and nonlinearity on the phase matching is studied. For degenerate FWM, the phase mismatch can be expressed as k = β + 2γ P p , where β = 2β p − β s − β i is the linear phase mismatch between pump, signal, and idler waves, and β p , β s and β i are the propagation constants for pump, signal and idler, respectively. 2γ P p is the nonlinear phase term induced by self-phase modulation (SPM) and cross-phase modulation (XPM). The β is related to the dispersion profile by using the following relation [37]: where β 2 and β 4 are second-and fourth-order dispersion parameters at pump wavelength, respectively, and is the angular frequency separation between pump and signal. Operating in the undepleted pump regime [38], the FWM conversion efficiency can be calculated by γ 2 P p 2 L eff 2 η, where L eff = (1 − e −αL )/α is the effective length of the waveguide (α: the loss per unit length and 3 dB/cm [6] is used in this calculation, L: the waveguide length). The phase matching factor η can be expressed as: As is shown in Fig. 4(d), the calculated β 2 and β 4 dispersion profiles express different signs in three wavelength ranges where a discrete frequency conversion based on high-order phasematching can be potentially achieved with a large pump-signal frequency detuning [39], [40]. However, the discrete conversion is generally narrowband and thus limits the practical applications. Therefore, in order to realize broadband continuous frequency conversion, the effects of pump wavelength and waveguide length on the phase matching should be studied [28]. Fig. 5(a) shows the simulated phase-mismatch (| β · L/π |) for different pump and signal wavelengths setting in the Ge 11.5 As 24 Se 64.5 /SiO 2 hybrid waveguide with an optimized cross-section parameter (W = 1400 nm, Hu = 305 nm, Hl = 710 nm, Hs = 110 nm) and a length of 1 cm. The green contour line indicates the near phase-matched condition (| β · L/π | = 1), where the conversion efficiency is half that of the perfect phase-matched case, and the blue dash lines denote four zero-dispersion wavelengths (ZDW1-ZDW4, numbered from short wavelength to long wavelength). When pumping at the red-detuned of the second ZDW (2200 nm, the red dash line in Fig. 5(a)), the fundamental conversion band can be merged with high-order phase-matching bands to realize an ultra-broad continuous conversion band. There are CW fiber laser sources below 2.21 μm that can provide enough pump power of >60 mW, considering a 3 dB fiber-to-chip coupling loss [41], [42]. Fig. 5(b) shows the simulated normalized conversion efficiency evolution as the waveguide length increases when the waveguide is pumped at 2200 nm. The black line and two white dash lines correspond to the pump wavelength and high-order phase-matched wavelengths, respectively. The black dash contour indicates a normalized conversion efficiency of −3 dB. As shown in Fig. 5(c), the conversion efficiency increases with the waveguide length due to the enhanced interaction length, while the 3 dB conversion bandwidth shows the opposite trend, resulting from the accumulation of phase mismatch between signal and pump in the waveguide. Note that the conversion bandwidth exhibits a sharp decline at 1.5 cm, because the high-order phase-matching bands are separate from the fundamental band. It is shown in Fig 5(b) that the continuous conversion band appears as long as the waveguide length does not exceed 1 cm. Thus, the waveguide length of 1 cm is selected for the next calculation of conversion efficiency in this work.
Considering both damage threshold of materials and available pump power (with 3 dB fiber-tochip coupling loss), a pump power of 60 mW is used. Fig. 5(d) shows the conversion efficiency as a function of signal wavelength when the waveguide is pumped at 2200 nm with a power of 60 mW. The 3 dB continuous conversion bandwidth can be extended to 3067 nm (from 1454 to 4521 nm), i.e., 140 THz, with a peak conversion efficiency of −38.43 dB. Correspondingly, the performance of frequency conversion between MIR band and telecom band is also demonstrated in Fig. 5(d).
Signal at MIR band (covering 3357-4380 nm wavelength range) can be transferred to the telecom band (covering 1460-1625 nm wavelength range). Moreover, the conversion efficiency is flat within the operating wavelength range. With high detectivity of telecom-band detectors, this conversion efficiency level creates enough power for detection. Compared with the previous reports [37], [39], [40], [43], [44], our result achieves the widest frequency conversion bandwidth in a monolithic integrated waveguide.

Analysis of Fabrication Tolerance
Practically, the overall dispersion shape and bandwidth are also affected by the changes of the slot height from fabrication errors. Accordingly, we propose a fabrication scheme for the hybrid waveguide, as shown in Fig. 6, to further improve the fabrication tolerance for dispersion engineering. Firstly, the lower Ge 11.5 As 24 Se 64.5 film is deposited via thermal evaporation onto a silicon wafer with a 300μm SiO 2 layer (TOX). Then a thin SiO 2 layer is deposited on it by ALD. Next, the upper Ge 11.5 As 24 Se 64.5 layer is deposited using similar parameters of the lower layer. The thicknesses of the Ge 11.5 As 24 Se 64.5 and SiO 2 films are accurately measured by AFM, respectively. After films deposition, the photoresist film (PR) is spin-coated onto the wafer and the waveguide is patterned by electron-beam lithography (EBL) and etched in an inductively coupled plasma (ICP) reactive ion etcher with CHF 3 gas [45]. Note, the Ge 11.5 As 24 Se 64.5 and SiO 2 can be etched by CHF 3 simultaneously. Finally, a 5-nm protective Al 2 O 3 layer is deposited on the surface of our sample by ALD. Enabled by state-of-the-art film deposition and nano-lithography techniques, the slot film thickness can be controlled within 2 nm accuracy while the slab layer thickness and waveguide width controlled within 10 nm accuracy.
To analyze the fabrication tolerance, we randomly change the structural parameters within the aforementioned accuracy range to simulate practical fabrication error. Six different structures are listed in Table 1. Fig. 7 demonstrates the dispersion profiles of these waveguide structures. The overall dispersion variation is about ±25 ps/nm/km. The peak efficiencies, conversion bandwidths and corresponding simulation parameters of these six waveguides are also shown in Table 1. Note that all the results are simulated with a pump power of 60 mW. As we can see, some bandwidths are narrowed to several hundred nanometers because the high-order phase-matching bands are separate from the fundamental conversion band. However, we can still achieve our  target at bridging NIR and MIR-band through tuning pump wavelength, which simultaneously tune the positions of the high-order phase-matching bands. The peak efficiency ranges from −37.96 dB to −40.4 dB, which is acceptable since photodetectors operated in telecom-band have relatively high detectivity. Based on the above analysis, we can emphasize that the dispersion of the hybrid waveguide has a good fabrication tolerance. This indicates that achieving broadband frequency conversion should consider several key elements altogether, including the effective nonlinearity and dispersion of the waveguides, as well as accurate fabrication process allowing precise control of dispersion and low optical loss.

Conclusion
A Ge-As-Se/SiO 2 hybrid waveguide with a low and flat dispersion has been proposed for broadband frequency conversion. A flat dispersion with four ZDWs across 1530 nm with a total variation of 10 ps/nm/km is achieved by fine dispersion engineering. A 3 dB conversion bandwidth of 3067 nm, i.e., 140 THz, with peak conversion efficiency of −38.43 dB is achieved when pumped at 2200 nm with a power of 60 mW. A fabrication scheme is proposed for the precise control of dispersion. The results highlight that the photonic chip-based frequency conversion based on FWM has potential in detecting fingerprints of the molecules.