Broadband Supercontinuum Generation Using Dispersion Engineered As₂Se₃-GeAsSe-GeAsS Waveguide at 6 μm

This paper reports a theoretical study of supercontinuum generation with a novel dispersion-engineered reverse rib waveguide design using chalcogenide materials such as As2Se3 glass as a core, GeAsSe and GeAsS as cladding. This structure achieves an ultrawide bandwidth supercontinuum spectrum because of its high nonlinear property of core material and the low mode loss. The waveguide operates at 170fs laser sech pulses pumping at <inline-formula> <tex-math notation="LaTeX">$6~\mu \text{m}$ </tex-math></inline-formula> as a central wavelength. The proposed waveguide shows an ultra-wide spectrum of up to <inline-formula> <tex-math notation="LaTeX">$16~\mu \text{m}$ </tex-math></inline-formula> at 10kW peak power and up to <inline-formula> <tex-math notation="LaTeX">$13~\mu \text{m}$ </tex-math></inline-formula> broad spectrum at 5kW peak power. Results of spectral broadening for 2kW peak power are also discussed. The designed waveguide structure should be helpful in supercontinuum sources, bio-molecule sensing, and spectroscopy.

Supercontinuum (SC) generation is a nonlinear optical process by pumping ultrashort (preferably femtosecond or picosecond) pulses into any optical waveguides. When light passes through the fiber or waveguide (around the core region) results in a spectral broadening by the interaction of the light source with the waveguide. SC generation has The associate editor coordinating the review of this manuscript and approving it for publication was Md. Selim Habib . attracted much attention in recent years because of its wide range of applications in optical fiber communication [11], [12], coherence tomography [13], ultrafast amplifiers [14], frequency metrology, and many other fields. The supercontinuum spectrum generated in the infrared region is by the four-wave mixing between solitons and dispersive waves, self-frequency shift, and soliton fission [15], and the visible region of SC generation is by Cherenkov radiation [16], soliton trapping and cross-phase modulation [17].
Over the years, single and multi-mode fibers, tapered fibers, Photonic crystal fibers (PCF), and optical waveguides have been used to produce supercontinuum for different applications [18], [19]. The materials used to fabricate waveguides depend on the respective application. It is based on the range of wavelengths needed for the cause. Silicon glass (SiO 2 ) fibers were used when the range needed was visible and near-infrared region. Apart from this, heavy metal oxides were also used in this wavelength region. Fluoride glass fibers (ZBLAN, InF 3 , ZrF) [20], [21] and liquid core fibers (CS 2 , Ethanol) [22], [23] operate in the wavelength region of the visible, near-infrared, and near mid-infrared regions up to 4µm. Gas-filled hollow-core fibers (Ar, Xe, Ne, Kr, H 2 ) [24], [25] can spread the spectrum from ultraviolet (0.2µm) to the near-mid infrared region up to 6µm. Moreover, silicon core and silicon-based fibers are used in the region between 0.4 and 8µm [26], [27]. Recently, chalcogenide glass fibers (S, Se, Te) have been utilized from nearinfrared to mid-infrared regions, and studies are undergoing for mid-infrared to far-infrared regions [28], [29].
Low losses of chalcogen materials made these useful in all-optical switching, which is very important in the field of optical communication. There is a chance of TPA and MPA at lower wavelengths of the visible region, which helps broaden the spectrum. Using Degenerate four-wave mixing (DFWM), an experiment by Kanbara et al. [30] showed that an ultra-fast response time that is less than a picosecond can be achieved using chalcogenide materials.
The materials commonly considered to fabricate a waveguide or a PCF to generate SC generation are Silicon on Insulator (SOI) structures. David Duchesne et al. reported that a silicon waveguide with a core nonlinear index value of n 2 = 5 × 10 −18 m 2 /W does not demonstrate a wide range of spectral broadening [31]. However, it gave the idea to design waveguides to produce a broad spectrum. In the nearinfrared and mid-infrared regions, Ahmad et al. modeled Ge 11.5 As 24 Se 64.5 chalcogenide waveguides with a broadband spectrum [32].
Step index fiber design modeled by Siwach P et al. used Ge 11.5 As 24 Se 64.5 to simulate SC generation has a high core nonlinear index value of n 2 = 4.3 × 10 −18 m 2 /W. They considered the central wavelength as 3.1µm, showing the dispersion of −11.36ps/(nm.km) using 10µm fiber pumped with 50fs pulse. It generates a spectrum from 2µm to 13µm pumping in a normal dispersion regime, which covers both near and part of mid-infrared regions [33]. Sharma R et al. modeled a 10µm long waveguide using GAP-Se and MgF 2 materials pumping with 45 to 135ps pulses at the center wavelength of 3100nm. This structure reports a chromatic dispersion of +21.63ps/(nm km) with a nonlinearity of 991(1/W.km), and the structure offers a supercontinuum spectrum ranging from 1.4 -7.6µm [34].
Generation of supercontinuum by considering the optical waveguides with As 2 Se 3 as a core material has a prominent role due to its higher refractive index over long wavelengths. Moreover, the linear and nonlinear properties of As 2 Se 3 material show a good dispersion with the low loss with low latency interaction with the pulses. Yuan Wu demonstrated a single-mode PCF with As 2 Se 3 material as a core of the fiber. The structure results in a spectral broadening from 2 to 10µm with a central wavelength of approximately 4µm [35]. Saini et al. reported mid-infrared SC generation with graded index As 2 Se 3 PCF pumped at 4.1µm having 3.5kW peak power with 50fs pulses, which spans the supercontinuum from 2 µm to 15µm wavelength [36]. Yingying Wang et al. proposed a chalcogenide step-index fiber with As 2 Se 3 as a core and As 2 -As 2 S as cladding pumped with 150fs pulses at 6.5µm central wavelength. The design achieved supercontinuum broadband from 2µm to 12.7µm [37]. Cherif et al. gave a numerical study on As 2 Se 3 -based chalcogenide PCF spanning 2 octaves using a central wavelength of 2.8µm [38]. Zhlutova et al., demonstrated a spectrally demonstrated flat SC generation in Silica-based dispersion decreasing fibers (DDF) with different core diameters and achieved a significant difference in the temporal and spectral transformation of radiation depending on the direction of wave propagation [39]. Kalashnikov et al., studied the Raman response in soft-glass PCFs in infrared supercontinuum generation to show that the Raman shift is double as high in the soft-glass as compared to fused silica [40]. Saini and Sinha gave a review about the Supercontinuum generations in Soft-glass PCFs in Mid-Infrared Region [41].
SC spectrum from any optical waveguides has been analyzed by numerically solving the Generalized Nonlinear Schrodinger Equation (GNLSE). This equation contains the interaction parameters of each phenomenon that occurs from linear and nonlinear effects. Several mathematical models and computational approaches are required to solve these equations and simulate high-energy pulse propagation in a waveguide. In this paper, the designing of waveguide and the propagation modes are obtained using COMSOL Multiphysics software. The Interaction picture method of Runge Kutta (RKIP4) in the frequency domain is used to calculate and produce SC generation.
Recently, Ashok et al. designed a reverse rib waveguide design for dispersion analysis. The structure shows a high negative dispersion, and the author discussed the fabrication tolerances [3]. The generation of the spectrum from waveguides depends upon the material properties, dimensions & design of waveguides, the central wavelength of input wave pumping, and power of the pulse, etc. In this paper, a reverse rib waveguide structure optical waveguide is discussed. The materials used to design and simulate the waveguide contain chalcogenide glasses like As 2 Se 3 as a core covered with Ge 11.5 As 24 Se 64.5 around the core, and GeAsS covers the base and top. The proposed waveguide is optimized by changing the dimensions of the waveguide in order to obtain desired dispersion and to get a broad spectrum. At 6µm central wavelength, the designed waveguide has a loss of 1.9 dB/cm.

II. THEORY AND NUMERICAL ANALYSIS
In the present paper, a reverse rib-optical waveguide structure is proposed. The dimensions of the proposed waveguide are optimized for low loss at the pump wavelength. Optimization is done for the design for near-zero dispersion value around the central wavelength to achieve broad SC generation.
Chalcogenide glass materials have high Kerr nonlinearity. Its nonlinear index is roughly some hundred times that of silica at various operating wavelengths. That is why they are one of the most prominent in χ 3 (optical third-order nonlinear susceptibility) materials. The transmission range, ZDW, and refractive indices of the different materials are shown in Table 1 [28], [42].
The top and bottom strips of a waveguide are made by GeAsS with a height of 'f' (1.0µm) and a length of 'c'(16.0µm). The proposed waveguide's core is designed  with a combination of a strip and a rectangle. The core strip height is 'd'(1.2µm). The rectangle core has a width of 'b' (6.5µm) and a height of 'a' (2.6µm) made with As 2 Se 3 chalcogenide material. The length between the strip of core and the bottom strip of the waveguide is covered by GeAsSe material with the height 'e' (5.2µm). The designed waveguide is shown in Fig 1. n The refractive indices of materials are plotted in Fig. 2 and calculated by utilizing the Sellmeier equation, shown in (1) (Here λ is in micrometer). The values of Sellmeier coefficients for Ge 11.5 As 24 Se 64.5 , As 2 Se 3 , and GeAsS are given by Karim et al. [43], [44], and those are listed in Table 2: (Here B i is in micrometer).  The ''Reverse-Rib'' waveguide structure proposed here has some advantages in comparison with conventional designs. This structure confines the light modes more efficiently and also the fabrication of these types of designs is also easy [45]. Reverse ridge waveguide design can be fabricated in a crack-free manner. A groove should be created using GeAsSe substrate by reactive ion etching process (RIE), lower and upper slabs can be fabricated through Chemical Vapour Deposition (CVD) method. The core material As 2 Se 3 can be filled in predefined trenches on the substrate using low-pressure chemical vapor deposition [3], [46], [47], [48].
Dispersion (D) can be calculated using two diverse ways, using n eff or using β(ω). Here, the dispersion is solved numerically using (2) [1], [49], which results in values of dispersion for different wavelengths. From the dispersion graph, Zero Dispersion Wavelength (ZDW) is observed near 6µm, which helps in choosing the central wavelength to produce a supercontinuum.
By choosing appropriate waveguide parameters, the reverse waveguide structure shows −0.172ps/(nm.km) dispersion at the central wavelength of 6 µm.
For the analysis of ultrashort pulses propagating through a waveguide, solving the Generalized nonlinear Schrodinger equation shown in (3) is necessary [1], [50]. Where A = A(z,t) is a time-varying input pulse at central frequency ω o , α is a loss in the waveguide, and β k 's are the dispersion coefficients undergoing Taylor series expansion. β k where (k ≤ 2) are called Higher-order dispersion parameters (HODP), and it can be calculated by using (5) [49].
The second-order dispersion coefficient(β 2 ) is calculated by (4), and its higher-order dispersion coefficients are calculated by differentiating β 2 with respect to angular frequency(ω) (5). The nonlinear parameter (γ ) is plotted as a function of wavelength in Fig. 3 and calculated using (6) [1], [24]: where n 2 is the nonlinear index of core material (As 2 Se 3 ) valued 1.1×10 −17 m 2 /W with A eff = 24.045 µm 2 , the nonlinear parameter value is 479.06 1/(W . km). Loss of waveguide is also considered and its variation with the wavelength is plotted in Fig. 4. Raman scattering is one of the significant phenomena during SC generation, which is also considered while solving GNLSE, where f R is the Raman factor. At the center wavelength coefficients of Raman are τ 1 = 23fs, τ 2 = 164.5fs, and f R = 0.148 [43].
The energy band gap of As 2 Se 3 is significantly more than the combined energy of two and three incident photons, which is 0.413eV and 0.619eV. Due to an enormous difference between the energies. The effect of two and three-photon absorption can be neglected [9], [10]. In the present structure with the optimized waveguide parameters, the modes of waveguides are calculated in order to measure the effective mode index and loss. Fundamental TE mode is considered in this paper, and the mode intensity profile is shown in Fig 5.
The tolerance study of core height is shown in Fig. 6. By increasing core height(a), the curve becomes slanted away from the horizontal axis, and by decreasing the value of 'a', the curve becomes flat towards the horizontal axis. For low values of core height, flat dispersion is achieved throughout some parts of the wavelength region. Such a flat dispersion curve is a good candidate for supercontinuum generation. Increasing the core height from 2.2 µm to 3.0 µm noticed that the dispersion values are increasing and the ZDW is moving towards the lower wavelength region. Fixing all the waveguide parameters except the core width, the effect of core width on the dispersion curve is analyzed. To adjust the central wavelength near to zero dispersion line, analysis of core width plays a crucial role in the proposed structure. To investigate the core width effect, calculation of the dispersion curve for five different values of core width(b) are obtained and results are plotted in Fig 7. In the dispersion curve, as the core width increases, the line crossing zero dispersion shifts towards the lower end of the wavelength. As core width decreases, the curve is getting flattened in the middle of the wavelength range taken. From the figure, it is clear that for a core width of 5.5 µm, the curve shows zero dispersion at 7.9µm wavelength. As increasing core width to 6 µm, 6.5 µm, 7 µm, and 7.5 µm, the dispersion curve shows zero value near 7.1, 6, 5.65, and 5.45 µm wavelengths, respectively. From this result, it is evident that the effect of core width will help in choosing the central wavelength for SC generation.
Analysis of the effect of change in slab height(d) and the distance between core and cladding slab height(e) on the dispersion curve is considered. The obtained dispersion values are plotted in Fig 8(a) & Fig 8(b), respectively. From Fig. 8(a), The trend of the dispersion curve remains almost the same and is noticeable. The impact of slab height changes is insignificant at the lower and upper end of the spectral range. However, there are some small widenings in a span of 5.5 to 8 µm wavelength range.
Changes in distance between the core slab and the cladding slab highly impacted the far side of the wavelength spectrum near, i.e., 9 to 10µm. Remarkable changes by tuning the value of 'e' shown in Fig 8(b) can be observed. This is because of the variation in the mode confinement of the input pulse. The lower index of the cladding material, with respect to the core material, pushes the mode towards the upper core when the lower slab is near the core region. If the lower slab is placed far from the core region, the propagation of the light spreads freely in core GeAsSe material.
The obtained results reveal that by choosing appropriate reverse rib-waveguide parameters, such as a strip height of 1.2µm, core width of 6.5 µm, a core height of 2.6µm, and distance between the core slab and the bottom strip of 5.2 µm. A low dispersion of −0.172ps/(nm.km) is observed at 6 µm wavelength and low loss at the same wavelength.

IV. SUPERCONTINUUM GENERATION
The fundamental Transverse Electric (TE) mode is considered for simulations. The sech pulse with a width of 12.5ps operating at 6µm wavelength is used to generate SC. The equation for the sech pulse is given in (9) [1]. The Full-width half maximum (FWHM) of the pulse is taken to be 170fs, and outputs are taken with different peak power of 2kW, 5kW, and 10kW.
Due to the high nonlinearity of As 2 Se 3 , the dispersion graph shows impressive results. The dispersion curve for the optimized waveguide parameters is plotted on Fig. 9. Values of HODP are calculated using the dispersion values with respect to frequency, and the accuracy of these values is important to solve GNLSE [49].
At central wavelength the dispersion lies in a normal dispersion regime, and the dispersion is found to be -0.172 ps/(nm.km). Loss at central wavelength is calculated, and it was found to be 1.9 dB/cm. SC generation needs a solver for the propagation of light through waveguides. Python code has been used to run the simulation based on a highly effective step-size implementation of the fourth order Runge-Kutta in the Interaction Picture (RK4IP) method [51], [52]. V. Hitaishi, N. Ashok: Broadband Supercontinuum Generation Using Dispersion Engineered As 2 Se 3 -GeAsSe-GeAsS Waveguide  To generate broadband supercontinuum, 6µm wavelength pump is used near the zero dispersion wavelength value [43]. Inputs in the present calculation are chosen to be 2kW, 5kW, and 10kW power with 170fs pulse duration (FWHM). Results from simulations of the supercontinuum spectra for the 2kW power spectral intensity is plotted in Fig 10(a) and its spectral evolution for same power is plotted in Fig. 11(a). It has been noticed that solition formations are less in this low-power input. However, the SPM and dispersions spam the spectra from 3.9 to 9.1 µm, hence covering a 5.2 µm wide spectrum.
Spectral analysis for 5kW input power is calculated for generating SC from the proposed waveguide, and supercontinuum results are plotted in Fig. 10(b). By choosing appropriate waveguide parameters, the reverse rib waveguide reports a wide spectrum broadening from 3.45 to 13.1 µm with 9.65 µm widening. Solitions formation can be seen around the central wavelength, and the solition fission occurs after input wave propagation towards half of the length of the waveguide. Dispersive wave radiations are near the 4 µm region of the spectra, and the higher end of spectra occurs with Raman dispersion and SPM. The spectral evolution for 5kW peak power is plotted in Fig. 11(b).
Next, analysis of the supercontinuum spectrum for 10kW peak power is undertaken. Fig. 10(c) reports the SC generation for a peak power of 10kW. Here SPM leads to a spectral broadening. Some of the incident lights are blue shifted towards the short wavelength side by fundamental solitons. Considering the suitable parameters with a change in power of 10kW leads to a spectral broadening of 12.9µm from 3.1 to 16µm. Soliton fission occurs around 5µm length of the waveguide, and Blue shifted dispersive waves (DW) are noticed because of higher order dispersion before ZDW. The evolution of spectra for 10kW peak power is plotted in Fig. 11(c). From the above analysis, it is evident that the proposed structure achieves a broadband spectrum with the following designed parameters of a = 2.6µm, b = 6.5µm, c = 16.0µm, d = 1.2µm, e = 5.2µm and f = 1.0µm.

V. CONCLUSION
The waveguide proposed here is made by using GeAsS and Ge 11.5 As 24 Se 64.5 as cladding around the As 2 Se 3 core and is modeled by taking into consideration of good dispersion curve around the center wavelength. The structure achieves a dispersion of -0.172 ps/(nm.km) at 6µm center wavelength. The reverse rib waveguide generates a 12.9 µm supercontinuum spectrum at the central wavelength of 6µm at 10kW peak power. We have also numerically simulated the supercontinuum for 5kW and 2kW peak power, and the structure results in 9.65 µm and 5.2 µm broad spectrums, respectively. The reported broadband spectrums are achieved with an input pulse of 170fs. The designed reverse rib waveguide can be used as a source for supercontinuum sources. These sources can be used to measure optical attenuation in photonic crystal fibers and to evaluate the laser and amplifiers [53].