Compact Nonvolatile Reconfigurable Mode Converter by Sb₂S₃ Embedded in 4H-Silicon-Carbide-on-Insulator Platform

Abstract

Nonvolatile switching is emerging and shows potential in integrated optics. A compact nonvolatile reconfigurable mode converter implemented on a 4H-silicon-carbide-on-insulator (4H-SiCOI) platform with a footprint of 0.5 × 1 × 1.8 μm³ is proposed in this study. The functional region features an Sb₂S₃ film embedded in a 4H-SiC strip waveguide. The functionality is achieved through manipulating the phase state of the Sb₂S₃. The high refractive index contrast between the crystalline Sb₂S₃ and 4H-SiC enables high-efficiency mode conversion within a compact footprint. The incident TM0 mode is converted to the TM1 mode with a high transmittance (T) beyond 0.91 and a mode purity (MP) over 91.72% across the 1500–1600 nm waveband. Additionally, when the Sb₂S₃ transitions to its amorphous state, the diminished refractive index contrast efficiently mitigates the mode conversion effect. In this state, the TM0 mode propagates through the functional region with minimal perturbation, exhibiting T ≥ 0.99 and MP_TM0 ≥ 97.65% within a 1500–1600 nm waveband. Furthermore, the device performances were investigated under partially crystallized states of Sb₂S₃. The proposed structure offers a broad range of transmittance differences (−16.42 dB ≤ ΔT ≤ 17.1 dB) and mode purity differences (−90.91% ≤ ΔMP ≤ 96.11%) between the TM0 mode and TM1 mode. The proposed device exhibits a high robustness within ±20 nm Δl and ±10 nm Δw. We believe that the proposed multi-level manipulation can facilitate a large communication capacity and that it can be deployed in neuromorphic optical computing.

1. Introduction

Phase-change materials (PCMs), a category of compounds, possess amorphous (disordered) and crystalline (ordered) structural states, enabling dramatic changes in their optical properties, e.g., refractive index (n) and extinction coefficient (k) [1]. The phase states are switched reversibly by external electric or optical stimuli. Furthermore, PCMs stably maintain their phase states without the application of constant power, resulting in huge potential in terms of nonvolatile optical switching and memory applications [2]. Ge₂Sb₂Te₅ (GST), a well-established PCM, provides a high refractive index contrast (Δn~2.8) near the wavelength of 1550 nm but suffers from a large extinction coefficient in both the amorphous and crystalline states [3]. In order to minimize the optical loss, Ge₂Sb₂Se₄Te₁ (GSST) has been explored, offering a refractive index contrast of ~1.7 and an ultralow loss in the amorphous state [4]. However, the extinction coefficient in the crystalline state should not be ignored. To deal with this issue, Muskens et al. [5] reported two wide-bandgap PCMs, i.e., Sb₂Se₃ and Sb₂S₃, with ultralow losses (k < 10⁻⁵) in both the amorphous and crystalline states. The low-loss Sb₂S₃ features a high refractive index contrast of 0.6 in the telecommunications C-band at 1550 nm, thereby rendering it highly suitable for nonvolatile optical switching in programmable photonic integrated circuits (PICs).

Mode-division multiplexing (MDM) leverages distinct spatial modes of light as independent data channels, and it is acknowledged as a promising technique for solving the exponential growth in data consumption [6]. A critical component of MDM is integrated mode-order converters, which enable seamless transitions between waveguide modes, unlocking the potential of spatial multiplexing in PICs. The principles of mode conversion can be summarized into three types: mode reconstitution, mode coupling, and mode evolution [7]. Mode reconstitution converters rely on the manipulation of the phase relationship within the eigenmodes, employing Mach–Zehnder interferometers (MZIs) [8,9], grating-assisted couplers [10,11], slot waveguides [12,13], and metawaveguides [14,15] dedicated to mode decomposition, phase shift, and mode reconstitution. Mode coupling converters need to fulfill the phase-matching condition between the fundamental and high-order modes through asymmetric directional couplers [16,17], Bragg gratings [18,19], metasurfaces [20,21], and so on. Mode evolution converters are based on the adiabatic transformation of the mode field, which fundamentally requires close matching of the modal effective indices. The reported schemes mainly comprise multichannel branching waveguides [22], asymmetric Y-junctions [23], and tapered waveguides [24,25]. Furthermore, reconfigurable mode-order converters can provide flexibility, scalability, and adaptability, crucial for advancing optical technologies in communication, sensing, quantum systems, and beyond. The ability to dynamically manipulate spatial modes opens new avenues for innovation across interdisciplinary applications. Reconfigurable mode-order converters assisted by PCMs, e.g., GSST [26,27], Sb₂S₃ [28], and Sb₂Se₃ [29], have been explored and developed. These devices deliver remarkable performance but compromise on their compact device footprint.

Herein, we propose a nonvolatile reconfigurable mode converter implemented on the emerging 4H-SiCOI platform. In the functional region, the Sb₂S₃ film is embedded in a 4H-SiC slab waveguide with a compact footprint of 0.5 × 1 × 1.8 μm³. When the Sb₂S₃ is in its crystalline state, its refractive index at a wavelength of 1550 nm is higher than that of 4H-SiC. Such a high refractive index contrast results in remarkable mode conversion. On the condition that the Sb₂S₃ is switched to its amorphous state, this mode-conversion effect becomes negligible due to the low refractive index contrast between the 4H-SiC and the amorphous Sb₂S₃ (a-Sb₂S₃). Through this, a nonvolatile reconfigurable mode-order converter is achieved that is assisted via manipulating the phase state of the Sb₂S₃.

2. Design and Principle

A schematic diagram of the method is sketched in Figure 1a,b. The proposed nonvolatile reconfigurable mode converter is deployed on the emerging 4H-SiC platform. In order to perfectly support both the TM0 and TM1 modes, the width W and height H of the 4H-SiC strip waveguide were set to 1 μm and 0.5 μm, respectively. An Sb₂S₃ film, a low-loss PCM in both crystalline and amorphous states near the 1550 nm wavelength, is embedded in a 4H-SiC strip waveguide. To improve the fabrication accuracy and reduce the fabrication difficulty, its height h was also fixed at 0.5 μm. Then, its width w and length l were separately set to 0.22 μm and 1.8 μm through parametric sweeps for attaining the highest mode conversion efficiency. As depicted in Figure 1c, the crystalline and amorphous states of Sb₂S₃ can be converted reversibly and fast by electrical or optical stimulations. The refractive index of Sb₂S₃ will change with the phase state. According to this rule, a high refractive index contrast exists between the 4H-SiC and the crystalline Sb₂S₃ (c-Sb₂S₃), which enables intense mode decomposition, phase shifting, and mode reconstitution effects within the specially designed structure, resulting in a remarkable mode conversion between the TM0 mode and TM1 mode. Once the Sb₂S₃ is switched in the amorphous state, the refractive index contrast becomes low, resulting in the mode conversion effect being negligible. Thus, a reconfigurable TM0-to-TM1 mode conversion is realized by the manipulation of the Sb₂S₃ within a compact footprint of 0.5 × 1 × 1.8 μm³.

The key element is the mode conversion that happens with the crystalline Sb₂S₃. The hybridized-mode interface method is used for the mode conversion [10]. Figure 2a,b depict the two lowest-order hybridized supermodes (HP₁ and HP₂), which generate, produce the phase shift, and synthesize in the specially designed functional region. In the process of the mode exchange, the transfer matrixes are described as follows:

$$M=\left[\begin{array}{cc}{\kappa }_{11}& {\kappa }_{12}\\ {\kappa }_{21}& {\kappa }_{22}\end{array}\right],$$

(1)

and

$$L=\left[\begin{array}{cc}{e}^{-j({\beta }_1-{\beta }_2)l}& 0\\ 0& 1\end{array}\right],$$

(2)

where κ_mn (m, n = 1, 2) denotes the coupling coefficient between the incident TM(n − 1) mode and the hybridized supermode HP_m, β₁ and β₂ denote the propagation constants of HP₁ and HP₂, respectively, and l is the length of the Sb₂S₃ film. As the middle functional region is mirror-symmetrical, the transfer matrix M can be written as M^T because of the optical reciprocity [30]. The matrix elements of M and M^T should fulfill the following: ${\kappa }_{ik}^2+{\kappa }_{jk}^2\le 1$ and ${\kappa }_{ki}^2+{\kappa }_{kj}^2\le 1$(i ≠ j and k = 1, 2). According to the transfer matrix method, the output of the converter is expressed as follows:

$$\left[\begin{array}{c}{k}_{\mathrm{out}1}\\ k_{\mathrm{out}2}\end{array}\right]=M^{T}LM\left[\begin{array}{c}{k}_{\mathrm{in}1}\\ k_{\mathrm{in}2}\end{array}\right]=\left[\begin{array}{cc}{e}^{-j({\beta }_1-{\beta }_2)l}{\kappa }_{11}^2+{\kappa }_{21}^2& {\kappa }_{21}{\kappa }_{22}+{\kappa }_{11}{\kappa }_{12}{e}^{-j({\beta }_1-{\beta }_2)l}\\ {\kappa }_{21}{\kappa }_{22}+{\kappa }_{11}{\kappa }_{12}{e}^{-j({\beta }_1-{\beta }_2)l}& e^{-j({\beta }_1-{\beta }_2)l}{\kappa }_{12}^2+{\kappa }_{22}^2\end{array}\right]\times \left[\begin{array}{c}{k}_{\mathrm{in}1}\\ k_{\mathrm{in}2}\end{array}\right],$$

(3)

where κ_in m and κ_out m denote the complex amplitudes of the incident TM(m − 1) mode and the output TM(m − 1) mode (m = 1, 2), respectively. To attain a complete mode conversion, it must achieve M^TLM = [0 1; 1 0], which should satisfy the conditions |k_mn| = sqrt(2)/2 and e^{−j(β1−β2)l} = −1. To ensure the first condition |k_mn| = sqrt(2)/2, various structural designs have been reported, such as Mach–Zehnder interferometers, gratings, slot waveguides, and so on. Herein, we chose a high-refractive-index material (crystalline Sb₂S₃) to be inlaid in a slab 4H-SiC waveguide for a compact footprint. Such a specially designed structure can support the pair of desired hybridized supermodes.

Apart from the optimal coupling coefficients, the second condition is e^{−j(β1−β2)l} = −1, i.e., the desired phase-shifting is equally crucial. To calculate the phase shift between HP₁ and HP₂, boundary model analyses were conducted by a finite-difference eigenmode (FDE) solver (Ansys Mode Solutions: Waveguide Simulator) [31]. The effective refractive index is expressed as follows [32]:

$$n_{eff}=\beta {\displaystyle \frac{\lambda }{2\pi }},$$

(4)

where β, i.e., the propagation constant, is the wavevector along the guiding direction x-axis. The effective refractive indices (n_eff) of HP₁ and HP₂ were calculated as 2.445 and 2.052 with a wavelength of 1550 nm, respectively. The spectral responses of the propagation constants are depicted in Figure 2c. It can be deduced from the second condition, e^{−j(β1−β2)l} = −1, that the π phase shift is vital for the mode conversion. The corresponding coupling length (CL) is described as follows [33]:

$$CL={\displaystyle \frac{\pi }{\Delta \beta }}={\displaystyle \frac{\pi }{({\beta }_1-{\beta }_2)}},$$

(5)

which is illustrated in Figure 2d. The sample (1.55, 1.97) means that the π phase shift can be obtained at a wavelength of 1550 nm when the coupling length is equal to 1.97 μm. Therefore, the length l of the Sb₂S₃ was initially fixed to 1.97 μm, which is further optimized in the three-dimensional simulation for propagation in Section 3.

3. Simulation and Performance

To calculate the device’s performance, we utilized a three-dimensional finite-difference time-domain (3D FDTD) method (Ansys Lumerical FDTD Solutions: 3D Electromagnetic Simulator) [34]. The refractive indices of silica and 4H-SiC were set to 1.44 and 2.6, respectively. The crystalline and amorphous Sb₂S₃ contents were set to 3.308 and 2.716, respectively. The simulated area had dimensions of 5 × 5 × 8 μm³. The boundary conditions were set to the perfectly matched layers (PMLs). The mesh-override section was fixed to dx = dy = dz = 10 nm to guarantee precision in the simulation. The transmittances of both the TM0 and TM1 modes were extracted by a mode expansion solver [35]. The target length l was optimized to 1.8 μm from 1.97 μm by parameter sweeping to attain the highest mode conversion efficiency. The finite-size field distributions and boundary conditions in the 3D FDTD simulations influenced the phase accumulation, resulting in an optimal length shift. When the inlaid Sb₂S₃ was crystalline, the proposed structure converted the incident TM0 mode to the TM1 mode with a high transmittance (T) of 0.91 and a mode purity (MP) of 93.03% at a wavelength of 1550 nm, as depicted in Figure 3a. The transmission losses were primarily caused by the high refractive index contrast between the crystalline Sb₂S₃ and the 4H-SiC, which can be mitigated through introducing some structural elements such as tapers, smoothing of the index transitions, or field matching at the expense of higher fabrication accuracy and difficulty. The mode purity is defined as follows:

$$MP (\%)={\displaystyle \frac{T_{TMi}}{T_{total}}}\times 100\%,$$

(6)

where T_TMi denotes the transmittance of the output TMi mode (i = 0, 1), and T_total is the total transmittance. Actually, apart from the output dominant TM1 mode, the other output power consists of the remaining TM0 mode and a higher-order mode (i.e., the TM2 mode). According to the optical reciprocity of the mirror-symmetrical functional region, it can be observed in Figure 3b that the used TM1 mode was converted to the TM0 mode with T = 0.94 and MP = 89.65%. Such a mode conversion relies on the high refractive index contrast between the 4H-SiC and the crystalline Sb₂S₃. However, abrupt refractive index transitions at the material interfaces induce significant light scattering and Fresnel reflections, which impose inherent limitations on the mode conversion efficiency. The proposed approach can obtain a compact device footprint but compromises in terms of the mode conversion efficiency. Once the Sb₂S₃ is switched to its amorphous state, its refractive index contrast becomes low, causing the mode conversion effect to disappear. Figure 3c,d show that the TM0 and TM1 modes propagated smoothly through the proposed structure with an ultrahigh transmittance (0.99) and mode purity (98.02% and 96.81%).

The spectral responses of the transmittance and mode purity were calculated with the incident TM0 mode with a 1500–1600 nm waveband. As illustrated in Figure 4a, the transmittance of the TM1 mode (T_TM1) remained beyond 0.83, and the transmittance of the TM0 mode (T_TM0) remained below 0.041 at a 1600 nm wavelength. As shown in Figure 4b, the mode purity of the TM1 mode (MP_TM1) remained above 91.72%, and the mode purity of the TM1 mode (MP_TM0) remained lower than 4.49% at a 1600 nm wavelength. Obviously, the TM0-to-TM1 conversion was remarkable with the crystalline Sb₂S₃. Figure 4c illustrates that the used TM0 mode was almost unaffected through the proposed structure with T_TM0 ≥ 0.97 and T_TM1 ≤ 0.021 at a 1500 nm wavelength. It is worth noting, as shown in Figure 4d, that MP_TM0 ≥ 97.65% and MP_TM0 ≤ 2.1% at a 1500 nm wavelength. It can be inferred that the mode conversion effect became negligible with the amorphous Sb₂S₃.

4. Discussion of the Partially Crystallized States of Sb₂S₃

Apart from their crystalline and amorphous states, phase-change materials (PCMs) also possess intermediate states. It is rather challenging to ascertain whether PCMs are in a completely crystalline or amorphous state. It is essential to conduct an investigation into the performances of devices in intermediate states. Multi-level partially crystallized states have been employed in diverse applications, e.g., multi-level memory [36], image displays [37,38], and photonic convolutional neural networks [3]. Sb₂S₃ is an emerging PCM that exhibits intriguing intermediate states between its amorphous and crystalline phases. These states are typically induced by normally incident laser pulses and have been validated through Raman spectroscopy. An intermediate state denotes a composite of amorphous and crystalline molecules, characterized by a specific crystallization ratio. The precise selection of peak intensities and durations of control pulses is indispensable for achieving an exact intermediate state. The corresponding effective dielectric constant ε_eff can be estimated via the effective medium theory in combination with the Lorent–Lorenz relation, as follows [39,40]:

$${\displaystyle \frac{{\epsilon }_{eff}(\lambda )-1}{{\epsilon }_{eff}(\lambda )+2}}=m{\displaystyle \frac{{\epsilon }_c(\lambda )-1}{{\epsilon }_c(\lambda )+2}}+(1-m){\displaystyle \frac{{\epsilon }_a(\lambda )-1}{{\epsilon }_a(\lambda )+2}}$$

(7)

where ε_c and ε_a denote the wavelength-dependent permittivity of crystalline and amorphous Sb₂S₃, respectively. m is the crystallization ratio, ranging from 0 (amorphous) to 1 (crystalline). The calculated refractive indices n are shown in Figure 5, with 10% crystallization ratio step. The theoretical refractive indices were used in the simulations to calculate the device performances.

The device performances encompass the transmittance (T), transmittance difference between the TM0 mode and TM1 mode (ΔT), mode purity (MP), and mode purity difference between the TM0 mode and TM1 mode (ΔMP). The TM0 mode was used in the proposed structure with a wavelength of 1550 nm. Figure 6 depicts the relationship between the above four performances and the crystallization ratio. It can be observed in Figure 6a that T_TM0 diminished as T_TM1 escalated with the increase in the crystallization ratio. The reason lies in the fact that the mode conversion effect was enhanced as the crystallization ratio was increased. Figure 6b depicts the transmittance difference between the TM0 mode and TM1 mode (ΔT = T_TM0 − T_TM1), ranging from −16.42 dB to 17.1 dB. When the crystallization ratio was 63%, the transmittances of the TM0 and TM1 modes were equal, so ΔT = 0 dB. As illustrated in Figure 6c, the mode purities of the output TM0 and TM1 modes both equalled 50% at a crystallization ratio of 63%. It is worth noting that the mode purity difference (ΔMP = MP_TM0 − MP_TM1) possessed a wide range, from −90.91% to 96.11%. To sum up, the proposed structure can provide a broad transmittance difference (−16.42 dB ≤ ΔT ≤ 17.1 dB) and mode purity difference (−90.91% ≤ ΔMP ≤ 96.11%) between the TM0 mode and TM1 mode by controlling the phase state of the Sb₂S₃. Such multi-level manipulation could attain a large communication capacity and could be deployed in convolutional neural networks for neuromorphic optical computing [3].

5. Robustness Analysis and Suggested Fabrication

As a theoretical study, it was necessary to conduct a robustness analysis. In the functional region, the inlaid Sb₂S₃ film is pivotal, so the variations in its length Δl and width Δw were considered. In the simulations, the TM0 mode was used in the proposed structure with a wavelength of 1550 nm. When the Sb₂S₃ was in its crystalline state, the incident TM0 mode was converted into the TM1 mode. As depicted in Figure 7a, the transmittance remained above 91% within ±20 nm deviations of Δl and Δw. It should be noted, as shown in Figure 7b, that the mode purity of the output TM1 mode remained beyond 90% within ±20 nm Δl and ±10 nm Δw. Figure 7c illustrates that the mode purity of the remaining output TM0 mode was below 5.28% within ±20 nm Δl and ±10 nm Δw. In a way, the width w of the Sb₂S₃ is more sensitive than the length l. Additionally, when the Sb₂S₃ was switched to its amorphous state, the mode conversion effect became inappreciable because of the low refractive index contrast. As shown in Figure 7d, the transmittance remained over 99.92%. It can be observed in Figure 7e,f that MP_TM1 ≤ 2.4% and MP_TM0 ≥ 97.4% were achieved within ±20 nm deviations of Δl and Δw. In short, the proposed device held its functionality within ±20 nm Δl and ±10 nm Δw. Finally, the suggested fabrication process is sketched in Figure 8. Commercial high-purity semi-insulating 4H-silicon carbide on insulator (4H-SiCOI) material can be fabricated through sublimation growth [41]. An amorphous Sb₂S₃ film can be deposited using electron-beam deposition (EBD) [42,43,44,45]. The cladding material, silica (SiO₂), is deposited onto the 4H-SiC substrate via the process of plasma-enhanced chemical vapor deposition (PECVD). The process for creating the 4H-SiC strip pattern and performing Sb₂S₃ lift-off necessitates two-step electron-beam lithography (EBL) procedures, succeeded by reactive ion etching (RIE). The phase state of the Sb₂S₃ film can be manipulated through a single-pulse laser with over 7000 switching cycles between amorphous and crystalline Sb₂S₃ [46,47]. Intermediate states can be reproducibly achieved through precise control of external laser pulses, and this has been confirmed via Raman spectroscopy. We anticipate that this will be conducive to the fabrication process.

6. Conclusions

In conclusion, a compact nonvolatile reconfigurable mode converter is proposed, deployed on a 4H-silicon-carbide-on-insulator (4H-SiCOI) platform with a footprint of 0.5 × 1 × 1.8 μm³. The functional region features an Sb₂S₃ film inlaid in a 4H-SiC strip waveguide. The functionality is realized via manipulating the phase state of the Sb₂S₃. When the Sb₂S₃ is crystalline, the high refractive index contrast between the crystalline Sb₂S₃ and 4H-SiC facilitates high-efficiency mode conversion. The incident TM0 mode is converted into the TM1 mode with a high transmittance (T) of 0.91 and a mode purity (MP) of 93.03% at a wavelength of 1550 nm. It is worth noting that T ≥ 0.91 and MP_TM1 ≥ 91.72% were achieved across a 1500–1600 nm waveband. Once the Sb₂S₃ transitions to its amorphous state, its refractive index contrast is significantly diminished, thereby rendering the mode conversion effect negligible. The used TM0 mode was barely affected through the functional region, with a high transmittance of 0.99 and a mode purity of 98.02% at a wavelength of 1550 nm. It should be noted that T ≥ 0.99 and MP_TM1 ≥ 97.65% were maintained within a 1500–1600 nm waveband. Furthermore, the proposed structure exhibits remarkable versatility, offering a broad range of transmittance differences (−16.42 dB ≤ ΔT ≤ 17.1 dB) and mode purity differences (−90.91% ≤ ΔMP ≤ 96.11%) between the TM0 mode and TM1 mode via precise control of the Sb₂S₃ phase state. The fabrication tolerance analyses revealed its robust performance, maintaining stability within ±20 nm Δl and ±10 nm Δw. We believe this innovative approach to multi-level manipulation not only facilitates enhanced communication capacity but also holds significant potential for deployment in neuromorphic optical computing systems. The unique characteristics and robust performances position it as a promising candidate for advanced photonic applications.