Realizing Large Topological Bandgaps and Edge Modes in Symmetric Silicon-on-Insulator Photonic Crystals

Introduction

Photonic crystals (PhCs) exhibiting topological bandgaps and edge modes have garnered significant research interest due to their robustness against disorder-induced scattering and potential applications in one-way waveguides. However, most studies have focused on air-bridge (or membrane) PhC slabs to maximize the refractive index contrast and achieve wider photonic bandgaps. While these structures offer desirable properties, they are challenging to fabricate and lack mechanical robustness. Conversely, non-membrane PhCs, although simpler to fabricate and mechanically robust, have been overlooked due to their lower refractive index contrast and the expectation of smaller and ill-defined photonic bandgaps.

In a recent study, researchers from the National Institute for Materials Science (NIMS) and the University of Tsukuba proposed a design to attain rigorous photonic bandgaps even in non-membrane structures, leveraging the advantages of topological PhCs. They examined the photonic bandgap width and dispersion relation of the topological edge modes in symmetric silicon-on-insulator (SOI) PhCs.

Design and Fabrication

The researchers designed a symmetric SOI PhC by covering the PhCs with a thick layer of SiO2, as illustrated in Fig. 1(a). Because the cladding and capping SiO2 layers are sufficiently thick, the PhC slabs can be considered symmetric about the center of the top Si layer. This symmetry restricts the mixing between the lowest symmetric TE (transverse electric)-like modes and the lowest antisymmetric TM (transverse magnetic)-like modes.

Fig. 1. (a) Diagram of a symmetric SOI photonic crystal (PhC) showing a side view with a SiO2 capping layer and an enlarged view of the x-y plane at the mid-section of the silicon slab. (b) and (c) Dispersion relations of PhC-t and PhC-n calculated by finite element method (FEM) with solid and dashed lines, respectively, and measured by angle resolved reflection spectroscopy, depicted with circles and triangles. Top-view SEM images of PhCs before SiO2 capping are shown alongside their respective dispersions.

Using finite element method (FEM) simulations with COMSOL Multiphysics, the researchers found a 4.1% complete bandgap shared by topologically trivial (PhC-t) and non-trivial (PhC-n) PhCs. The calculated dispersion relations for PhC-t and PhC-n are shown in Fig. 1(b) and (c) by solid and dashed lines, respectively.

Furthermore, they discovered edge modes localized at the zig-zag boundary between the PhC-t and PhC-n regions. The dispersion relation of the edge modes, shown in Fig. 2(a) with the grey area denoting the bulk mode region and maroon lines representing the edge modes, revealed a gap of 12 cm^-1 at kx = 0 due to the absence of mirror symmetry at the zig-zag boundary. This gap results in a linear polarization of the edge modes at kx = 0.

Fig. 2. (a) Displays an enlarged view of the edge mode dispersion and frequency ranges of bulk modes at the zig-zag boundary between PhC-t and PhC-n, calculated by FEM (maroon solid lines and grey shading), and measured by angle-resolved reflection spectroscopy (solid and open circles and triangles). (b) Shows an enlarged view of the edge mode dispersion and frequency ranges of bulk modes at the armchair boundary between PhC-t and PhC-n.

The researchers fabricated the PhC slabs in the top Si layer of the SOI wafer using electron beam lithography, followed by Si-deep etching by the Bosch RIE process. Subsequently, they buried the PhCs in SiO2 using plasma-enhanced chemical vapor deposition (PECVD), as shown in the insets of Fig. 1(b) and (c).

Results and Discussion

The researchers examined the dispersion relations of the PhC-t, PhC-n, and edge-mode (zig-zag boundary) specimens by high-resolution angle-resolved reflection spectroscopy in the mid-infrared region. They mapped the eigenfrequencies using circles and triangles in Fig. 1(b) and (c) for the individual PhC slabs and in Fig. 2(a) for the edge modes at the zig-zag boundary.

The results confirmed the complete common bandgaps of individual PhCs, as seen in Fig. 1(b) and (c), and the presence of edge modes at the zig-zag boundary. The edge modes were detected with linear polarization at normal incidence (kx = 0) due to the gap between the edge modes.

To reduce the gap between the edge modes and ensure spin-locking, the researchers switched to an armchair boundary between PhC-t and PhC-n. The calculated dispersion relation for this configuration, shown in Fig. 2(b), exhibits a negligible gap of 0.29 cm^-1, promising a wider spin-locking region and reduced backscattering loss.

Conclusion

The researchers from NIMS and the University of Tsukuba successfully fabricated symmetric SOI PhCs that materialized wide topological bandgaps and edge modes for the lowest-order symmetric TE-like modes. They confirmed the complete bandgaps by high-angle-resolution reflection measurements and polarization selection rules and detected the presence of edge modes.

This work demonstrates the potential of symmetric non-membrane PhCs in realizing rigorous photonic bandgaps comparable to previously reported PhC membranes. By utilizing the merits of topological PhCs, this design offers a simpler and more mechanically robust alternative to air-bridge structures, paving the way for practical applications in one-way waveguides and topological photonics.

Reference

[2] Begum et al., "Large and Complete Topological Bandgaps with Edge Modes in Symmetric SOI Photonic Crystal Slabs," Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan; Department of Applied Physics, University of Tsukuba, Tsukuba, Japan, 2024, pp. 1-6, doi: 979-8-3503-9404-7/24/$31.00 ©2024 IEEE.