SOI-Compatible Degenerate Band Edge Photonic Structure: Design Rules and Robustness Analysis

TL;DR

The paper addresses realizing a degenerate band edge (DBE) exceptional point in a realistic SOI platform consisting of two coupled waveguides with asymmetric gratings. It develops a design flow and uses three-dimensional FDTD to map dispersion, Bloch modes, and near-field profiles, confirming quartic dispersion near the stationary point and identifying DBE and RBE behaviors in two coupling regimes. Finite-size analysis shows that DBE resonances exhibit steep Q-factor growth with the number of unit cells ($Q\sim N^5$) while RBEs scale as $Q\sim N^3$, validating the DBE nature; the DBE resonance is sharper and more spectrally confined than the RBE. The study also demonstrates robustness to fabrication tolerances, with the DBE dispersion shape preserved under realistic parameter variations, and highlights potential applications in high-power optical amplification and narrow-linewidth lasers using SOI-compatible nanophotonic platforms.

Abstract

Optical periodic structures exhibiting a degenerate band edge (DBE) are of significant interest for various applications such as switching, sensing, high-power amplification, and lasing. At the edge of the bandgap in such structures, a fourth-order exceptional point degeneracy arises, leading to an extremely flat dispersion band. We propose and study a Silicon-on-Insulator-compatible structure composed of two coupled waveguides with asymmetric gratings. The dispersion relations and the field profiles are obtained using three-dimensional finite-difference time-domain simulations, and we provide a set of practical guidelines for the design and optimization of such structures, in order to obtain a DBE. We analyze the transmission and reflection spectra of finite-size devices, and investigate their spectral properties near the stationary points. The scaling of the resonance quality factor with the number of unit cells is studied, revealing a performance that surpasses that of conventional periodic structures. Finally, we examine the robustness of the DBE with respect to fabrication tolerances and structural imperfections.

Figures (9)

• Figure 1: Schematic of the proposed structure, composed to two coupled Silicon waveguides with gratings, on SiO$_2$ substrate.
• Figure 2: Dispersion relations of a single waveguide (gray circles) and two coupled waveguides (red 'x' - even mode, blue '+' - odd mode). (a) Waveguides without gratings. (b) Waveguides with gratings.
• Figure 3: TE eigen-modes of two coupled waveguides. The panels show a cross section of real part of $E_y$ in the xy plane. (a) Even mode. (b) Odd mode.
• Figure 4: Bloch dispersion relations corresponding to Set 1 and Set 2 designs. Orange dots and light blue circles mark a DBE and an RBE at the center of the Brillouin zone, respectively. (a) Weak coupling case (Set 1). inset - zoom in on the DBE and RBE at the center of the Brillouin zone. (b) Strong coupling case (Set 2).
• Figure 5: Electrical field intensity, $|E_y|^2$, profile inside the structure, near the DBE frequencies (a) Geometrical parameters of Set 1. (b) Geometrical parameters of Set 2.