Improved formulation of the film mode matching method for mode field calculations in dielectric waveguides

Passive Photonic Integrated Circuits Elements Fabricated on a Silicon Nitride Platform

The fabrication processes for silicon nitride photonic integrated circuits evolved from microelectronics components technology—basic processes have common roots and can be executed using the same type of equipment. In comparison to that of electronics components, passive photonic structures require fewer manufacturing steps and fabricated elements have larger critical dimensions. In this work, we present and discuss our first results on design and development of fundamental building blocks for silicon nitride integrated photonic platform. The scope of the work covers the full design and manufacturing chain, from numerical simulations of optical elements, design, and fabrication of the test structures to optical characterization and analysis the results. In particular, technological processes were developed and evaluated for fabrication of the waveguides (WGs), multimode interferometers (MMIs), and arrayed waveguide gratings (AWGs), which confirmed the potential of the technology and correctness of the proposed approach.

Thin-ridge Silicon-on-Insulator waveguides with directional control of lateral leakage radiation

In this paper, we propose a Silicon-On-Insulator waveguide structure which when excited with TM guided light emits controlled TE polarized radiation from one side of the structure only. The validity of the proposed structure is analyzed using eigenmode expansion and supermode techniques. It is shown that care must be taken to select the gap between the radiating elements such that both the phase and the amplitude of the radiating modes are maintained along the propagation direction to achieve the desired directional control of radiation. Steps toward practical demonstration of the proposed structure are identified.

Lateral leakage of TM-like mode in thin-ridge Silicon-on-Insulator bent waveguides and ring resonators

We present the first prediction of lateral leakage behavior of the TM-like mode in thin-ridge SOI curved waveguides and ring resonators. A simple phenomenological model is first presented which predicts that the lateral leakage in these structures is significantly impacted by both the ring radius and waveguide width. This prediction is verified using full vectorial mode matching and finite element methods. We show that specific combinations of waveguide width and ring radius can lead to very low-loss propagation in the TM-like mode. This finding is critical for the design of high-Q resonators on such waveguide platforms and will have major impact on the field of silicon lasers and sensing applications.

Evanescent modes in out-of-plane band structure for two-dimensional photonic crystals

Reflection, diffraction and transmission of optical waves at the interface between a photonic crystal and the surrounding air can be described by propagating and evanescent Bloch modes. We have found such modes for one of the canonical two-dimensional photonic crystals, identical circular cylinders in a square pattern. We present computed out-of-plane band diagrams for propagating as well as evanescent modes, obtained with a numerical method based on Fourier-Bessel expansions. For a given frequency, all the modes are evanescent, except for a few low-order propagating modes. We find that most of the evanescent modes have a purely imaginary z-component of the Bloch wave vector, but many of the modes have a complex z-component.

Vectorial modal analysis of dielectric waveguides based on a coupled transverse-mode integral equation. I. Mathematical formulation

We propose a rigorous full-vector integral-equation formulation for analyzing modal characteristics of the complex, two-dimensional, rectangular-like dielectric waveguide that is divisible into vertical slices of one-dimensional layered structures. The entire electromagnetic mode field is completely determined by the y-component electric and magnetic field functions on the interfaces between slices. These interfacial functions are governed by a system of vector-coupled transverse-mode integral equations (VCTMIE) whose kernels are made of orthonormal sets of both TE-to-y and TM-to-y modes from each slice. To solve for the unknown functions, we construct sets of suitable expansion functions and turn VCTMIE into a nonlinear matrix equation via orthogonal projection. The eigenvectors of the matrix provide the mode field solutions of the complex dielectric waveguide.

Photonic bandgap structures in planar waveguides

If a one-dimensional (1D) or two-dimensional (2D) photonic bandgap (PBG) structure is incorporated into a planar optical waveguide, the refractive-index nonuniformity in the direction perpendicular to the waveguide plane responsible for waveguiding may affect its behavior detrimentally. Such influence is demonstrated in the paper by numerical modeling of a deeply etched first-order waveguide Bragg grating. On the basis of physical considerations, a simple condition for the design of 1D and 2D waveguide PBG structures free of this degradation is formulated; it is, in fact the separability condition for the wave equation. Its positive effect is verified by numerical modeling of a modified waveguide Bragg grating that fulfills the separability condition.