The coupled-mode theory (CMT) for optical waveguides is reviewed, with emphasis on the analysis of coupled optical waveguides. A brief account of the recent development of the CMT for coupled optical waveguides is given. Issues raised in the debates of the 1980’s on the merits and shortcomings of the conventional as well as the improved coupled-mode formulations are discussed. The conventional coupled-mode formulations are set up in a simple, intuitive way. The rigorous CMT is established on the basis of a linear superposition of the modes for individual waveguides. The cross-power terms appear logically as a result of modal nonorthogonality. The cross power is necessary for the self-consistency of the CMT for dissimilar waveguides. The nonorthogonal CMT, though more complicated, yields more-accurate results than the conventional orthogonal CMT for most practical applications. It also leads to the prediction of cross talk in directional couplers. The conventional orthogonal CMT is, however, reliably accurate for describing the power coupling between two weakly coupled, nearly identical waveguides. For dissimilar waveguides, a self-consistent orthogonal CMT can be derived by a redefinition of the coupling coefficients, and it predicts the coupling length and therefore the power exchange between the waveguides accurately if the two waveguides are far apart. Three typical coupler configurations—the uniform, the grating-assisted, and the tapered—are examined in detail. The accuracy, scope of validity, limitations, and extensions of the coupled-mode formulations are discussed in conjunction with each configuration. To verify the arguments in the discussions, comparisons with the exact analytical solutions and the rigorous numerical simulations are made.

Coupled-mode theory for optical waveguides: an overview

A full-vectorial imaginary-distance beam propagation method based on a finite element scheme is newly formulated and is effectively applied to investigating the problem of leakage due to a finite number of arrays of air holes in photonic-crystal holey fibers (HFs). In order to treat arbitrarily shaped air holes and to avoid spurious solutions, a curvilinear edge/nodal hybrid element is introduced. Furthermore, in order to evaluate propagation characteristics of not only bound modes but leaky modes in HFs, an anisotropic perfectly matched layer is also employed as a boundary condition at computational window edges. It is confirmed from numerical results that the propagation loss increases rapidly with increasing wavelength, especially for HFs with one ring of smaller air holes, and that the propagation loss is drastically reduced by adding one more ring of air holes to the cladding region.

Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers

Silicon Photonics technology is rapidly maturing as a platform for larger-scale photonic circuits. As a result, the associated design methodologies are also evolving from componentoriented design to a more circuit-oriented design flow, that makes abstraction from the very detailed geometry and enables design on a larger scale. In this paper, we review the state of this emerging photonic circuit design flow and its synergies with electronic design automation (EDA). We cover the design flow from schematic capture, circuit simulation, layout and verification. We discuss the similarities and the differences between photonic and electronic design, and the challenges and opportunities that present themselves in the new photonic design landscape, such as variability analysis, photonic-electronic co-simulation and compact model definition. Silicon Photonics Circuit Design: Methods, Tools and

https://www.onlinelibrary.wiley.com/doi/epdf/10.1002/lpor.201700237

Silicon Photonics Circuit Design: Methods, Tools and Challenges

Simulations of optical guided waves in three-dimensional waveguide structures by a full vector beam propagation method are described. Two sets of coupled equations governing the propagation of the transverse electric and magnetic fields are derived systematically. Polarization dependence and coupling due to the vectorial nature of the electromagnetic fields are considered in the formulations. The governing equations are solved subsequently by finite-difference schemes. The vector BPM is first assessed for a step-index circular fiber by comparing the numerical results with the exact analytical solutions. The guided modes of a rib waveguide are then investigated in detail. Comparisons among the scalar, semi-vector and full-vector simulations of the rib waveguide are made. Finally polarization rotation of a periodically loaded rib waveguide operated fully based on the vector nature of the electromagnetic waves is modeled and simulated. >

Simulation of three-dimensional optical waveguides by a full-vector beam propagation method

In this paper, we propose a numerical scheme to solve the two-dimensional (2D) time-dependent Schrodinger equation using collocation points and approximating the solution using multiquadrics (MQ) and the Thin Plate Splines (TPS) Radial Basis Function (RBF). The scheme works in a similar fashion as finite-difference methods. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme.

A numerical method for two-dimensional Schrödinger equation using collocation and radial basis functions

The newly developed finite-difference vector beam propagation method (FD-VBPM) is analyzed and assessed for application to two-dimensional waveguide structures. The general formulations for the FD-VBPM are derived from the vector wave equations for the electric fields. The stability criteria, the numerical dissipation, and the dispersion of the finite-difference schemes are analyzed by applying the von Neumann method. Important issues regarding the implementation, such as the choice of reference refractive index, the application of numerical boundary conditions, and the use of numerical solution schemes, are discussed. The FD-VBPM is assessed by calculating the attenuation coefficients and the percentage errors of the propagation constants of the TE and TM modes of a step-index slab waveguide. Several salient features of the FD-VBPM are illustrated. >

The finite-difference vector beam propagation method: analysis and assessment

An in-depth study of the beam propagation method for the vector mode calculation of optical waveguides is presented. It is established that the imaginary-distance propagation method may be generalized to vectorial modes for arbitrary structures by combining it with the finite-difference vector beam propagation method (FD-VBPM). A simple, unified theory and analysis are developed. An assessment of the accuracy and efficiency is carried out by comparing the simulated results with the analytical solutions for well-known structures. >

Efficient and accurate vector mode calculations by beam propagation method

The fiber-optic LP/sub 01/ from or to LP/sub 11/ mode transducers are analyzed by a scalar coupled-mode theory with vector correction. The authors deal with fiber-optic mode transducers made of a single fiber with periodic perturbations due to microbends, acoustic waves, or a photoinduced index grating. Both the couplings caused by the index perturbations and by the vector property of the fields (polarization effect) are taken into account in the analysis. Approximate analytical solutions to the coupled-mode equations are obtained. The power exchange among the modes along the fiber and spectral properties of the mode transducers are examined. The functions of the mode transducers used as wavelength filters and polarizers are studied. >

Modeling and analysis of fiber-optic mode transducers: single fiber with periodic perturbations

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The finite-difference vector beam propagation method: analysis and assessment

Efficient and accurate vector mode calculations by beam propagation method

Modeling and analysis of fiber-optic mode transducers: single fiber with periodic perturbations