Coupled-mode Theory Equations Research Articles

Physics-Driven Machine-Learning Approach Incorporating Temporal Coupled Mode Theory for Intelligent Design of Metasurfaces

Metasurfaces find a wide variety of applications in the last decades due to their powerful ability to manipulate electromagnetic (EM) waves. Traditional approaches for metasurface design require massive full-wave EM simulations to achieve optimal geometrical parameter values, resulting in an inefficient design process of metasurfaces. In this article, we propose a physics-driven machine-learning (ML) approach incorporating temporal coupled mode theory (CMT) to improve the design efficiency and implement an intelligent design of metasurfaces. In the proposed approach, a surrogate model (i.e., neuro-CMT model) is developed to speed up the prediction of EM responses of metasurfaces. A three-stage method is used to develop the neuro-CMT model. First, we perform full-wave EM simulations of unit cells only containing single-and double-resonators for different geometrical design parameter values. Second, we extract the single-and double-resonator CMT parameters for each geometrical parameter value by fitting the corresponding EM responses based on CMT equations. Third, we train neural networks to learn the relationships between the CMT parameters and geometrical parameters for single-and double-resonator systems, respectively. These trained neural networks, in conjunction with the multiresonator CMT equation, become an efficient tool to accurately predict the EM responses of any arbitrary coupled multiresonator systems. The proposed neuro-CMT model can be further utilized for metasurface design optimizations. Two metasurface absorbers are given as examples to demonstrate the efficient and intelligent advantages of our proposed approach.

Analysis of coupling from core mode to counter-propagating radiation modes in tilted fiber Bragg gratings

Radiation-mode coupling is stronger and more efficient in tilted fiber Bragg gratings than in other fiber gratings; it has good advantage in such fields as optical communication and optical sensors. A simplified coupled-mode theory (CMT) approach is proposed for what we believe to be the first time, whose validity is demonstrated by comparing its simulation results with that of the complete CMT equations. With the simplified CMT approach, a theoretical spectral analysis of coupling from core mode to counter-propagating radiation modes in reflective tilted fiber Bragg gratings is presented. The influence of grating length, refractive index modulation amplitude and tilt angle is exhaustively investigated on the transmission spectrum characteristics. The different dependences between s-polarized and p-polarized radiation-mode coupling on grating tilt angle are discussed, and the coupling strength of 45°-tilted gratings shows the greatest polarization dependence with the limitation of backward-propagating radiation-mode coupling.

Analysis of radiation-mode coupling in reflective and transmissive tilted fiber Bragg gratings

Radiation-mode coupling is stronger and more efficient in tilted fiber Bragg gratings than in other fiber gratings; it can be used to good advantage in such fields as optical communication and optical sensors. A simplified coupled-mode theory (CMT) approach to the analysis of radiation-mode coupling is proposed for what we believe to be the first time, whose validity and accuracy is demonstrated by comparing its simulation results with that of the complete CMT equations and the volume current method (VCM). With the simplified CMT approach, a theoretical spectral analysis of coupling from core mode to radiation modes in both reflective and transmissive tilted fiber Bragg gratings is presented. The influence of tilt angle on the transmission spectrum characteristics is comprehensively investigated. The different dependences between s-polarized and p-polarized radiation-mode coupling on grating tilt angle are discussed, and an analysis is performed on how to obtain a high-performance in-fiber polarizer that involves a compromise between polarization extinction and insertion loss.

Extension of Coupled Mode Analysis to Infinite Photonic Superlattices

Coupled-mode theory (CMT) is extended to the case of infinite 2-D photonic arrays, made of periodically repeated identical groups of different waveguides (supercells). Born-Karman boundary conditions, applied to the CMT equations for this system, are used to compute the photonic band structure. This method was found to be more efficient and much less resource-consuming than the existing approaches, for the analysis of finite large-sized arrays.

Resonant coupling of dielectric optical waveguides via rectangular microcavities: the coupled guided mode perspective

Placed between two waveguides that serve as input and output ports, a wide segment of a third high contrast multimode dielectric waveguide can constitute the cavity in an integrated optical microresonator. We consider these devices in a spatial 2D setting by means of a bidirectional coupled mode theory (CMT) based on the guided fixed-frequency modes of the two port waveguides and the cavity segment. Combined with the numerically computed reflectivity of the cavity facets, the CMT equations can be solved for the power transmission of the resonators, in good agreement with rigorous mode expansion simulations. The CMT model allows to virtually detach the cavity from the port waveguides. Resonant configurations can thus be found as singularities in the matrix denominator of the CMT equations. Inspired by the field shape and the quality of some of the resonances, a more detailed look at the cavity facets reveals an effect of almost total reflection for specific slab mode superpositions. Both results together show that a slab waveguide mode solver is in principle sufficient for an approximate identification and classification of the resonances in the rectangular cavities. Several numerical examples illustrate the design procedure.