A Modified Coupled Mode Equation For Parallel Dielectric Waveguides
Abstract
Despite the fact that the coupled mode theory is widely used for practical applications, the majority of researchers still employ the conventional (or so-called orthogonal) formulation of this theory. It is shown that this formulation lacks accuracy and yields erroneous results in the case of strongly coupled modes. Those who model compact devices using the effects of distributed coupling between dielectric waveguides or analyze parasitic energy transfer phenomena in systems with tightly packed dielectric waveguides would inevitably encounter significant deviation of theoretical predictions from reality. A modified (or non-orthogonal) formulation is proposed which yields better accuracy. Previously a preliminary corollary of the theory of waveguide excitation by arbitrary sources was used for deriving the coupled mode equation in a non-orthogonal formulation, and the sought equation has been derived proceeding from these results. Despite the fact that such approach allows the obtained results to be interpreted in the most general physical manner, it seems to be excessive for deriving the equation for coupling of parallel dielectric waveguides; in addition, the approach is difficult to analyze and check. Prior to use this approach, it is necessary to determine the equivalent currents induced by the fields for each individual waveguide (from the associated modes of adjacent waveguides). The article presents a method for deriving the coupled mode equation in the non-orthogonal formulation based on using solely Maxwell's equations and an ansatz involving the sum of modes of individual waveguides and initially unknown additional fields related to the mutual influence of closely located waveguides. The expressions for these fields in terms of the fields of waveguide modes and the additional coefficients of volume and surface coupling are obtained. In the considered case, the discrete spectrum of modes was adopted instead of the continuous one to simplify the derivation and owing to its accessibility for experimental analysis.
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Для цитирования: Андреев А.С., Крутских В.В. Модифицированное уравнение связанных мод параллельных диэлектрических волноводов // Вестник МЭИ. 2018. № 1. С. 112—118. DOI: 10.24160/1993-6982-2018-1-112-118.
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4. Shalaby H.M.H. Bi-directional Coupler as a Mode- division Multiplexer/Demultiplexer. J. Lightwave Techn. 2016;34;15:3633—3640.
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For citation: Andreev A.S., Krutskikh V.V. A Modifi ed Coupled Mode Equation For Parallel Dielectric Waveguides. MPEI Vestnik. 2018;1:112—118. (in Russian). DOI: 10.24160/1993-6982-2018-1-112-118.
