Method of adiabatic modes in studying problems of smoothly irregular open waveguide structures
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EMENTARY PARTICLES AND FIELDS Theory
Method of Adiabatic Modes in Studying Problems of Smoothly Irregular Open Waveguide Structures L. A. Sevastianov1), 2)* , A. A. Egorov3), and A. L. Sevastyanov1) Received February 29, 2012; in final form, May 18, 2012
Abstract—Basic steps in developing an original method of adiabatic modes that makes it possible to solve the direct and inverse problems of simulating and designing three-dimensional multilayered smoothly irregular open waveguide structures are described. A new element in the method is that an approximate solution of Maxwell’s equations is made to obey “inclined” boundary conditions at the interfaces between the media being considered. These boundary conditions take into account the obliqueness of planes tangent to nonplanar boundaries between the media and lead to new equations for coupled vector quasiwaveguide hybrid adiabatic modes. Solutions of these equations describe the phenomenon of “entanglement” of two linear polarizations of an irregular multilayered waveguide, the appearance of a new mode in an entangled state, and the effect of rotation of the polarization plane of quasiwaveguide modes. The efficiency of the method is demonstrated by considering the example of numerically simulating a thin-film generalized ¨ waveguide Luneburg lens. DOI: 10.1134/S1063778813010134
1. INTRODUCTION Problems concerning the application, adaption, and development of the Kantorovich method [1, 2]—that is, reduction to ordinary differential equations [3]—as well as the method of adiabatic representation in the three-body problem [4, 5] and in lowdimensional quantum systems in applied fields [6], were considered among other things at the seminar dedicated to the 60th anniversary of the birthday of Professor S.I. Vinitsky, a renowned physicist. In the studies performed by the hero of the anniversary, together with his disciples and colleagues, it was shown that a combination of these methods is an efficient tool for analyzing spectral and optical properties of models of low-dimensional quantum systems and superconductor nanostructures (quantum wells, wires, or dots and rings, which are bounded in, respectively, one, two, or three spatial dimensions) in applied fields [7–22], as well as geometric phases in polarization optics and interferometric systems [23–28]. In the present article, we describe basic steps in developing a new method of adiabatic modes for solv1)
Peoples’ Friendship University of Russia, ul. MiklukhoMaklaya 6, Moscow, 117198 Russia. 2) Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia. 3) Prokhorov General Physics Institute, Russian Academy of Sciences, ul. Vavilova 38, Moscow, 119991 Russia. * E-mail: [email protected]
ing the problem of describing the waveguide propagation of electromagnetic radiation in a smoothly irregular integrated-optical waveguide. The importance of this problem is associated with the development of constructive methods in the theory of the direct and inverse scattering problems and with practical applications in pr
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