Magnetooptics in Cylindrical Structures

Štefan Višňovský

doi:10.3390/app8122547

Abstract

Understanding magnetooptics in cylindrical structures presents interest in the development of magnetic sensor and nonreciprocal devices compatible with optical fibers. The present work studies wave propagation in dielectric circular cylindrical structures characterized by magnetic permeability and electric permittivity tensors at axial magnetization. The Helmholtz equations deduced from the Maxwell equations in transverse circularly polarized representation provide electric and magnetic fields. With the restriction to terms linear in off-diagonal tensor elements, these can be expressed analytically. The results are applied to magnetooptic (MO) circular cylindrical waveguides with a step refractive index profile. The nonreciprocal propagation is illustrated on waveguides with an yttrium iron garnet (YIG) core and a lower refractive index cladding formed by gallium substituted yttrium iron garnet (GaYIG) at the optical communication wavelength. The propagation distance required for the isolator operation is about one hundred micrometers. The approach may be applied to other structures of cylindrical symmetry in the range from microwave to optical frequencies.

Highlights

Electromagnetic waves in magnetized media depend on magnetization and often show nonreciprocal propagation
T, dependence of harmonic waves propagating with the angular frequency, ω, and described by a factor exp, the Maxwell equations in a linear medium (i ) characterized by the electric permittivity tensor, ε(i), and magnetic permeability tensor, μ(i), become
Solutions to the eigenvalue equation, Equation (20), will be illustrated on a circular cylindrical dielectric waveguide operating at the wavelength λvac =1.550 μm with the core made from yttrium iron garnet, Y3 Fe5 O12 (YIG), and the cladding made from gallium substituted YIG, Y3 Fe5− x Gax O12 (GaYIG)

Summary

Introduction

Electromagnetic waves in magnetized media depend on magnetization and often show nonreciprocal propagation. The phenomenon is exploited in sensors and devices such as waveguide isolators, phase shifters, circulators, and modulators Their operation can be explained by considering circularly polarized (CP) transverse electromagnetic waves of opposite handedness (±) propagating in infinite lossless uniformly magnetized media. The effect of M is deduced from the tensor nature of magnetic permeability with the scalar electric permittivity [17] while in the near infrared and visible regions, the analysis assumes the tensor nature of electric permittivity with magnetic permeability reduced to its vacuum value [18,19] In both cases, the diagonal and off-diagonal tensor elements are even and odd functions of M, respectively [18,19,20,21,22,23].

Maxwell Equations

Helmholtz Equations

A Simple Cylindrically Layered Structure

Conclusions