Magnetooptics in Cylindrical Structures

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.

Compact Photonic-Crystals Based Isolator Using Ni–Zn Gyromagnetic Ferrite Posts

“…In the K waveband, if a ferrite post is magnetized in z-direction, its magneto-optical effect is usually described in terms of the tensor permeability [25]:…”

Nonreciprocal propagation in optical fibers

“…The z dependence is taken into account by a factor e −jβz , where β denotes the axial (or longitudinal) component of the propagation vector. With the z dependence removed, the field vector components acquire the meaning, 6) j…”

“…These can be specified, up to a common factor, using the boundary conditions for the corresponding isotropic waveguide. The required eigenvalue of effective guide index, b l p = [23][24][25] Alternatively, the eigenvalue equation in isotropic circular cylindrical waveguides can be expressed 6) n k g k g…”

“…( 68) and (69) in Eqs. ( 34)-( 37), provides the arguments of the Bessel functions for the core 6) 1 0 1 0…”

“…The work represents an extension of previous studies on the Helmholtz equation in isotropic cylindrical structures and on magneto-optics in cylindrical structures. 5,6) The focus is on the eigenmode configurations and on the differences between the configurations for ¹ + -k k important in the design of nonreciprocal structures. The notation with improved specifications of parameters in cylindrical functions is employed.…”