Elliptical Dielectric Waveguides

Abstract

The problem of electromagnetic wave propagation along a dielectric cylinder of elliptical cross section is considered. Two infinite determinants representing the characteristic equations for the two types of hybrid waves (the HEmne, and the HEmn0 waves) are derived. It is found that there exists two dominant waves which possess zero cutoff frequencies. The characteristic roots of these two dominant waves are computed for various values of eccentricity and relative dielectric constant. Theoretical propagation constants for the dominant waves are verified by experiments.

Birefringence Analysis of Photonic-Bandgap Fibers Using the Hexagonal Yee's Cell

“…3. The birefringence of this simple fiber, predicted exactly using Mathieu elliptical functions [26], [27], is 11.22 cm (dashed line in Fig. 3).…”

“…The operators and can then simply be obtained by substituting this permittivity tensor for in (9) of [24], i.e., (21) (22) The scaling of the unperturbed fiber geometry in the transverse plane, in general, can be expressed in the scaled coordinates as (23) The transverse curl of the field in the scaled coordinate and in the unperturbed coordinate are related by [24] (24) where (25) and and [24]. Substituting (24) and (25) in (22), one obtains the operator in the scaled coordinates (26) where is the operator of the unperturbed fiber, which has the same form as (22), and is shown in (27) at the bottom of the page.…”

Ray-Optics Analysis of Single Mode Condition for Optical Waveguides With Rectangular Cross-Section

“…Optical waveguides with a wide variety of shapes have been studied during the past decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. As one of the most basic structures among them, rectangular waveguides undoubtedly attracted the attention of early researchers.…”

Modal Dispersion Characteristics of a Single Mode Dielectric Optical Waveguide With a Guiding Region Cross-Section Bounded by Two Involuted Spirals

“…Unconventional waveguides with core cross-sections such as elliptical, rectangular, triangular, pentagonal, annular, spiral, cardioids etc. have been studied by the several researchers [1][2][3][4][5][6][7][8][9][10][11][12][13]. Such unconventional waveguides play an important role in the design and operation of many integrated optical devices such as wavelength filtering, coupling and semiconductor laser technology.…”