Modal Analysis of Multilayer Conical Dielectric Waveguides for Azimuthal Invariant Modes

Abstract

Abstract-By using field expansion in terms of the Legendre polynomials and Schelkunoff functions, Maxwell's equations in the spherical coordinate system are cast into a matrix form which lends itself to the analysis of a multilayer conical waveguide. The matrix formulation is then used to obtain an eigen-value problem whose eigen-values are the allowable wave-numbers for propagation in the radial direction. To verify the proposed numerical approach, it is used to evaluate the resonance frequency of a partially filled spherical resonator. The computed resonance frequencies are then compared with those obtained using commercial software based on the finiteelement method. The computation time is enormously reduced using the semi-analytical method of this work. Although results are shown for lossless isotropic dielectrics, the method is also applicable to conical waveguides made of lossy dielectrics even with negative permittivity.

Experimental and Theoretical Studies of a Broadband Superluminality in Fabry-Perot Interferometer

“…The conversion between high-order modes and the TE 10 mode modifies the magnitudes of transmission ( √ T and √ T ) and reflection ( √ R and √ R ) coefficients of the fundamental propagating wave (TE 10 ), as well as induces the extra phase changes (φ t , φ t , φ r , and φ r ) during the transmission and reflection processes. Such phenomenon is called the modal effect [27][28][29][30][31]. In this study, the regions I and III are WR-284 waveguides with a width of 2.84 inches (a = 72.14 mm) and a height of 1.34 inches (b = 34.04 mm).…”

“…These values are calculated using the modal analysis [27][28][29][30][31]. The round-trip phase change (2kL + 2φ r with L = 10 cm) is illustrated in (d).…”

“…Notably, the discontinuities of the undersized/oversized waveguide will excite high-order evanescent modes in addition to the fundamental mode, which is called the modal effect. The importance of the modal effect had long been noted [11][12][13][27][28][29][30][31], but its effect and extended application on the superluminality has never been studied.…”

A General Rule for Designing Multibranch High-Order Mode Converter

“…By coupling effect, the multibranch waveguides can be designed to operate as switches [8], wavelength-selective filter [9], and logic gates [10]. The design of mode converter [11][12][13][14] is another good guide for all-optical devices. Zhang et al [15] experimented and fabricated a TE mode converter.…”

Interaction of an Asymmetric Scanning Near Field Optical Microscopy Probe With Fluorescent Molecules

“…Since the proposal of the pioneering aperture structure, based on a metal coated dielectric with a subwavelength aperture left at the end, different options have been explored in order to overcome some of its fundamental drawbacks, i.e., the poor resolution limited by the size of the aperture, the low throughput and the asymmetric near field distribution at the probe apex resulting from the linearly polarized excitation [7][8][9]. Apertureless probes under far field external illumination have been indicated as a possible alternative [10][11][12][13]: although they allow the achievement of high field enhancement and high resolution, the far field illumination creates a strong background potentially deleterious for measurements on sensitive samples, as is the case for, e.g., fluorescent molecules.…”