# Determination of Power of Groove fields belonging to the wedge regions adjacent to a convex triangular obstacle associated with Dirichlet conditions subject to axially independent EM fields

## TL;DR

This paper calculates the power of electromagnetic groove fields near a convex triangular obstacle with Dirichlet boundary conditions, aiding the design of triangular gratings for wave propagation studies.

## Contribution

It introduces a method to determine groove field power for a convex triangular obstacle using Helmholtz equation solutions and advanced mathematical tools.

## Key findings

- Derived expressions for groove field power adjacent to convex triangular obstacles.
- Applied Fourier-Bessel series and Lommel's integral in the analysis.
- Provided insights for designing triangular corrugated structures.

## Abstract

A convex triangular obstacle forms a vital part of a periodic echellete grating. A triangular grating is characterized by three parameters like period, depth and flare angle. Knowledge of groove field is essential for precise designing of triangular corrugated structures for studying the blazing effect of propagating EM wave. In the present paper, an attempt has been made to determine the power of Groove fields belonging to a pair of groove regions adjacent to a convex triangular prism. Groove fields and their associated powers based on Dirichlet conditions on the groove surfaces have been determined. The governing Helmholtz wave equation has been solved for determining the free surface field and the groove field. Fourier-Bessel series, oblique coordinate transformations and Lommel's integral are used as tools.

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Source: https://tomesphere.com/paper/1901.07902