Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Legendre polynomial expansion for analysis of linear one-dimensional inhomogeneous optical structures and photonic crystals

Not Accessible

Your library or personal account may give you access

Abstract

A Legendre polynomial expansion of electromagnetic fields for analysis of layers with an inhomogeneous refractive index profile is reported. The solution of Maxwell’s equations subject to boundary conditions is sought in a complete space spanned by Legendre polynomials. Also, the permittivity profile is interpolated by polynomials. Different cases including computation of reflection–transmission coefficients of inhomogeneous layers, band-structure extraction of one-dimensional photonic crystals whose unit-cell refractive index profiles are inhomogeneous, and inhomogeneous planar waveguide analysis are investigated. The presented approach can be used to obtain the transfer matrix of an arbitrary inhomogeneous monolayer holistically, and approximation of the refractive index or permittivity profile by dividing into homogeneous sublayers is not needed. Comparisons with other well-known methods such as the transfer-matrix method, WKB, and effective index method are made. The presented approach, based on a nonharmonic expansion, is efficient, shows fast convergence, is versatile, and can be easily and systematically employed to analyze different inhomogeneous structures.

© 2006 Optical Society of America

Full Article  |  PDF Article
More Like This
Three-dimensional diffraction analysis of gratings based on Legendre expansion of electromagnetic fields

Amin Khavasi, Khashayar Mehrany, and Bizhan Rashidian
J. Opt. Soc. Am. B 24(10) 2676-2685 (2007)

Improved differential-transfer-matrix method for inhomogeneous one-dimensional photonic crystals

Mohammad Hadi Eghlidi, Khashayar Mehrany, and Bizhan Rashidian
J. Opt. Soc. Am. B 23(7) 1451-1459 (2006)

Polynomial expansion for extraction of electromagnetic eigenmodes in layered structures

Khashayar Mehrany and Bizhan Rashidian
J. Opt. Soc. Am. B 20(12) 2434-2441 (2003)

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (11)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (4)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (36)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved