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Analytical extraction of leaky modes in circular slab waveguides with arbitrary refractive index profile

Sarrafi, P ; Sharif University of Technology | 2007

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  1. Type of Document: Article
  2. DOI: 10.1364/AO.46.008656
  3. Publisher: 2007
  4. Abstract:
  5. Circular slab waveguides are conformally transformed into straight inhomogeneous waveguides, where-upon electromagnetic fields in the core are expanded in terms of Legendre polynomial basis functions. Thereafter, different analytical expression of electromagnetic fields in the cladding region, viz. Wentzel-Kramers-Brillouin solution, modified Airy function expansion, and the exact field solution for circular waveguides, i.e., Hankel function of complex order, are each matched to the polynomial expansion of the transverse electric field within the guide. This field matching process renders different boundary conditions to be satisfied by the set of orthogonal Legendre polynomial basis functions. In this fashion, the governing wave equation is converted into an algebraic and easy to solve eigenvalue problem, which is associated with a matrix whose elements are analytically given. Various numerical examples are presented and the accuracy of each of the abovementioned different boundary conditions is assessed. Furthermore, the computational efficiency and the convergence rate of the proposed method with increasing number of basis functions are briefly discussed. © 2007 Optical Society of America
  6. Keywords:
  7. Boundary conditions ; Brillouin scattering ; Eigenvalues and eigenfunctions ; Optical losses ; Polynomial approximation ; Refractive index ; Circular slab waveguides ; Hankel function ; Legendre polynomial basis functions ; Circular waveguides
  8. Source: Applied Optics ; Volume 46, Issue 36 , 2007 , Pages 8656-8667 ; 1559128X (ISSN)
  9. URL: https://www.osapublishing.org/ao/fulltext.cfm?uri=ao-46-36-8656&id=148521