Share Email Print
cover

Proceedings Paper

A new fundamental equation for the band spectra of dielectric layer films
Author(s): Frank Szmulowicz
Format Member Price Non-Member Price
PDF $14.40 $18.00

Paper Abstract

This paper derives a new fundamental equation for the frequency spectra ω(q) of one-dimensional photonic crystals as a function of Brillouin wave vector q in the form of a novel factored expression, tan2 qd / 2 = tan(kNaNN) × tan(kNaN - βN), where N the number of layers per period is, d is the unit cell width, and ki = niω/c is the local wave vector in the ith layer of width 2ai and refractive index ni. Angles(αNN) depend on the parameters of all N layers but are independent of aN . For two layers, (α2, β2) correspond to the even/odd parity solutions at the center and the edge of the Brillouin zone. The derived spectral expression provide separate eigenvalue conditions for consecutive band edges at the center and the edge of the Brillouin zone for any N and is useful in finding the Bloch phase that is necessary in finite crystal calculations. The formalism is convenient for tailoring band gaps and for calculating impurity modes in dielectric stacks.

Paper Details

Date Published: 16 February 2009
PDF: 10 pages
Proc. SPIE 7223, Photonic and Phononic Crystal Materials and Devices IX, 72230S (16 February 2009); doi: 10.1117/12.809262
Show Author Affiliations
Frank Szmulowicz, Univ. of Dayton Research Institute (United States)


Published in SPIE Proceedings Vol. 7223:
Photonic and Phononic Crystal Materials and Devices IX
Ali Adibi; Shawn-Yu Lin; Axel Scherer, Editor(s)

© SPIE. Terms of Use
Back to Top