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Phys. Rev. E 71, 056608 (2005) [9 pages]

Analytic properties of photonic crystal superprism parameters

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M. J. Steel1,2, R. Zoli2,3, C. Grillet2, R. C. McPhedran2, C. Martijn de Sterke2, A. Norton4, P. Bassi3, and B. J. Eggleton2
1RSoft Design Group, Inc., 65 O’Connor St, Chippendale, New South Wales 2008, Australia
2Centre for Ultrahigh-Bandwidth Devices for Optical Systems (CUDOS) and School of Physics, A28, University of Sydney, New South Wales 2006, Australia
3DEIS—Dipartimento di Elettronica Informatica e Sistemistica, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy
4Centre for Ultrahigh-Bandwidth Devices for Optical Systems (CUDOS) and Department of Applied Mathematics, University of Technology, Sydney, New South Wales 2008, Australia

Received 6 October 2004; published 19 May 2005

We study the analytic properties of the photonic crystal superprism resolution parameters p, q, and r introduced previously by Baba and Matsumoto Appl. Phys. Lett. 81 2325 (2002)], which characterize the potential dispersive power of a superprism. We find closed form expressions for these quantities that greatly simplify their accurate evaluation and reveal significant insights about their behavior. The expressions imply general properties of the parameters which are true for all bands and all photonic crystals. In particular, we demonstrate that all photonic crystals exhibit infinite resolution as measured by the parameter r along particular contours in any photonic band.

© 2005 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.71.056608
DOI:
10.1103/PhysRevE.71.056608
PACS:
42.25.Fx, 42.70.Qs, 42.82.Gw
 
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