## Approximate analysis of two-dimensional photonic crystals with rectangular geometry. I. *E* polarization

JOSA B, Vol. 25, Issue 7, pp. 1135-1143 (2008)

http://dx.doi.org/10.1364/JOSAB.25.001135

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### Abstract

Using analytical techniques the dispersion relations for two-dimensional photonic crystals with rectangular geometry are analyzed. In this part of the work *E* polarization is presented. By comparing with accurate numerical calculations, we show that our analysis provides a good description of the physical properties for this type of photonic crystal. Besides the significantly shorter calculation time, the analytical treatment provides an important insight into the photonic bands’ formation and their properties. The presented approach and derived analytical expressions can be useful for the investigation of photonic band structures as well as for the design of novel photonic crystal devices.

© 2008 Optical Society of America

**OCIS Codes**

(260.2110) Physical optics : Electromagnetic optics

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

(160.5293) Materials : Photonic bandgap materials

(230.5298) Optical devices : Photonic crystals

**ToC Category:**

Photonic Crystals

**History**

Original Manuscript: February 14, 2008

Manuscript Accepted: March 30, 2008

Published: June 23, 2008

**Citation**

Inna Nusinsky and Amos A. Hardy, "Approximate analysis of two-dimensional photonic crystals with rectangular geometry. I. E polarization," J. Opt. Soc. Am. B **25**, 1135-1143 (2008)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-25-7-1135

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### References

- K. Inoue and K. Ohtaka, eds., Photonic Crystals, Physics, Fabrication and Applications (Springer, 2004).
- M. Plihal, A. Shambrook, and A. A. Maradudin, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199-204 (1991). [CrossRef]
- A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).
- J. B. Pendry, “Calculating photonic band structure,” J. Phys.: Condens. Matter 8, 1085-1108 (1996). [CrossRef]
- S. N. Kawakami, “Analytically solvable model of photonic crystal structures and novel phenomena,” J. Lightwave Technol. 20, 1644-1650 (2002). [CrossRef]
- I. Ponomarev, “Separation of variables in the computation of spectra in 2-D photonic crystals,” SIAM J. Appl. Math. 61, 1202-1218 (2000). [CrossRef]
- K. Samokhvalova, C. Chen, and B.-L. Qian, “Analytical and numerical calculations of the dispersion characteristics of two-dimensional dielectric photonic band gap structures,” J. Appl. Phys. 99, 63104 (2006). [CrossRef]
- T. J. Shepherd, P. J. Roberts, and R. Loudon, “Soluble two-dimensional photonic crystal model,” Phys. Rev. E 55, 6024-6038 (1997). [CrossRef]
- A. Figotin and P. Kuchment, “Band gap structure of spectra of periodic dielectric and acoustic media. II. Two-dimensional photonic crystals,” SIAM J. Appl. Math. 56, 1561-1620 (1996). [CrossRef]
- L. Chang, C.-C. Ho, H.-S. Wei, and G. Y. Wu, “Effective medium theory with dimensionality reduction for band structures of photonic crystals,” J. Appl. Phys. 101, 053109 (2007). [CrossRef]
- M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
- K. Sakoda, Optical Properties of Photonic Crystals, 2nd ed. (Springer-Verlag, 2005).
- D. J. Griffiths, Introduction to Quantum Mechanics (Prentice-Hall, 1995).
- S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell's equations with shifting materials boundaries,” Phys. Rev. E 65, 066611 (2002). [CrossRef]
- W. Magnus and S. Winkler, Hill's Equation (Wiley, 1966).
- I. Nusinsky and A. A. Hardy, “Band gap-analysis of one-dimensional photonic crystals and conditions for gap closing,” Phys. Rev. B 73, 125104 (2006). [CrossRef]
- A. H. Nayfen, Introduction to Perturbation Techniques (Wiley, 1993).
- P. E. Barclay, K. Srinivasan, and O. Painter, “Design of photonic crystal waveguides for evanescent coupling to optical fiber tapers and integration with high-Q cavities,” J. Opt. Soc. Am. B 20, 2274-2284 (2003). [CrossRef]
- H. Kitahara, N. Tsumura, H. Kondo, M. W. Takeda, J. W. Haus, Z. Yuan, N. Kawai, K. Sakoda, and K. Inoue, “Terahertz wave dispersion in two-dimensional photonic crystals,” Phys. Rev. B 64, 045202 (2001). [CrossRef]

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