A semi-analytic method, based on scattering approach is applied to analyze the finite size photonic crystal cavities surrounded by cylindrical dielectric rods.The resonant frequency and the quality factor (Q) are determined by this method.Also, with a source at the center of the cavity, field and energy distribution can be obtained at different frequencies.The algorithm is simple to simulate on PCs. There is no need for absorbing boundary conditions which are required in most numerical methods.Using the symmetry of the structure the computational cost is reduced to 1/8 and 1/12 those of the square and hexagonal lattices respectively.Since the computational time is very low (in the order of one minute) the variation in size and dielectric constant of the rods can be examined easily.It is shown as an example that by varying the radius of the rods according to their distance from the center of the cavity, the Q factor is increased considerably in comparison with that of uniform structures.
2. Mekis, A., J.C.Chen, I.Kurland, S.F un, P.R.Villeneuve, and J.D.Joannop oulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett., Vol. 77, No. 18, 3787-3790, Oct.1996.
3. ablonovitch, E., "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett., Vol. 58, 2059-2062, May 1987.
4. Joannopoulos, J.D., R.D.Meade, and J.N.Winn, Photonic Crystals: Molding the Flow of Light, Ch.7, Princeton University Press, Princeton, NJ, 1995.
5. Sakoda, K., Optical Properties of Photonic Crystals, Ch.6, Springer-Verlag, New York, 2001.
6. Sakoda, K., "Numerical study on localized defect modes in twodimensional triangular photonic crystals," J. Appl. Phys., Vol. 84, 1210-1214, Aug.1998.
7. Hwang, J.K., S.B.Hyun, H.Y.Ryu, and Y.H.Lee, "Resonant modes of two-dimensional photonic bandgap cavities determined by the finite-element method and by use of the anisotropic perfectly matched layer boundary condition," J. Opt. Soc. Amer. B., Vol. 15, 2316-2324, Aug.1998.
8. Dibben, D.C. and R.Metaxas, "Frequency domain vs.time domain finite element methods for calculation of fields in multimode cavities," IEEE Trans. Magn., Vol. 33, No. 2, 1468-1471, Mar.1997.
9. Rodriguez-Esquerre, V.F., M.Koshiba, and H.E.Hernandez-Figueroa, "Finite-element analysis of photonic crystal cavities: Time and frequency domain," IEEE J. Lightw. Technol., Vol. 23, No. 3, 1514-1521, Mar.2005.
10. Tayeb, G. and D.Ma ystre, "Rigorous theoretical study of finitesize two-dimensional photonic crystals doped by microcavities," J. Opt. Soc. Am. A, Vol. 14, No. 12, 3323-3332, Dec.1997.
11. Maystre, D., "Electromagnetic scattering by a set of objects: An integral method based on scattering properties," Progress In Electromagnetic Research, Vol. 57, 55-84, 2006.
12. Maystre, D., M. Saillard, and G. Tayeb, "Special methods of wave diffraction," E-M Waves Scattering, Approximate and Numerical Methods, Chap. 1.5.6, 2001.
13. Painter, O., K.Sriniv asan, and P.E.Barklay, "Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals," Phys. Rev. B., Vol. 68, 35214, July 2003.
14. Harrington, R. F., Time-Harmonic Electromagnetic Fields, Chap.5, McGraw-Hill, 1961.
15. Song, B.S., S.No da, and T.Asano, "Ultra-high-Q photonic double hetero-structure nanocavity," Nat. Mater., Vol. 4, No. 3, 207-210, 2005.
16. Asano, T., B.S.Song, and S.Noda, "Analysis of the experimental Q factors (∼ 1 million) of photonic crystal nanocavities," Opt. Express, Vol. 14, No. 5, 1996-2002, Mar.2006.