Exact Calculation of Local Density of States in Two-Dimensional Photonic Crystals
HUANG Yong-Gang1,2, FAN Heng1, WANG Xue-Hua2
1Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190 2State Key laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University Guangzhou 510275
Exact Calculation of Local Density of States in Two-Dimensional Photonic Crystals
HUANG Yong-Gang1,2, FAN Heng1, WANG Xue-Hua2
1Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190 2State Key laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University Guangzhou 510275
摘要An exact calculation method of local density of states (LDOS) in two-dimensional (2D) photonic crystals (PCs) is presented. In order to calculate the LDOS, the eigen-equation of magnetic field is first solved by the plane-wave expansion method, then the eigen-modes of electric-field are obtained. There are two different ways to solve the eigen-equantion of magnetic field and three different ways to obtain the eigen-modes of the electric-field. In comparison of the numerical results from these different ways, an exact and fast method for calculating the LDOS in PCs is found. With use of this method, we investigate the LDOS of the 2D PCs consisting of a triangular lattice of cylinders. The results show the large LDOS is favorable to reside in higher dielectric-constant medium in high frequency region, rather than in lower dielectric-constant medium.
Abstract：An exact calculation method of local density of states (LDOS) in two-dimensional (2D) photonic crystals (PCs) is presented. In order to calculate the LDOS, the eigen-equation of magnetic field is first solved by the plane-wave expansion method, then the eigen-modes of electric-field are obtained. There are two different ways to solve the eigen-equantion of magnetic field and three different ways to obtain the eigen-modes of the electric-field. In comparison of the numerical results from these different ways, an exact and fast method for calculating the LDOS in PCs is found. With use of this method, we investigate the LDOS of the 2D PCs consisting of a triangular lattice of cylinders. The results show the large LDOS is favorable to reside in higher dielectric-constant medium in high frequency region, rather than in lower dielectric-constant medium.
HUANG Yong-Gang;FAN Heng;WANG Xue-Hua. Exact Calculation of Local Density of States in Two-Dimensional Photonic Crystals[J]. 中国物理快报, 2010, 27(10): 104213-104213.
HUANG Yong-Gang, FAN Heng, WANG Xue-Hua
. Exact Calculation of Local Density of States in Two-Dimensional Photonic Crystals. Chin. Phys. Lett., 2010, 27(10): 104213-104213.
[1] Purcell E M 1946 Phys. Rev. 69 681
[2] Grätzel M 2001 Nature 414 338
[3] Painter O et al 1999 Science 284 1819
[4] Altug H, Englund D and Vučković J 2006 Nature Physics 2 484
[5] Chen W et al 2009 Chin. Phys. Lett. 26 084210
[6] Sapienza L et al 2010 Science 327 1352
[7] Khitrova G et al 2006 Nature Physics 2 81
[8] Zhou Y S, Wang X H, Gu B Y and Wang F H 2006 Phys. Rev. Lett. 96 103601
[9] Yablonovitch E 1987 Phys. Rev. Lett. 58 2059
[10] John S 1987 Phys. Rev. Lett. 58 2486
[11] Wang X H, Gu B Y et al 2003 Phys. Rev. Lett. 91 113904.
[12] Wang X H et al 2003 Phys. Rev. Lett. 93 073901
[13] John S and Wang J 1990 Phys. Rev. Lett. 64 2418
[14] Bay S, Lambropoulos P and Molmer K 1997 Phys. Rev. Lett. 79 2654
[15] Faraon A, Majumdar A and Vučković J 2010 Phys. Rev. A 81 033838
[16] Hennessy K, Badolato A, Winger M, Gerace D, Atatüre M, Gulde S, Fält S, Hu E L and Imamoğlu A 2007 Nature 445 896
[17] Zhu S Y, Chen H and Huang H 1997 Phys. Rev. Lett. 79 205
[18] Wang R Z, Wang X H, Gu B Y and Yang G Z 2003 Phys. Rev. B 67 155114
[19] Kim T T, Lee S G, Park H Y, Kim J E and Kee C S 2010 Opt. Express 18 5384
[20] Faraon A, Fushman I et al 2008 Nature Physics 4 859
[21] Panajotov K and Dems M 2010 Opt. Lett. 35 829
[22] Hughes S 2005 Phys. Rev. Lett. 94 227402
[23] Shen L F and He S L 2002 J. Opt. Soc. Am. A 19 1021
[24] Plihal M and Maradudin A A 1991 Phys. Rev. B 44 8565
[25] Busch K and John S 1998 Phys. Rev. E 58 3896
[26] Ho K M, Chan C T and Soukoulis C M 1990 Phys. Rev. Lett. 65 3152
[27] Wang X H, Gu B Y and Wang R Z 2003 Phys. Lett. A 308 116
[28] Zhou Y S, Wang X H, Gu B Y and Wang F H 2005 Chin. Phys. 14 2241
[29] Wang R Z and Wang X H 2001 J. Appl. Phys. 90 4307
2010, Vol. 27 
