The Wannier function approach to photonic crystal circuits

被引:109
作者
Busch, K
Mingaleev, SF
Garcia-Martin, A
Schillinger, M
Hermann, D
机构
[1] Univ Karlsruhe, Inst Theorie Kondensierten Materie, D-76128 Karlsruhe, Germany
[2] Bogolyubov Inst Theoret Phys, UA-03143 Kiev, Ukraine
[3] CSIC, Inst Microelectron Madrid, Madrid 28760, Spain
关键词
D O I
10.1088/0953-8984/15/30/201
中图分类号
O469 [凝聚态物理学];
学科分类号
070205 ;
摘要
We introduce a novel approach to the accurate and efficient calculation of the optical properties of defect structures embedded in photonic crystals (PCs). This approach is based on an expansion of the electromagnetic field into optimally adapted photonic Wannier functions, which leads to effective lattice models of the PC structures. Calculations for eigenmode frequencies of simple and complex cavities as well as the dispersion relations for straight waveguides agree extremely well with the results from numerically exact supercell calculations. Similarly, calculations of the transmission through various waveguiding structures agree very well with the results of corresponding finite-difference time domain simulations. Besides being substantially more efficient than standard simulation tools, the Wannier function approach offers considerable insight into the nature of defect modes in PCs. With this approach, design studies and accurate simulation of optical anisotropic and non-linear defects as well as detailed investigations of disorder effects in higher-dimensional PCs become accessible.
引用
收藏
页码:R1233 / R1256
页数:24
相关论文
共 69 条
[1]   Photonic crystal modelling using a tight-binding Wannier function method [J].
Albert, JP ;
Jouanin, C ;
Cassagne, D ;
Monge, D .
OPTICAL AND QUANTUM ELECTRONICS, 2002, 34 (1-3) :251-263
[2]   Generalized Wannier function method for photonic crystals [J].
Albert, JP ;
Jouanin, C ;
Cassagne, D ;
Bertho, D .
PHYSICAL REVIEW B, 2000, 61 (07) :4381-4384
[3]   Two-dimensional local density of states in two-dimensional photonic crystals [J].
Asatryan, AA ;
Fabre, S ;
Busch, K ;
McPhedran, RC ;
Botten, LC ;
de Sterke, CM ;
Nicorovici, NAP .
OPTICS EXPRESS, 2001, 8 (03) :191-196
[4]  
Ashcroft N. W., 1973, SOLID STATE PHYS
[5]   Tight-binding description of the coupled defect modes in three-dimensional photonic crystals [J].
Bayindir, M ;
Temelkuran, B ;
Ozbay, E .
PHYSICAL REVIEW LETTERS, 2000, 84 (10) :2140-2143
[6]   Models and measurements for the transmission of submicron-width waveguide bends defined in two-dimensional photonic crystals [J].
Benisty, H ;
Olivier, S ;
Weisbuch, C ;
Agio, M ;
Kafesaki, M ;
Soukoulis, CM ;
Qiu, M ;
Swillo, M ;
Karlsson, A ;
Jaskorzynska, B ;
Talneau, A ;
Moosburger, J ;
Kamp, M ;
Forchel, A ;
Ferrini, R ;
Houdré, R ;
Oesterle, U .
IEEE JOURNAL OF QUANTUM ELECTRONICS, 2002, 38 (07) :770-785
[7]  
Birner A, 2001, ADV MATER, V13, P377, DOI 10.1002/1521-4095(200103)13:6<377::AID-ADMA377>3.3.CO
[8]  
2-O
[9]   Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres [J].
Blanco, A ;
Chomski, E ;
Grabtchak, S ;
Ibisate, M ;
John, S ;
Leonard, SW ;
Lopez, C ;
Meseguer, F ;
Miguez, H ;
Mondia, JP ;
Ozin, GA ;
Toader, O ;
van Driel, HM .
NATURE, 2000, 405 (6785) :437-440
[10]   Liquid-crystal photonic-band-gap materials: The tunable electromagnetic vacuum [J].
Busch, K ;
John, S .
PHYSICAL REVIEW LETTERS, 1999, 83 (05) :967-970