Numerical methods for calculation of optical properties of layered structures

Three methods, namely 2×2 and 4×4 transfer matrix methods as well as scattering matrix method, for simulation of the transmission and reflection spectra of the layered structures are described in this paper. The advantages of each of these methods for simulation of the optical spectra of one-dimensional photonic crystals are analyzed. The modified 2×2 transfer matrix method is suggested for calculation of the reflection and transmission coefficients of the layered structures in situation when the incident light beam has a cone-like shape.

[1]  T. Ishihara,et al.  Quasiguided modes and optical properties of photonic crystal slabs , 2002 .

[2]  Pochi Yeh,et al.  Electromagnetic propagation in birefringent layered media , 1979 .

[3]  Jean-Michel Lourtioz,et al.  Two-dimensional photonic crystals in macroporous silicon: from mid-infrared (10 /spl mu/m) to telecommunication wavelengths (1.3-1.5 /spl mu/m) , 1999 .

[4]  Reflection and transmission characterization of a hexagonal photonic crystal in the mid infrared , 1998 .

[5]  E. Astrova,et al.  Optical properties of one-dimensional photonic crystals fabricated by photo-electrochemical etching of silicon , 2010 .

[6]  Ko,et al.  Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems. , 1988, Physical review. B, Condensed matter.

[7]  T. Perova,et al.  1D photonic crystal fabricated by wet etching of silicon , 2005 .

[8]  E. Astrova,et al.  Photo‐electrochemical etching of macro‐pores in silicon with grooves as etch seeds , 2009 .

[9]  Kurt Busch,et al.  Photonic crystals : advances in design, fabrication, and characterization , 2004 .

[10]  Jean-Michel Lourtioz,et al.  LETTER TO THE EDITOR: An optical drill for the fabrication of photonic crystals , 1999 .

[11]  J. Pallarès,et al.  Tunable Fabry–Pérot filter based on one-dimensional photonic crystals with liquid crystal components , 2009 .

[12]  Amnon Yariv,et al.  Optical Waves in Crystals , 1984 .

[13]  D. Larkman,et al.  Photonic crystals , 1999, International Conference on Transparent Optical Networks (Cat. No. 99EX350).

[14]  E. Astrova,et al.  Formation of deep periodic trenches in photo-electrochemical etching of n-type silicon , 2009 .

[15]  R. Azzam,et al.  Ellipsometry and polarized light , 1977 .

[16]  Hoda A. ElMaraghy,et al.  Advances in Design , 2006 .

[17]  David J. Lockwood Pavesi,et al.  Silicon Fundamentals for Photonics Applications , 2004 .

[18]  A. Chelnokov,et al.  Two-dimensional photonic bandgap reflectors for free-propagating beams in the mid-infrared , 1999 .

[19]  Steven G. Johnson,et al.  Photonic Crystals: Molding the Flow of Light , 1995 .

[20]  F. Abelès.  La détermination de l'indice et de l'épaisseur des couches minces transparentes , 1950 .

[21]  T. Perova,et al.  Experimental evidence of photonic band gap extension for disordered 1D photonic crystals based on Si , 2006 .

[22]  E. H. Linfoot.  Principles of Optics , 1961 .

[23]  Ekaterina V. Astrova,et al.  Tunable photonic structures based on silicon and liquid crystals , 2007, SPIE Micro + Nano Materials, Devices, and Applications.