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Physics of the Solid State

Transmission of light through a plane-parallel plate of a two-dimensional resonant photonic crystal

Stepan Ya. Vetrov, Ivan V. Timofeev, Natalya V. Rudakova

Published Jan 1, 2011• 1 citation
Publisher

Abstract

The transmission spectra of two-dimensional resonant photonic crystals of two types have been investigated. Crystals of one type consist of dielectric cylinders forming a square lattice filled by a resonant gas with mercury atoms, and crystals of the other type consist of cylindrical holes filled with a gas and forming a square lattice in a dielectric matrix. It has been established that characteristics of the spectrum of additional transmission arising in the band gap of the photonic crystal can be changed significantly by varying the gas pressure and the angle of incidence. It has been demonstrated that the calculated features in the transmission spectrum of the photonic crystal are stable with respect to a significant increase in the width of the atomic resonance.

DOI
10.1134/s1063783411010355

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The transmission spectra of two-dimensional resonant photonic crystals of two types have been investigated. Crystals of one type consist of dielectric cylinders forming a square lattice filled by a resonant gas with mercury atoms, and crystals of the other type consist of cylindrical holes filled with a gas and forming a square lattice in a dielectric matrix. It has been established that characteristics of the spectrum of additional transmission arising in the band gap of the photonic crystal can be changed significantly by varying the gas pressure and the angle of incidence. It has been demonstrated that the calculated features in the transmission spectrum of the photonic crystal are stable with respect to a significant increase in the width of the atomic resonance.
The crystal under consideration is a layered structure consisting of alternating layers of two materials, one of which is a resonantly absorbing gas. It is shown that the combination of the dispersion of an atomic gas with the dispersion of a photonic-bandgap structures allows one to efficiently control the transmission spectra of s - and p -polarized modes in these combined systems. It is found that the spectrum is highly sensitive to the position of the gas resonance frequency with respect to the bandgap edge and to a change in the gas pressure. The transmission, reflection, and absorption spectra of the resonant photonic crystal are studied at an angle of incidence equal to the Brewster angle of a seed photonic crystal. Possible applications of the found particular features of the dispersion of resonant photonic crystals are discussed.
We studied the specular and nonspecular remittances and the absorptance of two-dimensional photonic crystals (PCs) comprising a periodic array of dielectric rods immersed in a coherent atomic gas (CAG). Illumination by obliquely incident, s-polarized plane waves was considered. Minipassbands that may include peaks of nearly complete transmission appear within the stop bands of the corresponding gas-free PCs, due to the strong frequency dispersion in the relative permittivity of the CAG. As a result, high-efficiency passbands of a gas-free PC and those arising due to the CAG can coexist. The latter can be tuned in a simpler way than by varying the constitutive parameters of the CAG, i.e., via variation of the incidence angle. In contrast with the earlier studied metallic PCs immersed in a CAG, new passbands may also appear when the CAG behaves as a medium with ultralow positive permittivity. Also, complete absorptance bands (with zero overall reflectance and overall transmittance) can be obtained, which are well correlated with the frequency-dependent characteristics of the CAG.
We study the photonic spectrum of a one-dimensional optical lattice possessing a double primitive cell, when the atoms are well localized at the lattice minima. While a one-dimensional lattice with a simple Wigner-Seitz cell always possesses a photonic band gap at the atomic resonance, in this configuration the photonic transmission spectrum may exhibit no, double, or multiple photonic band gaps depending on the ratio between the interparticle distance $\ensuremath{\varrho}$ inside the cell and the cell size aaa. The transmission spectra of a weak incident probe are evaluated when the atoms are trapped in free space and inside an optical resonator for realistic experimental parameters.
The lifetime distribution functions of the spontaneous emission (SE) of the excited atoms embedded in two-dimensional (2D) photonic crystals (PCs) with square lattice, consisting of square air rods in dielectric medium with different filling factors, are calculated by using the plane wave expansion method. The numerical results show that the SE in the 2D PCs cannot be prohibited completely but it can be inhibited intensively by the pseudo-PBG of the PCs. In the pseudoband edges, the SE is accelerated obviously. The reduced average lifetime of the excited atoms and the extension of the reduced lifetime distribution in the 2D PCs both are the same as those in the 3D PCs in the order of magnitude. Our results provide an available way to control the behavior of the SE by changing the structures of the 2D PCs.
A two_dimensional array of resonant absorptive and dispersive medium is proposed. The transmission,reflection and absorption spectra of optical field transmitting in the structure are calculated. The photonic band gap caused by resonance(PBG), similar as the case of one_dimensional active photonic crystal, is observed. It’s found that the resonance between the border of the Brillouin zone and the resonant center of the atom in the array is the key condition for the formation of the PBG. Further discussion is carried on the study of the dependence of transmission spectrum on the structure,the resonant center and the absorption linewidth of the atoms in the array.