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Acta Sinica Quantum Optica

The Transmission Spectrum of the 1D Photonic Crystal with Dispersive Cavity

Nian-Hua Liu

Published Jan 1, 2006• 0 citations
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Abstract

The transmission spectrum of the 1D photonic crystal with dispersive cavity is studied in this paper.The dispersive medium is described by the Lorentz oscillator model,and the frequency of the cavity mode is set at the center of the gap.When the absorption is negligible,the density of states near the cavity mode is very high,and there is a comparatively wider transmitted band appearing in the transmission spectrum.When absorption is included,the transmission at the central frequency disappears,but the transmission still exists near the tail of the transmission band.

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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.

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Nov 10, 2008•2 citations
The transmission spectrum of the 1D photonic crystal with dispersive cavity is studied in this paper.The dispersive medium is described by the Lorentz oscillator model,and the frequency of the cavity mode is set at the center of the gap.When the absorption is negligible,the density of states near the cavity mode is very high,and there is a comparatively wider transmitted band appearing in the transmission spectrum.When absorption is included,the transmission at the central frequency disappears,but the transmission still exists near the tail of the transmission band.
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.
The transfer matrix, which represents the dispersive medium's layer, can be rigorously obtained by using Lorentz model and considering boundary conditions. The detailed investigation on polaritons in a symmetric photonic crystal with absorptive type of dispersive medium's layer is presented by adjusting parameters of the dispersive medium's layer. It's found that the absorptive type of dispersive cavity and reinforced dispersive cavity may demonstrate similar properties in normal modes coupling, the homogeneous broadening effect, and the detuning effect. But there exists evident differences in transmitted intensity and frequency shift. Finally, the optical bistability in one-dimensional symmetric photonic crystal both with absorptive type of dispersive medium's layer and with Kerr nonlinear layer is also investigated. It's found that optical bistability threshold of the photonic crystal with dispersive medium layer is a little lower than that of structure without dispersive medium laver.
The normal-mode coupling dispersive medium in a symmetric one-dimension photonic crystals(1D PCs) was studied.The frequency shift effect,homogeneous broadening effect,and the detuning effect of the normal(coupled) modes can be well controlled by adjusting the parameters of the dispersive medium.It is found that the separation between the two transmission peaks enlarges with increasing the dimensionless coupling strength.It implies that we can modulate the frequency shift of the dispersive defect by adjusting the parameter of the dispersive medium.The broadening effect of normal coupled modes is related to the reduced oscillator HWHM linewidth.Detuning effect of dispersive layer will make one peak rapidly drop and the other relatively much higher.It can be understood by Fabry-Perot cavity analysis.
The probe absorption-dispersion spectrum of a double V-type four-level atom in a double-band photonic crystal is investigated. In the model used, the double V-type transitions are, respectively, coupled by the free vacuum modes and the photonic band gap modes, leading to the two possible types of quantum interference. Three types of zero absorption (transparency) appear in this model. In the first type, there exist two zeroes at the band edge frequencies in the case of isotropic photonic band gap. In the second type, a zero emerges at the middle frequency of two upper levels in the case that the quantum interference takes place in both V-type transitions. Finally, in the third type, a zero occurs at or around the middle frequency of two upper levels in the case that the quantum interference takes place only in the V-type transitions coupled to the free vacuum modes. Ultimately, the probe absorption-dispersion spectrum in the case of the single-band photonic band gap reservoirs compared to those of the double-band photonic band gap reservoirs. The results show that the dispersion property of the system depends on the two types of the quantum interference and the density of states of the photonic band gap reservoir.
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 investigate superradiant lasing in 1D photonic crystal taking into account both homogeneous and inhomogeneous broadening in a two-level active medium. The latter may be based on, e.g., the quantum-well heterostructures and the fibers activated by color centers where Bragg structure can be fabricated artificially by means of a periodic modulation of the cladding layers. The truncated Maxwell-Bloch equations for the counter-propagating waves, the polarization and inversion of an inhomogeneously broadened two-level medium are used to analyze numerically the interplay between the back-scattering, amplification, dispersion, and de-phasing of waves. It is found that, if the photonic band gap is less than the coherent amplification bandwidth, there is a wide range of the pumping and relaxation parameters of a two-level medium where superradiant lasing exists and results in generation of a quasi-periodic and/or chaotic series of powerful and short pulses similar to those of Dicke superfluorescence. It is the cavity mode selection due to distributed feedback caused by the resonant Bragg structure which is responsible for the existence of superradiant lasing. Typical parameters of superradiant photonic-crystal lasers, including lengths, photonic band gaps and relaxation rates, are indicated.