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arXiv:quant-ph/9908026 · Physical Review A

Transparency near a photonic band edge

Emmanuel Paspalakis, Niels J. Kylstra, P. L. Knight

Published Jul 1, 1999• 103 citations
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Abstract

We study the absorption and dispersion properties of a \ensuremath{\Lambda}-type atom that decays spontaneously near the edge of a photonic band gap (PBG). Using an isotropic PBG model, we show that the atom can become transparent to a probe laser field, even when other dissipative channels are present. This transparency originates from the square-root singularity of the density of modes of the PBG material at threshold.

DOI
10.1103/physreva.60.r33

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Communications in Theoretical Physics•Jan 1, 2011•3 citations
We study the absorption and dispersion properties of a \ensuremath{\Lambda}-type atom that decays spontaneously near the edge of a photonic band gap (PBG). Using an isotropic PBG model, we show that the atom can become transparent to a probe laser field, even when other dissipative channels are present. This transparency originates from the square-root singularity of the density of modes of the PBG material at threshold.
We study the spontaneous emission, absorption, and dispersion properties of a \ensuremath{\Lambda}-type atom where one transition interacts near resonantly with a double-band photonic crystal. Assuming an isotropic dispersion relation near the band edges, we show that two distinct coherent phenomena can occur. First the spontaneous emission spectrum of the adjacent free-space transition obtains ``dark lines'' (zeros in the spectrum). Second, the atom can become transparent to a probe laser field coupling to the adjacent free-space transition.
We investigate the dispersive property of a Λ-type atomic system embedded in photonic band gap structures. The atomic coherence is established by the structured reservoir which consists of a double-band photonic band gap (PBG) and defect modes. With an atomic density of 7×10 15 atoms/cm 3 , the group velocity of a probe laser being detuned far away from the gap is shown to be reduced to 3×10 2 m/s near the transparency window associated with the PBG edges and 6×10 3 m/s at the transparency window associated with the defect modes, without using any deriving field. The influence of the smoothness of the density of modes and the decay rate of the second ground state of atoms are analysed.
We derive the properties of self-induced transparency (SIT) solitary waves in a one-dimensional periodic structure doped uniformly with resonance two-level atoms. In our model, the electromagnetic field is treated classically and the dopant atoms are described quantum mechanically. The resulting solitary waves take the form of ultrashort (picosecond) laser pulses which propagate near the band edge of the nonlinear photonic band gap (PBG) material doped with rare-earth atoms such as erbium. Solitary wave formation involves the combined effects of group velocity dispersion (GVD), nonresonant Kerr nonlinearity, and resonant interaction with dopant atoms. We derive the general Maxwell-Bloch equations for a nonlinear PBG system and then demonstrate the existence of elementary solitary wave solutions for frequencies far outside the gap where GVD effects are negligible and for frequencies near the photonic band edge where GVD effects are crucial. We find two distinct new types of propagating SIT solitary wave pulses. Far from Bragg resonance, we recapture the usual McCall-Hahn soliton with hyperbolic secant profile when the nonlinear Kerr coefficient ${\ensuremath{\chi}}^{(3)}=0.$ However, when the host nonresonant Kerr coefficient is nonzero, we obtain the first new type of soliton. In this case, the optical soliton envelope function deviates from the hyperbolic secant profile and pulse propagation requires nontrivial phase modulation (chirping). We derive the dependence of the solitary wave structure on the Kerr coefficient ${\ensuremath{\chi}}^{(3)},$ the resonance impurity atom density, and the detuning of the average laser frequency from the atomic transition. When the laser frequency and the atomic transition frequencies are near the photonic band edge we obtain the second type of soliton. To illustrate the second type of soliton we consider two special cases. In the first case, GVD facilitates the propagation of an unchirped SIT-gap soliton moving at a velocity fixed by the material's parameters. The soliton structure changes dramatically as the laser frequency is tuned through the atomic resonance. In the second illustrative case we set the Kerr coefficient ${\ensuremath{\chi}}^{(3)}=0.$ In this case, the solution is a chirped pulse which arises from the balance between GVD and the resonance interaction with the dopant atoms. Finally, we show that under certain circumstances, these solitary wave solutions may persist even in the presence of (subpicosecond) dipolar dephasing of the dopant atoms and absorption losses of the host PBG material, provided that the system is incoherently pumped. These results may be relevant to the application of PBG materials as optical devices in fiber-optic networks.
The novel dynamical and spectral features of (single photon) spontaneous emission from an atomic transition near a photonic band edge are investigated by frustrating these features by spontaneous emission through another atomic transition far from the photonic band edge and deep in the photon continuum, the two atomic transitions forming the two dipole-allowed transitions of a three-level atom in a Λ configuration. Though spontaneous emission through the atomic transition far from the photonic band edge (the “far” transition) is not directly affected by the photonic band gap (PBG), it is indirectly affected by the PBG through its coupling to the atomic transition near the photonic band edge (the “near” transition) via the Λ configuration. As a result of this coupling, spontaneous emission through the “far” transition can be used as a probe to measure the strength of the effects of the PBG on spontaneous emission through the “near” transition. We have shown that the effects of the PBG on spontaneous emission via the “near” transition are strongly affected (and, therefore, can be controlled by) not only by the detuning of the “near” transition from photonic band edge but also by the vacuum decay rate of spontaneous emission through the “far” transition which is coupled to the “near” transition through the Λ configuration. In particular, we have shown that the oscillatory behavior of spontaneous emission near a photonic band edge as well as the Autler-Townes doublet of the spontaneous emission spectrum (due to the splitting of the atomic level near the photonic band edge) are strongly dependent on the decay rate of spontaneous emission through the probe transition which is far from the band edge.
We investigate the dispersive property of a A-type atomic system embedded in photonic band gap structures. The atomic coherence is established by the structured reservoir which consists of a double-band photonic band gap (PBG) and defect modes. With an atomic density of 7×10^15 atoms/cm^3, the group velocity of a probe laser being detuned far away from the gap is shown to be reduced to 3×10^2 m/s near the transparency window associated with the PBG edges and 6×10^3 m/s at the transparency window associated with the defect modes, without using any deriving field. The influence of the smoothness of the density of modes and the decay rate of the second ground state of atoms are analysed.
The probe absorption-dispersion spectra of a radio-frequency (RF)-driven five-level atom embedded in a photonic crystal are investigated by considering the isotropic double-band photonic-band-gap (PBG) reservoir. In the model used, the two transitions are, respectively, coupled by the upper and lower bands in such a PBG material, thus leading to some curious phenomena. Numerical simulations are performed for the optical spectra. It is found that when one transition frequency is inside the band gap and the other is outside the gap, there emerge three peaks in the absorption spectra. However, for the case that two transition frequencies lie inside or outside the band gap, the spectra display four absorption profiles. Especially, there appear two sharp peaks in the spectra when both transition frequencies exist inside the band gap. The influences of the intensity and frequency of the RF-driven field on the absorptive and dispersive response are analyzed under different band-edge positions. It is found that a transparency window appears in the absorption spectra and is accompanied by a very steep variation of the dispersion profile by adjusting system parameters. These results show that the absorption-dispersion properties of the system depend strongly on the RF-induced quantum interference and the density of states (DOS) of the PBG reservoir.