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Journal of the Optical Society of America B

Tunable double photonic bandgaps in a homogeneous atomic medium

Shang-qi Kuang, Ren-Gang Wan, Jun Kou, Yun Jiang, Jin-Yue Gao

Published Jul 8, 2010• 18 citations
Publisher

Abstract

Double photonic bandgaps (PBGs) can simultaneously appear when double dark resonances in uniform cold atoms are spatially modulated by a resonance standing-wave. Theoretical calculations show that variable and efficient coherent optical control of the PBGs can be achieved by modulating the coupling field and standing-wave. The structures of double PBGs induced by the atomic coherence effect are better than those obtained in the photonic crystal heterostructures. We anticipate that this scheme has potential applications in optical networks for dual-channel all-optical switching or a dual-frequency optical Bragg reflector.

DOI
10.1364/josab.27.001518

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Double photonic bandgaps (PBGs) can simultaneously appear when double dark resonances in uniform cold atoms are spatially modulated by a resonance standing-wave. Theoretical calculations show that variable and efficient coherent optical control of the PBGs can be achieved by modulating the coupling field and standing-wave. The structures of double PBGs induced by the atomic coherence effect are better than those obtained in the photonic crystal heterostructures. We anticipate that this scheme has potential applications in optical networks for dual-channel all-optical switching or a dual-frequency optical Bragg reflector.
A tripod atomic system driven by two standing-wave fields (a coupling and a driving) is explored to generate tunable double photonic bandgaps in the regime of electromagnetically induced transparency. Both photonic bandgaps depend critically on frequency detunings, spatial periodicities, and initial phases of the two standing-wave fields. When the coupling and driving detunings are very close, a small fluctuation of one standing-wave field may demolish both photonic bandgaps. If the two detunings are greatly different, however, each standing-wave field determines only one photonic bandgap in a less sensitive way. Dynamic generation and elimination of a pair of photonic bandgaps shown here may be exploited toward the end of simultaneous manipulation of two weak light signals even at the single-photon level.
We investigate a four level double lamder system with spontaneously generated coherence( SGC) for achieving photonic band gaps( PBG) by a standing- wave field. When the coupling field is far away from resonance or resonant,we can obtain one- phonon bandgap or two- phonon bandgap due to spontaneous emission coherent from two decay pathways. When the SGC is absent,the probe field is absorbed by the medium,so the PBG cannot be generated. The numerical calculations show that the induced PBG result from the Kerr nonlinear modulation between the probe and coupling field,and by controlling the detunings of coupling field,one PBG can be dynamically tuned into two PBGs in this system.
We analyze the optical response of a standing-wave driven four-level atomic system with double dark resonances. Fully developed double photonic band gaps arise as a result of periodically modulated refractive index within the two electromagnetically induced transparency widows. We anticipate that the dynamically induced band gaps can be used to coherently control the propagation of light-pulses with different center frequencies and may have applications in all-optical switching and routing for quantum information networks.
By using the technique of electromagnetically induced transparency and solving density matrix equations for atoms and transfer matrix equations of fields, we study the steady optical properties of a four-level system of cold atoms driven by a traveling-wave field and a standing-wave field. It is found that a nearly perfect structure of double photonic band-gap can be generated with specific parameters. In particular, the reflectivity inside each photonic band-gap is homogeneous over 95%. It is convenient to modulate the positions and widths of both photonic band-gaps by changing intensities and frequencies of the driving fields. The double photonic band-gaps can be used to achieve all-optical routing and switching and therefore may have applications in all-optical information networks.
We study a five-level $\text{quasi}\ensuremath{-}\ensuremath{\Lambda}$ system of cold atoms for achieving high-order photonic band gaps (PBGs) probed by an ultraviolet field in two cases where either an infrared or a visible control field works in the standing-wave configuration to induce one atomic grating. Transfer-matrix calculations for appropriate rubidium levels demonstrate that three fifth-order band gaps or two second-order band gaps can be generated near the probe resonance when the standing-wave control field is modulated to satisfy relevant Bragg conditions in the regime of electromagnetically induced transparency. These high-order PBGs, as characterized by homogeneous high reflectivities, can be dynamically tuned in positions and widths on demand and may be extended to develop efficient devices (like diodes and reflectors) for manipulating weak high-frequency light with strong low-frequency light.
The absorption–dispersion properties of a microwave-driven five-level atom embedded in an isotropic photonic bandgap (PBG) have been studied. Due to the singular density of modes (DOM) in the isotropic PBG and the dynamically coherence induced by the coupling fields, modified reservoir-induced transparency and quantum interference-induced transparency emerge simultaneously. Their interaction leads to ultra-narrow spectral structure. As a result of closed-loop configuration, these features can be manipulated by the amplitudes and relative phase of the coherently driven fields. The position and width of PBG also have an influence on the spectra. The theoretical studies can provide us with more efficient methods to control the atomic absorption–dispersion properties, which have applications in optical switching and slow light.