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Physical Review A

Dynamic control of the photonic stop bands formed by a standing wave in inhomogeneous broadening solids

Qiongyi He, Jin‐Hui Wu, Tie-Jun Wang, Jin-Yue Gao

Published May 12, 2006• 18 citations
Publisher

Abstract

When a three-level system is coherently driven by a strong modified standing wave, photonic band gaps are viable to realize. Theoretically detailed calculations, for ${\mathrm{Pr}}^{{3}^{+}}$-doped yttrium orthosilicate crystal with inhomogeneously broadening, further show that the gap structure can be dynamically controlled and optimized by modulating the Rabi frequency, the spatial periodicity of the standing wave, the reflectivity of mirror, and the angle of incidence. This adjustable photonic band gap determined by the external pump control parameters in a doped solid crystal should hold more potential for applications than that in typical photonic crystals which are determined once for all by the way the material periodic structure is grown.

DOI
10.1103/physreva.73.053813

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When a three-level system is coherently driven by a strong modified standing wave, photonic band gaps are viable to realize. Theoretically detailed calculations, for Pr3+{\mathrm{Pr}}^{{3}^{+}}Pr3+-doped yttrium orthosilicate crystal with inhomogeneously broadening, further show that the gap structure can be dynamically controlled and optimized by modulating the Rabi frequency, the spatial periodicity of the standing wave, the reflectivity of mirror, and the angle of incidence. This adjustable photonic band gap determined by the external pump control parameters in a doped solid crystal should hold more potential for applications than that in typical photonic crystals which are determined once for all by the way the material periodic structure is grown.
Inhomogeneously broadened doped solids supporting electromagnetically induced transparency are viable materials where optically tunable photonic band gaps may be observed and results are shown for Pr:YSO and nitrogen-vacancy color center materials. Such crystals, when coherently driven by a strong pump beam in a suitably designed standing wave configuration, exhibit a tunable stop-band with rather different values of the reflectivity. The different propagating behavior is investigated and characterized for a weak probe across the gap region of the two materials.
Abstract Inhomogeneously broadened optical transitions in nitrogen‐vacancy color centers in diamond and Pr3+ doped yttrium orthosilicate may be employed to attain all‐optically controlled Bragg structures with photonic band‐gaps of high reflectivities and large bandwidths. Such a control mechanism is valuable for improving performance and scalability of solid quantum memory devices. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2722–2726, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24723
We illustrate a mechanism based on coherent optical nonlinearities to realize optically tunable photonic crystals built from media supporting electromagnetically induced transparency. These exhibit specific periodic patterns where a light probe can experience a fully developed photonic band-gap with negligible absorption. An analytical method based on a two-mode approximation is developed to study the optical response of such a periodically modulated medium driven into a regime of standing-wave electromagnetically induced transparency. A comparison with a transfer matrix approach and with techniques based on the coupled Maxwell–Liouville equations shows that our method is very accurate to describe the optical properties of such photonic metamaterials in the frequency region of interest. Nearly perfect reflectivities may be attained for ultracold 87Rb atoms samples which are seen to reflect with little loss and deformation light pulses whose frequency components are contained within the gap. When the same mechanism is implemented for inhomogeneously broadened optical transitions of nitrogen-vacancy centers in diamond, which is more amenable to device applications, fully developed photonic band-gap structures with negligible absorption, reflectivities very close to unity and sufficiently large bandwidths may also be attained. We further examine more flexible schemes based on four level systems under double driving conditions showing more accurate and efficient coherent optical control of the photonic band-gap. The remarkable experimental simplicity of the schemes that we presented is set to ease quantum nonlinear optics applications.
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.
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.