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Quantum Electronics

Propagation of frequency-modulated pulses in active one-dimensional photonic crystals

И. О. Золотовский, Dmitry A. Korobko, Vladimir A. Ostatochnikov

Published Feb 27, 2015• 3 citations
Publisher

Abstract

The propagation of frequency-modulated pulses in one-dimensional photonic crystals with gain is considered. A correct expression is derived for the delay time of the pulse maximum. This expression takes into account the input pulse characteristics: duration, frequency modulation and spectrum position in the photonic band gap. The analytical results are basically in agreement with the results of numerical simulation. The influence of gain in the photonic-crystal structure is considered. It is shown that the parameters of a transmitted pulse can be controlled by changing the input-pulse frequency modulation.

DOI
10.1070/qe2015v045n02abeh015581

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The propagation of frequency-modulated pulses in one-dimensional photonic crystals with gain is considered. A correct expression is derived for the delay time of the pulse maximum. This expression takes into account the input pulse characteristics: duration, frequency modulation and spectrum position in the photonic band gap. The analytical results are basically in agreement with the results of numerical simulation. The influence of gain in the photonic-crystal structure is considered. It is shown that the parameters of a transmitted pulse can be controlled by changing the input-pulse frequency modulation.
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The present thesis is devoted to theoretical studies of light pulse propagation through different linear and nonlinear media. One dimensional holographic photonic crystals and one dimensional impurity band based photonic crystals are investigated as linear media. The effects of angular dependence of the band structures and pulse delay with respect to the light polarization are analyzed. A strict theory of nonlinear propagation of a few strong interacting light beams is presented and applied in the field of nonlinear optics. The key idea of this approach is a self-consistent solution of the nonlinear wave equation and the density matrix equations of the material beyond the so-called rotating wave approximation. The results of numerical studies led to a successful interpretation of recent experimental data [Nature, 415:767, 2002]. A theoretical study of the NO molecule by means of two-color infrared -- X-ray pump probe spectroscopy is presented. It was found that the phase of the infrared field strongly influences the trajectory of the nuclear wave packet, and hence, the X-ray spectrum. The dependence of the X-ray spectra on the delay time, the duration and the shape of the pulses are studied.
We report on experimental measurements of the propagation behavior of short optical pulses in a three-dimensional photonic crystal in the visible spectrum. The propagation delay of 70 fs light pulses transmitted through a sample of a fcc synthetic opal at frequencies lying in a photonic stop band was measured directly using a time-of-flight technique. Taking into account spectral reshaping of the transmitted pulses as well as the residual frequency chirp of the incoming pulses, it is found that the pulses significantly slow down at the photonic band edges.
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.
Photonic crystals (PCs) are periodic systems that consist of dielectrics with different refractive indices. Photonic crystals have many potential technological applications. These applications are mainly based on the photonic bang gap effect. However the band gap is not only effect that follows from the periodic changing of the refractive index in the photonic crystal. The periodic change of the photon-matter interaction in photonic crystal medium gives rise to the fact that the mass of an electron in the photonic crystal must differ from its mass in vacuum. Anisotropy of a photonic crystal results in the dependence of the electromagnetic mass correction on the orientation of the electron momentum in a photonic crystal. This orientation dependence in turn gives rise to the significant correction to the transition frequencies in an atom placed in air voids of a photonic crystal. These corrections are shown to be comparable to the atomic optical frequencies. This effect allows one to control the structure of the atomic energy levels and hence to control resonance processes. It can serve as the basis for new line spectrum sources. The effect provides new ways of realization of quantum interference between decay channels that can be important for quantum information science.