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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Photonic-crystal superradiant laser: effects of homogeneous and inhomogeneous broadening of an active medium

N. S. Ginzburg, E. R. Kocharovskaya, Alexander S. Sergeev, Alexander A. Telnykh

Published Nov 10, 2008• 2 citations
Publisher

Abstract

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.

DOI
10.1117/12.818016

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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 find and investigate numerically the self-starting superradiant lasing and the strongly modified superfluorescence regimes in a two-level active sample of one-dimensional photonic crystal (responsible for the resonance wave back-scattering) for various values of the light bandgap and the amplification bandwidth. The simplest oscillators of this type are the quantum-well injection heterostructures and the laser fibers with active colour centres where one-dimensional Bragg back-scattering can be fabricated artificially by means of a periodic modulation of the cladding layers. Of special interest is the case where the single-site reflections from the facets of a sample are weaker than the total distributed reflections owing to the resonance wave back-scattering either introduced artificially or present in an inverted two-level medium due to a photonic crystal structure.
Peculiarities of the implementation of a superradiant generation mode in a laser with a distributed feedback of the waves and an inhomogeneously broadened spectral line of the active medium are investigated. Based on a numerical solution of the semiclassical Maxwell-Bloch equations for the amplitudes of counterpropagating electromagnetic waves, polarization, and inversion of a two-level medium population, it is shown that a sequence of coherent high-power pulses is generated by the Bragg structure in a wide range of the laser parameters as a result of the selected mode and the cw pumping.
Using one-dimensional semiclassical Maxwell — Bloch equations with account for the coherent polarisation dynamics, we have studied spike generation regimes of a superradiant distributed feedback laser in the case of inhomogeneous broadening of the spectral line of an active medium. By analysing the dynamic spectra of inversion of the active medium and laser radiation, we have revealed the relationship of individual spikes of radiation and their modulation with specific parts in the spectral line of the active medium and mode beatings. It has been shown that the broadening and shift of the lasing spectrum with respect to the initial electromagnetic Bragg-cavity modes is accompanied by a strong spectral gradient of inversion that is typical of the superradiant regimes.
Abstract On the basis of numerical solution to the Maxwell–Bloch equations within the one-dimensional two-level model of a superradiant laser with a symmetric cavity in which the photon lifetime is less than the incoherent relaxation time of the optical-dipole oscillations of active centers, the phenomenon of the spontaneous asymmetric generation of counter-propagating waves under continuous uniform pumping of the active medium is revealed. It is shown that the observed symmetry breaking of the spatial profiles of counter-propagating waves of the electromagnetic field and, the polarization and inversion of the population of active-medium levels in the case of a small inhomogeneous broadening of the spectral line of its working transition occurs due to the asymmetric half-wave nonlinear grating of inversion of the energy-level population produced by these waves.
By means of numerical modeling of nonlinear and analytical solution of linearized Maxwell-Bloch equations, we find an intriguing regime of a superradiant laser with a symmetric low-Q Fabry-Perot cavity equipped with a distributed feedback of counter-propagating waves. We find that, in a wide range of parameters, there is lasing of a strongly-asymmetric self-modulated powerful polariton mode accompanied by excitation of several almost symmetric weak polariton or electromagnetic modes. The frequency of the powerful mode is approximately coincides with a center of the laser spectral line, and the frequencies of the weak modes are outside the spectral line of an active medium. We show that such a lasing takes place due to formation of a self-consistent inhomogeneous asymmetric grating of population inversion of active centers that provides undamped Rabi oscillations of the population inversion and dipole moments of centers. The grating makes the powerful ‘central’ mode strongly asymmetric, and the Rabi oscillations of active centers excite the weak ‘sideband’ modes due to the quadratic resonant nonlinearity of the two-level active medium.