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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Self-Starting Superradiant Lasing in Photonic Crystals

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

Published Jun 1, 2007• 0 citations
Publisher

Abstract

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.

DOI
10.1109/cleoe-iqec.2007.4386568

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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.
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 carry out numerical modelling of the Maxwell-Bloch equations for a CW superradiant lasing of a homogeneous two-level active medium in a symmetric low-Q Fabry-Perot cavity and find a remarkable phase transition. Namely, at a pumping level n > n ( a ) exceeding by several times the lasing threshold, n ( s ) , a stationary (or nonstationary multimode) lasing of more or less symmetric counter-propagating electromagnetic waves is replaced with a steady-state monochromatic (or weakly modulated) lasing of asymmetric counter-propagating waves with different amplitudes a + , a − . The spontaneous transition to a new field structure is accompanied by formation of a highly asymmetric strongly nonlinear half-wavelength grating of the self-consistent polarization and population inversion of active medium n z [1] , [2] . Many similar numerical runs with noise taking into account show that in a rather wide range of laser parameters the grating appears with equal probabilities 50:50 at one and the same distance from left or right ends of an active sample and has always one and the same asymmetric profile n z ( ζ ) with maximum at symmetric points with respect to the cavity center ζ = 0. As a rule, a formation of the steady-state grating takes a long transient period of time and includes generation of several superradiant pulses (see Fig. 1a ).
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.
The subject of the review is the diffraction of an electromagnetic wave on a periodic condensed matter where the Bragg condition is satisfied at the frequency of resonance excited in this medium. The Bragg systems known as resonant photonic crystals in general have been considered, and the propagation, reflection, transmission, and diffraction of electromagnetic radiation in different objects—(I) periodic quantum-well structures near the exciton resonance, (II) optical lattices of atoms cooled in a laser field, and (III) bulk crystals and multilayers with gamma-ray resonance intranuclear transitions—have been described in a unified context. The main attention has been paid to the steady-state linear diffraction, including resonant reflection and transmission, which is the best studied and allows a comparison of the three aforementioned systems with the aim of revealing specific characteristics and common features. A characteristic common property of the considered systems is the suppression of non-radiative channels and an inhomogeneous broadening of the resonance frequency. The second fundamental property of resonant photonic crystals is that the interaction of light with resonant excitation can occur in two regimes depending on the thickness of the sample. In the superradiant regime realized for a small number of resonant layers N (fine structures), the height of the peak and half-width of the reflection spectrum monotonically increase with increasing value of N. With a further increase in N, there occurs a transition to a photonic-crystal regime where the half-width of the reflection spectrum is saturated, which manifests itself in the form of an optical stop band. The theoretical description is illustrated by experimental spectra measured for all three resonant Bragg systems.
We demonstrate the existence of self-consistent Bloch modes in resonant nonlinear photonic crystals with a complex, intensity-dependent, and frequency-dependent dielectric function. Such a dielectric response may arise by "doping" the photonic crystal with resonant quantum dots, atomic impurities, or other two-level light emitters. These exact solutions of the nonlinear electromagnetic wave equation exhibit Bloch periodicity and describe fundamental eigenmodes of an active photonic crystal under incoherent pumping. In a simple model two-dimensional photonic crystal, doped with active two-level atoms, the optical field intensity of these waves shows a laserlike threshold behavior with pumping. This appears to be a universal property of active, nonlinear photonic crystals and photonic band gap materials, arising from multidirectional distributed feedback. We describe an iterative technique for computing the detailed properties of these exact, self-consistent nonlinear waves in strongly scattering photonic crystal architectures with regions of gain and loss.