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Quantum Optics Journal of the European Optical Society Part B

A review of local field effects in lasing without inversion

Aaron S. Manka, Jonathan P. Dowling, C. M. Bowden, Michael Fleischhauer

Published Aug 1, 1994• 28 citations
Publisher

Abstract

We review the effects of density dependent near dipole-dipole, or local field, interactions on lasing without inversion. In particular, we consider the nonlinear behaviour of the macroscopic electric susceptibility of a dense, coherently prepared, three-level Lambda system. For certain values of the atomic density, we observe enhancement of the absorptionless index of refraction and inversionless gain by more than two orders of magnitude. We also predict a piezophotonic switching effect whereby a small change in density induces the system to flip from a strong absorber into a local field enhanced inversionless amplifier.

DOI
10.1088/0954-8998/6/4/014

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Local-field effects in lasing without inversion: An enhancement of gain and absorptionless index of refraction

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Summary form only given. It is well known that in dense media the effective field acting on an atom/molecule is no longer the macroscopic field but the so-called local field, which is due to all external sources and to all dipole moments of the atoms/molecules within the sample except the one under consideration. The inclusion of the local field effects gives rise to the prediction of a large number of interesting phenomena in optical systems, such as spectral red shifts, mirrorless optical bistability, "piezophotonic" effects, and enhancement of inversionless gain and absorptionless index in lasing without inversion. As an example, a density of 10/sup 17/ atoms/cm/sup 3/ of sodium atoms is sufficient to give rise to a shift of about 1 GHz of the sodium D line. We analyze here the role of the local field effects on the spatiotemporal dynamics of broad-area homogeneously broadened three-level lasers. In these three-level systems, laser emission in one atomic transition is investigated while an external plane-wave driving laser couples an adjacent transition. Due to the interplay between atomic nonlinearities and light diffraction, the optical wavevector of the generated laser field develops a small component in the transverse plane, i.e., the emitted laser beam is slightly tilted with respect to the cavity-axis.

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Journal of Modern Optics•Jul 1, 1995•5 citations
We review the effects of density dependent near dipole-dipole, or local field, interactions on lasing without inversion. In particular, we consider the nonlinear behaviour of the macroscopic electric susceptibility of a dense, coherently prepared, three-level Lambda system. For certain values of the atomic density, we observe enhancement of the absorptionless index of refraction and inversionless gain by more than two orders of magnitude. We also predict a piezophotonic switching effect whereby a small change in density induces the system to flip from a strong absorber into a local field enhanced inversionless amplifier.
We study the effect of near dipole-dipole interactions on the electric susceptibility of a coherently prepared three-level $\ensuremath{\Lambda}$ system. We discuss the influence of atomic nonlinearities on the recently predicted enhancement of the absorptionless index of refraction and inversionless gain due to local field effects [J.P. Dowling and C.M. Bowden, Phys. Rev. Lett. 70 1421 1993] and predict a density dependent, or piezophotonic, switching between absorption and amplification.
It is well known that, for static fields, the local microscopic electric field EL, that couples to the atomic dipole moment p, is related to the macroscopic field E and volume polarization P, in a dense dielectric medium, by the Lorentz-Lorenz (LL) relation.1 For dense media, this relation implies a nonlinear relationship between the microscopic molecular polarizability α and the macroscopic susceptibility χ, for a material volume density N. The LL relation also holds for arbitrary time-dependent fields in a nonlinear medium.2 What this implies is that all of quantum optics that uses an external electric field rather than the local field is internally inconsistent and will yield only approximate results for an optically dense medium. We consider the effect of the local field interaction on a simple three-level A system predicted to exhibit lasing without inversion and a high index of refraction at zero absorption.3 A threshold transition allows us to choose a value of this parameter that enhances inversionless gain and absorptionless dispersion by at least two orders of magnitude over that foundin usual lasing without inversion.4
Summary form only given. It is well known that in dense media the effective field acting on an atom/molecule is no longer the macroscopic field but the so-called local field, which is due to all external sources and to all dipole moments of the atoms/molecules within the sample except the one under consideration. The inclusion of the local field effects gives rise to the prediction of a large number of interesting phenomena in optical systems, such as spectral red shifts, mirrorless optical bistability, "piezophotonic" effects, and enhancement of inversionless gain and absorptionless index in lasing without inversion. As an example, a density of 10/sup 17/ atoms/cm/sup 3/ of sodium atoms is sufficient to give rise to a shift of about 1 GHz of the sodium D line. We analyze here the role of the local field effects on the spatiotemporal dynamics of broad-area homogeneously broadened three-level lasers. In these three-level systems, laser emission in one atomic transition is investigated while an external plane-wave driving laser couples an adjacent transition. Due to the interplay between atomic nonlinearities and light diffraction, the optical wavevector of the generated laser field develops a small component in the transverse plane, i.e., the emitted laser beam is slightly tilted with respect to the cavity-axis.
A V-type three level system with two closely spaced upper levels interacting with a single mode of the electromagnetic field is studied for the absorptive and dispersive lineshapes. A semiclassical description for the atom-field interaction is being adopted to obtain the usual optical Bloch equations. The approximate analytical solutions for the density matrix elements are obtained by solving coupled optical Bloch equations. Through the off-diagonal density matrix elements, the introduction of phase angles between the levels participating in dipole allowed transitions are automatic. It is shown that these phases are appreciable if the applied electromagnetic field is strong. These field dependent phases (coherence) are responsible for the reduction of the inversionless gain and the absorptionless dispersion. For large decay constants, it is found that the energy gap between the upper two levels has no role to play on the laser without inversion and on the absorptionless dispersion. However, for large population per unit decay, a significant increase of the absorptionless dispersion and the inversionless gain is obtained. The condition for large population decay and a possible experimental realization of the field dependent phases are discussed.
The steady-state behaviour for a Λ-type, three-level atomic system has been analysed by taking into account the effect of the phase fluctuation. It is shown that, for a monochromatic driving field, even if the probe field is in resonance with the corresponding atomic transition, a large refraction index can still be generated; for a finite linewidth of the driving field, inversionless lasing and index enhancement tends to disappear. Furthermore, the linewidth prevents the transparency of the medium.