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Physical Review A

Semiclassical study of spectral evolution under propagation in an active medium

Li You, J. Cooper

Published May 1, 1995• 1 citation
Publisher

Abstract

We study the propagation of a near-resonant strong laser light with a broad background continuum spectrum in a dense gaseous two-level medium. Due to the nonlinear saturation caused by the driving of the coherent component of the field, spectral regions close to the Rabi sidebands with significant gain exist close to the resonance. The subsequent evolution of the spectrum of the propagating field displays interesting features, and in the stationary limit a broadening of the spectral line always eventually happens in the end which contradicts the coherent narrowing phenomenon for pulsed propagation. This may shed some new light on the mechanisms of cone emission.

DOI
10.1103/physreva.51.4194

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We study the propagation of a near-resonant strong laser light with a broad background continuum spectrum in a dense gaseous two-level medium. Due to the nonlinear saturation caused by the driving of the coherent component of the field, spectral regions close to the Rabi sidebands with significant gain exist close to the resonance. The subsequent evolution of the spectrum of the propagating field displays interesting features, and in the stationary limit a broadening of the spectral line always eventually happens in the end which contradicts the coherent narrowing phenomenon for pulsed propagation. This may shed some new light on the mechanisms of cone emission.
This is the first of a series of papers on the theory of cone emission from a laser-pumped two-level atomic medium. Starting from microscopic quantum theory for both the active medium and the field, equations for the slowly varying macroscopic quantities are derived. In the steady-state limit, which experimentally corresponds to cw excitation, we find that the sources for the paraxial fields of interest have a long coherence length despite the random nature of spontaneous emission. These radiation sources enter into the equations for the fields in the same form as the source generated by four-wave mixing and therefore may be considered as a ``spontaneous four-wave mixing,'' since the photons emitted in the Rabi sidebands are correlated. This has far-reaching consequences on the physics of cone emission and also sheds some new light on the fluoresence from strongly driven atomic systems.
A time-dependent theory for conical emission during near-resonant propagation of laser light in an atomic vapor, which includes full propagation for the laser and frequency sidebands in a nonlinear two-level medium is presented. The density-matrix equations for the dipole moment and population are solved in the dressed atomic frame. The polarization source terms are accurate to order \ensuremath{\gamma}/R, where \ensuremath{\gamma} is a damping constant and R is the generalized Rabi frequency. Analytical plane-wave solutions and numerical, cylindrically symmetric propagation simulations including diffraction are presented. It is shown that the calculations with cylindrically symmetric fields and atomic excitation profiles are incapable of accounting for the high levels of optical gain that are responsible for the intense conical emission observed in experiments. This result is at first surprising, since the model accounts rigorously for all of the physical phenomena that have been previously proposed as being responsible for generating large gains, and the calculation matches the symmetry of the observations. The lack of large calculated gain seems to imply the existence of higher-order (m>0)(m>0)(m>0) radial modes in the field for the experimental conditions that give rise to cone emission. In the simulations, however, the cylindrically symmetric fields do produce weak red-detuned cones with angular-frequency distributions similar to those seen in experiments.
We undertake a theoretical investigation of the coherent optical propagation of Stokes light in a collisionally broadened three-level Raman amplifier. The Stokes light consists of two distinct spectral components: off-resonance stimulated Raman scattering and on-resonance stimulated fluorescence, induced by collisional transfer of population to a near-resonant intermediate state of the atomic system. Our model is based on the semiclassical Maxwell-Bloch formalism where the separation of the Stokes light into two components results in an expansion from the usual 9 to 13 atomic variables. We investigate the model both analytically and numerically. We point out the physical contributions to the simultaneous evolution of pump, fluorescence, and Raman light. We discuss the development during propagation of these separate pulses, emphasizing the nonlinear effects that lead to saturation.
We investigated the sideband instability by numerical integration of the Maxwell-Bloch equations for propagation of a nearly resonant pump laser and a weak probe laser in a system of two-level atoms. In an optically thick medium, the probe gain (absorption) spectrum becomes a function of propagation distance. We find that the well-known gain resonance at the generalized Rabi frequency Ω' is suppressed and a broad asymmetric gain region forms on each side of the laser frequency. For probe-pump detunings inside these gain regions, the field envelope breaks up into periodic traveling waves that are compared to the polycnoidal solutions of the sine-Gordon equation with periodic boundary conditions.
The spectrum evolution of a few-cycle optical pulse in a resonant two-level atom medium is studied theoretically by using the full Maxwell-Bloch equations. On the propagating pulse, significantly much faster oscillation components separated with the main pulse appear due to strong self-phase modulation and pulse reshaping. In this case, ideal self-induced transparency cannot occur for a 2π pulse. The spectrum of the 4π pulse shows an evident oscillatory feature because of the continuum interference of the separate pulses. For larger pulse areas, continuum generation from near ultraviolet to infrared occurs.
The spectrum evolution of a few-cycle optical pulse in a resonant two-level atom medium is studied theoretically by using the full Maxwell-Bloch equations. On the propagating pulse, significantly much faster oscillation components separated with the main pulse appear due to strong self-phase modulation and pulse reshaping. In this case, ideal self-induced transparency cannot occur for a 2 pi pulse. The spectrum of the 4 pi pulse shows an evident oscillatory feature because of the continuum interference of the separate pulses. For larger pulse areas, continuum generation from near ultraviolet to infrared occurs.