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Physical Review A

Using the eigenmode expansion for computing the supercontinuum spectral distribution from a slab of two-level atoms

Jamal T. Manassah

Published Dec 24, 2014• 2 citations
Publisher

Abstract

This Brief Report gives the spectral distribution of the supercontinuum generated from a system of initially partially excited two-level atoms. The expansion in the eigenfunctions of the one-dimensional Li\'enard-Wiechert kernel which was successful in obtaining previously the results in the linear regime is generalized to the nonlinear regime. The detailed spectral distribution of the emitted radiation is computed without invoking either the phenomenological simplified physical model for the active medium or the mathematical approximations commonly used in treating propagation in absorbing media. The numerical solutions presented are those of the complete set of the coupled Maxwell-Bloch equations.

DOI
10.1103/physreva.90.065801

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This Brief Report gives the spectral distribution of the supercontinuum generated from a system of initially partially excited two-level atoms. The expansion in the eigenfunctions of the one-dimensional Li'enard-Wiechert kernel which was successful in obtaining previously the results in the linear regime is generalized to the nonlinear regime. The detailed spectral distribution of the emitted radiation is computed without invoking either the phenomenological simplified physical model for the active medium or the mathematical approximations commonly used in treating propagation in absorbing media. The numerical solutions presented are those of the complete set of the coupled Maxwell-Bloch equations.
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Using eigenmode analysis I calculate in the linear regime the emission characteristics from a slab of two-level resonant atoms excited by a delta-pulse propagating normal to the surface of the slab. I show that the qualitative features of the emitted spectra in the forward and backward directions to be different from each other; I also find the effects of the total linewidth of the resonance line and of the deviation in the spatial periodicity of the initial atomic polarization from k 0, where k 0 = ω0/c and ω0 is the two level resonant frequency, on the spectra. The dominant spatial mode of the system is identified as the key parameter for determining the forward emission spectral width.
We have studied the spectral behaviour of few-cycle soliton pulses in a non-resonant two-level atom medium by solving the full Maxwell-Bloch equations. It is demonstrated further that the carrier effects play an important role in the propagation of the few-cycle pulse laser. When the frequency detuning is not very large, both the population distribution and the refractive index of the medium follow the oscillatory carrier field instantaneously; in this case, carrier-wave compression or carrier shock occurs and a supercontinuum broader than that in the resonant medium may be generated. When the frequency detuning is large, the carrier shock is weak and the spectrum is not continuous, only showing an odd harmonic radiation.
We have studied the spectral behaviour of few-cycle soliton pulses in a non-resonant two-level atom medium by solving the full Maxwell-Bloch equations. It is demonstrated further that the carrier effects play an important role in the propagation of the few-cycle pulse laser. When the frequency detuning is not very large, both the population distribution and the refractive index of the medium follow the oscillatory carrier field instantaneously; in this case, carrier-wave compression or carrier shock occurs and a supercontinuum broader than that in the resonant medium may be generated. When the frequency detuning is large, the carrier shock is weak and the spectrum is not continuous, only showing an odd harmonic radiation.
Starting from first principles we simulate numerically the dynamics of a system of two-level atoms interacting with a multimode electromagnetic field in a one-dimensional cavity. In particular, we investigate the spontaneous emission of an excited two-level atom in the cavity. We show how the decay depends on the mode spectrum and on the position of the atom in the cavity. We study how the spontaneous emission is modified when the initially excited atom is surrounded by a material medium modeled as a system of two-level atoms. We also study the propagation of photon wave packets emitted by the atom within the material media. Our microscopic model provides us with a deeper understanding of the atom-field interaction and offers us a framework for a systematic investigation of the transition from a microscopic to a macroscopic (phenomenological) description of the spontaneous decay in material media (e.g., dielectrics).