Simulation of a spectral inhomogeneous broadening

Abstract

The standard approach that is used to simulate effects of inhomogeneous spectral broadening in a medium consisting of two- or multilevel systems is to calculate the microscopic polarization (the dipole moment of an individual system) as a function of the frequency detuning and further to average this quantity over detunings with corresponding weights. This just leads to the macroscopic polarization that appears in Maxwell’s equations of electrodynamics of continuous media. Here, we study and develop an alternative method that has been recently proposed by N.V. Vysotina, N.N. Rozanov, and V.E. Semenov (Opt. Spectrosc. 106 (5), 713 (2009)) for calculation of the macroscopic polarization and that has been aimed at solving problems of computational quantum optics. In this approach, the frequency detuning is considered as a stochastic function of coordinates; in one-dimensional problems, of longitudinal coordinate z. At each step of evolution, the microscopic polarization is calculated for a randomly chosen fixed value of the detuning. Therefore, calculating the macroscopic polarization does not need an additional averaging over detunings; it is replaced by averaging over spatial coordinates, which is naturally performed when describing the radiation propagation through an ensemble of quantum systems. This radically reduces the amount of computations, especially in the context of the finite-difference time domain (FDTD) method.