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Optics and Spectroscopy

Simulation of a spectral inhomogeneous broadening

V. V. Kozlov, N. N. Rosanov

Published Jun 1, 2014• 2 citations

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.

DOI: 10.1134/s0030400x14060150

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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.

Abstract—A numerical model based on the finite-difference time-domain method is developed to simulate fluctuations which accompany the dephasing of atomic polarization and the decay of excited state’s population. This model is based on the Maxwell-Bloch equations with c-number stochastic noise terms. We successfully apply our method to a numerical simulation of the atomic superfluorescence process. This method opens the door to further studies of the effects of stochastic noise on light-matter interaction and transient processes in complex systems without prior knowledge of modes. Index Terms—Noise, spontaneous emission, stochastic processes, FDTD methods, Maxwell equations I.

A technique for the numerical simulation of coherent optical responses of the photon echo type formed in resonance media with strong inhomogeneous broadening under the action of femtosecond laser pulses is developed. This approach is based on solving the Maxwell-Bloch equations using the finite-difference time-domain (FDTD) method without application of a fast rotating field and slowly varying envelope approximations. The method can be used to simulate coherent responses in different resonance media with a complex structure of energy levels. The technique was validated using the example of describing experiments on narrowing a photon echo pulse and femtosecond echo processing.

We employ another approach to quantize electromagnetic fields in the coordinate space, instead of the mode (or Fourier) space, such that local features of photons can be efficiently, physically, and more intuitively described. To do this, coordinate-ladder operators are defined from mode-ladder operators via the unitary transformation of systems involved in arbitrary inhomogeneous dielectric media. Then, one can expand electromagnetic field operators through the coordinate-ladder operators weighted by non-orthogonal and spatially-localized bases, which are propagators of initial quantum electromagnetic (complex-valued) field operators. Here, we call them QEM-CV-propagators. However, there are no general closed form solutions available for them. This inspires us to develop a quantum finite-difference time-domain (Q-FDTD) scheme to numerically time evolve QEM-CV-propagators. In order to check the validity of the proposed Q-FDTD scheme, we perform computer simulations to observe the Hong-Ou-Mandel effect resulting from the destructive interference of two photons in a 50/50 quantum beam splitter.

We present a one-dimensional iterative predictor-corrector finite-difference time-domain method for modeling of broadband optical pulse propagation and interaction with inhomogeneously broadened materials. The simulator is used to demonstrate two- and three-pulse photon echoes resulting from bandwidth limited pulse and matched chirp interactions with a material modeled with hundreds of equally spaced, discrete spectral lines of detuning. The results are illustrated as Bloch-sphere evolution movies.

Propagation and amplification of an ultrashort laser pulse in a two-level medium is numerically investigated with the use of the finite-difference time-domain (FDTD) procedure simultaneously solving Maxwell and Schrodinger equations with no assumptions characteristic of slowly varying envelope approximation. Comparison of the results of FDTD numerical simulations with the predictions of the pulse area theorem has demonstrated that the developed numerical procedure provides an adequate description of pulse evolution in a two-level medium. Amplification of ultrashort light pulses in a two-level medium is analyzed. Two methods of improving the gain of ultrashort pulses in a two-level medium by modulating the spatial distribution of dipole moments of resonant transitions and using initially chirped frequency-detuned pulses are explored.