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arXiv:2007.09329

Modeling lasers and saturable absorbers via multilevel atomic media in the Meep FDTD software: Theory and implementation

Alexander Cerjan, Ardavan F. Oskooi, Song-Liang Chua, Steven G. Johnson

Published Jul 18, 2020• 2 citations

Abstract

This technical note describes the physical model, numerical implementation, and validation of multilevel atomic media for lasers and saturable absorbers in Meep: a free/open-source finite-difference time-domain (FDTD) software package for electromagnetics simulation. Simulating multilevel media in the time domain involves coupling rate equations for the populations of electronic energy levels with Maxwell's equations via a generalization of the Maxwell--Bloch equations. We describe the underlying equations and their implementation using a second-order discretization scheme, and also demonstrate their equivalence to a quantum density-matrix model. The Meep implementation is validated using a separate FDTD density-matrix model as well as a frequency-domain solver based on steady-state ab-initio laser theory (SALT).

DOI: 10.48550/arxiv.2007.09329

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This technical note describes the physical model, numerical implementation, and validation of multilevel atomic media for lasers and saturable absorbers in Meep: a free/open-source finite-difference time-domain (FDTD) software package for electromagnetics simulation. Simulating multilevel media in the time domain involves coupling rate equations for the populations of electronic energy levels with Maxwell's equations via a generalization of the Maxwell--Bloch equations. We describe the underlying equations and their implementation using a second-order discretization scheme, and also demonstrate their equivalence to a quantum density-matrix model. The Meep implementation is validated using a separate FDTD density-matrix model as well as a frequency-domain solver based on steady-state ab-initio laser theory (SALT).

A faster numerical method based on FDTD for the four energy level atomic system is present here. The initial conditions for the electrons of each level are achieving while the fields are in steady state. Polarization equation, rate equations of electronic population and Maxwell’s equations were used to describe the coupling between the atoms and electromagnetic wave. Numerical simulations, based on a finite-difference time-domain (FDTD) method, were utilized to obtain the population inversion and lasing threshold. The validity of the model and its theory is confirmed. The time, which we can observe the lasing phenomenon, is much shorter in our new model. Our model can be put into using in large scale simulations in mutiphysics to reduce the total simulated time.

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.

Time-domain electromagnetic modelling of complex structures which include both non-dispersive media and media exhibiting electromagnetically induced transparency (EIT) require a general, robust calculation method such as finite-difference time-domain (FDTD). We propose a complex-valued, exact two-pole representation of the permittivity of a three-level system which is suitable for integration into the FDTD algorithm via the auxiliary differential equation method. Our calculation model confirmed reported results which were calculated with an approximate representation of the EIT permittivity. Additionally, propagation calculations which mimic slow light experiments were performed. A major advantage of our representation is the ease with which changes in the control field Rabi frequency can be implemented by using a time-dependent permittivity.

Recent progress in ultrafast technology has led to the generation of optical pulses as short as 8 fs. The propagation of such short pulses in nonlinear optical media requires new computational techniques in which the standard approximations such as the slowly-varying envelope approximation (SVEA) and rotating-wave approximation (RWA) are not made while using the Maxwell-Bloch equations [1]. Previous calculations, which used the finite-difference time-domain (FDTD) method, found that for a a Kerr-like instantaneous nonlinearity [2] significant differences can occur when the full vector Maxwell equations are used instead of the nonlinear Schrodinger equation. Recently, the FDTD method has been extended to the case of a homogeneously broadened two-level atomic system [3].