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Optics Express

Multilevel Maxwell-Bloch simulations in inhomogeneously broadened media

Robert Marskar, Ulf L. Österberg

Published Aug 15, 2011• 34 citations
Publisher

Abstract

A compact numerical method for simulating ultrafast pulse interaction with inhomogeneously broadened multi-level media is reported. We use a low-dispersion pseudospectral scheme with fourth order time stepping for Maxwell's equations, and a weakly coupled operator splitting method for the Bloch equations where inhomogeneous broadening and relaxations are also taken into account. The underlying physics is briefly discussed with emphasis on the formalism used.

DOI
10.1364/oe.19.016784

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A compact numerical method for simulating ultrafast pulse interaction with inhomogeneously broadened multi-level media is reported. We use a low-dispersion pseudospectral scheme with fourth order time stepping for Maxwell's equations, and a weakly coupled operator splitting method for the Bloch equations where inhomogeneous broadening and relaxations are also taken into account. The underlying physics is briefly discussed with emphasis on the formalism used.
An accurate and effective numerical method is presented to solve the Maxwell-Bloch equations that are used to describe the optical pulse propagation and interaction with inhomogeneously broadened two-level medium.The convergence and stability of this numerical method are proved by comparing with the analytic solutions and area theorem derived under special condition.The simulations of arbitrary conditions is discussed by employing this method and analyze the pulse evolution for different detunings,relaxation times and inhomogeneously broadened linewidthes.The established numerical method provides a good way to have further study about the coherent interaction of short optical pulses with resonant mediums,and can be used to solve the corrections of Maxwell-Bloch equations.
An accurate and effective numerical method is presented to solve the Maxwell-Bloch equations,which describe the optical pulse propagation and interaction with homogeneously broadened two-level medium.The convergence and stability of this numerical method are also proved by comparing with the analytic solutions derived under special condition,and the method maintains its erroneous exponents and is applicable.Simulations of arbitrary conditions are discussed by employing this new method,and the evolutions of pulse and Bloch vectors for different detunings,relaxation times and initial input pulse power are analyzed.The established numerical method can be used to solve the Maxwell-Bloch equations and their corrections.
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.
Coherent amplification of short-pulse XeCl lasers is studied theoretically by using multilevel Maxwell–Bloch equations in which the vibrational–rotational structures of a XeCl gain spectrum are included. The model used considers 100 transitions each in the P and R branches for six different vibrational transitions of XeCl(B, υ = 0) → XeCl(X, υ′ = 0–5). Coherence components between sublevels in the B and X states are also properly calculated. The model can successfully predict coherent effects such as a quantum beat caused by the spectrum overlap of the several vibrational–rotational transitions involved in a short-pulse laser spectrum. During amplification, laser pulses experience some nonlinear effects caused by the complex gain spectrum structure and by the coherent interactions; thus a considerable change in the laser pulse shape and a substantial reduction in the duration of the amplified laser pulse are predicted. The Frantz–Nodvik equation in the rate-equation limit and even single-level Maxwell–Bloch equations are not applicable for short-pulse propagation analyses in inhomogeneously broadened gain media.
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).