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Acta Scientiarum Naturalium Universitatis Sunyatseni

Numerical Method and Application for Optical Maxwell-Bloch-Equations in Inhomogeneously Broadened Medium

Cheng Li, Huarong Zhang, Xiangyang Yu

Published Jul 25, 2009• 0 citations
OpenAlex

Abstract

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.

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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.
We present a numerical method for solving the Maxwell-Bloch equations describing pulse propagation for a two-level medium. The method is accurate, efficient, stable, and well suited for this type of simultaneous equations. By applying the numerical scheme we investigate the evolutions of pulse area, pulse propagation, pulse velocity, and spectral shapes under both homogeneous and inhomogeneous broadening conditions. The results show that the area evolution and pulse-reshaping procedure are significantly influenced by detuning and inhomogeneous line shape, which also impact the oscillation tail and pulse peak. In addition, the pulse-peak traces indicated the pulse velocity always increases with greater deviation in pulse-area value from the value 2\ensuremath{\pi}. We also demonstrate the pulse velocity increased for a larger detuning or a wider inhomogeneous line shape. Furthermore, the spectral feature shows that pulse spectra evolve into an oscillating shape.
Important applications in optical information storage and processing based on photon echo have been developed.An accurate and effective numerical method to solve the Maxwell-Bloch equations that are used to describe the optical pulse propagation and interaction with inhomogeneously broadened two-level medium will be introduced.Two-pulse photon echo is calculated then photon echo and multiple-pulse photon echoes are stimulated in optical thin(thick) media by using the method,and the physical properties of those echoes are analyzed.The results show that the approach to storage and retrieval of light using multiple-pulse photon echoes based on stimulated photon echo is an effective mode.
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.