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Propagation of Laser Pulses in Media with Non-stationary optical and Magnetic Response

Любен Иванов, K Kovachev, V Serkin, L Kovachev

Published Jan 1, 2010• 0 citations
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Abstract

We investigate the propagation of laser pulses in media with non-stationary optical and magnetic response. A new amplitude integro-differential equation, governing the evolution of wave packets with one and few cycles under the envelope, is derived. The application of slowly varying amplitude approximation to this equation reduces it to a nonlinear Slowly Varying Equation of Amplitudes (SVEA) in a second approximation of the linear dispersion. It is important to point out that the SVEA obtained in media with non-stationary optical and magnetic response is similar to the SVEA equation with stationary magnetic response. The only difference is in the expressions for the group velocity and for the dispersion parameters. In particular, in paramagnetic media near to the magnetic resonances and also in experiments with a strong DC longitudinal magnetic field, it is possible to attain negative group velocity and group velocity, higher than the velocity of light in vacuum.

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We investigate the propagation of laser pulses in media with non-stationary optical and magnetic response. A new amplitude integro-differential equation, governing the evolution of wave packets with one and few cycles under the envelope, is derived. The application of slowly varying amplitude approximation to this equation reduces it to a nonlinear Slowly Varying Equation of Amplitudes (SVEA) in a second approximation of the linear dispersion. It is important to point out that the SVEA obtained in media with non-stationary optical and magnetic response is similar to the SVEA equation with stationary magnetic response. The only difference is in the expressions for the group velocity and for the dispersion parameters. In particular, in paramagnetic media near to the magnetic resonances and also in experiments with a strong DC longitudinal magnetic field, it is possible to attain negative group velocity and group velocity, higher than the velocity of light in vacuum.
We shell investigate the propagation dynamics of optical pulses in media with non stationary optical and magnetic response. We derived a new amplitude integro-differential equation describing their propagation in transparency region of such media. The applied method of the slowly varying amplitude approximation to this equation reduces it to nonlinear Slowly Varying Equation of Amplitudes (SVEA) in second approximation of linear dispersion and in first approximation to the nonlinear dispersion (SVEA). It is important to point out, that the obtained SVEA in media with no stationary optical and magnetic response is similar to the SVEA equation with stationary magnetic response. The only difference is the expression for group velocity and dispersion parameters. Partially, in paramagnetic media near to magnetic resonances it is possible to reach group velocity higher than velocity of light in vacuum.
The semiclassical Maxwell–Bloch equations beyond the slowly varying envelope approximation (SVEA) are derived in order to study the propagation of the ultrashort pulse in a two-level medium. The evolutions of the pulse shape, the group velocity and the pulse peak of 2[Formula: see text] ultrashort pulse are investigated as well as the pulse splitting of 4[Formula: see text] ultrashort pulse. By comparing the numerical results with those obtained using the SVEA, the error introduced by the approximation is quantitatively evaluated with respect to the pulse width and the applicable condition of the SVEA is discussed consequently. The envelope solutions presented by us allow clear observation on the evolution of the envelope.
The propagation of ultrashort few-cycle laser pulses through a quantum nonlinear medium with resonant properties is studied using the method of slowly varying amplitudes with allowance for dispersion effects. A self-consistent system of nonlinear wave equation for the evolution of laser field and the nonstationary Schrödinger equation that determines the material polarization response is numerically solved. Specific features of the propagation of laser pulse caused by a relatively large spectral width and the nonadiabatic character of the laser pulse are established. The rise of the slowly dumping polarization at the eigenfrequency of the medium and the consequent stretching of the laser pulse are observed. The role of the resonant absorption of the laser energy in the medium is analyzed. The nonlinear spectral broadening is demonstrated for the laser pulse propagating through the medium.
We derive the propagation equation for the slowly varying envelope (SVE) of the electric field in a homogeneous dispersive nonisotropic medium. Terms in the propagation equation of the field envelope that originate because of finite beam size are obtained and explained, including generalized Fresnel diffraction terms and a term that rotates the SVE wave packet in a uniaxial crystal about an axis perpendicular to the optical plane. Numerical estimates of these terms in the propagation of short pulses in the uniaxial crystal β-barium borate are presented. We obtain an analytic expression for the SVE for an initial Gaussian wave packet by keeping terms up to second order in the wave equation for the SVE.
The evolution of slowly varying wave pulses in strongly dispersive and absorptive media is studied by a recursive method. It is shown that the resulting envelope function may be obtained by including correction terms of arbitrary dispersive and absorptive orders. Different definitions of pulse velocity are discussed in some detail and finally, qualitative examples of a Gaussian pulse in a cold plasma and an atomic medium are given, illustrating the importance of higher-order terms in the velocity expression. Particularly, the packet velocity is shown to be dependent on pulse width besides dispersion.
We performed a series of experiments to examine the arrival of phase nonanalytical points in fast- and slow-light media, using a Gaussian-shaped temporal pulse and encoding phase nonanalytical points at various positions within the pulse envelope. For the phase nonanalytical points, the amplitude of the slowly varying pulse envelope, as well as any order of the derivatives, is continuous, but the phase of the carrier wave is discontinuous. The phase nonanalytical points were neither advanced nor delayed, but appeared at the same instance as they entered the fast- and slow-light media, in good accordance with the idea that the information velocity was equal to the velocity of light in a vacuum, ccc, or in the background medium.