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Elektronika ir Elektrotechnika

Determination of the characteristic frequency of two–level system in the modulated optical field

ZIGMANTAS JANKAUSKAS, VYGAUDAS KVEDARAS, V. Zaveckas

Published Mar 19, 2006• 0 citations
Publisher

Abstract

Interaction between a two-level system and strong nonmonochromatic electromagnetic field has been the focus of attention of the laser technique and fiber optics for a long time. The influence of the modulated optical signal on the active medium, when the amplitude and phase (or frequency) vary arbitrary in time, is important in many problems, such as interaction of ultrashort pulses with the resonant amplifier, change of the line shape, the emission perturbation theory, self-focusing of light, etc. In this article, a new computational procedure is proposed for a two-level system in the strong harmonically modulated optical field. Expressions for polarization and population difference of a quantum system have been obtained in the form of the Fourier series. The characteristic frequency has been determined numerically. It depends not only upon the intensity of the carrier wave and the detuning magnitude but also upon the depth and frequency of modulation. The computational technique is applicable both for amplitude and phase modulation. Ill. 6, bibl. 3 (in English; summaries in English, Russian and Lithuanian).

DOI
10.5755/j02.eie.10634

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Interaction between a two-level system and strong nonmonochromatic electromagnetic field has been the focus of attention of the laser technique and fiber optics for a long time. The influence of the modulated optical signal on the active medium, when the amplitude and phase (or frequency) vary arbitrary in time, is important in many problems, such as interaction of ultrashort pulses with the resonant amplifier, change of the line shape, the emission perturbation theory, self-focusing of light, etc. In this article, a new computational procedure is proposed for a two-level system in the strong harmonically modulated optical field. Expressions for polarization and population difference of a quantum system have been obtained in the form of the Fourier series. The characteristic frequency has been determined numerically. It depends not only upon the intensity of the carrier wave and the detuning magnitude but also upon the depth and frequency of modulation. The computational technique is applicable both for amplitude and phase modulation. Ill. 6, bibl. 3 (in English; summaries in English, Russian and Lithuanian).
Expressions for polarization and population difference of a quantum system in the modulated optical field at the modulation frequency exceeding the transition line width have been obtained in the form of the Fourier series. The characteristic frequency of the system, or the Rabi frequency, has been determined numerically. It depends not only on the intensity of the carrier wave and the detuning magnitude but also on depth and frequency of modulation. The computational technique is applicable both for amplitude and phase modulation.
The propagation of a weakly modulated light beam through a nonlinear material is treated. The optical field representing such a beam consists of a strong carrier-frequency component and two weak, symmetrically displaced sidebands that combine to form a field, which may be purely amplitude modulated (AM), frequency modulated (FM), or some combination of these two modulation forms. It is shown that, for any optical nonlinearity, two modulation forms exist that have the property that the form of modulation is invariant under propagation of the beam. If a modulation form other than one of these natural modes is injected into the nonlinear medium, the modulation form will change as the beam propagates, asymptotically approaching the natural mode that experiences the lower attenuation. Explicit expressions for these natural modes are presented for the case in which the nonlinear medium can be modeled as a collection of two-level atoms. For the special case of an on-resonance pump beam, the natural modes correspond to pure amplitude modulation and pure frequency modulation. This formalism provides a general description of saturation spectroscopy for both AM and FM fields. Formulas are derived for the rate at which a pure FM beam is converted to an AM beam owing to its interaction with a two-level atomic medium. We also consider the variation that is due to propagation of the depth of modulation of an AM wave interacting resonantly with two-level atoms. The formalism predicts the existence of spectral features whose shape depends sensitively on the internal relaxation processes of the material. Experimental spectra are presented for ruby, alexandrite, and fluorescein in glass and are interpreted.
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.
Full space-time numerical modeling of near-resonance self-action of a beam, whose frequency is harmonically modulated in time, is presented. Maxwell-Bloch equations describing the propagation of the beam through a two-level medium with saturable absorption and refraction are solved using an original stable numerical scheme for multidimensional nonlinear Schrodinger equations. Delayed redistribution of intensity over the beam cross-section due to nonlinear self-focusing and self-phase-modulation effects is shown to affect the phase and the amplitude dynamics of the output signal in a rather nontrivial way, depending on the carrier laser frequency.
Numerical modeling of self-action of a beam, whose amplitude is periodically modulated in time, in a two-level saturable absorbing medium is reported. For describe a beam self-action we solve numerically the full set of Maxwell-Bloch equations. We study the influence of the non-stationary self-action of the beam on the transmission of modulation signal through the medium. It is shown that in the time dependence of the polarization and population difference the nonlinear distortions of the modulation signal can be much stronger than in the output field intensity.
On-resonance self-action of a beam with periodically modulated amplitude in a two-level saturable absorber is studied numerically. When the period of modulation is comparable with relaxation times, one cannot describe the medium by means of susceptibility, and the response of the medium to the amplitude variation is not immediate. We solve the Bloch equations in each point of the medium to find this response correctly. Transient behavior followed by stable oscillations of population difference and polarization vector is shown to depend strongly on the frequency and amplitude of modulation. Beam propagation is considered using a simplified model of a thin absorber followed by free space, the propagation distance being small compared with the modulation wavelength. Manifestations of non-stationary response of the medium in the output intensity behavior are analyzed.