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Quantum Electronics

Analysis of the amplitude — phase parameters of time-dependent optical signals and transfer functions

V. A. Zubov

Published Jun 30, 2002• 5 citations
Publisher

Abstract

The possibilities of obtaining information on the time dependence of the amplitude and phase of an optical signal by the spectral modulation method are analysed. Three variants of the signal analysis are considered: a direct analysis of the signal whose parameters are changing in time; studies of the time-dependent optical characteristics of an object or a medium under study by probing them with radiation of the known structure; and measurements of the parameters of radiation propagated through the object and simultaneous determination and analysis of time-dependent structures of the signal and transfer function describing the effect of the transfer medium, the object, or an optical system on the propagated signal.

DOI
10.1070/qe2002v032n06abeh002227

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 8, 2005•0 citations
The possibilities of obtaining information on the time dependence of the amplitude and phase of an optical signal by the spectral modulation method are analysed. Three variants of the signal analysis are considered: a direct analysis of the signal whose parameters are changing in time; studies of the time-dependent optical characteristics of an object or a medium under study by probing them with radiation of the known structure; and measurements of the parameters of radiation propagated through the object and simultaneous determination and analysis of time-dependent structures of the signal and transfer function describing the effect of the transfer medium, the object, or an optical system on the propagated signal.
The solution is obtained of the problem of simultaneous determination of the characteristics of an amplitude—phase signal and of the instrumental function, which acts on the signal amplitude and phase. This avoids the need for separate determination of the instrumental function. The solution follows from an analysis of measurements of the intensities in the spectral representations of signals acted upon by the instrumental function and subjected to additional modulation created in a specified manner.
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).
We propose a theoretical scheme for creating a two-dimensional Electromagnetically Induced Grating in a three-level [Formula: see text]-type atomic system interacting with a weak probe field and two simultaneous position-dependent coupling fields-a two dimensional standing wave and an optical vortex beam. Upon derivation of the Maxwell wave equation, describing the dynamic response of the probe light in the atomic medium, we perform numerical calculations of the amplitude, phase modulations and Fraunhofer diffraction pattern of the probe field under different system parameters. We show that due to the azimuthal modulation of the Laguerre-Gaussian field, a two-dimensional asymmetric grating is observed, giving an increase of the zeroth and high orders of diffraction, thus transferring the probe energy to the high orders of direction. The asymmetry is especially seen in the case of combining a resonant probe with an off-resonant standing wave coupling and optical vortex fields. Unlike in previously reported asymmetric diffraction gratings for PT symmetric structures, the parity time symmetric structure is not necessary for the asymmetric diffraction grating presented here. The asymmetry is due to the constructive and destructive interference between the amplitude and phase modulations of the grating system, resulting in complete blocking of the diffracted photons at negative or positive angles, due to the coupling of the vortex beam. A detailed analysis of the probe field energy transfer to different orders of diffraction in the case of off-resonant standing wave coupling field proves the possibility of direct control over the performance of the grating.
We present a theoretical analysis of high-frequency optical heterodyne saturation spectroscopy in Doppler-broadened coupled three-level systems. The saturating beam, which is assumed to be amplitude modulated at frequency δ (double-sideband suppressed carrier amplitude modulation) is resonant for one of the transitions. Through non-degenerate four-wave mixing processes, this modulation is transferred to a probe beam, resonant for the coupled transition. Saturating and probe fields may be either co-propagating or counter-propagating. The lineshape of the probe modulation is analysed via a third-order perturbation expansion of the atomic density matrix with respect to the incident field amplitudes. The resulting signal is integrated over velocities, in the Doppler limit approximation. Both population saturation effects and coherent (Raman-type, or two-photon) processes contribute to the signal. The various contributions appear as Lorentzian-type resonance doublets. We show that, in the absence of relaxation processes (collisional dephasing, or radiative cascades), destructive interferences between population saturation and coherent two-photon processes are responsible for the disappearance of one resonance doublet. Phase-interrupting collisions are thus predicted to lead to the existence of a « pressure-induced extra-resonance » (PIER) doublet, which could yield information on collisional processes in the impact regime. The properties of the predicted PIER doublets are analysed in relation with other types of PIER signals studied in four-wave mixing, and in time-resolved saturation spectroscopy.
As it is known the optical Kerr's effect changes cubic medium refraction index and in a nonlinear ring interferometer (NRI) causes to generation of optical structures and chaos. Besides in nonlinear media enough high emission power stimulates a multiphoton process. For example in a cubic medium three-photon absorption is possible. The process in a ring interferometer containing Kerr's medium through which the two-frequency light field is propagated are considered. The influence of mulitiphoton processes to dynamics of nonlinear phase shift in Kerr's medium is investigated. The mathematical model is constructed as differential partial equation, ordinary differential equation, discrete map. Maps of Lyapunov's characteristic exponents as functions of the interferometer and light field parameters are constructed. The influence of these parameters to possibility of determined chaos is discussed. It is shown that the act of three-photons absorption (N=3) produces an amplification of nonlinear effects in NRI due to generation of the third harmonics. And the position of the obrder of nonlinearity is determined by a value Kb0 s which is proportional to [2βbl(N-1)]-1/(N-1), where l is length of the medium, βb is a measure of three harmonics generation productivity.