<title>Method of phase portrait for analysis of nonstationary coherent optical fields</title>

Abstract

The method dwells upon observed estimate of nonstationary field density operator in the form of two-dimensional joint distribution of variables related to the field envelope or correlation function and their Hubert-images.It is oriented to recognition and estimation of the parameters of both stationary and non-stationary optical fields.Consideration is given to apply it for experimental study of low-frequency transients in optical quantum generators and nonstationary light scattering in liquid media. . IntroductionA method of experimental estimation of nonstationary field density operator in the form of twodimensional joint distribution of variables related to the field envelope or correlation function and their Hubert-images is discussed. The paperdescribes its application to experimental analysis of low-frequency transients in optical quantum generators and nonstationary light scatter in liquids.The spectral methods have certain disadvantages. At observing coherent field E+(r,t) = e(r,t) Xx exp(f w0t) (complex envelope e+(r, t) and optical carrier w) , it is field correlation function C(r, t) = <E+(r, t) E(r', t + r)> = <e+(r, t) e(r', t + -r)> exp(jw0t) that is investigated depending, for stationary fields, only on a single time argument r and is related by the Fourier transform to the spectral power S(w) of field envelope. One can judge from spectrum width Aw about the interval A v 1 /z\ w of temporal field coherence characterizing the temporal correlation of the stationary process generating filed envelope. COrrelational or identical spectral descriptions suffice for many processes associated, for example, with molecular continuum dynamics because of random nature of phase relations in motions of individual molecules. This phase information is known to be disregarded in these descriptions that preserve only values averaged over all possible phases in the ensemble of molecules (denoted by <>) . Correlational C(r, t) or timefrequency S(w, t) descriptions of nonstationary fields depend on two appropriate arguments. It is well known that for high-frequency fluctuations (noises), stationary descriptions can be constructed by averaging C(v, t) or S(w, t) by greater observation time T (T/A oo) [1]. For low-frequency processes, however, averaging results in degenerate descriptions, that is loss of 'phase information about cause-effect relations between temporal components of processes. For instance, nonstationarity of transients in high-molecular compounds or phase transitions in ordered media may be due to cooperative intermolecular interaction or environmental interaction, correlation function trend variations characterizing interaction features. Direct correlational or 0-8194-1 224-4/93/$6.oo SPIE Vol. 1978 / 193 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/17/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

<title>Use of the Fresnel transform for optical pattern recognition</title>

“…( 3) This field with the accuracy of constant multiplier has the absolute meaning of a coherence degree coincided with (2). The affirmation about the equivalence of a wave field with an envelope (2) and a mutual coherence function (1) is called a van Zittert-Zemike theorem1…”