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Soviet Journal of Quantum Electronics

Optimal measurement and phase conjugation algorithms used in the case ofa prioriindeterminacy of the statistics of the received signal

V. E. Kirakosyants, Vadim A. Loginov

Published Jan 31, 1988• 0 citations
Publisher

Abstract

An analysis is made of the task of measuring and phase conjugation of the optical field against the background of noise in the case of a priori indeterminacy of the statistical properties of the received signal. Mode expansion of a useful signal is employed to show that the optimal algorithm may be realized in at least two variants: either on the basis of multichannel heterodyne reception and phase conjugation of the filtered signal at a radio frequency or with the aid of "physical" phase conjugation methods directly at an optical frequency. Expressions are obtained for estimating the quality of the measurements and phase conjugation. It is shown that practical realization of the latter variant of the optimal algorithm may result in a significant deterioration of the potential characteristics.

DOI
10.1070/qe1988v018n01abeh011232

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An analysis is made of the task of measuring and phase conjugation of the optical field against the background of noise in the case of a priori indeterminacy of the statistical properties of the received signal. Mode expansion of a useful signal is employed to show that the optimal algorithm may be realized in at least two variants: either on the basis of multichannel heterodyne reception and phase conjugation of the filtered signal at a radio frequency or with the aid of "physical" phase conjugation methods directly at an optical frequency. Expressions are obtained for estimating the quality of the measurements and phase conjugation. It is shown that practical realization of the latter variant of the optimal algorithm may result in a significant deterioration of the potential characteristics.
An analysis is made of the efficiency of compensation of distortions of the angular distribution by a phase-conjugate adaptive system of the heterodyne type. Numerical estimates are given of the time and energy characteristics of adaptive systems obtained for different values of the signal/noise ratio in the measuring scheme. It is shown that when the signal/noise ratio in a homogeneous system is of the order of unity, the use of adaptive correction is not very effective. Analytic and numerical results obtained in the present study make it possible to estimate approximately the potential characteristics of phase-conjugate adaptive systems.
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The problem of estimating a member of a discrete-time vector process from past and present quantum mechanical measurements is considered; specifically, the minimum-variance linear estimator based on optimal present measurements is studied. Necessary and sufficient conditions that characterize the optimal processing matrix coefficients and the optimal measurements are discussed and interpreted. The optimal linear filter is compared to the optimal quantum estimator without postprocessing of past data. When the signal sequence is pairwise Gaussian and the optimal quantum measurement without postproccssing has the properties that it is linear in a specific sense and that its outcome and the corresponding element of the signal sequence are jointly Gaussian, then the optimal linear filter separates. That is, the optimal measurement can be taken to be the same as thc optimal measurement without regard to past data, and the past and present data are processed classically. Thc results are illustrated by considering the filtering of the in-phase and quadrature amplitudes of a laser field received in a single-mode cavity along with thermal noise. In this case, when the random signal sequence satisfies a linear recursion, the estimate can be computed recursively in a very efficient manner.
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In fundamental papers from 1962, Heffener and Haus showed that it is not possible to construct a linear noiseless amplifier [ Proc. IRE 50 , 1604 ( 1962 ) PIREAE 0096-8390 10.1109/JRPROC.1962.288130 ; Phys. Rev. Lett. 128 , 2407 ( 1962 ) PHRVAO 0031-899X 10.1103/PhysRev.128.2407 ]. This implies that amplifier intrinsic noise sources induce random perturbations on the phase of the incoming optical signal, which translates into spectral broadening. Achieving the minimum induced phase fluctuation requires a phase measurement method that introduces minimum uncertainty, i.e., optimum phase measurement. We demonstrate that a measurement method based on heterodyne detection and extended Kalman filtering approaches optimum phase measurement in the presence of amplifier noise. A penalty of 5 dB (numerical) and 15 dB (experimental) compared to quantum limited spectral broadening is achieved. Spectral broadening reduction of 44 dB is achieved, compared to when using the widely employed phase measurement method, based purely on the argument of the signal field. Our results reveal new scientific insights by demonstrating a phase measurement method that enables to approach minimum phase fluctuation, induced by amplifier noise. An impact is envisioned for phase-based optical sensing systems, as optical amplification could increase sensing distance with minimum impact on the phase.