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Wave Electronics and its Application in Information and Telecommunication Systems (WECONF)

Methods of Signals Theory in the Problems of Optical Radiation Description

Oleg D. Moskaletz

Published Nov 1, 2018• 1 citation
Publisher

Abstract

On the critical evaluation basis of the signals theory it is shown that it is necessary to develop its physical aspect, based on the quantum ideas. Within the framework of the quantum approach, where the energy of radiation changes over time in jump, the existence of frequency-temporal duality of photons is shown and the absence of operator connection between the time and frequency characteristics of the optical signal. The instantaneous power of the optical signal is described by a sequence of delta functions, similar to the sampled signal in the communication theory. Methods of communication theory and properties of photon spin allowed to make the transition to the classical approximation of the optical signal.

DOI
10.1109/weconf.2018.8604388

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On the critical evaluation basis of the signals theory it is shown that it is necessary to develop its physical aspect, based on the quantum ideas. Within the framework of the quantum approach, where the energy of radiation changes over time in jump, the existence of frequency-temporal duality of photons is shown and the absence of operator connection between the time and frequency characteristics of the optical signal. The instantaneous power of the optical signal is described by a sequence of delta functions, similar to the sampled signal in the communication theory. Methods of communication theory and properties of photon spin allowed to make the transition to the classical approximation of the optical signal.
Based on the critical estimation of modern information theory and signal theory, the necessity of developing the physical aspect of signal theory, which is based on an abrupt change in the energy of an optical signal during its formation, is substantiated. It is shown that the inflow of information in time has a quantum nature and is due to the action of the photon production operators. Quantum forms of optical signals were obtained and, based on the methods of communication theory, a transition was made to the classical approximation of an optical signal. The role of the probabilistic nature of quantum processes in the stochastic essence of the optical signal is noted.
Based on the quantum postulates of Planck and Einstein, without the use of quantum formalism, a quantum description of optical signals in the form of discrete sequences of instantaneous power and instantaneous values of the electrical component of optical radiation is proposed. The classical approximation of the quantum representation of optical signals is carried out using the methods of signal theory and communication theory. A quantum description of photodetection of optical signals is proposed, within the framework of which the photocurrent is given in the form of a discrete sequence, and its classical description is carried out.
The necessity of development of the physical signal theory (ST) as component of laser theory is justified, and its principles are stated. These principles include quantum description of signals in the form of electromagnetic (EM) field and their classical representation. The submitted researches are based on Planck hypothesis about discrete levels of energy of EM radiation, Einstein hypothesis about light quantum and Bohr rule of frequencies only, and in so doing Heisenberg indeterminateness principle is taken into account.
Communication theory problems incorporating quantum effects for optical-frequency applications are discussed. Under suitable conditions, a unique quantum channel model corresponding to a given classical space-time varying linear random channel is established. A procedure is described by which a proper density-operator representation applicable to any receiver configuration can be constructed directly from the channel output field. Some examples illustrating the application of our methods to the development of optical quantum channel representations are given. Optimizations of communication system performance under different criteria are considered. In particular, certain necessary and sufficient conditions on the optimal detector in M-ary quantum signal detection are derived. Some examples are presented. Parameter estimation and channel capacity are discussed briefly.
Hitherto communication theory was based on two alternative methods of signal analysis. One is the description of the signal as a function of time; the other is Fourier analysis. Both are idealizations, as the first method operates with sharply defined instants of time, the second with infinite wave-trains of rigorously defined frequencies. But our everyday experiences—especially our auditory sensations—insist on a description in terms of both time and frequency. In the present paper this point of view is developed in quantitative language. Signals are represented in two dimensions, with time and frequency as co-ordinates. Such two-dimensional representations can be called “information diagrams,” as areas in them are proportional to the number of independent data which they can convey. This is a consequence of the fact that the frequency of a signal which is not of infinite duration can be defined only with a certain inaccuracy, which is inversely proportional to the duration, and vice versa. This “uncertainty relation” suggests a new method of description, intermediate between the two extremes of time analysis and spectral analysis. There are certain “elementary signals” which occupy the smallest possible area in the information diagram. They are harmonic oscillations modulated by a “probability pulse.” Each elementary signal can be considered as conveying exactly one datum, or one “quantum of information.” Any signal can be expanded in terms of these by a process which includes time analysis and Fourier analysis as extreme cases.These new methods of analysis, which involve some of the mathematical apparatus of quantum theory, are illustrated by application to some problems of transmission theory, such as direct generation of single sidebands, signals transmitted in minimum time through limited frequency channels, frequency modulation and time-division multiplex telephony.