In this analysis the quantum statistics of the received signal of a frequency modulated laser communication system are derived. In particular the detection statistics for heterodyne and electric field detection of the frequency modulated laser beam are determined. These detection statistics are used to define a measure of the communication system performance in terms of a signal to noise ratio. The development of the quantum electromagnetic field in terms of the photon annihilation eigenstates is the basis for determining these statistics. The derivation used accounts for fluctuations in the carrier, fluctuations due to background radiation introduced after modulation, fluctuations due to the local laser oscillator, and zero point field fluctuations. The results of this analysis indicate the probability distribution for the optical heterodyne detection is not a familiar one of classical communication theory, but it is of the form of probability distribution that satisfies experimentally measured photocount statistics of unmodulated laser radiation. The probability distribution for the electric field intensity detection of the frequency modulated laser beam is the familiar Gaussian distribution. (Author)
In this analysis the quantum statistics of the received signal of a frequency modulated laser communication system are derived. In particular the detection statistics for heterodyne and electric field detection of the frequency modulated laser beam are determined. These detection statistics are used to define a measure of the communication system performance in terms of a signal to noise ratio. The development of the quantum electromagnetic field in terms of the photon annihilation eigenstates is the basis for determining these statistics. The derivation used accounts for fluctuations in the carrier, fluctuations due to background radiation introduced after modulation, fluctuations due to the local laser oscillator, and zero point field fluctuations. The results of this analysis indicate the probability distribution for the optical heterodyne detection is not a familiar one of classical communication theory, but it is of the form of probability distribution that satisfies experimentally measured photocount statistics of unmodulated laser radiation. The probability distribution for the electric field intensity detection of the frequency modulated laser beam is the familiar Gaussian distribution. (Author)
The problem of including quantum effects within existing methods of communication system analysis is investigated.A mathematical model is postulated for describing narrow bandwidth systems.Utilizing the Glauber P representation, the model permits analysis of both real field detection (measurement of electric and magnetic field magnitudes) and photon detection.The resulting equation which describes photon detection is shown to be consistent with previous work which has been proven experimentally.Unique aspects of the postulated model are its ability to describe both random and deterministic modulation functions in conventional terms, and its ability to demonstrate the inapplicability of the "photon channel" model for describing present-day systems.An analysis of quantum effects at the transmitter shows that modulation of the radiated field must take place by one of two distinctly different processes.Wave modulation is defined as a process which conveys information in the amplitude and phase of the electromagnetic field.Photon modulation is defined as a process which conveys information in the exact number of photons per pulse of the transmitted field (i.e., the "photon channel" of Stern, Gordon, ani othfrs).A wave modulated signal is shown to describe present-day modulation schemes and, moreover, to yield random photon fluctuations.It is concluded a wave modulated signal is not capable of describing a photon modulated signal.In contrast, a photon modulated signal is shown to possess a completely random phase fluctuation thus demonstrating the inability of the "photon channel" to describe presently used wave modulation schemes.For wave modulation the Glauber P function is shown to be identical (with a change of variable) to the classical joint probability density of the quadrature components of a narrowband sinusoid used in conventional analysis.Equations are derived which "transform" classical probability distributions into distributions which include quantum effects.The "partitioning noise" studied by Hagfors and Bowen is found to constitute a source of noise only in the "photon channel."The "partitioning effect" is shown to merely preserve the Poisson character of photon counts in wave modulated fields and therefore does not introduce a noise in present-day systems.For a wave modulated system with real field detection it is shown that photon noise can be included in conventional analysis by adding to the normal input noise, a noise density of hf c /2 Watts/Hertz where h is Planck's constant and f is the system carrier frequency.Use of photon heterodyne detection requires the addition of an input noise density of hf c Watts/Hertz.The photon noise is exactly additive Gaussian for real field detection and approximately additive Gaussian for photon heterodyne detection.Detection by counting the received photons is shown to yield neither Gaussian nor Poissonian statistics.However, with an "ideal measurement process," when the effective received noise density n c is much less than hf c , the variance of the counts are found to approach that of a Poisson distribution.Conversely, when nc is much larger than hf c , the .variance approaches that derivable from a classical analysis.A channel capacity equation for a wave modulated system is found which is equal to those derived by Lachs and Jelsma.The equation is shown to give capacities less than that derived by Gordon.
The theory of balanced homodyne and heterodyne detection is developed for inputs in which the signal field is in an arbitrary quantum state and the local-oscillator field is in a highly excited coherent state. Exact expressions are derived for the photocount moment-generating functions in the special case of a coherent signal. For more general signals, the first two moments of the photocount probability distribution are determined. The moments are evaluated for the examples of a coherent signal with a chaotic noise component, and for squeezed light derived from a degenerate and from a non-degenerate parametric amplifier. The corresponding moments for direct detection are obtained so that comparisons can be made. The Kelley-Kleiner photocount distribution formula is adapted to balanced detection schemes. Light beams are characterized throughout by their energy fluxes, and the theory accordingly describes steady-state experiments.
The basic equations governing noise phenomena are derived from first principles and applied to examples in optical communications. Quantum noise arises from two sources, the momentum fluctuations of electrons at optical frequencies and the uncertainty-related fluctuations of the electromagnetic field. Shot noise results from the beating of the noise sources with the signal field. In high-gain amplifiers, the spontaneous-emission noise dominates shot noise and results in a noise figure of at least 3 dB. It is shown explicitly how, at high power, both the laser field and the laser noise source become classical. The increase in noise in lasers with open cavities is not due to enhanced spontaneous emission as once thought, but to single-pass amplification. The noise fields and spontaneous currents have Gaussian distributions, while nonlasing modes have exponential photon-number distributions. Low-frequency intensity fluctuations arise from the electric current driving the laser and can be sub-Poissonian, in contrast to shot noise, which has a Poissonian distribution. The calculational tools are a wave equation for the field operator and a rate equation for the carrier-number operator, each containing spontaneous current noise sources. The correlation functions of these sources are determined by the fluctuation-dissipation theorem. [S0034-6861(96)00503-X]
The paper contains a quantum theoretical analysis of laser beam fluctuations and of the light beat experiments with two lasers. With the help of experimental results on photon counting fluctuations in a single-mode laser field, some correlation properties of the field are derived. It is shown that the correlation equations are satisfied by states of the field which are much more general than "coherent" states. The equations lead directly to the spectral density of the intensity operator in the light beat experiments, which can be obtained from photoelectric measurements. The resulting expression is practically identical to that found by Forrester for light having thermal statistical properties. The reasons for this are discussed by a comparison of the corresponding probability distributions of photon counts and of the classical wave amplitude.
This paper is concerned with the determination of the quantum statistics of the photoelectric detection, and the E-field detection of multiple-mode superposed chaotic and coherent radiation. The Glauber P-representation is utilized extensively, and results are obtained by a fully quantum-mechanical treatment. The generating function, the mean, and the variance of the photocount statistics are derived for illumination times of arbitrary duration and for modes of arbitrary statistical interdependence. For short illumination times, the complete photocount distribution is obtained. The distribution has the same form as that for a single mode of superposed chaotic and coherent radiation. The multiple-mode distribution, however, is nonstationary. The difference between experimental determinations of the mean and variance which utilize periodic sampling and those which utilize random sampling is derived. A method for determining the P-representation for modulated fields is described, and the detection statistics are derived. The statistics of the E field are found to be Gaussian, and it is found that for multiple-mode classical statistics and quantum statistics differ.
In Part I of this three-part study it was shown that the use of two-photon coherent state (TCS) radiation may yield siginificant performance gains in free-space optical communicatinn if the receiver makes a quantum measurement of a single field quadrature. In Part II it was shown that homodyne detection achieves the same signal-to-noise ratio as the quantum field quadrature measurement, thus providing a receiver which realizes the linear modulation TCS performance gain found in Part I. Furthermore, it was shown in Part il that ff homodyne detection does exactly correspond to the field quadrature measurement, then a large binary communication performance gain is afforded by homodyne detection of antipodal TCS signals. The full equivalence of honmdyne detection and single-quadrature field measurement, as well as that of heterodyne detection and two-quadrature field measurement, is established. Furthermore, a heterodyne configuration which uses a TCS image-band oscillator in addition to the usual coherent state local oscillator is studied. This coafiguration termed TCS heterodyne detection is shown to realize all the quantum measurements described by arbitrary TCS. The foregoing results are obtained by means of a representation theorem which shows that photoemissive detection realizes the photon flux density measurement.