An experimental investigation was made of the efficiency of a regenerative optical quantum amplifier in detection of scattered laser radiation. In agreement with theoretical estimates, the experimental results demonstrated that the average energy of the scattered field amplified in this amplifier did not exceed the energy in the spatial coherence area. The relative variance of the output signal, which was distributed exponentially under linear conditions, was close to unity and was independent of the relationship between the correlation radius of the spatially random field and the receiver aperture radius.
An experimental investigation was made of the efficiency of a regenerative optical quantum amplifier in detection of scattered laser radiation. In agreement with theoretical estimates, the experimental results demonstrated that the average energy of the scattered field amplified in this amplifier did not exceed the energy in the spatial coherence area. The relative variance of the output signal, which was distributed exponentially under linear conditions, was close to unity and was independent of the relationship between the correlation radius of the spatially random field and the receiver aperture radius.
A theory is devloped of the propagation of a spatially random signal, resulting from the scattering of coherent radiation, through a single-pass optical quantum amplifier. Attention is drawn to the need to allow for the channeling of the radiation by the walls of a gas-discharge cell. The spatial selectivity of optical quantum amplifiers is discussed. It is shown that the optimal size of the aperture of a receiver system with a single-pass amplifier may be considerably greater than the spatial coherence radius. Estimates are obtained for the scattered-radiation gain. The theoretical conclusions are confirmed by an experimental study.
Conditions for the efficient detection of reflected laser radiation by means of optical quantum amplifiers are considered theoretically. It is shown that in the case of a strongly disturbed spatial coherence, there is no need to take it into account and a simple geometrical consideration is sufficient. The expressions relating the effective radius of the input aperture and the angular magnification of a projecting optical system with the laser radiation divergence and amplifier parameters are obtained. The theoretical results are confirmed by experiments.
We examine application of optical amplification to coherent lidar for the case of a weak return signal (a number of quanta of the return optical field close to unity). We consider the option that has been explored to date, namely, incorporation of an optical amplifier operated in a linear manner located after reception of the signal and immediately prior to heterodyning and photodetection. We also consider alternative strategies where the coherent interaction, the nonlinear processes, and the amplification are not necessarily constrained to occur in the manner investigated to date. We include the complications that occur because of mechanisms that occur at the level of a few, or one, quantum excitation. Two factors combine in the work to date that limit the value of the approach. These are: (1) the weak signal tends to require operation of the amplifier in the linear regime where the important advantages of nonlinear optical processing are not accessed, (2) the linear optical amplifier has a -3dB noise figure (SN(out)/SN(in)) that necessarily degrades the signal. Some improvement is gained because the gain provided by the optical amplifier can be used to overcome losses in the heterodyned process and photodetection. The result, however, is that introduction of an optical amplifier in a well optimized coherent lidar system results in, at best, a modest improvement in signal to noise. Some improvement may also be realized on incorporating more optical components in a coherent lidar system for purely practical reasons. For example, more compact, lighter weight, components, more robust alignment, or more rapid processing may be gained. We further find that there remain a number of potentially valuable, but unexplored options offered both by the rapidly expanding base of optical technology and the recent investigation of novel nonlinear coherent interference phenomena occurring at the single quantum excitation level. Key findings are: (1) insertion of linear optical amplifiers in well optimized conventional lidar systems offers modest improvements, at best, (2) the practical advantages of optical amplifiers, especially fiber amplifiers, such as ease of alignment, compactness, efficiency, lightweight, etc., warrant further investigation for coherent lidar, (3) the possibility of more fully optical lidar systems should be explored, (4) advantages gained by use of coherent interference of optical fields at the level of one, or a few, signal quanta should be explored, (5) amplification without inversion, population trapping, and use of electromagnetic induced transparency warrant investigation in connection with coherent lidar, (6) these new findings are probably more applicable to earth related NASA work, although applications to deep space should not be excluded, and (7) our own work in the Ultrafast Laboratory at UAH along some of the above lines of investigation, may be useful.
In super-regenerative detection, a weak external signal is amplified in an oscillator that is periodically switched on and then quenched. It is shown that very weak optical signals, slightly above the noise level, can be detected effectively by a laser used as a super-regenerative receiver. The detector output for different signal levels and its operating characteristics are determined by numerical integration of stochastic differential equations that represent the growth of laser radiation from a background consisting of signal and noise.
The amplification before detection of the carrier of a modulated optical signal by a narrow-band quantum amplifier enhances the signal-to-noise ratio, particularly when the signal wave-front is distorted. A further improvement is obtained by using a combination of wide-band and narrow-band quantum amplifiers. The practical application of these schemes requires a degenerate regenerative ring-type amplifier capable of amplifying arbitrary transverse field configurations. Experiments show that such an amplifier with a gain of 24 dB and a bandwidth of 1 MHz is feasible. The incident beam axis can be displaced by as much as ten times the beam-waist radius without losing more than 4 dB in gain. Frequency modulation may be converted into amplitude modulation by the phase shift introduced in the carrier.
We derive the photon-number probability distribution and the resulting degree of second-order optical coherence for light emission from a uniformly distributed active species within a multiple-light-scattering medium. This is obtained from a master equation describing the probability distribution for photons in the vicinity of position r, traveling with a wave vector k, related, in turn, to a coarse-grained average of the optical Wigner coherence function. Using a simple model for isotropic, spatially uncorrelated scatterers, this reduces to a generalization of the master equation of a conventional laser in which the medium behaves like a random collection of low-quality factor cavities that are coupled by photon diffusion between a given cavity and its neighbors. Laserlike coherence, on average, is obtained in the random laser above a specific pumping threshold. Photon-number statistics above and below the lasing threshold are computed by first assuming that the atomic response to the local electromagnetic fields is nearly instantaneous. Corrections to this simple model, arising from nonadiabatic atomic dynamics, are then estimated. The dependence of the photon statistics on scatterer density, gain concentration, and position within a sample reveal that, on average, increase of the scattering strength (decrease of the photon transport mean free path) in the medium leads to a sharper peak in the local photon-number distribution, characteristic of increased local coherence in the optical field. We also evaluate the coherence of the output field at points outside the random-laser medium. This is a weighted average of radiation emitted at different positions in the sample, exhibiting varying degrees of coherence due to variations in the local pumping intensity.