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Physical Review A

Laser-amplifier gain and noise

R. Loudon, Michael Harris, Terence J. Shepherd, J. Michael Vaughan

Published Jul 1, 1993• 37 citations
Publisher

Abstract

A theoretical study is presented of the gain and the noise spectra of laser amplifiers at pumping rates both above and below the oscillation threshold. The theory is valid for both class-A and class-B laser systems, where the decay rate of the collective atomic dipole moment greatly exceeds the decay rates of the atomic population inversion and the laser cavity. The gain and the noise properties are shown to be strongly influenced by a four-wave mixing of the signal and image frequencies via a modulation of the population inversion. Particular attention is paid to the residual noise flux that persists in the laser output above threshold and to the typical characteristics of a second-order phase transition displayed by the gain in the threshold region. The results for the above-threshold laser amplifier are compared with experimental measurements of both gain and noise for the argon-ion (class-A) and ${\mathrm{CO}}_{2}$ (class-B) lasers. The signal-to-noise ratios for both heterodyne and direct-detection measurements are evaluated, and the conditions are determined under which optical amplification can lead to an enhancement of sensitivity.

DOI
10.1103/physreva.48.681

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Communications in Theoretical Physics•Feb 10, 2025•0 citations
A theoretical study is presented of the gain and the noise spectra of laser amplifiers at pumping rates both above and below the oscillation threshold. The theory is valid for both class-A and class-B laser systems, where the decay rate of the collective atomic dipole moment greatly exceeds the decay rates of the atomic population inversion and the laser cavity. The gain and the noise properties are shown to be strongly influenced by a four-wave mixing of the signal and image frequencies via a modulation of the population inversion. Particular attention is paid to the residual noise flux that persists in the laser output above threshold and to the typical characteristics of a second-order phase transition displayed by the gain in the threshold region. The results for the above-threshold laser amplifier are compared with experimental measurements of both gain and noise for the argon-ion (class-A) and CO2{\mathrm{CO}}_{2}CO2​ (class-B) lasers. The signal-to-noise ratios for both heterodyne and direct-detection measurements are evaluated, and the conditions are determined under which optical amplification can lead to an enhancement of sensitivity.
The theory of small-signal laser amplification is developed for homogeneously broadened systems in which the three main decay rates, for the collective atomic dipole moment, the population inversion, and the field in the laser cavity, have arbitrary relative magnitudes. The calculations extend previous work on class-AAA and -BBB lasers, where the dipole decay rate greatly exceeds the other two rates, to class-CCC lasers, where the dipole decay rate is comparable to the others. The free-running laser is assumed to excite a single longitudinal mode of the cavity, whose frequency generally differs from that of the coupled atomic transition. The linear gains of the laser are derived for input signals whose frequencies are close to that of the lasing mode or to one of its adjacent nonlasing longitudinal modes. Divergences in the gain that occur for these two arrangements are associated with the previously studied single-mode and multimode instabilities of the free-running laser, respectively.
It has been customary to ignore the key role of the cavity Langevin force on the laser noise fluxes. Here, the noise fluxes of the laser pump and spontaneous and stimulated emission (laser) radiation are calculated for class-B lasers by considering the cavity Langevin force alone. They have a symmetrical double-peak profile around the cavity resonance frequency, which is in complete agreement with the experimental results of the heterodyne gain profile of class-B laser amplifiers. This agreement indicates the lasers undertake the same mechanism in amplifying an input signal as superimposing noise fluxes on their variables. Meanwhile, the noise flux profiles of the cavity Langevin force are consistent with those produced by two other Langevin forces, associated with atomic population inversion and the atomic dipole moment. Finally, the noise fluxes generated by the cavity Langevin force are confirmed by demonstrating the flux conservation law.
We calculate the input-output characteristics of an optical amplifier that consists of an inverted-population medium placed inside a high-Q Fabry-P\'erot cavity. Expressions are derived for the output second- and fourth-order spectral and temporal correlation functions, and more generally for the output characteristic functional, in terms of the corresponding input quantities. The photocount first and second factorial moments are obtained for both homodyne and direct detection of the amplifier input and output. The general results are applied to several cases of practical interest, including inputs that have coherent or chaotic coherence properties. Particular attention is paid to the effects of amplification on specific nonclassical varieties of input light. It is shown that a maximum of only twofold amplification is permitted if any squeezing present in the input is to survive as squeezing in the output light. Similarly, for the preservation of photon antibunching in amplification, we show, by consideration of a kind of free-space number-state input, that only small gains are allowed. The amplifier model treated here provides a detailed example of the limitations imposed by quantum mechanics on the minimum noise generated by a multimode linear amplifier. In particular, we show that minimum noise occurs in a cavity that is asymmetric with respect to mirror reflectivities, for which we derive the corresponding conditions. In addition, we demonstrate the ability of the amplifier to improve upon signal-to-noise ratio, otherwise limited by low detector quantum efficiency.
Abstract The noise feature of a single-mode class-A laser amplifier is investigated by solving the Maxwell–Bloch equations of motion in the presence of the fluctuation force of cavity Langevin. The aim is to calculate the simultaneous fluctuations that are superimposed on the amplitude and phase of the cavity electric field, as well as the atomic population inversion. The correlation function of these fluctuations yields the amplitude, phase, and spontaneous emission noise fluxes, respectively. The amplitude and spontaneous emission noise fluxes exhibit the Lorentzian profiles in both the below-threshold state and the injection-locking region of the above-threshold state. While noise is typically viewed negatively in science and engineering, this research highlights its positive role as a valuable tool for measuring the optical properties of a laser amplifier. For instance, the degree of first-order temporal coherence (DFOTC) is derived by taking the Fourier transform of the amplitude noise flux. The damping rate of DFOTC is associated with the coherence time of the light emitted by the laser amplifier. Furthermore, the uncertainty relation between noise bandwidth and coherence time is confirmed. Finally, it is demonstrated that the input pumping noise flux, together with the output amplitude and spontaneous emission noise fluxes, satisfy the principle of flux conservation.