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Physical Review

Maser Noise Considerations

J. Weber

Published Nov 1, 1957• 40 citations
Publisher

Abstract

The contribution of the saturation field to the noise figure of a three-level maser is calculated. It is shown that the effect is very small, under ordinary circumstances.Certain aspects of spontaneous-emission noise are considered. It is shown that the spontaneous-emission equivalent temperature for a free-electron vacuum-tube amplifier is one-half that of a maser.The possibility of eliminating spontaneous-emission noise is considered and it is concluded that more general quantum-mechanical amplifiers can in principle be constructed which will not have spontaneous-emission noise.

DOI
10.1103/physrev.108.537

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Journal of the Physical Society of Japan•Jun 1, 1957•315 citations
The contribution of the saturation field to the noise figure of a three-level maser is calculated. It is shown that the effect is very small, under ordinary circumstances.Certain aspects of spontaneous-emission noise are considered. It is shown that the spontaneous-emission equivalent temperature for a free-electron vacuum-tube amplifier is one-half that of a maser.The possibility of eliminating spontaneous-emission noise is considered and it is concluded that more general quantum-mechanical amplifiers can in principle be constructed which will not have spontaneous-emission noise.
Since the demonstration of the possibility of achieving very low noise amplification of signals in the centimetric wavebands, a great deal of work has been carried out in various laboratories with a view to producing and testing devices. The major part of the present article focuses attention on one particular device, the three-level solid-state maser. The physical principles underlying the process of stimulated emission of radiation are in many cases unfamiliar to electronic engineers, and study of the growing literature on the subject can be confusing without a clear understanding of the physics involved. The present article outlines the general theory of emission and radiation processes, particularly as they apply to the microwave spectrum. A quantum mechanical description is employed throughout, and a brief and not very rigorous account is given of the relevant portions of this theory as it applies to the investigation of transistors between energy levels. Well-known expressions are derived for the operating characteristics of a three-level maser, particular attention being given to the significance of the various factors involved and their relationship to easily measured quantities. Little information is included concerning practical maser amplifiers; at the time of writing, few practical devices had been constructed. A survey of recent literature indicates the rapid progress which has since been made, and shows the interest in the development of masers.
In a three-level maser, a transition between two energy levels is saturated in order to produce an induced emission of power at a lower frequency corresponding to a transition between an intermediate energy level and one or the other of the two saturated levels. In this paper, certain effects are discussed which cannot be predicted from a theory in which the population differences alone are considered in this process. For instance, it is shown that, in some cases it is possible to obtain for the same system an induced emission of power at two frequencies given by the resonances between the intermediate energy level and both of the saturated levels. Also, it is shown that, even in the absence of inhomogeneous broadening of the spectral line, one can obtain a net induced emission at some portions of a resonant line and a net absorption at other frequencies within the line widths. Such effects become important even in early stages of saturation in cases where T1=T2{T}_{1}={T}_{2}T1​=T2​ which is true for ordinary gaseous systems and individual spin systems in a majority of very dilute paramagnetic solids. A complete theory is discussed for a gaseous system and extended to two limiting cases of paramagnetic materials with T1=T2{T}_{1}={T}_{2}T1​=T2​ and ${T}_{2}\ensuremath{\ll}{T}_{1}$ for each individual spin system. Furthermore, it is shown that for a saturating field of fixed frequency, the integral of induced power over the entire line is in full agreement with the results of a semiclassical treatment in which the population differences alone are considered. Some remarks are made as to the practicability of certain systems of this type.
The noise figure or limiting sensitivity for both traveling-wave and resonant-cavity quantum-mechanical amplifiers, sensitive to one direction of propagation, is derived with spontaneous emission as the limiting noise. The concept of effective temperature is introduced as an analytical parameter; thus negative temperatures appear in a natural fashion. It is pointed out that the results of this calculation can be considered the solution to the problem of linear counting of coherent particles. In this case the least count is one and the signal-to-noise ratio (for constant photon flux) increases as the reciprocal of the band width. The limiting temperature sensitivity of properly designed quantum-mechanical amplifiers is given as $\frac{h\ensuremath{\nu}}{k}$ degrees because of the drastic difference between negative and positive temperatures.
Fluctuations in the amplification and absorption of waves by quantum processes are considered. Assuming for each quantum the probability (per unit time) a of producing another quantum, probability b of being absorbed, and assuming a probability c that a new quantum is introduced, a set of differential equations is obtained. By solving these equations, a complete expression for the probability of distribution of quanta is obtained, as well as expressions for the average values and fractional fluctuation. The expressions developed are applied in particular to maser-type amplifiers, and certain fluctuations in the amplification of electromagnetic waves are pointed out which are important when their quantum character becomes significant. This condition can occur in maser-type amplifiers, where thermal and extraneous noises may be very small. For such an amplifier, a is proportional to the number of excited molecules, whereas b consists of a term proportional to the number of molecules in the ground state plus terms due to certain other losses. The noise temperature of a maser-type traveling-wave amplifier is the "effective temperature" a ( a - b ) -1 h ν/ k . In superregenerative and regenerative amplifiers using resonant cavities, the noise temperature is rather similar, if losses through the input coupling hole are excluded from b . In any case, the limiting noise for an ideal amplifier corresponds to a classical noise temperature of h ν/ k .