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European Microwave Conference (EuMC)

Pump Noise Coupling in Parametric Amplifiers

Marcella E. Dean, John L. Clarke

Published Oct 1, 1974• 0 citations
Publisher

Abstract

A simple theory for predicting the effects of pump noise on the performance of parametric amplifiers has been developed and verified. It is shown that AM noise on the pump injects both FM and AM noise on the signal magnified by approximately the amplifier gain. It is also shown that FM noise on the pump can yield both FM and AM noise on the amplified signal : in this case the coupling coefficient for simple amplifiers is shown to be a function of the idler bandwidth. Analytic expressions for the maximum coupling factors are quoted for the case of a simple amplifier. Experiments on two different amplifiers are described which both support the theoretical predictions.

DOI
10.1109/euma.1974.332068

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A simple theory for predicting the effects of pump noise on the performance of parametric amplifiers has been developed and verified. It is shown that AM noise on the pump injects both FM and AM noise on the signal magnified by approximately the amplifier gain. It is also shown that FM noise on the pump can yield both FM and AM noise on the amplified signal : in this case the coupling coefficient for simple amplifiers is shown to be a function of the idler bandwidth. Analytic expressions for the maximum coupling factors are quoted for the case of a simple amplifier. Experiments on two different amplifiers are described which both support the theoretical predictions.
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In a parametric amplifier (PA) driven by two pump waves the signal sideband is coupled to three idler sidebands, all of which are frequency-converted (FC) images of the signal, and two of which are phaseconjugated (PC) images of the signal. If such a device is to be useful, the signal must be amplified, and the PC and FC idlers must be produced, with minimal noise. In this paper the quantum noise properties of two-sideband (TS) parametric devices are reviewed and the properties of many-sideband devices are determined. These results are applied to the study of two-pump PAs, which are based on the aforementioned four-sideband (FS) interaction. As a general guideline, the more sidebands that interact, the higher are the noise levels. However, if the pump frequencies are tuned to maximize the frequency bandwidth of the FS interaction, the signal and idler noise-figures are only slightly higher than the noise figures associated with the limiting TS interactions.
The parametric amplifier is usually studied under the assumption that the pump mode is in a large-amplitude coherent state. We consider what happens when this is no longer the case. We first derive some exact relations between the number fluctuations of the pump and signal, the pump and the idler, and also the signal and the idler. It is then determined how much phase noise can be tolerated in the initial pump state if two-mode squeezing is to be produced in the signal-idler field. The relation between the rotational symmetry in phase space of the initial pump state and that of the signal-idler subsystem is determined. We find that the sum phase distribution of the signal and idler has twice the rotational symmetry as that of the initial pump state. Finally, we generalize the parametric approximation to treat pump states which are not coherent states. We examine the effect of a phase-squeezed pump state and find that the pump squeezing can actually decrease the two-mode squeezing of the signal-idler field while enhancing a form of higher-order squeezing, sum squeezing, for these fields.
We describe a novel noise mechanism which should effect all externally pumped parametric amplifiers. The theory is developed specifically for the four-wave Josephson paramp. We predict a noise temperature rising in direct proportion to the amplifier gain; this prediction agrees perfectly with all previously published data for both the three- and four- wave Josephson amplifiers. An explicit expression for the noise temperature of the four-wave device is derived and compared to previous experiments.
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We derive the fundamental noise properties of a parametric amplifier (paramp) which is driven by a monochromatic pump but which has many lossy signal and idler modes. We use a quantum-mechanical approach similar to that employed by Louisell and co-workers in their treatment of paramps and lasers with lossless modes. Our results are not directly deducible from the lossless mode analysis, but they do give the same limiting noise temperature as that analysis. This minimum noise temperature is the same as that of an ideal laser. In fact, we find that one can always design a laser whose field correlation functions would be the same as those of any given paramp. Many results for laser noise in various configurations can be carried over directly and applied to parametric amplifiers by using correspondence substitutions which we set down. For example, in analogy to Pound's description of the maser (in terms of a Nyquist theorem extended to negative temperatures), the calculation of paramp noise is found to be equivalent to applying Nyquist's theorem to both the active and passive elements in the (classically computed) equivalent circuit of a signal mode of interest. From this one obtains the spectra of effective noise generators which, when amplified in the circuit, duplicate the "quantum" as well as thermal noise that is present in the output. The Nyquist theorem is extended to apply to each active element by simply taking the element temperatures to be minus the real temperature of the corresponding idler mode (whose parametric coupling into the signal circuit gives rise to that element) multiplied by the ratio of the pump minus the idler to the idler frequencies.