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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Higher order effect of regular pumping in lasers and masers

Shi-Yao Zhu, Marlan O. Scully, Chang Su

Published Sep 1, 1991• 0 citations
Publisher

Abstract

The higher-order terms in the expansion of ln(1 + pu) with respect to the pumping regularity p are considered. The effects of higher-order terms, due to regular pumping, on the photon statistics are found to be significant in maser cases, and can be neglected in laser cases. The right order approximation must be used to ensure correct results.

DOI
10.1117/12.46781

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The higher-order terms in the expansion of ln(1 + pu) with respect to the pumping regularity p are considered. The effects of higher-order terms, due to regular pumping, on the photon statistics are found to be significant in maser cases, and can be neglected in laser cases. The right order approximation must be used to ensure correct results.
In laser systems, regular pumping always reduces the photon noise. In micromaser systems, however, regular pumping may lead to photon noise reduction as well as photon noise increase depending on the operation conditions. The effect of higher-order terms in the expansion of ln(1+pu) with respect to the pumping regularity parameter p is discussed. These terms have a significant effect on the photon statistics in micromaser systems. Their effect in laser systems is quite small compared with the second order and can be neglected.
We show that regularization of pumping leads to large photon-number noise reduction in one- and two-photon micromasers, and is much more important than in macroscopic lasers and masers. Our calculations are based on a step-by-step microscopic approach and are compared to results obtained from a pumping-statistics-dependent master equation, which is shown not to be entirely reliable in the micromaser case. Although noise reduction and the discrepancies betwen the two approaches are more important for monokinetic beams, they are still relevant when a 10% velocity dispersion is allowed.
We present a theory of the micromaser including the effect of the arrival-time statistics of the active atoms in the theoretical treatments. Our starting point is an approach that explicitly incorporates the effect of pump statistics into the dynamical description of lasers and masers. We show that the application of standard laser theory to the micromaser is tantamount to the tacit assumption of Poissonian arrival-time statistics. Hence standard laser theory and the theory of the micromaser are, in general, not equivalent, but the latter contains the former, as a limiting case, for completely random arrival times. We show, as an application, that the steady-state value of the average photon number (first moment) is essentially unaffected by the pump statistics since it depends only on the flux of active atoms (average number of atoms entering the cavity per unit time) provided the flux is constant. The intensity fluctuations (second moment), however, exhibit a stronger dependence on the pump statistics. In particular, for sub-Poissonian pump statistics the sub-Poissonian character of the field is enhanced.
A higher order calculation of the theory of an optical maser is carried out for the purpose of obtaining more accurate theoretical expressions of the Lamb dip. The amplitude of maser oscillation is calculated in the approximations up to the fifth order and the calculated power vs. frequency characteristics by the third and the fifth order approximations are compared. The Lamb dip becomes considerably shallower if the fifth order term is included. The fifth order calculation should therefore be employed for a more accurate determination of the linewidth parameters of the active atoms from observed shapes of the Lamb dip. It is shown, however, that the correction due to the fifth order calculation is small when the relative excitation is very close to the threshold. The fifth order calculation in the case when the “Doppler limit” does not apply is also discussed as well as in the case of the “Doppler limit”.