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Journal of Applied Physics

Effect of a Small Stokes Shift on the Operation of Three-Level Masers

Peter J. Warter

Published Oct 1, 1963• 2 citations

Abstract

Small differences between the emission and absorption spectra of three-level maser centers can have a pronounced effect on maser operation. This paper considers the effects of a Stokes shift, the simplest and most probable difference. If there is a Stokes shift which is large compared to the linewidth, the operation of the maser will be essentially four level. If there is a small Stokes shift (some fraction of the linewidth) the operation will still be three level, but the Stokes shift will significantly affect the operation of the maser. The principal effects will be a shift of the maser line from the peak in the fluorescent emission line (away from the absorption peak) and a reduction in the upper level population required to reach the threshold of oscillation. The evidence is not conclusive as to whether there is a Stokes shift in the ruby R1 line, but if there is a shift it is at most a small fraction of the fluorescent linewidth at room temperature. Shifts of the ruby maser line to the red have been observed by D'Haenens and Asawa and have been attributed to large temperature changes. It is likely that the temperature shift, while important, will not explain the shift which has been observed. Gires and Mayer have found the lower state population of an operating ruby maser to be approximately 75% of the unexcited population rather than approximately 50% and have suggested a Stokes shift as a possible cause of the reduction in the upper state population at threshold. This paper considers the effect of such a small Stokes shift on the operation of an otherwise ideal three-level maser.

DOI: 10.1063/1.1729103

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Fujio Saito

Pulsed oscillation of a three-level ruby maser of which pumping microwave was modulated by pulse was investigated. The time lag t d of the oscillation pulse behind the pumping pulse was determined experimentally as a function of the peak level P of the pumping power, and the period T and the width τ of the pumping pulse. A semi-empirical formula t d =t 0(\frac{P_{c}}{P}) k exp [b(\frac{T}{\tau})1-δ\frac{P_{c}}{P}] was obtained. The minimum pulse width τ m required for the oscillation to occur was determined as a function of P and T, which was approximately expressed by τ m =c\frac{T^{m}}{P^{n}}. The above results were qualitatively interpreted in terms of excess population Δ n,

Japanese Journal of Applied Physics•Aug 1, 1962•1 citation

Small differences between the emission and absorption spectra of three-level maser centers can have a pronounced effect on maser operation. This paper considers the effects of a Stokes shift, the simplest and most probable difference. If there is a Stokes shift which is large compared to the linewidth, the operation of the maser will be essentially four level. If there is a small Stokes shift (some fraction of the linewidth) the operation will still be three level, but the Stokes shift will significantly affect the operation of the maser. The principal effects will be a shift of the maser line from the peak in the fluorescent emission line (away from the absorption peak) and a reduction in the upper level population required to reach the threshold of oscillation. The evidence is not conclusive as to whether there is a Stokes shift in the ruby R1 line, but if there is a shift it is at most a small fraction of the fluorescent linewidth at room temperature. Shifts of the ruby maser line to the red have been observed by D'Haenens and Asawa and have been attributed to large temperature changes. It is likely that the temperature shift, while important, will not explain the shift which has been observed. Gires and Mayer have found the lower state population of an operating ruby maser to be approximately 75% of the unexcited population rather than approximately 50% and have suggested a Stokes shift as a possible cause of the reduction in the upper state population at threshold. This paper considers the effect of such a small Stokes shift on the operation of an otherwise ideal three-level maser.

Virtually simultaneous measurements of the emission and absorption profiles of the ruby R1 line show that no significant Stokes' shift is present. Observations were made on rubies of 0.0055% and 0.0186% Cr by weight with both crystallographic orientations and both polarizations in the temperature range from 77° to 153°K. The position of the peaks in the absorption line matched those of the emission line to within 0.002 cm−1. Shifts of this size or smaller cause no significant change in the operating characteristics of a laser.

Optical maser action at the R2 line in ruby has been observed. Because of a fast thermal relaxation between the two 2E levels, it is not usually possible to satisfy the maser conditions at the R2 line when stimulated emission is occurring at the R1 line. However, if maser action can be suppressed at the R1 line, even at high inversion, it can be made to occur at the R2 line by the appropriate selection of operating conditions. This has been accomplished by using, for end reflectors, multilayer dielectric interference filters which have high transmission at the R1 line and low transmission at the R2 line. The selection of the operating conditions requires a correction of the absorption coefficients for the R1 and R2 lines based on the Boltzmann distribution between the two excited states. When the Boltzmann correction is made, the calculations show reasonable requirements on pumping threshold and reflectivities.

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

{T}_{1}={T}_{2}

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

{T}_{1}={T}_{2}

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.

In the case when the pumping transition in a three-level system of a molecule does not exactly coincide with the output frequency of a maser oscillator, four different types of operation at off-resonance of the three-level maser detector are discussed. At first the use of pressure broadening is considered; secondly a method which observes the double-quantum transition and thirdly the other method which measures a change in population caused by the double-quantum pumping are considered, and finally the level shift due to the far-infrared input is considered. It is found that the third method of double-quantum pumping in which three waves are involved is the most sensitive. The minimum detectable power of order 10-6W/cm2 with the resolving time of about 10-6s is expected in detecting the maser output at the far-infrared which differs from the resonant frequency of the detector by as large as 10 GHz.

Pulsed oscillation of a three-level ruby maser of which pumping microwave was modulated by pulse was investigated. The time lag t d of the oscillation pulse behind the pumping pulse was determined experimentally as a function of the peak level P of the pumping power, and the period T and the width τ of the pumping pulse. A semi-empirical formula t d =t 0(\frac{P_{c}}{P}) k exp [b(\frac{T}{\tau})1-δ\frac{P_{c}}{P}] was obtained. The minimum pulse width τ m required for the oscillation to occur was determined as a function of P and T, which was approximately expressed by τ m =c\frac{T^{m}}{P^{n}}. The above results were qualitatively interpreted in terms of excess population Δ n,