Effect of axial modes on Doppler experiments with gas lasers

Abstract

Power output modulation was obtained by using a moving mirror reflecting one beam back into the laser interferometer.The strong dependence of modulation amplitude on the distance between moving mirror and laser is related to the number, n , of excited axial modes for n > 1.With gas lasers Doppler experiments with moving mirrors are easily performed in two ways. In one type (A) of experiment [l] a Michelson interferometer is used. The fringe shift obtained can be described as due to beats between two coherent waves with a frequency difference equal to the Doppler shift. Another type (B) of experiment [2] is based on the interference effect observed by King and Steward [3], that occurs when the laser radiation is reflected back into the laser interferometer by means of a single external mirror. It this mirror moves continuously along the beam direction, the laser output, observed at the other end, is modulated at the Doppler frequency. A change in external optical path length equal to one wavelength results in one cycle of laser output modulation. Similar feed-back effects are commonly used in plasma diagnostics [4].A great advantage of Doppler experiments of type B is the very easy optical adjustment. Here we show that in performing Doppler experiments with a gas laser the multimode character of the laser radiation should be taken into account. Actually, information on the number of axial modes present may be gained from the simply measured dependence of the modulation amplitude on the path-length covered by the moving mirror.Starting from well-known expressions for the intensity in the interference pattern in the general case of two-beam interference [5] one may derive for the variable component in the laser output power (disregarding non-linear effects and omitting a non-interesting constant factor) I = ) C(Z) ( cos 2k,Z ,where k, is the wave number of the atomic transition, Z is the varying distance between external mirror and laser end face, and 88 C(Z) = 2sj(x) cos (2x1) dx .(2) In eq. (2) the integration is taken over the total spectral profile of the laser radiation determined by the distribution function j(x) [xz k -ko] which was assumed to be symmetrical in deriving eq. (1). When the external mirror moves with constant velocity parallel to the beam direction eq. (1) yields for the a. c. component in the laser outputwhere IQ is the Doppler frequency. Eqs. (2) and (3) show that the amplitude of I is a (slowly-varying) function of I, which depends on the spectral composition of the laser light i. e. the number of modes and their relative intensities. We note that

Resonator Q modulation of gas lasers with an external moving mirror

“…We note that the non-sinusoidal shape of the modulation is due to the non-sinusoidal modulation of Q rather than to the non-* Another feature of external moving mirror modulation is that the number of axial modes can, in principle, be determined from the amplitude of the a.c. power output as a function of l [10,11 e.f. also 12]. We note that sinusoidal laser output modulation may also be treated as a case of two-beam interference, as shown in [10]. The relative contribution of each mode to the total modulation amplitude should be taken proportional to A(E 2) rather than to E 2 (see [li D.…”