The laser-power-output modulation, obtained by reflection of the laser beam back into the resonator by means of an external moving mirror (EMM), is analyzed in terms of resonator Q modulation. The variation of the amplitude of the output-power modulation as a function of the distance EMM laser is characteristic for the number of excited axial modes. Experiments were performed with various commercially available He-Ne lasers, showing clearly one, two, three, and more modes. A comparison is made with similar experiments which may be made in a Michelson moving-mirror interferometer. An additional feature of EMM modulation is that the saturation of the laser transition in a single-mode laser can easily be demonstrated. The experimental procedure and arrangement are simple, and it is believed that the work presented may have value for demonstration and education.

The predicted central tuning dip in the modulated power output of gas lasers was observed by applying resonator Q modulation. The modulation was obtained by means of an external moving mirror. The signal shapes observed are explained for the quasistatic case.Saturation and gain of single-mode gas lasers can be studied by analysis of the modulated power output [1][2][3]. For instance, we predicted in the a.c. power output a central tuning dip which reveals the saturation more clearly than the well-known Lamb-dip. The dip we observed previously by applying excitation density modulation [1]. Here we report our observation of the modulation dip in case of resonator Q modulation obtained by reflecting the laser beam back into the resonator by means of an external moving mirror [4].If, for simplicity, we consider transmission losses only, the resonator quality Qo of a twomirror laser isHere L is the distance between the laser mirrors M 1 and M2, andR 1 and R 2 are their intensity reflectivities. The external mirror M 3 (reflectivity R3) and the nearest laser mirror M2 form a Fabry-Perot interferometer with length I. Its intensity reflectivity R can easily be derived [5][6][7]. To find the resonator quality Q with M 3 present we merely replace R 2 by R in eq.(1). The steady-state laser intensity in singlemode operation is [8]where el ---ol' -~/Q is the unsaturated net gain and fl is the saturation parameter. Eq. (2) holds for low excitation level only. We find the change in laser intensity due to the presence of M 3 in the 128 quasistatic casewhere 5 = 41rlu/c is the external phase difference. When the external moving mirror has constant velocity v along the beam direction, eq. (3) indicates that E2 is modulated at the Doppler frequency WD = 4~vv/c and that, in general, the shape of the modulation is non-sinusoidal. Sinusoidal modulation is obtained if 2(R2R3)½ << 1 +R 2R3 . The time-dependent part of EZcan then be writtenThe resonator quality can then be put into the form Q ~ Q + AQcOswDt, with (AQ/~) << 1 and U~ slightly abobe Qo" These conditions were needed in ref.3 in the general case of resonator Q modulation.We made experiments with a single-mode 1.15 tt He-Ne laser provided with plane internal mirrors [9] and with a hemispherical multimode 0.6328~t He-Ne laser (OIP type 160-G). The experimental arrangement was as described in ref. 10; R 3 was varied from 0.01 up to 0.75 by using beam splitters in the external interferometer. The output was detected through mirror M 1.At low modulation level we observed a dip in the a.c. power output, which is shown for the

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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