Resonator Q modulation of gas lasers with an external moving mirror

Abstract

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

Nonstationary Casimir Effect and Analytical Solutions for Quantum Fields in Cavities with Moving Boundaries

“…The explicit form of "two-dimensional" coefficients g kj is more complicated than a simple formula (19). However, these coefficients remain antisymmetrical: g kj = −g jk , due to the normalization of functions ψ k , {L} 0 dr ψ m ψ n = δ mn , and due to zero boundary conditions at x = L. (Moreover, they do not depend on the cavity dimensions.)…”

“…For u = 0 (the left wall at rest) the equations like (18)- (19) were derived in [174,177]. If the wall comes back to its initial position L 0 after some interval of time T , then the right-hand side of equation (18) disappears, so at t > T one can write…”

“…The detailed paper by Baranov and Shirokov [17] can be considered, in a sense, as a concluding study of the one-dimensional problem with a uniformly moving boundary (although many publications on this subject continued to appear up to last years). The experiments on laser cavities with uniformly moving mirrors were described, e.g., in [18][19][20][21][22]. In these experiments, the constant velocity of the mirror varied from 7 cm/s [18] to 400 m/s [22].…”