Discharge modulation noise in HeNe laser radiation

Abstract

Discharge modulation noise in He-Ne laser radiation is considered theoretically, including explicitly the laser oscillator properties. Experiments reported previously by us and other authors are in agreement with our analysis.The radiation of d.c. excited He-Ne lasers may show a large amount of low-frequency noise [1] which is due to modulation of the internal laser field by discharge current fluctuations [2][3][4][5][6][7]. Here we give an analysis of this modulation noise which includes explicitly the laser oscillator properties as derived by Lamb [8], in contrast to the analysis given by other authors [5,7].As a result of discharge current fluctuations the number of excited metastable He atoms and Ne atoms in the upper laser level fluctuate. This fluctuation in the driving force of the laser oscillation may be described by including a stochastic, slowly varying term AN(t) in N, which is defined by Lamb [8] as the excitation density in absence of optical oscillations. Thus we write N = N + +AN(t), with AN(t) << N. Using Lamb's differential equation for the amplitude E(t) of the electric field in the laser interferometer dE~dr = ~E -~E 3, and its steady-state solution, Eo2 = a/~, we find for the fluctuating part AE(t) in E [cf. 9,10] dAE/dt + 2otAE = (½v/Q) (Eo/N)AN(t),( 1) where we assumed AE(t) << E o. The quantities and ~ respresent the unsaturated net gain and the saturation, respectively, as defined by Lamb [8].Eq. (1) is a typical Langevin equation wellknown in noise analysis. The relation between the spectral noise intensities SAN(f) and SAE (f) can easily be found by making a Fourier analysis of eq. (1). The spectral noise intensity of the laser power output ccE2 follows from SA(E2 ) (f~ = = 4Eo2SAE (f). We have(2) where ¢o = 21rf. We assumed implicitly that f is much smaller than the decay rates of the laser levels (f << 10 Mc/s in case of He-Ne lasers). It is seen from eq. (2) that for a given SAN(f)the intensity fluctuations decrease with increasing average excitation density N and saturation B, as may be expected. The saturation of a gas laser transition is known to become stronger near atomic line center [8]. It follows then from eq. (2) that for w << 2a the noise intensity of a singlemode gas laser versus interferometer detuning should show a dipnear line center, which we observed indeed [4]*. In ref. 4 also reported the noise intensity near threshold detuning varied proportionally to the square of the d. c. laser output with varying interferometer detuning. Close to threshold we have w >> 2~ [cf. 10], so that according to eq. (2) SA(E 2) (f) cc (~/~)2 = Eo4 ' indeed.In discussing the noise spectrum of the laser radiation we have also to consider the noise spectrum SAN(f) , being determined by relaxation effects in the discharge. Let us discuss briefly some factors which affect the noise spectrum. In case of He-Ne lasers the slowest decay rate in the (de-)excitation processes involved is the inverse lifetime T of the metastable He atoms (23S or 21S) which at low electron densities describes t...