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Physical Review A

Effect of detuning on a single-mode modulated laser

Binoy Krishna Goswami, Dhruba J. Biswas

Published Jul 1, 1987• 28 citations
Publisher

Abstract

We have compared the impact of loss, pump, and frequency modulations on a single-mode homogeneously broadened laser under varying detunings and modulation frequencies. In the case of loss and gain modulations the impact on intensity shows a minimal behavior at the line center for gain values more than twice the lasing threshold. The system relaxation time with respect to any transient perturbation depends on the magnitude of detuning and is minimal at the line center. In the case of frequency modulation, the impact on intensity vanishes at the line center irrespective of the gain values. These results are based on linear analysis.

DOI
10.1103/physreva.36.975

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Physical Review A•Dec 1, 1982•51 citations
We have compared the impact of loss, pump, and frequency modulations on a single-mode homogeneously broadened laser under varying detunings and modulation frequencies. In the case of loss and gain modulations the impact on intensity shows a minimal behavior at the line center for gain values more than twice the lasing threshold. The system relaxation time with respect to any transient perturbation depends on the magnitude of detuning and is minimal at the line center. In the case of frequency modulation, the impact on intensity vanishes at the line center irrespective of the gain values. These results are based on linear analysis.
We show that the dip in the intensity line shape of a single-mode laser can appear at definite experimental conditions in cases both of nonhomogeneously broadened line as well as homogeneously broadened line of the atomic transition. In both cases the dip is explained by the nonlinear character of the phenomenon. The saturation of the population difference of the involved atomic energy levels has its maximum in the vicinity of the line center. Therefore the saturation of the amplification is at maximum near the atomic line center, and, as a consequence, the lasing power is reduced.
Homogeneously broadened lasers are considered as intrinsically single mode monostable devices [1] where intensity and frequency are defined by the cavity mode that lies nearest to the center of the atomic line. Here we show theoretically and experimentally that this heuristic picture falls when the interaction between different cavity modes becomes relevant. In fact, for sufficiently high detuning between cavity and atomic resonance frequencies (δAC), self pulsing of the laser arise from the simultaneous operation in two modes (phase instability) even if it is operating near threshold (C ⪯ 1) and in the so-called good cavity limit (k ≪ γ⊥, γ‖). Using parameter values which are typical of many solid state and molecular gas lasers (γ‖, k ≪ γ⊥), the theory predicts a bistable behavior in both the output intensity and frequency, as δAC is varied (Fig. 1). These theoretical results have been confirmed by experiments carried out on a CO2 laser where the distance between modes was controlled by changing the losses inside the cavity and the detuning δAC was varied by a fine tuning of the distance between mirrors. The output intensity versus δAC is shown in Fig. 2 for two different values of losses and gas pressure. Direct comparison between Fig. 2b) and Fig. 1 shows a good qualitative agreement. Measurements of the transients during the jump of Fig.2b) confirmed the mode-mode competition interpretation.
An exact analysis has been carried out for general analytical expressions for the second threshold of a single-mode homogeneously broadened laser and for the initial pulsation frequency at the second threshold, for arbitary physical values of the relaxation rates, and at an arbitrary detuning between the cavity frequency and the atomic resonance frequency. These expressions also give correspondingly exact forms for asymptotic cases that have been previously studied with some approximations. Earlier approximate results are partly confirmed and partly improved by these more general expressions. The physical status of various expressions and approximations is reconsidered and specified more clearly, including an analysis of what reasonably can be attained in lasers or masers. A general analytical proof is given of the fact that, for a larger detuning of the laser cavity from resonance, a higher value of the laser excitation is required to destabilize the steady-state solution (the second threshold). We also present results for the minimum value of the second threshold at fixed detuning as a function of the other parameters of the system and for the dependence of the ratio of the second threshold to the first threshold as a function of detuning. Minima of the second threshold and of the threshold ratio occur only if the population relaxation rate is equal to zero. The minima of the threshold ratio are shown to be bounded from above as well as from below (as functions of the relaxation rates, so long as the second threshold exists). The upper bound on the minima ratio is equal to 17. The variation of the second threshold in the semi-infinite parameter space of the decay rates is shown at various detunings in plots with a finite domain by normalizing the material relaxation rates to the cavity decay rate.
Self-pulsing of a single-mode laser has been studied with the use of the inhomogeneously broadened 3.51-\ensuremath{\mu}m transition in xenon. Time-averaged intensity power spectra, average power output, and real-time observations of intensity fluctuations have been recorded for various detunings of the Fabry-Perot cavity. Two forms of self-pulsing have been observed, both of which can be explained in terms of the phase locking of several frequencies which simultaneously exist in the same spatial mode, made possible by the rapid variations of the index of refraction in the high-gain medium. One form of such mode splitting occurs in the wings of the atomic response due to the variations in the inhomogeneously broadened anomalous dispersion. The second form can occur anywhere in the tuning range of the laser as it is caused by distortions induced in the dispersion by the hole-burning effects of the oscillating mode. The pulsation frequency of this induced mode splitting varies with cavity tuning, shows a dip at the atomic line center, and may be absent for detuning of one or two homogeneous linewidths away from center. The instabilities have shown subharmonic bifurcations of the pulsation frequencies. Both high-QQQ pulsation frequencies and broad bands of frequencies in the power spectra have been observed for various operating conditions.