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Applied Optics

Dependence of laser intensity on cavity losses for a detuned, single-mode laser

S. C. Mehendale

Published Dec 20, 1994• 1 citation
Publisher

Abstract

It is shown that for a detuned, single-mode, homogeneously broadened laser, semiclassical laser theory predicts a transition from a nonlasing state to a lasing state when cavity losses are increased for a range of cavity detunings when dispersion is large. A physical explanation for this behavior is presented in which the influence of dispersion on the cavity resonance frequencies is considered.

DOI
10.1364/ao.33.008330

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It is shown that for a detuned, single-mode, homogeneously broadened laser, semiclassical laser theory predicts a transition from a nonlasing state to a lasing state when cavity losses are increased for a range of cavity detunings when dispersion is large. A physical explanation for this behavior is presented in which the influence of dispersion on the cavity resonance frequencies is considered.
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 study the five semiclassical laser equations in the mean-field limit for the simple model of two-level atoms with homogeneous broadening in a single-mode unidirectional ring cavity, taking into account detuning between atomic and cavity frequencies. Our analysis concentrates on the properties of the laser at and beyond the second thresh-old in the bad-cavity case. We first show that the position of the second threshold depends on the excitation mechanism: When the pump parameter is increased either adiabatically or abruptly, two different thresholds occur. The sequence of periodic and chaotic solutions beyond the second threshold is then discussed as a function of the detuning and the pump parameter.
This paper presents new results for the steady states of a detuned ring laser with a saturable absorber. We employ a semiclassical model which assumes homogeneously broadened two-level atoms. We proceed by solving the Maxwell-Bloch equations for the longitudinal dependence of the steady states of this system, and then simplify our solution by use of the uniform-field approximation. We present uniform-field results for squared electric field versus operating frequency, and for each of these versus cavity tuning and laser excitation. Various cavity linewidths and both resonant and nonresonant amplifier and absorber line-center frequencies are considered. The most notable finding is that cavity detuning breaks the degeneracies found in the steady-state solutions of the fully tuned case. This leads to the prediction that an actual system will bifurcate from the zero-intensity solution to a steady-state solution as laser excitation increases from zero, rather than to the small-amplitude pulsations found for the model with exactly resonant tuning of the cavity and the media line centers. Other phenomena suggested by the steady-state results include tuning-dependent hysteresis and bistability, and instability in both intensity and frequency due to the appearance of one or more new steady-state solutions as tuning is varied. These effects of detuning are being tested by a linearized stability analysis whose results will be reported separately.
We use the semiclassical strong-signal theory of the laser to predict and explain the onset of side-mode buildup in lasers with one oscillating mode. Two general categories are considered: one for which the side modes and the oscillating mode all have the same wavelength and the other for which they have different wavelengths. The treatments include an arbitrary amount of inhomogeneous broadening. Our approach unifies the treatments of the side-mode instabilities presented earlier and extends them to handle standing waves in addition to the previously treated running waves. We write the field and the population matrix elements as Fourier series in the adjacent-mode beat frequency. This approach has been used extensively in both multimode laser theory and saturation spectroscopy. This technique coincides with linear stability analyses used by others, provided that our beat frequency includes a contribution that is proportional to the complex side-mode gain. We give a solution that allows for detuned operation along with its simpler, centrally tuned special case. The connection with saturation spectroscopy clearly reveals that the side-mode instabilities require side-mode gain. For the single-wavelength case, nonlinear anomalous dispersion is also required. The side-mode gain and dispersion result from both inhomogeneous broadening and population pulsations. The lowest instability thresholds occur when both of these mechanisms play a role. The approach can also be used to treat instabilities in optical bistability by substituting the appropriate equation of state for the strong-mode intensity and by changing the sign of the absorption coefficient. In homogeneously broadened, standing-wave lasers, we show that multiwavelength instabilities depend strongly on the position of the medium in the cavity. We illustrate the theory by giving numerical results for the output pulsation frequency and for the instability threshold by using parameters that are appropriate for the He–Xe laser. These results correlate well with experimental observations.
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.