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Lasers & Sources
Probing solid-state laser characteristics through polarization behavior
Abruptly changing pump-beam polarization provides an effective probe of the physical mechanisms controlling solid-state laser polarization transition, and can help estimate some key laser properties.
13 July 2006, SPIE Newsroom. DOI: 10.1117/2.1200606.0278
It is difficult to accurately describe the polarization state of light emitted by lasers.1 Generally, laser polarization behavior is often probed by changing a single parameter, such as pump current, to see what happens. This kind of experiment can be used to formulate and validate theoretical models of the phenomenon. Detailed studies have found that many physical mechanisms contribute to the complex polarization behavior of semiconductor lasers.2,3 However, similar studies have yet to be performed on optically-pumped solid-state lasers. Here, we describe our efforts to remedy this situation.
Under some conditions, the polarization of solid-state lasers is known to depend on the pump-beam polarization and the stress-induced birefringence that determines the laser cavity polarization. While models have been developed that accurately describe the steady-state behavior, the dynamic evolution predicted by these models had not been compared to experiments.
We have been found that abruptly changing the pump beam polarization switches the laser's polarization state. However, contrary to the behavior seen in semiconductor lasers, the switching occurs after a significant delay. Further investigation has allowed us to accurately model the delay as due to three physical parameters.
In our experiments, an electro-optic modulator adjusted the polarization of the pump beam, which was applied to a Nd:YAG laser. The laser's polarization response to abruptly changing the pump beam's polarization by 90°, but keeping its power constant, appeared after a delay of several tens of microseconds (see Figure 1). The delay strongly increased as the pump amplitude approached the threshold pump strength. During this turn-on period, the output polarization angle was unchanged, although the intensity showed relaxation oscillations. After the delay, the angle evolved to its new steady-state value on a time scale much smaller than the relaxation period, followed by large fluctuations in the total intensity similar to those during turn-on.
Figure 1. The response of a Nd:YAG laser's linear polarization modes (black and blue lines) to a 90° change in pump polarization (vertical dashed line) is delayed. The pump strength is 116mW, or a factor of 1.26 higher than the threshold pump strength.
The experimental results are well represented with the rate-equation model proposed by Bouwmans et al.,4 which indicates that the slow recovery of the laser population inversion causes the delay. When the pump polarization changes, the existing laser steady-state condition does not immediately lose its stability because the population reservoirs relax toward their new steady-state values on a microsecond time-scale.5
However, this model does not clearly identify the key laser parameters that Influence the delay. We deduced these with an asymptotic analysis of the laser equations, taking advantage of the different time scales available on our system. The result was an expression for the delay6 that depends only on the medium decay rate γ, the gain anisotropy βL and the pump absorption anisotropy βP:
is proportional to the intensity of the polarization mode that is lasing before the switch. changes linearly with the pump strength, and depends on the parameters βL
. The delay calculated with Equation (1) is in excellent agreement with the measured delay (seeFigure 2
). We can therefore use equation (1) to estimate the gain and absorption anisotropy, quantities that are difficult to measure.
Figure 2. The polarization response delay calculated from Equation (1) (black line) compares very well with the measured delay (black circles) as a function of pump strength above threshold J (the ratio of pump strength to threshold pump strength). Parameter values used for the calculated delay: γ = 3.3 × 10-5, βL= 0.62, βP = 0.75.
We have shown that polarization can be a useful probe of solid-state laser properties. The dynamic-switching experiments, combined with an analysis of the laser rate equations, provided valuable insight on the physical mechanisms that control the polarization switching transition. Solid state lasers are Class B lasers characterized by the slow recovery of the population inversion, so our results are relevant to all Class B lasers exhibiting polarization dynamics.
This work was supported by the Belgian Inter-university Attraction Pole program. Jan Danckaert, Guy Van der Sande, and Guy Verschaffelt acknowledge the Fund for Scientific Research-Flanders for their fellowships and for project support. Thomas Erneux acknowledges the support of the Fonds National de la Recherche Scientifique.
Guy Verschaffelt, Guy Van der Sande, and Jan Danckaert
Dept. Applied Physics and Photonics (IR-TONA), Vrije Universiteit Brussel
Optique Nonlinéaire Théorique, Université Libre de Bruxelles
Bernard Ségard and Pierre Glorieux
Laboratoire de Physique des Lasers, Atomes et Molécules, Université des Sciences et Technologies de Lille
1. W. van Haeringen, Polarization properties of a single-mode operating gas laser in a small axial magnetic field,
Vol: 158, pp. 256-272, 1967.
2. M. San Miguel,
Polarization Properties of Vertical Cavity Surface Emitting Lasers,
pp. 339-366, 1999.
3. G. Verschaffelt, J. Albert, B. Nagler, M. Peeters, J. Danckaert, S. Barbay, G. Giacomelli, F. Marin, Frequency response of polarization switching in vertical-cavity surface-emitting lasers,
IEEE Journal of Quantum Electronics,
Vol: 39, no. 10, pp. 1177-1186, 2003.