- Solution to the 'Green Problem' Demonstrated
Intracavity frequency-doubled solid-state lasers are one of the photonics industry's all-time best sellers because they provide an efficient, compact and rugged source of coherent visible light for applications from surgery to spectroscopy to green laser pointers. But their success comes despite the inherent "green problem" that sometimes produces a deleterious fluctuation in the output power. Now researchers at Universität Hamburg in Germany have conceived and demonstrated a way to avoid the green problem by judicious placement of the gain medium and nonlinear crystal within the laser resonator.
Because the efficiency of frequency doubling is proportional to the fundamental power, most low-power frequency-doubled lasers are configured with the nonlinear crystal inside the resonator, where the fundamental power -- and, hence, the doubling efficiency -- is at least an order of magnitude greater than in the external beam. The green problem arises because the intracavity nonlinear crystal generates not only second-harmonic light, but also light at the sum frequencies of the laser's different longitudinal modes. This sum-frequency generation couples the competing longitudinal modes and gives rise to chaotic behavior as the modes gain and lose oscillating strength, producing an undesirable fluctuation in output power.
One straightforward solution to the green problem is to force the laser to oscillate in a single longitudinal mode. Unfortunately, single-longitudinal-mode lasers are very sensitive to mechanical and temperature perturbations, and they produce output powers lower than that of multimode lasers. Another solution is to allow a great many longitudinal modes to oscillate so that the fluctuations are averaged over many modes. But the only way to do this is to pull the mirrors far apart (the frequency spacing between adjacent modes is inversely proportional to resonator length), which can result in long, awkward resonators that may be unsuitable for practical applications.
The Hamburg researchers' solution is to place both the nonlinear crystal and the gain medium as close as possible to the center of the resonator. By placing the gain medium in the middle of the resonator, they ensure that only two adjacent longitudinal modes oscillate. Each mode burns holes in the population inversion at the maxima of its standing wave, but at the center of the resonator, the holes burned by adjacent modes have minimal overlap (Figure 1). Thus, the two adjacent modes uniformly saturate the gain, and there is no residual gain to support additional modes.
Figure 1. The spatial intensities of the standing waves of two adjacent longitudinal modes in a resonator whose length is 10λ indicate that if the gain medium is placed in the center of the resonator, these two standing waves will completely saturate the gain, leaving no spatial "hot spots" to support other modes. If the gain medium is placed near one of the mirrors, however, many modes can oscillate before the gain becomes saturated.
By placing the nonlinear crystal in the middle of the resonator, the researchers minimize the efficiency of sum-frequency generation between the two modes that are oscillating. For efficient sum-frequency generation at a given location, there must be energy at both modes. In the middle of the resonator, there is minimal overlap between the two modes and, hence, minimal sum-frequency efficiency (Figure 2). Because the sum-frequency generation is minimized, coupling between the longitudinal modes also is minimized, and the green problem disappears.
Figure 2. The efficiency of the second-harmonic generation (solid line) and of the sum-frequency generation between the two modes shown in Figure 1 (dotted line) indicate that sum-frequency generation is minimized at the center of the resonator because there is minimal spatial overlap between the two modes.
To demonstrate the effectiveness of the concept, the researchers constructed an Nd:YAG laser with an intracavity LiB3O5 doubling crystal. (The laser operated on the quasi-three-level, 946-nm transition, so in this case, the "green problem" was blue.) They mounted the nonlinear crystal on a translation stage so that it could be moved from its initial position in the middle of the resonator. When the crystal was in the middle of the resonator, the scientists observed very stable output, with residual fluctuation of less than 3 percent at the relaxation-oscillation frequency of approximately 107 kHz. But when they cranked it 4 mm farther away from the center of the resonator -- into a zone where there was more overlapping power at the two modes -- they observed fluctuations as great as 50 percent. When they moved the crystal another 6 mm from the center of the resonator, they encountered chaotic instabilities typical of the green problem.
The group also noted that the green problem could be eliminated if the gain medium and nonlinear crystal were placed at symmetrical locations away from the center of the resonator. For example, if both were placed a quarter cavity-length from respective mirrors, only two longitudinal modes oscillated, but they were next-to-adjacent modes rather than adjacent ones. As before, the efficiency of sum-frequency generation between the two modes was minimized by the location of the nonlinear crystal.
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