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Definition: the phenomenon that an input laser beam generates a beam with three times the optical frequency
German: Frequenzverdreifachung
Frequency tripling is a process of nonlinear frequency conversion where the resulting optical frequency is three times that of the input laser beam. In principle, this can be achieved with a χ(3) nonlinearity for direct third-harmonic generation [12–14], but this is difficult due to the small χ(3) nonlinearity of optical media and phase-matching constraints (except for tripling in gases). Therefore, frequency tripling is usually realized as a cascaded process, beginning with frequency doubling of the input beam and subsequent sum frequency generation of both waves, with both processes being based on nonlinear crystal materials with a χ(2) nonlinearity.
Figure 1: A typical configuration for frequency tripling: an infrared input beam at 1064 nm generates a green 532-nm wave, and these two mix in a second crystal to obtain 355-nm light.
The main application of frequency tripling is the generation of ultraviolet light. Most common is the generation of 355-nm light by frequency tripling of a laser beam with 1064 nm, as obtained from a Nd:YAG or Nd:YVO4 laser. A common approach is to use two LBO crystals, the first being phase-matched for second-harmonic generation and the second for sum frequency generation. It is easy to make this process efficient when using pulses from a Q-switched or mode-locked laser, but also possible in continuous-wave operation e.g. with intracavity frequency doubling and resonant sum frequency generation.
It is also possible to generate blue light by frequency tripling the output of a 1.3-μm neodymium laser.
Power Conversion Efficiency
Theoretically, the total power conversion efficiency of the frequency tripling process could be close to 100 %. For that, the frequency doubler should have a conversion efficiency of 2/3, so that the second-harmonic wave has twice the power of the remaining fundamental wave, and both have equal photon numbers. In practice, the efficiency of the frequency doubler is normally somewhat lower (often around 40 to 50 %), and in particular the sum frequency mixer is far from 100 % efficient. The latter problem can result from many effects, such as too low optical intensities, design limitations enforced by optical damage, effects of spatial walk-off, mismatch of pulse duration and/or temporal walk-off, etc. Tentatively, the conversion works best for high peak powers in not too short pulses, and when the beam quality is high and the optical bandwidth not too high.
With numerical modeling, the whole frequency tripling process can be simulated with fairly high accuracy and reliability of the results.
Bibliography
| [1] | G. H. C. New and J. F. Ward, “Optical third-harmonic generation in gases”, Phys. Rev. Lett. 19 (10), 556 (1967) |
| [2] | W. Seka et al., “Demonstration of high efficiency third harmonic conversion of high power Nd:glass laser radiation”, Opt. Commun. 34, 469 (1980) |
| [3] | R. Craxton, “High efficiency frequency tripling schemes for high-power Nd:glass lasers”, IEEE J. Quantum Electron. 17 (9), 1771 (1981) |
| [4] | G. Manneberg, “Phase-matched frequency tripling and phase conjugation in isotropic materials”, J. Opt. Soc. Am. B 4 (11), 1790 (1987) |
| [5] | A. Lago et al., “Coherent 70.9-nm radiation generated in neon by frequency tripling the fifth harmonic of a Nd:YAG laser”, Opt. Lett. 13 (3), 221 (1988) |
| [6] | R. Friedberg et al., “Optimizing third harmonic generation in gases”, J. Phys. B: At. Mol. Opt. Phys. 24, 2883 (1991) |
| [7] | R. Wu, “High-efficiency and compact blue source: intracavity frequency tripling by using LBO and BBO without the influence of birefringence”, Appl. Opt. 32 (6), 971 (1993) |
| [8] | L. Goldberg et al., “Tunable UV generation at 286 nm by frequency tripling of a high-power mode-locked semiconductor laser”, Opt. Lett. 20 (15), 1640 (1995) |
| [9] | D. Eimerl et al., “Multicrystal designs for efficient third-harmonic generation”, Opt. Lett. 22 (16), 1208 (1997) |
| [10] | J. Squier et al., “Third harmonic generation microscopy”, Opt. Express 3 (9), 315 (1998) |
| [11] | Z. Sun et al., “Generation of 4.3-W coherent blue light by frequency-tripling of a side-pumped Nd:YAG laser in LBO crystals”, Opt. Express 12 (26), 6428 (2004) |
| [12] | F. Gravier and B. Boulanger, “Cubic parametric frequency generation in rutile single crystal”, Opt. Express 14 (24), 11715 (2006) |
| [13] | K. Miyata et al., “Phase-matched pure χ(3) third-harmonic generation in noncentrosymmetric BiB3O6”, Opt. Lett. 34 (4), 500 (2009) |
| [14] | K. Miyata et al., “High-efficiency single-crystal third-harmonic generation in BiB3O6”, Opt. Lett. 36 (18), 3627 (2011) |
See also: frequency doubling, frequency quadrupling, nonlinear frequency conversion, nonlinear crystal materials, ultraviolet light, ultraviolet lasers
