This chapter has outlined the theory required to model the performance of cw-pumped OPOs. It has focused on two main aspects: pum p power thresholds and tuning characteristics. Both of these depend critically on the num ber of resonant fields within the OPO cavity, and the subsequent constraints placed on the cavity mirrors of the resonator.
Since the nature of these studies is three-wave mixing, then up to three fields can be brought to resonance within the OPO cavity. Their first effect is on the pum p power threshold. As expected, increasing the num ber of resonant fields within the OPO results in lower pump power thresholds. Predictably, full benefit is achieved only when all the resonant fields satisfy simultaneously exact cavity resonances.
The detuning of resonant fields also plays an important role in the tuning characteristics of cw OPOs. To obtain smooth frequency tuning from cw OPOs, the fields that are subject to resonance conditions must be tuned together so that the energy conservation relation is always satisfied. There are several different methods for continuously tuning cw OPOs. The first consideration is whether or not the pum p can be considered as a tuning parameter. This depends ultimately on the desired application. In any application that requires precisely determined, absolute frequencies, it is highly unlikely that the pump frequency can be considered to be tunable. For less demanding applications (e.g. spectroscopy), a tunable pump source may be tolerated.
j
î When the pum p frequency is tunable, then single-cavity, singly-
resonant and doubly-resonant OPOs allow for multiple parameter tuning. For the singly-resonant device, the resonant OPO field can remain fixed or be scanned with the pum p frequency. Either way, both sum and difference frequency selection arises. In the doubly-resonant OPO, tuning the pum p frequency must be matched by both the signal and idler resonance conditions. The addition of pump resonance effects to lower the pump power thresholds can only be decoupled from the tuning characteristics by resonating the pump field in a separately formed build-up cavity that does not affect directly the signal and/or idler resonance conditions.
When using a fixed pump frequency, only truly singly-resonant OPOs allow for difference frequency control in a simplified, free-running manner. If doubly-resonant OPOs are to match this performance, they must be formed with independent cavity length control via dual-cavity resonators. Dual cavity, doubly-resonant OPOs allow for pump power thresholds at the mW- level, smooth frequency tuning from either a fixed frequency pump source or a tunable pum p source, and a convenient m ethod of controlling independently the finesses and free spectral ranges of the signal and idler fields. The dual-cavity, doubly-resonant OPO can be regarded as the ideal OPO configuration for high precision frequency applications. Only when other applications are targeted in which the specifications are considerably relaxed (or w hen m ulti-watt, kHz, single-frequency lasers are available at any frequency from the ultra-violet to the mid-infra-red spectral regions) can other types of cw OPOs be considered.
This chapter also discussed conversion efficiencies in cw OPOs, mode- matching, and coherence properties of cw OPOs.
The internal conversion efficiencies of OPOs, irrespective of the fields resonated, are considerable. This is because, once above threshold, additional pum p power is diverted directly to signal and idler photons. The main differences arise in the external conversion efficiencies, dictated by the resonance conditions of the OPOs. When the signal or idler fields are constrained to high finesse cavities, then, as expected, the ratio of useful to parasitic losses governs the external conversion efficiency. The most practical method of providing high external conversion efficiencies is to eliminate the resonance condition for either the signal or idler field, as in a singly-resonant oscillator. However, as with any optical resonator, high external conversion
efficiencies can always be obtained by operating well above threshold, and adjusting the output coupling such that this value is significantly above the other (parasitic) cavity losses. In general, the extreme dependence of the pump power threshold on cavity finesses does not allow for such flexibility in experimental designs.
The mode-matching of the three fields over the length of the gain medium can be achieved by setting the cavity mirror spacings/curvatures to fix the resonant transverse beam dimensions, and focusing the pump field to optimize the three wave interaction. The degree of overlap between the three fields is optimized when all the fields are approximately collimated (low diffraction effects) in the focal zone of the gaussian beam profile. Perhaps the most im portant case to consider is when the input pum p field is itself resonant in the OPO cavity. In this case, the pum p enhancement factor depends upon the precise spatial mode overlap between the intra- and extra cavity pump fields.
While, in most cases, the stability of the OPO outputs is dictated by the pum p frequency stability, the limit to the signal and idler frequency is determined by phase-diffusion effects. Whereas the sum of the signal and idler phases remains fixed, the phase-difference diffuses randomly, similar to the effects of spontaneous emission on the coherence of a laser oscillator.
References.
1. See the following review papers: R. L. Byer,
in "Treatise in Quantum Electronics," (H. Rabin & C. L. Tang, Eds.), Academic Press, New York (1973).
R. G. Smith,
"Optical parametric oscillators,"
in "Lasers: a series of advances," vol. 4, (A. K. Levine & A. J. DeMaria Eds.) Marcel Dekker, New York, 189 (1976).
A. Yariv,
"Theory of the optical parametric oscillator," IEEE J. Quant. Electron. QE-2,418 (1966). V. W. Brunner, H. Paul, & A. Bandilla,
"The optical parametric oscillator. 1," Annalen der Physik. 7, 69 (1971).
2. J. A. Armstrong, N. Bloembergen, J. Ducuing, & P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127,1918 (1962).
3. G. D. Boyd & D. A. Kleinman,
"Parametric interaction of focused Gaussian light beams," J. Appl. Phys. 39, 3597 (1968).
4. J. F. Nye,
"Physical properties of crystals," Oxford University Press (1976). 5. F. Zernike & J. E. Midwinter,
"Applied nonlinear optics," Wiley Series in Pure & Applied Optics (S. S. Ballard Ed.) John Wiley, New York (1973).
6. A. Yariv,
"Quantum electronics," 3rd Edn., John Wiley, Singapore (1989). 7. M. Zahler & Y. Ben-Aryeh,
"Loss effects in classical non-degenerate parametric amplifier," Opt. Comm. 79,361 (1990).
8. G. D. Boyd & A. Ashkin,
"Theory of parametric oscillator threshold with single-mode optical masers and observation of amplification in LiNbOg,"
Phys. Rev. 146, 187 (1966). 9. W. Brunner & H. Paul,
in "Progress in Optics," (E. Wolf, Ed.), North-Holland, Amsterdam, pl5 (1977). 10. S. T. Yang, R. C. Eckardt, &c R. L. Byer,
"Continuous-wave singly resonant optical parametric oscillator pumped by a single frequency resonantly doubled NdtYAG laser,"
Opt. Lett. 18, 971 (1993).
"1.9-W cw ring-cavity KTP singly resonant optical parametric oscillator," Opt. Lett. 19, 475 (1994).
11. S. T. Yang, R. C. Eckardt, & R. L. Byer,
"Power and spectral characteristics of continuous wave parametric oscillators: the doubly to singly resonant transition,"