Crystal length
Each crystal has an associated pump acceptance bandwidth which is inversely dependent on length, so crystal length is an important factor when choosing a crystal. This acceptance bandwidth is due to the group velocity mismatch between the interacting waves.
For narrowband CW sources our longer crystal lengths, at 20 to 40mm, should give best efficiency. However, for pulsed sources, a long crystal can have a negative effect if the pump bandwidth is much broader than the crystal acceptance bandwidth. For nanosecond pulses, we typically recommend 10mm lengths and our shortest lengths at 0.5 to 1mm are ideal for femtosecond pulse systems.
For SHG of femtosecond pulses, if the pump bandwidth is significantly wider than the acceptance bandwidth, it is still possible to achieve high conversion efficiency. The pump frequencies outside of the acceptance bandwidth can still contribute to the conversion efficiency via sum frequency generation, essentially squeezing the broadband pump into a relatively narrower-band SHG pulse [1].
Polarization
In order to access the highest nonlinear coefficient of lithium niobate, the input light must e-polarized, i.e. the polarization must be aligned with the dipole moment of the crystal. This is accomplished by aligning the polarization axis of the light parallel to the thickness of the crystal. This applies to all nonlinear interactions.
This configuration is known as Type-0 phase matching (ee-e), as all the interacting beams have the same polarization.
Type I phase matching (oo-e) and type II phase matching (eo-e) schemes are also possible in PPLN, for example for the generation of heralded single photons. Please contact Covesion to discuss your requirements.
Focusing and the Optical Arrangement
Typically, Covesion crystals consist of several grating periods each with a 0.5×0.5mm2, or 1.0×1.0mm2 aperture and with a length of up to 40mm long. To achieve high conversion efficiency in PPLN, the pump beam should be focussed into a grating with the focus centred on the crystal length.
For SHG with CW lasers, a theoretical result from Boyd and Kleinmann shows that optimum efficiency can be achieved when the ratio of the crystal length to the confocal parameter is 2.84 [2]. (The confocal parameter is twice the Rayleigh range). This is also true for SFG interactions where the two pump beams should also have the same Rayleigh range.
For DFG and OPOs, optimum efficiency requires a confocal focussing condition i.e. the Rayleigh range is half the length of the crystal.
These focussing conditions apply to pulsed lasers too, but due to the high peak powers, the spot size requirements are less sensitive. (Be aware of the crystal damage threshold so as not to focus too tightly.)
In general, a good rule of thumb is that the spot size should be chosen such that the Rayleigh range is half the length of the crystal. The spot size can then be reduced in small increments until the maximum efficiency is obtained.
Temperature and Period
The poling period of a PPLN crystal is determined by the wavelengths of light being used. The quasi-phase-matched wavelength can be tuned slightly by varying the temperature of the crystal.
Covesion’s range of off-the-shelf PPLN crystals each include multiple different poling periods, which allow different wavelengths to be used at a given crystal temperature. Our calculated tuning curves give a good indication of the required temperature for phase-matching. The temperature dependence of conversion efficiency follows a sinc 2 function, describing a crystal temperature acceptance bandwidth. The longer the crystal, the narrower and more sensitive the acceptance bandwidth.
In many cases the efficiency of the nonlinear interaction is very sensitive to <1°C. For example, for SHG with a 1064nm pump in a 20mm long crystal, the temperature acceptance bandwidth is ~1°C. So if the temperature is 0.5°C off from the optimum phase matching temperature, then the SHG power is 50% lower than the optimum. If the crystal temperature can be maintained at the optimum phase matching temperature to within +/-0.1°C, then the SHG power is stable to within 2-3%.
The optimum temperature can be determined by heating the crystal to 20°C higher than the calculated temperature and then allowing the crystal to cool whilst monitoring the output power at the generated wavelength.
The Covesion PPLN oven is easy to incorporate into an optical setup. It can be paired with Covesion’s OC1 temperature controller to maintain the crystal temperature to within ±0.01°C, providing highly stable output power.
References
1. K. Moutzouris et al., Optics letters, vol. 31, no. 8, pp. 1148–50, (2006)
2. G. Boyd and D. Kleinman, Journal of Applied Physics, vol. 39, no. 8, p. 3597, (1968)