Second Harmonic Generation (SHG) is a fundamental nonlinear optical process where two photons at frequency ω combine to produce one photon at frequency 2ω. The efficiency of this process depends critically on the choice of nonlinear crystal, phase-matching conditions, and crystal dimensions.
Common Nonlinear Crystals
| Crystal | Transparency | d_eff (pm/V) | Best For |
|---|---|---|---|
| BBO | 190–3500 nm | 2.0 | UV generation, broadband SHG |
| LBO | 160–2600 nm | 0.85 | High-power SHG, NCPM |
| KTP | 350–4500 nm | 3.2 | CW and quasi-CW SHG |
| KDP/DKDP | 200–1600 nm | 0.44 | Large aperture, high energy |
Phase Matching
Efficient SHG requires the fundamental and harmonic waves to maintain a fixed phase relationship throughout the crystal. The two main approaches are:
- Critical Phase Matching (CPM): Achieved by angle-tuning the crystal. Offers broadband operation but introduces spatial walk-off.
- Non-Critical Phase Matching (NCPM): Temperature-tuned. No walk-off, ideal for high-power applications, but limited to specific wavelength ranges.
Crystal Thickness Selection
There is a fundamental trade-off between conversion efficiency and acceptance bandwidth. Thicker crystals offer higher efficiency but narrower spectral acceptance, making them unsuitable for ultrashort pulses. Use the BBO thickness calculator to find the optimal crystal length for your pulse parameters.
Walk-off Compensation
In Type I BBO, the extraordinary wave walks off from the ordinary wave at approximately 55 mrad at 800 nm. For beam diameters below 100 μm, this limits the useful crystal length. Consider using two thin crystals in a walk-off compensating arrangement.
Practical Tips
- Always verify the damage threshold of your crystal at the operating fluence
- Use AR-coated crystals to minimize reflection losses
- Mount crystals with proper thermal contact for temperature stability
- Measure output power to verify phase-matching angle optimization
For a complete phase-matching calculation including walk-off and efficiency estimates, use our online SHG calculators linked in the sidebar.