What is Second Harmonic Generation?
Second harmonic generation (SHG) is a nonlinear optical process where two photons at frequency ω combine in a nonlinear crystal to produce one photon at frequency 2ω (half the wavelength). It is the most widely used frequency conversion technique in laser science — converting 1064 nm Nd:YAG to 532 nm green, or 800 nm Ti:Sapphire to 400 nm UV.
Efficient SHG requires phase matching: the fundamental and second harmonic waves must maintain a fixed phase relationship throughout the crystal. Without phase matching, the generated SH signal destructively interferes with itself after a distance called the coherence length (~10 μm in most crystals).
Phase Matching Types
Type I Phase Matching
Both fundamental photons have the same polarization (ordinary or extraordinary), and the SH photon has the orthogonal polarization:
o + o → e or e + e → o
Advantages: Higher effective nonlinear coefficient, wider acceptance bandwidth. Best for CW and low-energy pulsed lasers.
Type II Phase Matching
The two fundamental photons have orthogonal polarizations:
o + e → e or o + e → o
Advantages: Naturally produces orthogonally polarized beams (useful for entangled photon sources). Narrower acceptance bandwidth can serve as a spectral filter.
Crystal Comparison: BBO vs LBO vs KTP
| Parameter | BBO (β-BaB₂O₄) | LBO (LiB₃O₅) | KTP (KTiOPO₄) |
|---|---|---|---|
| Transparency Range | 190–3500 nm | 160–2600 nm | 350–4500 nm |
| Effective deff | ~2.0 pm/V | ~0.85 pm/V | ~3.2 pm/V |
| Damage Threshold | ~5 GW/cm² (ns) | ~25 GW/cm² (ns) | ~0.5 GW/cm² (ns) |
| Walk-off Angle | 2.7° (at 800 nm) | <0.5° (NCPM) | 0.3° (at 1064 nm) |
| Acceptance BW | Moderate | Wide (NCPM) | Narrow |
| Hygroscopic | Yes (slight) | No | No |
| Best For | Ti:Sapphire SHG, UV generation, ultrafast pulses | High-power SHG, wide bandwidth, Nd:YAG | CW and low-rep-rate SHG of 1064 nm |
When to Use Each Crystal
Choose BBO when:
- You need UV generation (down to ~190 nm via SHG/THG/FHG)
- Working with ultrashort pulses (<100 fs) — high deff compensates for short crystal length
- Ti:Sapphire SHG (800 → 400 nm)
- Wide tunability is needed (OPO/OPA pump)
Choose LBO when:
- High average power is involved (>10 W) — highest damage threshold
- Non-critical phase matching (NCPM) is desirable — zero walk-off, circular beam
- Nd:YAG 1064 nm → 532 nm at high power
- Industrial applications requiring long crystal lifetime
Choose KTP when:
- CW or quasi-CW SHG of 1064 nm — highest deff
- Intracavity SHG in green laser pointers and DPSS lasers
- Moderate power levels (<1 W average)
- Type II phase matching for entangled photon pair generation (SPDC)
Calculating Phase Matching Angles
The phase matching angle depends on the crystal's Sellmeier equations and the fundamental wavelength. Use our SHG Phase Matching Calculator to instantly find:
- Phase matching angle (θ) for any wavelength
- Acceptance bandwidth and angular tolerance
- Walk-off angle and effective nonlinear coefficient
- Crystal length recommendation for your pulse parameters
Shop Nonlinear Crystals
Browse our nonlinear crystals collection for BBO, LBO, KTP, and other frequency conversion crystals. All crystals include damage threshold specifications and AR coating options.
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