Nonlinear Crystal Comparison
Second-harmonic generation of 1064 nm in BBO, LBO, KTP, BiBO, bulk MgO:LiNbO₃ and PPLN: d_eff of each phase-matched cut, and the focused-beam (Boyd–Kleinman) SH power and efficiency for a crystal length, pump power and waist.
type I (ooe), θ = 22.9°, 1064 → 532 nm: d_eff = 2.058 pm/V, n_ω = 1.6551, n_2ω = 1.6551; EKSMA BBO sheet (d₂₂, d₃₁, indices); θ from the indices.
Second-harmonic power
1.511 mW
P_2ω = K P_ω², 1064 → 532 nm
Conversion efficiency
0.03021 %
η = K P_ω (undepleted pump)
Normalized efficiency K
0.006043 %/W
ξ = 1.14, B = 8.72, h = 0.0792
Best focus at Δk = 0
0.006119 %/W
w₀ = 26.6 µm (ξ = 1.45, h = 0.0802)
Boyd–Kleinman optimum
0.006135 %/W
w₀ = 26.5 µm (ξ = 1.45) with Δk tuned to σ = 0.752, h = 0.0804
Walk-off B = 8.72: the SH beam leaves the fundamental within the crystal, so h falls from 0.646 to 0.0802; a shorter crystal or a noncritical/QPM cut converts more per W².
Normalized efficiency over crystal length
A fixed waist gives K ∝ L² while L stays below the confocal parameter, then ∝ L⁰; refocusing for each length keeps K ∝ L.
Crystals for 1064 → 532 nm
| Crystal | Cut | d_eff (pm/V) | n_ω / n_2ω | d²/(n_ω²n_2ω) (pm²/V²) | ρ (mrad) | K, best focus | Transparency (nm) | Source |
|---|---|---|---|---|---|---|---|---|
| β-BBO | type I (ooe), θ = 22.9° | 2.06 | 1.655 / 1.655 | 0.934 | 55.8 | 0.00612 %/W | 189–3500 | EKSMA BBO sheet (d₂₂, d₃₁, indices); θ from the indices |
| LBO | type I (ooe), XY plane, φ = 11.6° | 0.96 | 1.605 / 1.605 | 0.223 | 7.04 | 0.00823 %/W | 155–3200 | EKSMA LBO sheet |
| KTP | type II, XY plane, φ = 23.5° | 3.59 | 1.788 / 1.788 | 2.25 | 3.15 | 0.118 %/W | 350–4400 | EKSMA KTP sheet |
| BiBO | type I (ee → o), YZ plane, θ = 168.8° | 3 | 1.789 / 1.789 | 1.57 | 25.7 | 0.0226 %/W | 286–2500 | CASTECH BiBO sheet (d_eff); n and θ from Umemura et al. 2007 |
| MgO:LiNbO₃ (bulk) | type I (ooe), θ = 90°, temperature-tuned | 4.4 | 2.232 / 2.232 | 1.74 | 0 | 0.124 %/W | 420–5200 | d₃₁ Shoji et al. 1997; n_o Zelmon et al. 1997 |
| MgO:PPLN (QPM) | first-order QPM, eee | 15.9 | 2.156 / 2.234 | 24.4 | 0 | 1.68 %/W | 420–5200 | d₃₃ Shoji et al. 1997, d_eff = 2d₃₃/π; n_e Zelmon et al. 1997 |
Click a row to select the crystal. K is for the length above at the best phase-matched focus.
Model
P_2ω = K P_ω², K = 16π² d_eff² L h(σ, B, ξ) / (ε₀ c n_ω n_2ω λ³), ξ = L/b, b = 2πn_ω w₀²/λ, B = ρ√(L k_ω)/2
Boyd–Kleinman focused Gaussian beam with the focus at the crystal centre, no absorption and an undepleted pump. Without walk-off and at Δk = 0, h = arctan²ξ/ξ peaks at 0.646 for ξ = 1.39; tuning Δk slightly raises the optimum to h = 1.068 at ξ = 2.84. With walk-off, the best focus is looser and h smaller.
Walk-off is included through Boyd–Kleinman's h(σ, B, ξ), B = ρ√(L k_ω)/2. BBO (56 mrad) and BiBO (26 mrad) at 10 mm have B ≈ 8.7 and 4.2; LBO (7 mrad, B ≈ 1.1) and KTP (3 mrad) are still angle-critical cuts with smaller walk-off; only the 90° MgO:LiNbO₃ cut and PPLN have none. For type II KTP the one-walking-wave form is approximate. d_eff belongs to one cut at 1064 nm and changes with wavelength and angle, and published values differ by tens of per cent between sources. For pulses, use the peak power and keep the pulse longer than the group-velocity walk-off over L.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Boyd–Kleinman focused Gaussian beam with walk-off, h(σ, B, ξ) with B = ρ√(Lk_ω)/2, focus at the crystal centre, undepleted pump, no absorption; for type II the one-walking-wave form is approximate. d_eff comes from each source's d_ij and cut at 1064 nm (BBO's and BiBO's angles from their indices); published values differ by tens of per cent between sources. Mid-IR crystals (AgGaS₂, ZGP, GaSe, OP-GaAs) and acceptance and damage data are not included until sourced.
- Boyd G. D., Kleinman D. A. (1968). Parametric Interaction of Focused Gaussian Light Beams. J. Appl. Phys. 39, 3597–3639. Focusing function h(σ, ξ). doi:10.1063/1.1656831
- Shoji I. et al. (1997). Absolute scale of second-order nonlinear-optical coefficients. J. Opt. Soc. Am. B 14, 2268. Table 10: 5 % MgO:LiNbO₃ d₃₃ = 25.0, d₃₁ = 4.4 pm/V at 1064 nm. doi:10.1364/JOSAB.14.002268
- EKSMA Optics data sheets for BBO, LBO and KTP crystals: d_ij, indices at 1064 and 532 nm, cut angles, walk-off, transparency. eksmaoptics.com
- CASTECH. BiB₃O₆ (BiBO) properties: d_eff 3.0 pm/V and θ = 168.9° for SHG of 1064 nm. castech-us.com
- Umemura N., Miyata K., Kato K. (2007). New data on the optical properties of BiB₃O₆. Opt. Mater. 30, 532–534. Sellmeier equations (via the refractiveindex.info database): BiBO n_x(532 nm) and the type I cut computed from them (168.8°). doi:10.1016/j.optmat.2006.12.014
- Zelmon D. E., Small D. L., Jundt D. (1997). Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol.% magnesium oxide–doped lithium niobate. J. Opt. Soc. Am. B 14, 3319. doi:10.1364/JOSAB.14.003319