As one of the most important nonlinear optical crystals, beta-barium borate (β-BaB2O4，β-BBO) combines many outstanding features such as its high nonlinear optical coefficients, low group-velocity dispersion, broad transparency range (189–3500 nm) and high damage threshold. This unique combination ensures β-BBO crystal a promising candidate for a wide range of nonlinear optical applications such as frequency converters and optical parametric oscillators. In the realm of quantum optics, β-BBO crystal can be used to generate entangled photon pairs and ten-photon entanglement.
BBO is a negative uniaxial crystal, which provides phase matching for various second-order interactions almost over its entire transparency range (from 185 nm to 3.3 µm, as deduced from the transmittance measurements using crystal samples of several mm thickness), making it a widely used crystal for nonlinear frequency conversion in the ultraviolet, visible and near-infrared. In that regard, BBO is the most important nonlinear crystal for near infrared optical parametric chirped pulse amplifiers, which currently deliver few optical cycle pulses with high average and ultrahigh peak powers.
Physical and Chemical Properties
| Property | Value |
| Chemical formula | BaB2O4 |
| Crystal structure | trigonal, 3m |
| Lattice Parameter | a=b=12.532Å,c=12.717Å, Z=6 |
| Mass density | 3.85 g/cm3 |
| Moh hardness | 4 |
| Melting point | About 1095°C |
| Thermal conductivity | 1.2 W/m/K (⊥c); 1.6 W/m/K (//c) |
| Thermal expansion coefficient | α,4×10-6/K; c,36×10-6/K |
| Birefringence | negative uniaxial |
| Property | Value |
| Transparency Range | 189 – 3500 nm |
| Absorption Coefficient | α<0.1%/cm @1064nm |
| RefractiveIndices | |
at 1.0642 μm at 0.5321 μm at 0.2660 μm | ne = 1.5425, no = 1.6551 ne = 1.5555, no = 1.6749 ne = 1.6146, no = 1.7571 |
| Sellmeier Equations(λ in μm) | no2(λ) = 2.7359+0.01878/(λ2-0.01822)-0.01354λ2 ne2(λ) = 2.3753+0.01224/(λ2-0.01667)-0.01516λ2 |
| Property | Value |
| SHG Phase Matchable Range | 409.6 ∼ 3500nm (Type I); 525 ∼ 3500nm (TypeII) |
| NLO coefficients | d11= 5.8 x d36(KDP); d31 = 0.05 x d11; d22< 0.05 x d11 |
| deff(I)=d31sinθ+ (d11cos3φ – d22sin3φ)cosθ | |
| deff(II)=(d11sin3φ+ d22cos3θ)cos2θ | |
| Therm-Optic Coefficients | dno/dT = – 9.3 x 10-6/◦C |
| dne/dT = -16.6 x 10-6/◦C | |
| Electro-Optic Coefficients | g11= 2.7 pm/V, g22, g31< 0.1 g11 |
| Half-Wave Voltage | 48 KV (at 1064 nm) |
| Damage Threshold | |
| at 1.064 μm | 5 GW/cm2 (10 ns); 10 GW/cm2 (1.3 ns) |
| at 0.532 μm | 1 GW/cm2 (10 ns); 7 GW/cm2 (250 ps) |
| λ[µm] | α [cm-1] | Note |
| 0.1934 | 1.39 | T =295K |
| 0.29 | T =91K | |
| 0.213 | <0.21 | best crystals |
| 0.264 | 0.04±0.01 | ||c |
| 0.06±0.003 | ⊥c, o-wave | |
| 0.10±0.003 | ⊥c, e-wave | |
| 0.2661 | <0.17 | best crystals |
| 0.04–0.15 | ||
| 0.5321 | 0.01 | |
| <0.01 | ||
| 1 | 0.001–0.002 | |
| 1.0642 | <0.001 | |
| 2.09 | 0.0085 | e-wave |
| 0.07 | o-wave | |
| 2.55 | 0.5 |
Two-photon Absorption Coefficient
| λ[µm] | τp [ns] | β×1011[cm/W] | Note |
| 0.211 | 0.0009 | 243±85 | θ =30◦, φ =0◦ |
| 0.264 | 0.0008 | 93±33 | θ =30◦, φ =0◦ |
| 0.00022 | 68±6 | ||c | |
| 66±7 | ⊥c, o-wave | ||
| 47±5 | ⊥c, e-wave | ||
| 0.0002 | 61 | θ =48° | |
| 0.2661 | 0.015 | 90±10 | ||c |
| 0.3547 | 0.017 | 1.0±0.2 | ||c |
Experimental Values of Refractive Indices
| λ[µm] | no | ne |
| 0.40466 | 1.69267 | 1.56796 |
| 0.43583 | 1.68679 | 1.56376 |
| 0.46782 | 1.68198 | 1.56024 |
| 0.47999 | 1.68044 | 1.55914 |
| 0.50858 | 1.67722 | 1.55691 |
| 0.54607 | 1.67376 | 1.55465 |
| 0.57907 | 1.67131 | 1.55298 |
| 0.58930 | 1.67049 | 1.55247 |
| 0.64385 | 1.66736 | 1.55012 |
| 0.81890 | 1.66066 | 1.54589 |
| 0.85212 | 1.65969 | 1.54542 |
| 0.89435 | 1.65862 | 1.54469 |
| 1.01400 | 1.65608 | 1.54333 |
| λ[µm] | γ×1015[cm2/W] | Note |
| 0.2661 | 0.025±0.008 | ||c |
| 0.3547 | 0.36±0.08 | ||c |
| 0.5321 | 0.55±0.10 | ||c |
| 0.78 | 0.40±0.05 | [100] direction |
| 0.32±0.05 | [010] direction | |
| 0.85 | 0.37 ±0.06 | θ =29.2˚, φ =0◦ |
| 1.0642 | 0.29 ±0.05 | ||c |
Experimental Values of Phase-matching Angle (T =293K)
| Interacting wavelengths[μm] | θexp [deg] |
SHG, o+o ⇒ e | |
| 0.4096⇒0.2048 | 90 |
| 0.41⇒0.20 | 90 |
| 0.41152⇒0.20576 | 82.8 |
| 0.41546⇒0.20773 | 79.2 |
| 0.418⇒0.209 | 77.3 |
| 0.429⇒0.2145 | 71 |
| 0.4765⇒0.23825 | 57 |
| 0.488⇒0.244 | 54.5 |
| 0.4965⇒0.24825 | 52.5 |
| 0.5106⇒0.2553 | 50/50.6 |
| 0.5145⇒0.25725 | 49.5 |
| 0.5321⇒0.26605 | 47.3/47.5/47.6/48 |
| 0.589⇒0.2945 | 41.5 |
| 0.604⇒0.302 | 40 |
| 0.6156⇒0.3078 | 39 |
| 0.616⇒0.308 | 38 |
| 0.70946⇒0.35473 | 32.9/33/33.1/33.3/33.7 |
| 0.78⇒0.39 | 31/30 |
| 0.8⇒0.4 | 26.5 |
| 0.946⇒0.473 | 24.9 |
| 1.0642⇒0.5321 | 22.7/22.8 |
SFG, o+o ⇒ e | |
| 0.73865+0.25725⇒0.1908 | 81.7 |
| 0.72747+0.26325⇒0.1933 | 76 |
| 0.5922+0.2961⇒0.1974 | 88 |
| 0.5964+0.2982⇒0.1988 | 82.5 |
| 0.5991+0.29955⇒0.1997 | 80 |
| 0.60465+0.30233⇒0.20155 | 76.2 |
| 0.5321+0.32561⇒0.202 | 83.9 |
| 0.6099+0.30495⇒0.2033 | 73.5 |
| 0.5321+0.34691⇒0.21 | 71.9 |
| 0.7736+0.25787⇒0.1934 | 70.7 |
| 0.5321+0.35473⇒0.21284 | 70 |
| 0.51567+0.38675⇒0.221 | 64.7 |
| 0.804+0.268⇒0.201 | 64 |
| 0.75+0.375⇒0.25 | 61.7 |
| 1.0642+0.26605⇒0.21284 | 51.1 |
| 0.78+0.373⇒0.2523 | 47.4 |
| 1.0642+0.298⇒0.23281 | 46.1 |
| 0.5782+0.5106⇒0.27115 | 46 |
| 0.59099+0.5321⇒0.28 | 44.7 |
| 0.78+0.43⇒0.2772 | 43.4 |
| 1.0642+0.35473⇒0.26605 | 40.2 |
| 1.0641+0.53205⇒0.3547 | 31.3 |
| 1.0642+0.5321⇒0.35473 | 31.1/31.3/31.4 |
| 2.68823+0.5712⇒0.4711 | 21.8 |
| 1.41831+1.0642⇒0.608 | 21 |
SHG, e+o ⇒ e | |
| 0.5321⇒0.26605 | 81 |
| 0.70946⇒0.35473 | 48/48.1 |
| 1.0642⇒0.5321 | 31.6/32.4/32.7/32.9 |
SFG, e+o ⇒ e | |
| 1.0642+0.35473⇒0.26605 | 46.6 |
| 1.0642+0.5321⇒0.35473 | 38.4/38.5 |
SFG, o+e ⇒ e | |
| 1.0642+0.5321⇒0.35473 | 59.8 |
Experimental Values of Internal Angular, Temperature, and Spectral Bandwidths at T =293K
| Interacting wavelengths[μm] | θpm [deg] | Δθint [deg] | ΔT [℃] | Δν[cm-1] |
| SHG, o+o ⇒ e | ||||
| 1.0642⇒0.5321 | 22.8 | 0.021 | 37 | 9.7 |
| 22.7 | 0.03 | 51 | ||
| 0.5321⇒0.26605 | 47.3 | 0.01 | 4 | |
| 0.53⇒0.265 | 47.6(298K) | 0.006 | ||
| SFG, o+o ⇒ e | ||||
| 1.0641+0.53205⇒0.3547 | 31.3 | 0.011 | ||
| 1.0642+0.5321⇒0.35473 | 31.1 | 0.015 | 16 | |
| 2.44702+0.5712⇒0.4631 | 22.1 | 0.026 | ||
| 2.68823+0.5712⇒0.4711 | 21.8 | 0.028 | ||
| SHG, e+o ⇒ e | ||||
| 1.0642⇒0.5321 | 32.7 | 0.034 | 8.8 | |
| 32.4 | 0.046 | 37 | ||
| SFG, e+o ⇒ e | ||||
| 1.0642+0.5321⇒0.35473 | 38.4 | 0.02 | 13 | |
| SFG, o+e ⇒ e | ||||
| 1.0642+0.5321⇒0.35473 | 58.4 | 0.05 | 12 | |
Temperature Variation of Phase-matching Angle at T =293K
| Interacting wavelengths[μm] | θpm [deg] | dθpm/dT[deg/K] |
| SHG, o+o ⇒ e | ||
| 0.5321⇒0.26605 | 47.3 | 0.0025 |
| 1.0642⇒0.5321 | 22.7 | 0.00057 |
| SFG, o+o ⇒ e | ||
| 1.0642+0.5321⇒0.35473 | 31.1 | 0.00099 |
| SHG, e+o ⇒ e | ||
| 1.0642⇒0.5321 | 32.4 | 0.0012 |
| SFG, e+o ⇒ e | ||
| 1.0642+0.5321⇒0.35473 | 38.4 | 0.0015 |
| SFG, o+e ⇒ e | ||
| 1.0642+0.5321⇒0.35473 | 58.4 | 0.00421 |
Calculated Values of Inverse Group-velocity Mismatch for SHG Process in BBO
| Interacting wavelengths[μm] | θpm [deg] | β[fs/mm] |
| SHG, o+o ⇒ e | ||
| 1.2⇒0.6 | 21.18 | 54 |
| 1.1⇒0.55 | 22.28 | 76 |
| 1.0⇒0.5 | 23.85 | 104 |
| 0.9⇒0.45 | 26.07 | 141 |
| 0.8⇒0.4 | 29.18 | 194 |
| 0.7⇒0.35 | 33.65 | 275 |
| 0.6⇒0.3 | 40.47 | 415 |
| 1.0642+0.5321⇒0.35473 | 38.4 | 0.0015 |
| SHG, e+o ⇒ e | ||
| 1.2⇒0.6 | 29.91 | 103 |
| 1.1⇒0.55 | 31.46 | 130 |
| 1.0⇒0.5 | 33.73 | 164 |
| 0.9⇒0.45 | 36.98 | 210 |
| 0.8⇒0.4 | 41.67 | 276 |
| 0.7⇒0.35 | 48.74 | 373 |
| 0.6⇒0.3 | 60.91 | 531 |
Laser-induced Bulk Damage Threshold
| λ[µm] | τp[ns] | Ithr[GW/cm2] | Note |
| 0.2661 | 10 | 0.3 | 10Hz |
| 8 | >0.12 | ||
| 2 | grown by Czochralski method (CZ-BBO) | ||
| 3 | grown by flux method (flux-BBO) | ||
| 3.4 | CZ-BBO, annealed at 1193K (50 hours) | ||
| 0.308 | 12 | >0.2 | |
| 0.3547 | 10 | 0.9 | 10Hz |
| 8 | 25 | 1pulse | |
| 19 | 1800pulses | ||
| 0.03 | >0.4 | 10Hz | |
| 0.015 | >3 | ||
| 0.4 | 0.0002 | >150 | 10Hz |
| 0.5106 | 20 | >0.25 | 4kHz |
| 0.51–0.58 | 20 | 10 | |
| 0.5145 | CW | >0.0004 | |
| 0.5321 | 10 | 2.3 | 10Hz |
| 8 | 48 | 1pulse | |
| 32 | 1800pulses | ||
| 0.62 | 0.0002 | >50 | |
| 0.6943 | 0.02 | 10 | |
| 0.8 | 0.000025 | >3400 | 1–5kHz |
| 0.85 | 0.00025 | >93 | 1kHz |
| 1.054 | 0.005 | 50 | |
| 1.0642 | 14 | 50 | 1pulse |
| 23 | 1800pulses | ||
| 10 | 4.5 | 10Hz |
Laser-induced Surface Damage Threshold
| λ[µm] | τp[ns] | Ithr[GW/cm2] | Note |
| 0.266 | 10 | 0.15 | 10Hz |
| 0.355 | 10 | 0.50 | 10Hz |
| 0.51–0.58 | 20 | 1 | 4–14kHz |
| 0.532 | 10 | 1.3 | 10Hz |
| 1.064 | 10 | 2.6 | 10Hz |
| Linear Thermal Expansion Coefficient | ||
| T [K] | αt×106[K-1],||c | αt×106[K-1],⊥c |
| 293 | 0.36 | -2.54 |
| Mean Value of Linear Thermal Expansion Coefficient | ||
| T [K] | αt×106[K-1],||c | αt×106[K-1],⊥c |
| 298-1173 | 36 | 4 |
| Specific Heat Capacity at P =0.101325MPa | ||
| T [K] | cp[J/kgK] | |
| 298 | 490/496 | |
| Thermal Conductivity Coefficient | ||
| K[W/mK] ,||c | K[W/mK] ,⊥c | |
| 0.8 | 0.08 | |
| 1.6 | 1.2 | |
The range of transmission is from 190 nm to 3500nm
Good physical properties
Appropriate mechanical properties
Effective SHG(Second-harmonic generation) coefficient is large
Damage threshold of 100 ps pulse with 10 J/cm2 at 1064 nm
The range of phase matching is large from 409.6 nm to 3500nm
Temperature bandwidth is about 55℃
Optical homogeneity is high:δn≈10-6/cm
Material Processing
Optical Communication
Medical Applications