


More details about Lithium Triborate LiB_{3}O_{5} (LBO) crystal


Part I. Crystallographic facts. 

LBO is an orthorhombic biaxial crystal with mm2 point group symmetry. Its principal crystallophysical axes x, y, z (n_{z} > n_{y} > n_{x}, n_{x} > n_{y} > n_{z}) are parallel to the crystallographic axes a, b, c. The calculated angle between the optical axes is equal to 109° at l = 532 nm and to 108° at 635 nm, which defines LBO as a negative biaxial crystal. Its transmission range ranges from 155 to 3200 nm. The linear absorption coefficient of LBO is 3.1x10^{3} cm^{1} in the spectral range 351  364 nm and 3.5x10^{4} cm^{1} at l = 1064 nm.
Dispersion relations  Sellmeier equations for LiB_{3}O_{5} are the following:
n_{x}^{2} = 2.4542 + 0.01125/(l^{2}  0.01135)  0.01388l^{2}
n_{y}^{2} = 2.5390 + 0.01277/(l^{2}  0.01189)  0.01848l^{2}
n_{z}^{2} = 2.5865 + 0.01310/(l^{2}  0.01223)  0.01861l^{2}
Typical values of LBO refraction indices are presented in the table below:
Refractive indices: 
n_{x} 
n_{y} 
n_{z} 
1064 nm 
1.565 
1.590 
1.605 
532 nm 
1.578 
1.607 
1.621 
355 nm 
1.597 
1.627 
1.643 
266 nm 
1.626 
1.650 
1.676 


Part II. Optical and nonlinear optical properties. 

The phasematching directions for threewave interactions in the LBO crystal are determined for the practical case of light propagation in principal planes of a biaxial crystal. The picture below demonstrates the first octant of the LBO crystal in the crystallophysical coordinate system (x, y, z) with the corresponding dependences of refraction indices on light propagation direction (index surfaces). It is seen that in the xy (q = 90°) and xz (f = 0°, q < V_{z}) planes LBO is similar to the negative uniaxial crystal and in the yz (q = 90°) and xz (f = 0°, q > V_{z}) planes to the positive uniaxial one. Moreover, due to zero values of effective nonlinearity coefficients for some types of threewave interactions only interactions of Type I are possible in xy and xz (q > V_{z}) planes (o + o > e and e + e > o interactions, correspondingly), whereas interactions of Type II occur only in yz and xz (q < V_{z}) planes (o + e > o, e + o > o and e + o > e, o + e > e interactions, correspondingly).
The calculated values of the birefringence  "walkoff" angles for waves with extraordinary polarization propagating inside the LBO crystal in the phasematching direction corresponding to the generation of the different harmonics of Nd:YAG, Nd:YAP and Ti:Sapphire laser radiation are given in the next table:


Interacting wavelengths [nm] 
Phasematching angle [deg.] 
Birefringence angle [deg.] 
xy plane, q = 90° o + o > e 
f_{theor} 
r_{1} 
r_{2} 
r_{3} 
1079 > 539.5 
10.68 
 
 
0.37 
1064.2 > 532.1 
11.60 
 
 
0.40 
886 > 443 
24.05 
 
 
0.78 
870 > 435 
25.36 
 
 
0.81 
780 > 390 
33.72 
 
 
0.98 
760 > 380 
35.83 
 
 
1.02 
715 > 357.5 
41.34 
 
 
1.07 
1064 + 532 > 355 
37.21 
 
 
1.05 
1064 + 355 > 266 
60.63 
 
 
1.01 
yz plane, f = 90° o + e > o 
q_{theor} 
r_{1} 
r_{2} 
r_{3} 
1064.2 > 532.1 
20.45 
 
0.35 
 
870 > 435 
51.79 
 
0.52 
 
1064 + 532 > 355 
42.19 
 
0.53 
 


The dependences of refraction indices on light propagation direction (index surfaces) in the first octant of LBO in crystallophysical coordinate system (x, y, z). Designations: q is the polar angle, f is the azimuthal angle, V_{z} is the angle between one of the optical axes and the axis z. The similarity of LBO in its principal plane to a positive (+) or negative () uniaxial crystal is indicated.
The experimental phasematching angular (internal Df^{i}, Dq^{i} or external Df^{e}, Dq^{e}, FWHM) and temperature (DT, FWHM) bandwidth values in the case of SHG, THG and FHG processes induced in LBO at room temperature by Nd:YAG (l = 1064 nm), Nd:YAP (l = 1079 nm) and Ti:Sapphire (l = 0.71  0.89 nm) laser radiation are shown in the next table below.


Interacting wavelengths [nm] 
Angular bandwidth [deg.] 
Temperature bandwidth [°C] 
xy plane, q = 90° o + o > e 
Df^{e} 
Df^{i} 
Dq^{e} 
DT 
1079 > 539.5 
0.49 

 
 
1064.2 > 532.1 
0.43

0.24 
1.79 4.22 
6.7

886 > 443 



7.8 
870 > 435 

0.10 


780 > 390 

0.07 


760 > 380 



15.3 
715 > 357.5 

0.06 


1064 + 355 > 266 



3.8 
yz plane, f = 90° o + e > o 
Dq^{e} 

Df^{e} 
DT 
1064.2 > 532.1 
1.20 

4.70 
6.2 
1064 + 532 > 355 
0.29 

4.90 
3.7 


The expressions for the effective nonlinearity for an arbitrary direction inside the LBO crystal (mm2 point group symmetry, x, y, z > a, b, c assignment between the crystallophysical and crystallographic coordinate systems) in the principal planes are the following.


xy plane: 
d_{eff}^{ooe} = d_{32}cosf 
yz plane: 
d_{eff}^{oeo} = d_{eff}^{eoo} = d_{31}cosq 
zx plane, q < V_{z}: 
d_{eff}^{eoe} = d_{eff}^{oee} = d_{32}sin^{2}q+ d_{31}cos^{2}q 
zx plane, q > Vz: 
d_{eff}^{eeo} = d_{32}sin^{2}q+ d_{31}cos^{2}q 


where q and f are the polar and azimuthal angles in a polar coordinate system related to the crystallophisical coordinate system: q is measured from z and f from x (see the picture above).
The effective nonlinearity coefficients d_{31} and d_{32} for LBO with respect to d_{36} (KDP) with the most accurate value of 0.39 pm/V were obtained:
d_{31} = ±(1.05 ± 0.13)x10^{12} m/V
d_{32} = ±(0.98 ± 0.09)x10^{12} m/V
(note that d_{31} and d_{32} are of different sign, this is important for the calculation of d_{eff} in the xz plane).




Calculated values of effective nonlinearity for SHG and SFG processes in the principal planes of LBO crystal.


Interacting wavelengths [nm] 
Phasematching angle [deg.] 
Effective nonlinearity [pm/V] 
xy plane, q = 90° 
f_{theor} 
d_{eff}^{ooe} 
1908 > 954 
24.04 
0.89 
1500 > 750 
7.03 
0.97 
1079 > 539.5 
10.68 
0.96 
1064.2 > 532.1 
11.60 
0.96 
886 > 443 
24.05 
0.89 
870 > 435 
25.36 
0.88 
780 > 390 
33.72 
0.81 
760 > 380 
35.83 
0.79 
715 > 357.5 
41.34 
0.73 
1064 + 532 > 355 
37.21 
0.78 
1064 + 355 > 266 
60.63 
0.48 
yz plane, f = 90° 
q_{theor} 
d_{eff}^{eoe} = d_{eff}^{oee} 
1908 > 954 
49.00 
0.69 
1500 > 750 
14.19 
1.02 
1908 > 954 
24.04 
0.89 
1079 > 539.5 
18.59 
1.00 
1064.2 > 532.1 
20.45 
0.99 
870 > 435 
51.79 
0.65 
1064 + 532 > 355 
42.19 
0.78 
xz plane, f = 0° q < V_{z} 
q_{theor} 
d_{eff}^{eoe} = d_{eff}^{oee} 
1318.8 > 659.4 
5.10 
1.04 
xz plane, f = 0° q > V_{z} 
q_{theor} 
d_{eff}^{eeo} 
1318.8 > 659.4 
86.26 
0.96 


LBO is a very useful nonlinear optical material, especially for SHG of highintensity laser radiation, intracavity SHG, deepUV SFG and OPO applications.
To compare the nonlinear optical properties of LBO with those of other nonlinear materials such as BBO, KDP and KTP, the attention should be given to the following values: the experimental phasematching angles for the different interactions, the experimental values of angular and temperature bandwidths (FWHM), the calculated values of birefringence angle and effective nonlinearity in the phasematching direction. Such a comparison is shown in the table below for SHG of Nd:YAG laser radiation, one of the nonlinear processes frequently used in quantum electronics.
From this table it follows that LBO has a relatively large angular acceptance bandwidth, which permits effective frequency doubling of multimode laser radiation. It possesses a rather small temperature acceptance bandwidth and a low birefringence. Concerning effective nonlinearity LBO has nearly the same nonlinearity as BBO but overcomes significantly KDP and compares unfavorably with KTP. On the other hand, LBO exhibits very high resistance to laser damage and its transparency range spreads deep into the UV.
Comparison of Nd:YAG laser frequency doublers made from LBO, BBO, KDP and KTP (1064.2 nm > 532.1 nm).



LBO 
BBO 
KDP 
KTP 
Type of interaction 
ooe 
eoo 
ooe 
eoe 
ooe 
eoe 
eoe 
q_{pm} 
90.0° 
20.5° 
22.8° 
32.7° 
41.0° 
58.0° 
90.0° 
f_{pm} 
10.7° 
90.0° 
90.0° 
0.00° 
45.0° 
0.00° 
25.0° 
Dq^{e}_{exp} [ang. min] 
25.3 
7.20 
3.00 
4.40 
9.30 
18.2 
19.6 
Df^{e}_{exp} [ang. min] 
25.8 
30.0 




63.0 
DT_{exp} [°C] 
5.80 
6.20 
50.6 
37.1 
11.0 
13.2 
24.0 
r_{1} [deg] 

0.4 

3.8 

1.2 
0.2 
r_{3} [deg] 
0.4 

3.2 
4.0 
1.6 
1.4 
0.3 
d_{eff} [pm/V] 
0.96 
0.99 
2.00 
1.60 
0.26 
0.35 
3.30 
Cutoff of UV transmission 
155 
189 
177 
350 


