LCS, Inc. representsLaser Crystal Solutions projectStage I: Industrial Crystal Growth: Lithium Triborate (LBO)

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Nonlinear Crystal products:

LBO nonlinear crystals
Lithium Triborate
Chemical formula: LiB3O5
BBO nonlinear crystals
beta-Barium Borate
Chemical formula: BaB2O4
BBO e-o switches
KTP nonlinear crystals
Potassium Tytanil Phosphate
Chemical formula: KTiOPO4
KGW, KYW laser host material
Raman Shifters (KGW, KYW)
Optical Coatings
anti-reflection and protective

Laser products:

Optical Parametric Oscillator

Contact information:

Zelenaja gorka str. 1,
630060, Novosibirsk,
Russian Federation
Phone/Fax: +7 (383) 334 80 81

e-mail: sales@lc-solutions.com

Part I. Crystallographic facts.

LBO is an orthorhombic biaxial crystal with mm2 point group symmetry. Its principal crystallophysical axes x, y, z (nz > ny > nx, nx > ny > nz) 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 LiB3O5 are the following:
nx2 = 2.4542 + 0.01125/(l2 - 0.01135) - 0.01388l2
ny2 = 2.5390 + 0.01277/(l2 - 0.01189) - 0.01848l2
nz2 = 2.5865 + 0.01310/(l2 - 0.01223) - 0.01861l2
Typical values of LBO refraction indices are presented in the table below:

1.565

1.590

1.605

1.578

1.607

1.621

1.597

1.627

1.643

1.626

1.650

1.676

Part II. Optical and nonlinear optical properties.

The phase-matching directions for three-wave 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 < Vz) planes LBO is similar to the negative uniaxial crystal and in the yz (q = 90°) and xz (f = 0°, q > Vz) planes to the positive uniaxial one.
Moreover, due to zero values of effective nonlinearity coefficients for some types of three-wave interactions only interactions of Type I are possible in xy and xz (q > Vz) planes (o + o --> e and e + e --> o interactions, correspondingly), whereas interactions of Type II occur only in yz and xz (q < Vz) planes (o + e --> o, e + o --> o and e + o --> e, o + e --> e interactions, correspondingly).
The calculated values of the birefringence - "walk-off" angles for waves with extraordinary polarization propagating inside the LBO crystal in the phase-matching 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:

Birefringence angle [deg.]

xy plane, q = 90° o + o --> e ftheor r1 r2 r3

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

qtheor

r1

r2

r3

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, Vz 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 phase-matching angular (internal Dfi, Dqi or external Dfe, Dqe, 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.

Temperature bandwidth [°C]

xy plane, q = 90° o + o --> e Dfe Dfi Dqe 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

Dqe Dfe 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: deffooe = d32cosf yz plane: deffoeo = deffeoo = d31cosq zx plane, q < Vz: deffeoe = deffoee = d32sin2q+ d31cos2q zx plane, q > Vz: deffeeo = d32sin2q+ d31cos2q

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 d31 and d32 for LBO with respect to d36 (KDP) with the most accurate value of 0.39 pm/V were obtained:
d31 = ±(1.05 ± 0.13)x10-12 m/V
d32 = ±(0.98 ± 0.09)x10-12 m/V
(note that d31 and d32 are of different sign, this is important for the calculation of deff in the xz plane).

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

Effective nonlinearity [pm/V]

xy plane, q = 90°

ftheor

deffooe

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°

qtheor

deffeoe = deffoee

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 < Vz

qtheor

deffeoe = deffoee

1318.8 --> 659.4

5.10

1.04

xz plane, f = 0° q > Vz

qtheor

deffeeo

1318.8 --> 659.4

86.26

0.96

LBO is a very useful nonlinear optical material, especially for SHG of high-intensity laser radiation, intracavity SHG, deep-UV 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 phase-matching 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 phase-matching 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 multi-mode 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).

eoe

qpm

90.0°

20.5°

22.8°

32.7°

41.0°

58.0°

90.0°

fpm

10.7°

90.0°

90.0°

0.00°

45.0°

0.00°

25.0°

Dqeexp [ang. min]

25.3

7.20

3.00

4.40

9.30

18.2

19.6

Dfeexp [ang. min]

25.8

30.0

63.0

DTexp [°C]

5.80

6.20

50.6

37.1

11.0

13.2

24.0

r1 [deg]

0.4

3.8

1.2

0.2

r3 [deg]

0.4

3.2

4.0

1.6

1.4

0.3

deff [pm/V]

0.96

0.99

2.00

1.60

0.26

0.35

3.30

Cutoff of UV transmission

155

189

177

350