Title

Description

LBO crystal — the most excellent nonlinear crystal for Noncritical Phase Matched laser frequency doubling

LBO is one of the excellent non-linear crystals in the ultraviolet band. It has been successfully used in second and third harmonic generation of YLF, YAG, YAP lasers. LBO crystal has wide transmission band, good ultraviolet transmittance, slightly deliquescence, good physical and chemical properties, moderate non-linear optical coefficient, good optical uniformity, high damage threshold, large allowable angle and small walk-off angle. It has been widely used in high average power second harmonic, sum frequency, difference frequency, third harmonic, fourth harmonic and parametric oscillation field.

The greatest advantage of LBO is that temperature tuning can be used to achieve non-critical phase matching (NCPM). When the non-critical phase matching relationship is satisfied in the frequency doubling process, the walk-off angle between the fundamental frequency light and the second harmonic of frequency doubling is 0. At this time, the effective length of LBO crystal can theoretically reach infinity, which can compensate for its small non-linear coefficient. Because its damage threshold is very large, it means that high-power fundamental wave pumping can be realized. Therefore, the conversion efficiency of fundamental frequency light will be greatly improved by using the non-critical phase matching of LBO crystal for the extra-cavity frequency doubling of pulsed laser. The beam quality and stability of frequency light will be greatly improved.

Parameter

Chemical and Physical properties

Property	Value
Chemical formula	LiB3O5
Crystal structure	Orthorhombic, Space group Pna21, Point group mm2
Lattice Parameter	a=8.4473Å ,b=7.3788Å, c=5.1395Å, Z=2
Mass density	2.47 g/cm3
Moh hardness	6
Melting point	About 834°C
Thermal conductivity	3.5W/m/K
Birefringence	Negative biaxial crystal: 2Vz = 109.2˚ at λ = 0.5321μm

Coating

Crystal Dimension/mm	Length/mm	Application	Orientation Theta/Phi deg	ARCoatings S1/S2,nm/nm
5 x 5	15	THG@1064nm, Type II (e-oe)	42.2/90	1064 + 532 / 355
5 x 5	15	SHG@1064nm, Type I (e-oo)	90/11.6	1064 + 532 / 1064 + 532
6 x 6	0.9	SHG@1030nm	90/13.8	515 + 1030 / 515 + 1030
	1.9	SHG@1030nm	90/13.8	515 + 1030 / 515 + 1030
	2.8	SHG@1030nm	90/13.8	515 + 1030 / 515 + 1030
	3.7	SHG@1030nm	90/13.8	515 + 1030 / 515 + 1030
10 x 10	0.9	SHG@1030nm	90/13.8	515 + 1030 / 515 + 1030
	1.9	SHG@1030nm	90/13.8	515 + 1030 / 515 + 1030
	2.8	SHG@1030nm	90/13.8	515 + 1030 / 515 + 1030
	3.7	SHG@1030nm	90/13.8	515 + 1030 / 515 + 1030
3 x 3	10	THG@1064nm, Type II (e-oe)	42.2/90	1064 + 532 / 355
	15	SHG@1064nm, NCPM I Type	90/0	1064 + 532 / 1064 + 532
	15	THG@1064nm, Type II (e-oe)	42.2/90	1064 + 532 / 355
	15	SHG@1064nm, Type I (e-oo)	90/11.6	1064 + 532 / 1064 + 532
	20	SHG@1064nm, NCPM I Type	90/0	1064 + 532 / 1064 + 532

Polishing

Property	Value
Orientation Tolerence	< 0.5°
Thickness/Diameter Tolerance	±0.05 mm
Surface Flatness	<λ/8@632 nm
Wavefront Distortion	<λ/4@632 nm
Surface Quality	10/5
Parallel	30〞
Perpendicular	15ˊ
Clear Aperture	>90%
Chamfer	<0.2×45°

Linear Optical Properties

Property	Value
Transparency Range	169 – 2600 nm
Absorption Coefficient:	<0.1%/cm at 1064nm;<0.3%/cm at 532nm
Refractive Indices
at 1.0642 mm	nx = 1.5656, ny = 1.5905, nz=1.6055
at 0.5321 mm	nx = 1.5785, ny = 1.6065, nz=1.6212
at 0.2660 mm	nx = 1.5973, ny = 1.6286, nz=1.6444
Sellmeier Equations(λ in μm)	nx2=2.454140+0.011249/(λ2-0.011350)-0.014591λ2-6.60×10-5λ4
	ny2=2.539070+0.012711/(λ2-0.012523)-0.018540λ2+2.0×10-4λ4
	nz2=2.586179+0.013099/(λ2-0.011893)-0.017968λ2-2.26×10-4λ4

Nonlinear Optical Properties

Property	Value
SHG Phase Matchable Range	551 ~ 2600nm (Type I);790-2150nm (Type II)
NLO coefficients	deff(I)=d32cosΦ (Type I in XY plane)
	deff(I)=d31cos2θ+d32sin2θ (Type I in XZ plane)
	deff(II)=d31cosθ (Type II in YZ plane)
	deff(II)=d31cos2θ+d32sin2θ (Type II in XZ plane)
Non-vanished NLO susceptibilities	d31=1.05 ± 0.09 pm/V
	d32=-0.98 ± 0.09 pm/V
	d33= 0.05 ± 0.006 pm/V
Therm-Optic Coefficients(°C,λ in μm)	dnx/dT=-9.3X10-6
	dny/dT=-13.6X10-6
	dnz/dT=(-6.3-2.1λ)X10-6
Angle Acceptance	6.54mrad-cm (Φ, Type I,1064 SHG)15.27mrad-cm (q, Type II,1064 SHG)

Linear Thermal Expansion Coefficient

T [K]	αt×106[ K-1],\|\|X	αt×106[K-1 ],\|\|Y	αt×106[ K-1],\|\|Z
273	107.1	-95.4	33.7
323	108.2	-88	33.6
373	108.3	-80.9	33.2
423	107.3	-74.0	32.6
473	105.3	-67.3	31.7
523	102.3	-60.7	30.5
573	98.2	-54.4	29.1
673	87.0	-42.3	25.5
723	79.8	-36.5	23.3
773	71.6	-30.9	20.9
873	52.1	-20.3	15.3
923	40.8	-15.3	12.1
973	28.5	-10.6	8.7
1023	15.1	-5.9	5.0
1073	0.8	1.5	1.1

Experimental Values of Refractive Indices

λ[µm]	nX	nY	nZ
0.2537	1.6335	1.6582	1.6792
0.2894	1.6209	1.6467	1.6681
0.2968	1.6182	1.6450	1.6674
0.3125	1.6097	1.6415	1.6588
0.3341	1.6043	1.6346	1.6509
0.3650	1.59523	1.62518	1.64025
0.4000	1.58995	1.61918
0.4047	1.5907	1.6216	1.6353
0.4358	1.5859	1.6148	1.6297
0.4500	1.58449	1.61301	1.62793
0.4861	1.5817	1.6099	1.6248
0.5000	1.58059	1.60862	1.62348
0.5250	1.57906	1.60686
0.5321	1.57868	1.60642	1.62122
0.5461	1.5780	1.6057	1.6206
0.5500	1.57772	1.60535	1.62014
0.5780	1.5765	1.6039	1.6187
0.5893	1.5760	1.6035	1.6183
0.6000	1.57541	1.60276	1.61753
0.6328	1.5742	1.6014	1.6163
0.6563	1.5734	1.6006	1.6154
0.7000		1.59893	1.61363
0.8000	1.56959	1.59615	1.61078
0.9000	1.56764	1.59386	1.60843
1.0000	1.56586	1.59187	1.60637
1.0642	1.56487	1.59072	1.60515
1.1000	1.56432	1.59005	1.60449

Experimental Values of Phase-matching Angle (T =293K)

Interacting wavelengths[μm]	Φexp [deg]	θexp [deg]
XY plane θ=90° SHG, o+o ⇒ e
1.908⇒0.954	23.8
1.5⇒0.75	7
1.0796⇒0.5398	10.6/10.7
1.0642⇒0.5321	11.3/11.4/11.6/11.8
0.946⇒0.473	19.4/19.5
0.930⇒0.465	21.3
0.896⇒0.448	23.25
0.88⇒0.44	24.53
0.850⇒0.425	27
0.84⇒0.42	27.92
0.836⇒0.418	28.3
0.80⇒0.40	31.70
0.794⇒0.397	32.3
0.786⇒0.393	33
0.78⇒0.39	33.70
0.7735⇒0.38675	34.4
0.75⇒0.375	37.13/37
0.746⇒0.373	37.5
0.7094⇒0.3547	41.8/41.9/42/43.5
0.63⇒0.315	55.6
0.555⇒0.2775	86
0.554⇒0.277	90
SFG, o+o ⇒ e
1.3414+0.6707⇒0.44713	20
1.0642+0.5321⇒0.35473	37/37.1/37.2
1.053+0.5265⇒0.351	38.2
1.0642+0.35473⇒0.26605	60.7/61
0.86+0.43⇒0.2867	61
1.3188+0.26605⇒0.22139	70.2
0.21284+2.35524⇒0.1952	50.3
0.21284+1.90007⇒0.1914	63.8
0.21284+1.58910⇒0.18774	88
YZ plane, Φ=90◦ SHG, o+e ⇒ o
1.908⇒0.954		46.2
1.5⇒0.75		14.7
1.0796⇒0.5398		19.2
1.0642⇒0.5321		19.9/20.5/20.6/21.0
SFG, o+e ⇒ o
1.0641+0.53205⇒0.3547		42/42.7
1.0642+0.5321⇒0.35473		42.2/42.5/43.2
XZ plane, Φ=0◦, θ＜VZ SHG, e+o ⇒ e
1.3414⇒0.6707		3.6/4.2/5.0
1.3188⇒0.6594		5.2
1.3⇒0.65		5.4
XZ plane, Φ=0◦, θ＞VZ SHG, e+e ⇒ o
1.3414⇒0.6707		86.1/86.3/86.6
1.3188⇒0.6594		86.0
1.3⇒0.65		86.1
1.24⇒0.62		86

Experimental Values of Non-critical Phase Matching (NCPM) Temperature

Interacting wavelengths[μm]	T[℃]
along X axis SHG, typeⅠ
1.547⇒0.7735	117
1.46⇒0.73	50
1.252⇒0.626	3.5
1.25⇒0.625	-2.9
1.215⇒0.6075	21
1.211⇒0.6055	20
1.206⇒0.603	24
1.2⇒0.6	24.3
1.15⇒0.575	61.1
1.135⇒0.5675	77.4
1.11⇒0.555	108.2
1.0796⇒0.5398	112
1.0642⇒0.5321	148/148.5/149/149.5/151
1.047⇒0.5235	166.5/167/172/175/176.5/180
1.025⇒0.5125	190.3
SFG, typeⅠ
1.908+1.0642⇒0.6832	81
1.444+1.08⇒0.6179	23
1.135+1.0642⇒0.5491	112
1.547+0.7735⇒0.5157	141
DFG, typeⅠ
0.532-0.8⇒1.588	135
along Z axis SHG, type II
1.342⇒0.671	35
1.3⇒0.65	46

Experimental Values of Internal Angular, Temperature, and Spectral Bandwidths

Interacting wavelengths[μm]	T[℃]	Δφint [deg]	Δθint [deg]	ΔT[℃]
along X axis
SHG, type I
1.46⇒0.73	50			6
1.252⇒0.626	3.5			9
1.206⇒0.603	24			13
1.135⇒0.5675	77.4			4.7
1.0642⇒0.5321	148	3.54	2.57	3.9
	148.5			2.7
	149	2.3	1.9	4
	149.5			4.1
	151	2.1	2.1	2.9
1.047⇒0.5235	175			3.5
SFG, type I
1.908+1.0642⇒0.6832	81			7.4
1.444+1.08⇒0.6179	23	4.2	3
1.135+1.0642⇒0.5491	112			5
DFG, type I
0.532-0.8⇒1.588	135			3.8

Experimental Values of Internal Angular, Temperature, and Spectral Bandwidths

Interacting wavelengths[μm]	Φpm[deg]	θpm[deg]	Δφint[deg]	Δθint[deg]	ΔT[℃]	Δν[cm-1]
XY plane, θ =90(T=293K)
SHG, o+o ⇒ e
1.0796⇒0.5398	10.7		0.31
1.0642⇒0.5321	10.8		0.27	2.63
	11.4		0.24	1.79
	11.6				5.8
			0.34	2.64	6.7	8.8
0.886⇒0.443	24.1				7.8	15.9
0.870⇒0.435	25.4		0.12			141
0.78⇒0.39	33.7		0.08			194
0.7605⇒0.38025	35.9				15.3	10.5
0.715⇒0.3575	41		0.06
SFG, o+o ⇒ e
1.0642+0.3547⇒0.2661	60.7				3.8
YZ plane, φ =90(T=293K)
SHG, o+e ⇒ o
1.0642⇒0.5321		20.6	3.2	0.77
1.0642⇒0.5321			3	0.81		11.5
SFG, o+e ⇒ o
1.0641+0.53205⇒0.3547		42	0.79	0.16	6
1.0642+0.5321⇒0.35473		42.2		0.18
1.0642+0.5321⇒0.35473		41	3.07	0.18

Calculated Values of Inverse Group-velocity Mismatch for SHG Process in LBO

Interacting wavelengths[μm]	Φpm[deg]	θpm[deg]	β[fs/mm]
XY plane, θ =90◦
SHG, o+o ⇒ e
1.2⇒0.6	2.36		18
1.1⇒0.55	9.37		37
1.0⇒0.5	15.74		59
0.9⇒0.45	22.94		86
0.8⇒0.4	31.69		123
0.7⇒0.35	43.38		175
0.6⇒0.3	62.63		257
YZ plane, φ =90◦
SHG, o+e ⇒ o
1.1⇒0.55		15.98	82
1.0⇒0.5		28.96	106
0.9⇒0.45		45.36	139
0.8⇒0.4		76.88	186

Laser-induced Surface-damage Threshold

λ[µm]	τp [ns]	Ithr [GW/cm2]	Note
0.2661	12	>0.04
0.308	17	>0.05
0.308	0.0003	47,000	sharp focusing
0.3547	18	>0.18	10Hz
	8	>0.1
	7	>0.14
	0.03	>9.4	10Hz
	0.015	>2.8
	0.018	>5
	0.025	>6	10Hz
0.5145	CW	>0.00003
0.5235	0.055	>1.1	500Hz
0.5321	CW	>0.0004
	60	>0.07	900Hz
	10	>0.22
	0.1	>4.5	500Hz
	0.035	>3.1
	0.015	>4.4
0.592	0.0005	>50	1kHz
0.605	0.0002	>25
0.616	0.0004	31,000	sharp focusing
0.652	0.02	>0.81
0.7–0.9	10	>0.03	10Hz
0.71–0.87	25	1.1–1.4	25Hz
0.72–0.85	0.001	>8
0.77–0.83	0.00005	>22	80MHz
1.0642	CW	>0.001
	60	>0.06	1333Hz
	18	>0.6	10Hz
	9	>0.9	10Hz
	8	>0.5
	1.3	19
	1.1	45	bulk damage
	0.1	25
	0.035	>4.8
	0.025	>3.3	10Hz
1.0796	5	20	1–25Hz
1.0796	0.04	30

Temperature derivative of refractive indices

for spectral range 0.4–1.0µm and temperature range 293–338K (λ in µm):

dnX/dT=-1.8×10-6K-1

dny/dT=-13.6×10-6K-1

dnz/dT=-(6.3+2.1λ)×10-6K-1

for spectral range 0.4–1.0 µm and temperature range 293–383K (λ in µm):

dnX/dT=-(3.76λ-2.3)×10-6K-1

dny/dT=-(19.40-6.01λ)×10-6K-1

dnz/dT=-(9.70-1.50λ)×10-6K-1

for λ =0.6328µm and temperature range 293–473K (λ in µm, T in K):

dnX/dT=[0.20342-1.9697×10-2 (T-273)-1.4415×10-5(T-273)2]×10-6K-1

dny/dT=-[10.748+7.1034×10-2 (T-273) +5.7387×10-5(T-273)2]×10-6K-1

dnz/dT=-[0.85998+1.5476×10-1 (T-273) -9.4675×10-4(T-273)2+2.2375×10-6(T-273)3]×10-6K-1

Other Parameters

Specific Heat Capacity cp at P =0.101325 MPa
T [K]	cp[J/kgK]
298	1060
Linear Absorption Coefficient α
λ[µm]	α [cm-1]
0.35–0.36	0.0031
1.0642	0.00035
Two-photon Absorption Coefficient β
λ[µm]	τp[ns]	β×1011[cm/W]	Note
0.211	0.0009	103±36	θ =90°, Φ=30°
0.264	0.0008	15±5	θ =90°, Φ=30°
Nonlinear Refractive Index γ
λ[µm]	γ×1015[cm2/W]	Note
0.78	0.26±0.03	[100] direction
0.78	0.19±0.03	[010] direction
0.85	0 .19±0.04

Features

Low sensitivity to moisture
Dispertive angle is small
High optical homogeneity
The range of tunable wavelengths is large
The region of transparency is wide
Damage threshold is high
Wide acceptance angle

Applications

Material Processing

Optical Communication

Holography

671nm laser

Medical Applications

OPA(Optical parametric amplifiers) and OPO(oscillators)

SHG(Frequency harmonic doubling) and THG(Tripling harmonic doubling)

Diode laser pumped Nd: YLF laser and Nd:YAG laser. Alexandrite, Ti:Sapphire, Dye Lasers, Ultrashort Pulse Lasers