Nonlinear Optical Crystals

The nonlinear optical (NLO) crystals mentioned in oru crystal catalog are used in frequency conversion for lasers. Dayoptics has a complete line of NLO crystals including BBO , LBO, KTP , LiNbO 3 , MgO:LiNbO 3 , ZnO:LiNbO 3 , KNbO 3 , KDP , KD*P , ADP and LiIO 3 crystals. The basic properties, advantages and applications of these crystals are described in our catalog.

Frequency Conversion

The frequency conversion processes include frequency doubling (which is a special case of sum frequency generation), sum frequency generation (SFG), differential-frequency generation (DFG) and optical parametric generation (OPG) which are demonstrated in the following equations:

Sum Frequency Generation(SFG):

w 1 + w 2 = w 3 (or 1/ l 1 + 1/ l 2 = 1/ l 3 in wavelength) It combines two low energy (or low frequency) photons into a high energy photon (see Fig.1). For example:

1064 nm + 1064 nm ----> 532 nm

Fig. 1

Differential - Frequency Generation (DFG):

w 1 - w 2 = w 3 (or 1/ l 1 - 1/ l 2 = 1/ l 3 in wavelength)(or in wavelength) It combines two high energy photons into a low energy photon. For example:

532 nm - 810 nm ----> 1550 nm

Optical Parametric Generation (OPG):

w p = w s + w i (or 1/ l p = 1/ l s + 1/ l i in wavelength) It splits one high energy photon into two low energy photons (see Fig.2).

Fig. 2

Frequency Doubling

Frequency Doubling or Second Harmonic Generation (SHG) is a special case of sum frequency generation if the two input wavelengths are the same. The simplest scheme for frequency doubling is extracavity doubling. The laser passes through the nonlinear crystal only once as shown in the Fig. 3. However, if the power density of laser is low, focused beam (Fig. 4), intracavity doubling (Fig. 5) and external resonant cavity (Fig. 6) are normally used to increase the power density on the crystals, for example, for doubling of cw Nd:YAG laser and Argon lon lasers. If you meet any problems in scheme selection, please contact Dayoptics for a solution.

Fig. 3	Fig. 4
Fig. 5

Sum Frequency Generation

Freuency Tripling or Third Harmonic Generation (THG) is and example of Sum Frequency Geenration where, for THG) of Nd:YAG laser , w 1 = 1064 nm, w 2 =532 nm and generated wavelength w 3 = 355 nm. Bsum frequency of fundamental wavelength and THGof a Ti:Sapphire laser in BBO crystal, ti can generate wavelength as short as 193 nm.

Optical Parametric Oscillation

Optical Parametric Generation (OPG) is an inverse process of Sum Frequency Generation. It splits one high - frequency photon (pumping wavelength, l p) into two low - frequency photons (signal, l s, and idler wavelength, l i). If two mirrors are added to form a cavity as shown in Fig. 7 an Optical Parametric Oscillator (OPO) is established. For a fixed pump wavelength, an infinite number of singnal and idler wavelengths can be generated by tilting a crystal. Therefore, OPO is an excellent source for generating wide tunable rang coherent radiation, BBO, KTP, LBO and LiNbO3 are good crystals for OPO and Optical Parametric Amplifier (OPA) applications.

Fig. 7

Phase - Matching

In order to obtain high conversion efficiency, the phase vectors input beams and generated beams have to be matched:

D k = k 3 - k 2 - k 1 = 2 p n 3 / l 3 - 2 p n 2 / l 2 - 2 p n 1 / l 1 = 0 (for sum frequency generation) Where: D k is phase mismatchingm ki is phase vector at li and ni is refractive index at li. In low power case, the relationship between conversion efficiency and phase missmatching is: h - (sin( D kl)/ D kl) 2 (see Fig. 8)

Fig. 8

It is clear that the conversion efficiency will drop dramaticall if D k increases. The phase - matching can be obtained by angle tilting, temperature tuning or other methods. The angle tilting is mostly used to angle between optical axis and beam propagation ( q ) isn't eaual to 90?or 0?,we call it criticl phase - matching (CPM). Otherwise, 90?non-critical phase-matching (NCPM) is q = 90?and 0 NCPM is for q = 0?

Fig. 9

Two types of phase-matching are classified in consideration of polarization of lasers. If the polarizations of two input beams (for sum frequency ) are parallel to each other (see Fig. 10), it is called type I phase- matching . If the polarizaions are perpendicular to each other (see Fig. 11). it is called type II phase-matching.

Fig. 10	Fig. 11

Conversion Efficicncy

How to select a NLO crystal for a frequency conversion process with a certain laser? The most important thing is to obtain a high conversion efficiency. The conversion efficiency has the following relationship with effective nonlinear coefficient(deff), crystal length (L), input power density (P) and phase mismatching( D k )

h - PL 2 (d eff sin( D kl)/ D kl) 2

In general, higher power density, longer crystals length, larger nonlinear coefficients and smaller phase mismatching will result higher conversion efficiency. However, there is always some limitation coming from nonlinear crystals and lases. For example, the d eff is determined by the nonlinear crystal itself and the input power density has to be lower than the damage threshold of crystal. Therefore, itis important to select a right crystal for your applications. In the following Table we list the laser and crystal parameters for selecting right crystals:

Parameters For NLO Crystal Selection

Laser Parameters	Crystal Parameters
NLO Process Power or Energy Divergence Bandwidth Beam Size Pulse Width Repetition Rate Environment	Phase-Matching Type and Angle Damage Threshold, d eff Acceptance Angle Spectral Acceptance Crystal Size, Walk-Off Angle Group Velocity Mismatching Damage Threshold Temperature Acceptance, Moistrue

Crystal Acceptance

If a laser light propagates in the direction with angle Dq to phase matching direction, the conversion efficiency will reduce dramatically (see Fig. 12). We define the acceptance angle ( Dq ) as full angle at half maximum (FAHM), where q = 0?is phase-matching direction. For example, the acceptance angle of BBO for type I frequency doubling of Nk:YAG at 1064 nm is about 1 mrad-chm. Therefore, if a Nd:YAG laser doubling, over half fo the input power is useless. In this case, LBO may be better because of its larger acceptance angle, about 8 mrad-cm, For NCPM, the acceptance angle is normally much bigger than that for CPM, for example, 52 mrad-cm for type I NCPM LBO.

Fig. 12

In addition, you have to consider the spectral acceptance(Dl) of crystal and the spectral bandwith of your laser; crystal temperature acceptance (DT) and the temperature change of environment.

Walk-Off

Due to the birefringence of NLO crystals, the extraordinary wave(n e ) will experience Poynting vector walk-off as shown in Fig. 13 If the beam size of input laser is small, the generated beam and input will be separated at a walk-off angle (p) in the crystal Therefore, for focused beam of intracavity doubling, the walk-off is amain limitaion to high conversion efficiency.

Fig. 13

Group Velocity Mixmatching

For NLO processes of ultrafast lasers such as Ti:Sapphire and Dye lasers with femtosecond (fs) pulser width, the main limitation to conversion efficiency is group velocity is matching (GVM). The GVM is caused by group velocity dispersion fo NLO crystal. For frequency doubling a Ti:Sapphire laser at 800 nm, for example, the inverse group velocities(1/Vg)fo BBO are respectively 1/Vg=56.09 ps/cm at 800 nm and 1/Vg=58.01 ps/cm at 400 nm and GVM = 1.92 ps/cm. That means an 1 mm long BBO crystal witt make 192 fs separation between the pulses at two vavelengths. Terefor, for an 100 fs Ti:Sapphire laser, we normally recommend a 0.5 mm long BBO crystal (with 96 fs Separation )in order to obtain high efficiency without dramatric pulse broadening.

NLO Program

There are several other crystal parameters which have to be considered in selecting NLO crystals. Many of them can be found in this catalog. However, many other parameters change from one process to another, for example, acceptance angle, walk-off angle and deff, etc.

In order to help customers have a clear picture of nonlinear crystals. Dayoptics developed a computer program, NLO Program, to calculate parameters for all of the nonlinear crystals listed in this catalog. The NLO Program can provide the following parameters:

1. Type ofPhase Matching
2.Phase Matching angle
3.refractive Indices
4. Polarization Directions
5. Effective Nonlinear Coefficients
6. Figure of Merit
7.Walk- Off Angle
8. Acceptance Angles
9. Spectral Acceptance Bandwidth
10. Group Velocities
11. Group Velocity Mismatching (GVM)

We provide free services to calculate the parametres for your processes or you may contact us for buying NLO Program.

How To Handle A NLO Crystal

Keep Crystal Clean

When you receive crystals from Dayoptics. please look at the polished or coated crystal surfaces first. If the surfaces are contaminated, pleaser blow the surfaces with air ball. If there is still pollution on the crystal surfaces, please clean the surfaces with cleaning liquid and soft silk. For BBO crystal, the mixing liquid of 50% high purity alcohol and 50% high purity ether is recommended as cleaning liquid. Please note that the contaminated surfaces are very easy to be damaged.

Angle Tilting

In order to obtain maximum conversion efficiency, angle tilting is normally used to reach phase-matching direciton. There are tow axes for tilting crystal angles as shown in Fig. 14. Because the NLO crystals provided by Dayoptics are normally cut in a principla crystal plane, conversion efficiency isn't sensitive to the angle tilting around b-axis which is normal to marked face. However, it is very sensitive to the angle great attention when rotating the crystal around a-axis. Acrystal mount with angle accuracy of about 5 arc secong is recommenden.

Fig. 14

Optimum Crystal Size and Cut

When ordering a nonlinear optical crystal, crystal orientation (or crystal cut) and size have to be known. The orientation is solely determined by the nonlinear opticl process. For example, for type I frequency-doubling of 1.064 m m, BBO is cut at q =22.8?and f =0?.Dayoptics's salesmen and engineers will help customers in selecting correct orientation. If any problem is met in crystal orientaiton, please, please contact Dayoptics.

The crystal size is divided into three dimension noted as W x H x L mm3(see Fig.15). The careful desing of crystal size is important because the price of crystal changes with crystal size. More important. the conversion efficiency has direct relation to crystal length. To select the optimum crystal heght (H), the laser beam diameter upon the crystal should be taken into account. The optimun crystal height should be slightly (for instance, 1 mm to 2 mm ) larger than the laser beam diameter upon the crystal.

Fig. 15

Both of laser beam diameter upon NLO crystal and tunable wavelength range have to be considered when designing the optimum 532 nm, we select W=H, If it is wide wavelength tuning NLO process, for example, frequency doubling a Dye laser form 440 nm to 660 nm by useing BBO crystal, the crystal should be tuned from q =36?to q =66.6? The width (W) is set to H + tg((66.6?- 36?/2)xL. If the crystal height (H)is 4 mm and length (L) is 7mm, the W should be approximately 8mm long.

Every NLO crystal has a standard length (L) for frequency doubling lasers with pulse width longer than nanosecond (ns). For example, the standard crystal lengths for BBO and KTP are 7 mm and 5mm, respectively. However, OPO and OPA need longer length, for example, >12 mm for BBO, and the SHG and THG of ultrashort pulse lasers collected a series of standard crystal lengths for various applications. This information is provided free.