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Date: 2009-10-15hits: 1998

The** nonlinear optical (NLO) crystals** mentioned in our website are used in frequency conversion for lasers.CryLight has a complete line of NLO crystals including BBO , LBO , KTP , Nd:YAG and Nd:YVO4 crystals.The basic properties,advantages and applications of these crystals are described in our website.

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):**

ω_{1} + ω_{2} = ω_{3} (or 1/λ_{1} + 1/λ_{2} = 1/λ_{3} in wavelength) It combines two low-energy (or low- frequency) photons into a high-energy photon.

For example:

1064 nm + 532 nm -> 355 nm

**Sum Frequency Generation**

**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: 2w1 = w2 (or l1 = 2l2 in wavelength). The simplest scheme for frequency doubling is extracavity doubling. The laser passes through the nonlinear crystal only once as shown. However, if the power density of laser is low, focused beam, intracavity doubling and external resonant cavity are normally used to increase the power density on the crystals, for example, for doubling of cw Nd:YAG laser and Argon Ion lasers. If you meet any problems in scheme selection, please contact for a solution.

** Extracavity SHG** **SHG With Focused Beam**

**Intracavity SHG External Resonant cavity SHG**

**Frequency Tripling**

Frequency Tripling or Third Harmonic Generation (THG) is an other example of Sum Frequency Generation where, for THG of Nd:YAG laser, l1=1064nm, l2=532nm and generated wavelength l3=355nm. By sum frequency of fundamental wavelength and THG of a Ti:Sapphire laser in BBO crystal, it can generate wavelength as short as 193nm.

**Group Velocity Mismatching**

For frequency conversion of ultrafast lasers such as Ti:Sapphire and Dye lasers with femtosecond (fs) pulse width, the main concern is fs pulse broadening induced by group velocity mismatching (GVM)) or group velocity dispersion of NLO crystal. In order to keep efficiency frequency conversion without significant pulse broadening, the suggested thickness (LGVM) of crystals is less than Pulse Width divides GVM. For frequency doubling a Ti:Sapphire laser at 800 nm, for example, the inverse group velocities (1/VG) of 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 will make 192 fs separation between the pulses at two wavelengths. Therefore, 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 dramatic pulse broadening. SUWTECH is able to manufacture as thin as 0.02mm BBO crystals for as short as 5fs laser application.

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:

ω

For example:

1064 nm + 532 nm -> 355 nm

Frequency Tripling or Third Harmonic Generation (THG) is an other example of Sum Frequency Generation where, for THG of Nd:YAG laser, l1=1064nm, l2=532nm and generated wavelength l3=355nm. By sum frequency of fundamental wavelength and THG of a Ti:Sapphire laser in BBO crystal, it can generate wavelength as short as 193nm.

**Differential-Frequency Generation (DFG):
**ω

532 nm - 810 nm -> 1550 nm

**Differential Frequency Generation**

**Optical Parametric Generation (OPG):**

ω_{p} = ωs + ωi (or 1/λ_{p} = 1/λs + 1/λ_{i} in wavelength) It splits one high-energy photon into two low-energy photons.

For example:

355 nm -> 532 nm + 1064 nm

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

Phase-Matching

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

Δ_{k} = k_{3} - k_{2} - k_{1} = 2_{π3}/λ_{3} - 2πn_{2}/λ2 - 2πn1/λ1 = 0 (for sum frequency generation)

Where: k is phase mismatching, k_{i} is phase vector at λ_{i }and n_{i} is refractive index at λ_{i}.

**Conversion Efficiency Vs Δk
**

The phase-matching can be obtained by angle tilting, temperature tuning or other methods. The angle tilting is mostly used to obtain phasematching as shown in the left figure. If the angle between optical axis and beam ropagation (θ) isn't equal to 90^{o} or 0^{o}, we call it **critical phase-matching (CPM)**.Otherwise, **90 ^{o} non-critical phasematching (NCPM)** is for θ = 90

**Type I Phase Matching
Type II Phase Matching
**

Parameters For NLO Crystal Selection

NLO Process | Phase-Matching Type and Angle, deff |

Power or Energy, Repetition Rate | Damage Threshold |

Divergence | Acceptance Angle |

Bandwidth Spectral | Spectral Acceptance |

Beam Size | Crystal Size, Walk-Off Angle |

Pulse Width | Group Velocity Mismatching |

Environment | Moisture,Temperature Acceptance |

**Crystal Acceptance**

If a laser light propagates in the direction with angle △θto phase matching direction, the conversion efficiency will reduce dramatically (see the right Figure). We define the acceptance angle (△θ) as full angle at half maximum (FAHM), where θ = 0 is phase-matching direction. For example, the acceptance angle of BBO for type I frequency doubling of Nd:YAG at 1064 nm is about 1 mrad-cm. Therefore, if a Nd:YAG laser has beam divergence of 3 mrad for frequency-doubling, over half of 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-cm1/2 for type I NCPM LBO.

In addition, you have to consider the spectral acceptance (△λ) of crystal and the spectral bandwidth of your laser; crystal temperature acceptance (△T) and the temperature change of environment

**Walk-Off**

Due to the birefringence of NLO crystals, the extraordinary wave (ne) will experience Poynting vector walk-off. If the beam size of input laser is small, the generated beam and input beam will be separated at a walk-off angle (ρ) in the crystal and it will cause low conversion efficiency. Therefore, for focused beam or intracavity doubling, the walk-off is a main limitation to high conversion efficiency.

For frequency conversion of ultrafast lasers such as Ti:Sapphire and Dye lasers with femtosecond (fs) pulse width, the main concern is fs pulse broadening induced by group velocity mismatching (GVM)) or group velocity dispersion of NLO crystal. In order to keep efficiency frequency conversion without significant pulse broadening, the suggested thickness (LGVM) of crystals is less than Pulse Width divides GVM. For frequency doubling a Ti:Sapphire laser at 800 nm, for example, the inverse group velocities (1/VG) of 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 will make 192 fs separation between the pulses at two wavelengths. Therefore, 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 dramatic pulse broadening. SUWTECH is able to manufacture as thin as 0.02mm BBO crystals for as short as 5fs laser application.