2025-04-08

WHITE PAPER

Nonlinear crystals for frequency conversion: 

harmonics generation

OPTOGAMA and 4Lasers.com offers Potassium Dihydrogen Phosphate & Potassium Dideuterium Phosphate (KDP & DKDP), Potassium Titanyl Phosphate (KTP), Beta Barium Borate (BBO), and Lithium Triborate (LBO) nonlinear optical crystals for harmonics generation of commonly used lasers including Nd:doped, Yb:doped and Ti:Sapphire lasers. 

Physical and Optical Properties of nonlinear crystals

Nonlinear properties of crystals for harmonics generation

KDP and DKDP crystals are one of the oldest used nonlinear materials. They both exhibit excellent ultraviolet transmission and high damage threshold. The nonlinearity of these crystals is relatively low. These crystals can be grown in large size. KDP crystals are used for fourth harmonic generation (SHG @532 nm, Type I, θ=76.5o, j=45o ) of Q‑switched and modelocked Nd-lasers with high pulse energy. Absorption coefficient of KDP @266 nm is lower comparing to that of DKDP. DKDP crystals are used for second harmonic generation (SHG @1064 nm, Type I and Type II) and third harmonic generation (THG @1064nm, Type II) of Q-switched and mode-locked Nd-lasers with high pulse energy, as well as for fourth harmonic generation (SHG @532nm) of these same lasers under non-critical phase matching conditions (NPCM, T= 50 °C).The main drawback is that these crystals are highly hygroscopic, therefore sealed housing and dry operating conditions have to be ensured.

KTP crystals are advantageous due to their high nonlinearity, great mechanical stability, high optical quality, and transparency range of 350 nm - 4,5 µm. It is an excellent solution for frequency doubling applications of Nd-doped lasers (SHG@1064 nm, Type II), especially for low and medium power applications, both intra- and extra-cavity design. KTP is susceptible to photochromic damage (grey-tracking), which causes the deterioration of nonlinear conversion efficiency. Optogama provides high grey track resistance (HGTR) KTP crystals as a solution, which significantly improves the grey-track resistance and overall performance. HGTR KTP crystals extend the use of KTP as a nonlinear medium to high-power applications.

BBO crystals transparency ranges from 188 nm to 5,2 µm, which includes reasonable transparency from 3-5,2 µm for few tens µm thick crystals, while their phase-matchable range spans almost over the entire transparency range. BBO is favorable for frequency doubling (SHG @ 800 nm, Type I) and tripling (THG @ 800 nm, Type I) of femtosecond Ti:Sapphire lasers, as well as  second (SHG@1030 nm,Type I), third (THG@1030 nm,Type I) and fourth (SHG @ 515 nm, Type I)  harmonic generation of femtosecond Yb-doped crystal-based lasers. It is used also for  ultrashot pulse duration measurements by autocorrelation methods. BBO crystals have the highest nonlinearity in the UV range out of all common nonlinear crystals.

LBO crystals feature a broad transparency range, wide acceptance angle, small walk-off angle, and high damage threshold. Most common applications include high-power near-infrared wavelength second harmonic generation of Nd-lasers (SHG@1064 nm, Type I;  SHG @1064 nm, NCPM, T= 149 oC) and Yb-lasers  (SHG@1030 nm, Type I), sum-frequency generation (THG @1064 nm, Type II) to produce visible and ultraviolet laser light. Optogama are capable of providing uncoated super-polished LBO crystals designed, e.g. for high-power UV generation via sum-frequency generation of 1064 nm and 532 nm.

Optics of nonlinear crystals including calculations of phase matching angles, walk-off angle, conversion efficiency, acceptances (spectral, angular and temperature bandwidths) is described in Ref. [1]. Some usefull relations and formulas are given in Annex.

OPTOGAMA develops and supplies #nonlinear #crystals for #research and industrial applications grown by different crystal growth techniques.

References

1.   V.G. Dmitriev, G.G. Gurzadyan, D.N. Nikogosyan, Handbook of Nonlinear Optical Crystals, Third revised eddition, Springer, 1999.

Annex

1.    Phase Matching Types in Uniaxial Crystals

Negative crystals (no>ne)

Type I             ko1 + ko2 = ke3(θ)       or “ooe interaction”

Type II            ke1(θ) + ko2 = ke3(θ) or “eoe interaction”

Type II            ko1 + ke2(θ) = ke3(θ) or “oee interaction”

 

Positive crystals (ne>no)

Type I ke1(θ) + ke2(θ) = ko3   or “eeo interaction”

Type II            ko1 + ke2(θ) = ko3          or “oeo interaction”

Type II            ke1(θ) + ko2 = ko3          or “eoo interaction”

where k is wave propagation vector (k=2pn/λ); θ is phase matching angle in the crystal; o is ordinary polarization, e is extraordinary polarization; 1, 2, 3 indices  refer to the wave vectors with lower, mid and higher  frequency, respectively.

2. Walk-off angle

ρ(θ) = ± arctan[(no/ne)2 ×tan θ] -/+ θ,

where the upper signs refer to a negative crystal and the lower signs to a positive one. Beam displacement δ due to walk-off:   δ = L tan ρ

 3. Equations for calculating phase-matching angles in uniaxial crystals [1].

4. Effective nonlinearity deff in uniaxial crystals of different point groups

5. Expresions for angular (Dθ), temperature (DT), and spectral (Dv) bandwidths in fixed-field approximation [1]:

6. Thickness of nonlinear crystal limited by Group Velocity Mismatch (GVM)

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