Second Harmonic Generation Crystal
A second harmonic generation (SHG) crystal is a nonlinear optical crystal used to convert laser light at frequency ω (wavelength λ) into light at 2ω (wavelength λ/2). Two photons of the pump combine into one photon with twice the energy. The process is also called frequency doubling. It requires a material with a non-zero second-order susceptibility χ(2), which means the crystal must lack inversion symmetry.
The classic lab example is 1064 nm Nd:YAG or Nd:YVO₄ doubled in KTP or LBO to 532 nm green.
How it works:
The induced polarization contains a term ∝χ(2)E2. For a field at ω, that term drives a wave at 2ω. Efficient conversion needs phase matching: the pump and harmonic must stay in step so fields generated along the crystal add constructively.
Δk=k2ω−2kω=0⇔n(2ω)=n(ω)
Dispersion normally makes n(2ω)>n(ω). Birefringent crystals fix that by mixing ordinary and extraordinary indices:
Type I: two pump photons of the same polarization → harmonic of the other polarization (e.g. o+o→e).
Type II: pump photons of orthogonal polarizations → harmonic of one polarization (e.g. o+e→e).
Type 0 / quasi-phase matching (QPM): all waves same polarization; the sign of χ(2)\chi^{(2)}χ(2) is periodically flipped (PPLN, PPLT) so the mismatch resets every coherence length.
Critical phase matching uses crystal angle. Noncritical phase matching (NCPM) uses temperature (or a 90° cut) so walk-off is zero and the angular acceptance is large—preferred for high-power CW and tightly focused beams. LBO NCPM for 1064 → 532 nm is a standard high-power green recipe.
Conversion efficiency rises with intensity, effective nonlinear coefficient d/eff, and interaction length, and falls with walk-off, group-velocity mismatch (ultrashort pulses), and Δk. The crystal can sit outside the laser (extracavity) or inside the cavity (intracavity SHG) to raise the circulating fundamental intensity.
Common SHG crystals:
KTP (KTiOPO₄): high d/eff, wide angular acceptance; workhorse for 1064 → 532 nm. Flux-grown parts can gray-track at high green power; hydrothermal KTP is more robust. Family includes KTA, RTP.
LBO (LiB₃O₅): high damage threshold, wide transparency (~160–2600 nm), small walk-off, good NCPM. Preferred for high-average-power green and many UV mixing schemes.
BBO (β-BaB₂O₄): large birefringence and UV transparency; doubles and triples Ti:sapphire and Yb lasers; hygroscopic; tighter angular tolerance.
KDP / DKDP: large apertures, high pulse energy; hygroscopic; used on big Q-switched and fusion-class beams.
PPLN / PPLT (periodically poled LiNbO₃ / LiTaO₃): very high effective nonlinearity via QPM; efficient at modest CW power; photorefractive issues unless MgO-doped and/or heated.
Others: BIBO, CLBO (deep UV), KNbO₃, ZnGeP₂ (mid-IR, more often OPO than SHG).
Practical limits: damage threshold, hygroscopicity, gray tracking, thermal lensing, and AR coatings at both ω and 2ω.
Applications:
Green and blue sources from IR solid-state and fiber lasers (pointers, pumping, displays, alignment).
UV generation: 532 → 266 nm (fourth harmonic), or mixing for 355 nm (third harmonic) in the same or a second crystal.
Ultrashort-pulse lasers: thin BBO/LBO to limit group-velocity walk-off.
Intracavity-doubled DPSS lasers for multi-watt CW green.
Microscopy and spectroscopy (SHG imaging uses the same χ(2) process in tissue or a crystal sample).
Seed or pump wavelengths for OPOs and further mixing.
Metrology and quantum optics (squeezed light, entangled-photon sources often start with SHG into an OPO).
An SHG crystal is the standard way to reach colors that laser gain media do not emit directly, at the cost of phase-matching alignment, extra loss, and careful thermal and damage management.