■ Swiss Terahertz · Tools
Organic Crystal Phase Matching
How much terahertz an organic crystal actually produces, and how thick it should be. Generation is limited by one thing above all: the pump pulse and the terahertz it creates travel at different speeds, so the two walk apart and the new light starts cancelling what came before. Absorption then decides whether extra thickness helps or hurts. Everything runs in your browser.
Velocity mismatch—
Coherence length at 1 THz—
Best thickness—
Peak output at—
i
Generated spectrum
at the thickness set above
Output against thickness
at the peak frequency
Coherence length
how far pump and terahertz stay in step
What the numbers mean
Velocity mismatch is the whole game. The pump travels at the optical group index, the terahertz at its own index. When those two agree, every slice of crystal adds in phase and output grows with the square of thickness. When they disagree, output oscillates with thickness instead of growing, and beyond the coherence length a thicker crystal gives you less, not more.
Coherence length is the distance over which the two drift half a cycle apart. It falls as the terahertz frequency rises, which is why a crystal that works well at 1 THz can be useless at 5.
Absorption sets the other limit. The residual figure is quoted at 1 THz and rises as the square of frequency, which is how the non-resonant background behaves in these crystals; the phonon sits on top of it. Together they are usually what ends the band, not the phase matching.
Absorption also decides thickness. Even perfectly matched, output saturates once the crystal is a few absorption lengths thick, because the terahertz generated at the front is reabsorbed before it reaches the back. Best thickness is where these two effects cross.
Two absorptions, not one. The terahertz is absorbed on its way out, and the pump is absorbed on its way in — so the source driving the process gets weaker with depth. Pump absorption is what pulls the optimum thickness down to a few hundred microns in practice. Not modelled here: two-photon and free-carrier absorption, which depend on how hard you pump rather than on a fixed coefficient, and pump depletion.
The phonon is what gives an organic crystal its character. A lattice resonance both absorbs strongly at its own frequency and drags the refractive index around either side of it, so phase matching that holds below the phonon can fail above it. Set it to zero strength to see the crystal without one.
Pump duration caps the top of the band. A pulse of duration τ cannot produce frequencies much above roughly 1/τ, whatever the crystal does.
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Where the presets come from, and what they are not. The refractive indices are from
Jazbinsek, Puc, Abina and Zidansek, Organic Crystals for THz Photonics, Appl. Sci. 9,
882 (2019), Table 2, quoted at each crystal's velocity-matching pump wavelength. Phonon positions
come from the same review. The absorption figures are placeholders — that paper gives
absorption only as plotted curves, so the residual α here is not a measured number for any
crystal. Index and absorption also vary with axis, temperature and growth batch, which is why every
field above is editable. Put your own values in before trusting an answer.
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