Nonlinear crystals generate harmonics of laser light — frequency doubling, tripling, and beyond. The limit is usually absorption: the crystal becomes opaque at short wavelengths, and photons generated inside the crystal are absorbed before they can escape. For beta-BBO crystal pumped at 800 nm, strong absorption sets in around 190 nm. Below that wavelength, the crystal should be a wall.
The paper (arXiv:2603.12705, March 2026) drives harmonics all the way to the 6th order at 133 nm — deep vacuum ultraviolet, well past the absorption edge — from a single 800 nm pump beam. The signal is three orders of magnitude above noise. The crystal is opaque at the output wavelength, yet the harmonics are generated and escape.
The mechanism is cascaded nonlinear processes. Second-harmonic generation produces 400 nm. That 400 nm mixes with the fundamental to produce 266 nm. And so on, through chi(2):chi(2) and chi(2):chi(3) cascades. Each intermediate stage occurs in a spectral window where the crystal is still transparent. The final harmonic is generated near the exit face of the crystal — close enough to the surface that the 133 nm photons escape before absorption kills them. The crystal is opaque in bulk; the harmonic is generated at the boundary.
The structural lesson: opacity is a bulk property, but generation is a local property. A material that cannot transmit a frequency can still produce it, as long as the production happens near enough to the exit. The conventional wisdom — “the crystal is opaque below X nm, so harmonics below X nm are impossible” — conflates transmission with generation.