Hollow-core pulse compressor
A gas-filled capillary broadens the spectrum of an intense pulse; a negative-GDD compressor then makes it shorter — and an autocorrelator shows how far its reading can be trusted.
Open in the canvas →Background
A pulse cannot be shorter than its spectrum allows, so compressing an intense femtosecond pulse starts by giving it more bandwidth. Focused into a hollow glass capillary filled with a noble gas, the pulse travels as a guided mode over a metre or so at high intensity, and self-phase modulation adds new frequencies on both sides of the carrier — red on the rising edge, blue on the falling one. The capillary guides the light without the damage a solid fiber would suffer at millijoule energies, and the gas pressure tunes both the nonlinearity and the dispersion. The broadened, positively chirped pulse is then compressed by negative group-delay dispersion — chirped mirrors or a prism pair — into a pulse several times shorter than the input[1].
The guided mode loses light to the wall. For a smooth dielectric capillary the loss of the fundamental mode falls with the cube of the core radius and rises approximately with the square of the wavelength — the wall's dispersion adds a smaller factor — which is why compressors use wide cores[2]. The argon's refractive index and Kerr coefficient come from measurements[3,4].
Measuring the result is its own problem. An intensity autocorrelator records the correlation of the pulse with itself, which is wider than the pulse by a factor set by the pulse's shape — √2 for a Gaussian, 1.543 for sech². The instrument cannot know that shape, so its reading is only as good as the shape the user assumes.
What this setup demonstrates
A 800 nm, 100 fs, 30 µJ laser at 1 kHz is coupled into a 1 m capillary with a 250 µm core and 2 bar of argon. The capillary propagates the complex pulse envelope numerically — its dispersion, its Kerr self-phase modulation and its loss, 0.615 dB/m computed for a smooth silica wall at this core and wavelength. Select the gold cable to see the coupled energy, the nonlinear phase (about 2 rad) and the computed output.
A 10 % tap sends part of the output to one autocorrelator before compression; the rest goes through a −650 fs² compressor to a second. Each screen draws the numerical intensity autocorrelation of the computed pulse and reports the duration the way a real instrument does: the trace's width divided by the Gaussian factor. Beside it, SIM is the simulated pulse's intensity FWHM — model knowledge a real autocorrelator does not have, shown here for comparison. Before compression the pulse is still close to Gaussian, and the reading is right to about 1 %: 101 fs for a 102 fs pulse. After compression the pulse carries the wings self-phase modulation leaves behind, its own autocorrelation ratio is 1.64 rather than 1.41, and the Gaussian assumption reads 54 fs for a pulse that is really 47 fs — 16 % long. Switch an autocorrelator's assumed shape to sech² and it reads 50 fs, closer but still not exact.
Try the controls on the cable and the laser: pressure 0 for no gas, Kerr off for purely linear propagation, a smaller core for more nonlinearity and far more loss, or 1 W of average power — beyond the solver's bounds, where the light continues with argon's linear dispersion only and every readout downstream says so. Tune the compressor: for these settings, about −650 fs² gives the shortest computed pulse.
The capillary is a single-mode model with second-order dispersion, the Kerr effect and loss. It has no ionization, higher-order dispersion, higher modes, wall resonances, Raman response or self-steepening, and its effective area is the Gaussian approximation of the capillary mode, which makes the nonlinearity about 16 % stronger than the exact mode would. The loss is the ideal straight-capillary value at the carrier wavelength, applied to the whole broadened spectrum. The compressor is a lumped GDD, not a traced pair of chirped mirrors or prisms. The layout is illustrative, not the reconstruction of a particular experiment.
The autocorrelators compute the intensity autocorrelation of the pulse envelope; they do not model the second-harmonic crystal, its phase-matching bandwidth or the detector. Cross-correlation of two computed envelopes is not modelled.
Related components
References
- M. Nisoli, S. De Silvestri, O. Svelto, “Generation of high energy 10 fs pulses by a new pulse compression technique,” Applied Physics Letters 68, 2793–2795 (1996)
- E. A. J. Marcatili, R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell System Technical Journal 43, 1783–1809 (1964)
- E. R. Peck, D. J. Fisher, “Dispersion of argon,” Journal of the Optical Society of America 54, 1362–1364 (1964)
- S. Zahedpour, J. K. Wahlstrand, H. M. Milchberg, “Measurement of the nonlinear refractive index of air constituents at mid-infrared wavelengths” (2015), Table 1