Hawking Radiation from Ultrashort Laser Pulse Filaments
F. Belgiorno · S. L. Cacciatori · M. Clerici · V. Gorini · G. Ortenzi · L. Rizzi · E. Rubino · V. G. Sala · D. Faccio
Abstract and summary · read the original at the source
In one page
Hawking predicted in 1974 that the curvature at a black hole horizon is enough to excite photons out of the vacuum. It was realised soon after that the black hole is not the essential ingredient — the horizon is — and horizons can be built on a laboratory bench. Daniele Faccio and eight colleagues in Milan, Como and Edinburgh build one out of light. A short, intense laser pulse travelling through fused silica raises a moving bump in the glass’s refractive index; light catching up with the bump is slowed, and at the right speed it is brought to a standstill in the bump’s own frame. That is an analogue horizon, and this team went looking for the photons it should shed. They collected light at ninety degrees to the beam, where the ordinary nonlinear optical effects cannot reach, and found emission exactly inside the narrow wavelength window their dispersion calculation predicts, absent when the pulse velocity falls outside it.
Why it matters hereChapter 5 treats the vacuum as a medium whose excitations can be studied in a laboratory rather than only at a black hole, and this is one of the experiments that made that programme concrete: a horizon built from a laser pulse in a piece of glass, emitting photons the vacuum supplied. It belongs to chapter 2 as well, because what the apparatus is measuring is the vacuum responding to a structure imposed on it.
What it claims
01The horizon is made of light. An intense pulse in a Kerr medium raises a refractive index perturbation equal to the nonlinear Kerr index times the intensity; light approaching that perturbation sees a higher local index and slows, and at the right combination of frequency and perturbation velocity it is brought to rest in the frame moving with the perturbation. Each perturbation carries two horizons: the leading edge behaves as a black hole horizon, the trailing edge as its time-reversed white hole counterpart.Introduction, first and second columns, following Philbin and colleagues
Published and peer-reviewed02Dispersion turns that into a testable signature. Writing the index as a dispersive background plus the pulse-shaped perturbation, a horizon exists only for perturbation velocities lying between the two bounds set by the background index and the background index plus the perturbation — so the emission spectrum has well-defined upper and lower edges. The authors treat that bounded window, rather than the emission alone, as the feature peculiar to analogue Hawking radiation in this setting, and it is what separates the signal from Cerenkov-like emission, which has no upper bound.Equation 1 and the paragraph following it; exclusion (i)
Published and peer-reviewed03The measurement is built to exclude its own rivals. One picosecond pulses from a 10 Hz Nd:glass laser, up to 6 mJ, are shaped into a Bessel filament with a 7 degree cone angle by a fused silica axicon and sent into a 2 cm fused silica sample; light is collected at ninety degrees to the propagation axis and imaged onto a spectrometer and a cooled 16 bit CCD. At that angle four-wave mixing and self-phase modulation are forbidden by phase matching, Rayleigh scattering would need the other polarisation, and the three known fused silica fluorescence peaks are documented well enough to be fitted and subtracted. Tuning the pulse group velocity places the predicted window between 800 and 875 nm, where no known fluorescence sits and the camera is most sensitive.Figure 1 and the four numbered exclusions; Figure 2b
Published and peer-reviewed04The signal appears where predicted and scales as predicted. Photon emission is registered inside the predicted window, while a Gaussian reference pulse of the same peak intensity, whose velocity does not satisfy the horizon condition, shows no signal at all. The emitted light is unpolarised, supporting a spontaneous origin. The spectral peak shifts by about 40 nm as the input energy is raised, against a predicted 45 nm, and the bandwidth grows linearly with intensity; mapping bandwidth back onto the index perturbation returns a Kerr index of 2.8 plus or minus 0.5 times ten to the minus sixteen square centimetres per watt, against a tabulated value near three times ten to the minus sixteen.Figures 3a and 3b, and the accompanying text
Published and peer-reviewed05A second, independent geometry repeats it. Replacing the axicon with a 20 cm lens and loosely focusing a 50 µJ Gaussian pulse produces a spontaneous filament that accelerates as it propagates, so it should emit over a broader window — predicted between 270 and 450 nm — and the measured spectrum agrees. Narrowing the spectrometer slit onto the beginning and the end of the filament shows each section emitting only its own portion of the spectrum, in quantitative agreement with the velocity each section carries.Figure 4, panels a to d
Published and peer-reviewed06The paper names its own open question. Its analysis is built on phase velocity horizons, while other analogue systems rely on group velocity horizons, and for the Bessel pulse used here no group horizon exists at all — no frequency in the glass travels at the pulse’s group velocity. The measurement therefore indicates that in this setting a phase velocity horizon alone can produce photons in the predicted window, and the relative role of the two kinds of horizon is the question left standing, taken up directly in the published Comment and Reply that followed.Closing paragraph, second column of page 4
What to watch
The way in
https://doi.org/10.1103/PhysRevLett.105.203901Published as Physical Review Letters 105, 203901 (2010) under the APS default licence. The preprint is on arXiv as 1009.4634, version 1 posted 23 September 2010, under the arXiv.org perpetual non-exclusive licence, which permits arXiv to distribute and grants no redistribution right — checked on the arXiv record for this paper on 2026-09-08, where no Creative Commons statement appears, and the preprint text carries none. So this page holds the summary, the claims and the authors’ own abstract and sends the reader to the source; the claims are read against that preprint. The groups are at the Università degli Studi di Milano, INFN Milano, the Università dell’Insubria at Como, the Università di Milano-Bicocca and Heriot-Watt University in Edinburgh; Faccio is the corresponding author. The published exchange that followed is in this library as the Comment on Hawking Radiation from Ultrashort Laser Pulse Filaments by Ralf Schützhold and William Unruh, Physical Review Letters 107, 149401 (2011), to which the authors published a Reply.
How to cite it
F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, D. Faccio (2010) Hawking Radiation from Ultrashort Laser Pulse Filaments. doi:10.1103/PhysRevLett.105.203901
Where it sits in the curriculum