Historical research guide · 0769 · 2008
Fiber-Optical Analog of the Event Horizon
Thomas G. Philbin · Chris Kuklewicz · Scott Robertson · Stephen Hill · Friedrich König · Ulf Leonhardt
In one minute
Thomas Philbin and colleagues sent 70-femtosecond pulses through 1.5 metres of microstructured optical fibre. Each pulse briefly raises the fibre’s refractive index, so a moving change in optical properties travels through glass that itself stays still. A continuous probe beam approaching the pulse’s trailing edge slowed until it could no longer overtake that edge: a white-hole analogue for the probe. The measured probe spectrum gained a blue-shifted peak, matching the group’s model of light near this optical horizon. Fibre dispersion limits how far the frequency can shift. The team also calculated how vacuum fluctuations could produce photon pairs in this arrangement. This experiment measured the classical blue shift; it did not report detecting those quantum pairs or Hawking radiation.
Connection
A 70-femtosecond pulse changes the fibre’s refractive index as it travels; the glass stays still while an optical boundary moves. Philbin’s team measured the resulting blue shift of probe light at the pulse’s trailing edge. Their calculation asks what photon pairs that boundary could produce from initially empty optical modes. The paper gives chapter 5 a concrete distinction between a measured classical horizon effect and a quantum effect the same apparatus could test.
From the source
The physics at an event horizon resembles the behaviour of waves in a moving medium, and horizons form wherever the local speed of the medium exceeds the wave velocity — a black-hole horizon where the flow accelerates past the wave speed, a white-hole horizon where a fast flow slows down and waves can no longer enter.Abstract; Introduction, paragraphs 1 to 2
The medium does not have to move physically. An ultrashort pulse raises the refractive index of the fibre through the Kerr effect by an amount proportional to its instantaneous intensity, and that index change travels with the pulse — so the pulse establishes a moving medium, at the speed of light in the fibre, although nothing material is moving.Paragraph 5 and Eq. (1)
In the experiment, 70-femtosecond solitons at 803 nanometres carrier wavelength and 80 megahertz repetition rate were launched into 1.5 metres of microstructured fibre, with a continuous probe tunable from 1460 to 1540 nanometres chasing them; the fibre was chosen so the two group velocities match. The measured probe spectrum shows a clear blue-shifted peak, in very good agreement with the theory of light propagation in the presence of horizons — the classical optical effect of a white-hole horizon.Paragraphs 6 to 10; Fig. 2 and Fig. 3; Doppler formula Eq. (2)
The analogue supplies its own answer to the trans-Planckian problem. At an astrophysical horizon light freezes at wavelengths shorter than the Planck scale, where the physics is unknown; in the fibre the corresponding physics is known and simple — the frequency dependence of the refractive index blue-shifts the incoming modes and then limits the shift by tuning the probe out of the horizon.Paragraph 8
Near 300 nanometres the glass dispersion makes the effective medium superluminal for those modes, so each subluminal mode has a superluminal partner at the same co-moving frequency, and the pulse can convert them partially into one another. The authors’ model predicts that, even with every mode initially in its vacuum state, this process could create photon pairs at both the black-hole and white-hole analogues. Their calculated pairs would be separable from the pump by polarisation and by an octave in frequency, outside the phase-matching conditions of ordinary four-wave mixing. The paper proposes detecting both partners and testing their correlations; it does not report that measurement.Paragraphs 11 to 13
The Hawking temperature in this system does not depend on the size of the refractive-index change, only on how steeply it varies with retarded time — so even the tiny index changes of nonlinear fibre optics give a substantial temperature. Taking the steepness of the self-steepened optical shock front as comparable to twice the carrier frequency, 8 times ten to the fourteen hertz, the calculated temperature reaches about a thousand kelvin, many orders of magnitude above the condensed-matter analogues.Eq. (8) and the two closing paragraphs
The way in
https://doi.org/10.1126/science.1153625How to cite it
Thomas G. Philbin, Chris Kuklewicz, Scott Robertson, Stephen Hill, Friedrich König, Ulf Leonhardt (2008) Fiber-Optical Analog of the Event Horizon doi:10.1126/science.1153625