6.4 Fibre-optic models

A recent implementation of analogue models based on electrodynamics is that based on fibre-optic engineering [504Jump To The Next Citation Point, 505Jump To The Next Citation Point]. The basic idea in this case is to use long dispersive light pulses (solitons), generated with a suitable laser, to create a propagating front at which the refractive index of the fibre changes suddenly (albeit by a small amount). Basically, the refractive index of the fibre, n0, acquires a time- and position-dependent correction δn, which is proportional to the instantaneous pulse intensity I at a give space-time position, δn ∝ I(t,x ). The wavefront at which this change in the refractive index occurs will move naturally at a speed close to the speed of light (and fibre optic engineering allows one to control this feature). If one now sends a continuous wave of light, what we might call a probe, along the fibre in such a manner that the probe group velocity in the fibre is arranged to be slightly larger than the pulse group velocity, then it will be possible to obtain horizon-like effects. In fact, as the probe wave reaches the back of the pulse, the increase in the refractive index will slow it down, until the probe group velocity will match the pulse one. Effectively, the rear end of the pulse will act as a white hole for the probe wave. Similarly, there will be a point on the front side of the pulse where the two group velocities will match. This will be the equivalent of a black-hole horizon for the probe wave. In [504, 505] the behaviour of the probe waves at the pulse was investigated, and it was shown for the white hole case that the expected classical behaviour is theoretically reproduced. Since this behaviour lies at the core of the mechanism responsible for the mode conversion underlying the Hawking effect, it is then expected that the quantum counterpart should also be reproducible in this manner. Indeed, very recently Belgiorno et al. have reported experimental detection of photons from a black-hole–white-hole configuration possessing a “phase velocity horizon” [66Jump To The Next Citation Point]. The underlying theory behind their specific experiment is considered in [63, 64].
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