Optical black hole lasers

Arxiv – Optical black hole lasers (14 pages) You can amplify light by bouncing it between the horizons of a black hole and a white hole. Now physicists have worked out how to build such a device in the lab.

Their real triumph, however, is in showing how such a device could be made in the lab. They point out that the refractive index of certain materials depends on the intensity of light inside them. So the light itself changes the refractive index.

That means a very intense beam can create a huge gradient in the refractive index. This gradient can be so steep that it behaves like an event horizon. In fact, a single pulse can create black hole horizon at its leading edge and a white hole horizon at its trailing edge.

That’s exactly the condition these guys are looking for. They go on to say that it ought to be possible to do this in optical waveguides made of diamond. They’ve tested the idea numerically and say it works as expected.

Faccio and co are quick to point out that it is possible to grow diamond into more or less any shape so it ought to be possible to test this idea in the lab now. “This would therefore seem to indicate that this kind of novel amplification process could be observed in real settings,” they say.

That would be an extraordinary experiment– a black hole laser in a lab.

Using numerical simulations we show how to realize an optical black hole laser, i.e. an ampli fier formed by traveling refractive index perturbations arranged so as to trap light between a white and a black hole horizon. The simulations highlight the main features of these lasers: the growth inside the cavity of positive and negative frequency modes accompanied by a weaker emission of modes that occurs in periodic bursts corresponding to the cavity round trips of the trapped modes. We then highlight a new regime in which the trapped mode spectra broaden until the zero-frequency points on the dispersion curve are reached. Ampli fication at the horizon is highest for zero-frequencies, therefore leading to a strong modifi cation of the structure of the trapped light. For su fficiently long propagation times, lasing ensues only at the zero frequency modes.

We have numerically analysed the possibility of observing black hole lasing using laser-pulse induced (or optical) horizons. The general behaviour of the black-white hole horizon cavity is very similar to the behaviour of similar cavities studied theoretically and numerically in Bose-Einstein condensates. Our numerical simulations have been carried out over longer propagation distances (i.e. larger number of cavity round-trips) with respect to previous studies and highlight the onset of a regime in which the cavity leads to a broadening of the mode spectra until the two comoving zero-frequency modes are excited (in the laboratory frame, one mode lies at zero-frequency, the other lies in the visible or ultraviolet region, depending on the specifi c dispersion relation of the medium). Due to the 1=!0 dependence of the horizon ampli fication, the zero-frequency modes oscillate in the cavity with a much higher gain. These findings are summarised in the accompanying video animation that shows the evolution of the typical situation studied here: the initial optical pulse seeded in to the cavity is actually much shorter than the cavity itself (diff erently from typical cases studied so far in which the cavity length was of the same order of the input wavelength) and bounces back and forth until the zero-frequency modes take over and completely fills the cavity.

Our numerical simulations treat the case of a coherently seeded laser. Naturally, one would expect that if the laser were to be seeded by vacuum fluctuations, then most certainly laser oscillation would occur at the zero-frequency modes as these have the highest gain and lowest lasing threshold.

A remarkable and unique feature of black hole lasers is the coupling between the very low frequency and very high frequency components of the electromagnetic spectrum. However, more complicated dispersion relations that include also resonances at certain wavelengths are expected to complicate this picture although a full model that includes losses due to material absorption would be required in order to correctly model such a situation.

These simulations underline the fact that an experimental demonstration of black hole
lasing, although not simple may not be as far-fetched as one may think. Refractive
index perturbations of the order of 0.005 (or smaller) will give rise to signi ficant gain over distances of the order of 1 cm. The dispersion relation used in this work is very close to that of diamond, a material that is now widely used and can be shaped in to optical waveguides. Diamond exhibits not only a very simple dispersion curve but (as a consequence of this) also a remarkably wide transparency range that could easily sustain the zero-frequency amplifi cation regime reported here. The laser cavity, i.e. the black and white hole horizons could be generated by focusing for example two independent and ultrashort laser pulses, e.g. at 800 nm wavelength: each pulse would create an through the nonlinear Kerr eff ect and the relative delay between the two pulses would allow to control the laser cavity length. The main challenge would be to find a condition (laser wavelengths, durations, energies) such that the rising and falling edges of the laser pulses that form the horizons are maintained shorter than about 3 microns for significantly long propagation distances, e.g. more than 1 to 2 mm. Future studies will hopefully unravel other settings or combinations of materials and wavelengths that may indeed lead to the first experimental black hole laser. In the meantime, this remains a fascinating scenario in which to combine technologies and ideas developed in the area of photonics to the study of owing media and horizon physics.

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