Analogue of the Event Horizon in Fibers

Abstract

In 1974 Stephen Hawking predicted that gravitational black holes would emit thermal radiation and decay (Hawking, 1974). This radiation, emitted from an area called the event horizon, is since known as Hawking radiation. To date it is still one of the most intriguing physical effects and bears great importance for the development of a quantum theory of gravity, cosmology and high energy physics. The Hawking effect is one of a rich class of quantum properties of the vacuum (Birrell & Davies, 1984; Brout et. al., a; Milonni, 1994). For example, in the Unruh effect (Moore, 1970; Fulling, 1973; Davies, 1975; DeWitt, 1975; Unruh, 1976), an accelerated observer perceives the Minkowski vacuum as a thermal field. The physics of Hawking radiation leaves us with fascinating questions about the laws of nature at transplanckian scales, the conservation of information and physics beyond the standard model. Because of the thermal nature of the radiation, it is characterized by a temperature, the Hawking temperature. For stable astronomical black holes this lies far below the temperature of the cosmic microwave background, such that an observation of Hawking radiation in astrophysics seems unlikely. Laboratory analogues of black holes have the potential to make the effect observable (Unruh, 1981; Schleich & Scully, 1984). The space-time geometry of the gravitational field can be represented in coordinates that act as an effective flow (Novello et al., 2002; Volovik, 2003; Unruh, 1981; Jacobson, 1991; Rousseaux et al., 2008). The event horizon lies where the flow velocity appears to exceed the speed of light in vacuum. Analogue systems are thus inspired by the following intuitive idea (Unruh, 1981): the black hole resembles a river (Jacobson, 1991; Rousseaux et al., 2008), a moving medium flowing towards a waterfall, the singularity. Imagine that the river carries waves propagating against the current with speed c’. The waves play the role of light where c’ represents c, the speed of light in vacuum. Suppose that the closer the river gets to the waterfall the faster it flows and that at some point the speed of the river exceeds c’. Clearly, beyond this point no wave can propagate upstream anymore. The point of no return is the horizon. In this chapter we are explaining a recent approach to the realization of an event horizon in optics (Philbin et. al, 2008). We start by describing the propagation of light in optical fibers and show the analogy to a curved space-time geometry. In Sec. 4 we quantize the field equation and give a Hamiltonian. Then we can use the geometrical optics approximation in Sec. 5 to find the behavior of light at a horizon, before we describe the scattering process that Source: Advances in Lasers and Electro Optics, Book edited by: Nelson Costa and Adolfo Cartaxo, ISBN 978-953-307-088-9, pp. 838, April 2010, INTECH, Croatia, downloaded from SCIYO.COM