Prof. Xiang Zhang's Laboratory

at UC Berkeley

Site Updated:
10/24/2009

Mimicking celestial motion with optical metamatgerials

In general relativity, the existence of matter-energy densities results in curves space-time, and light follows the geodesic line.  On the other hand, the mapping between a real space and a curved virtual space can be realized by spatially designing the optical properties of an optical medium, one example is the invisible cloaking. Thus, an equivalence of light trajectories can be established between the curved space in the general relativity and spatially engineered inhomogenous optical medium, namely metamaterials. With this equivalence, we can study celestial phenomena using table-top experiments with spatially engineered optical metamaterials.

1. Optical black hole
The most interesting phenomena associated with the general relativity are the black holes. A black hole is defined as a spatial region where space and time are distorted in such a way nothing (including light) can escape. There are several interesting phenomena associated with black holes, such as event horizon, photon sphere and optical scattering. While the mimic of event horizon in an optical metamaterial requires extreme optical properties (index goes to infinity), and is difficult to realize, we show that with engineered dielectric metamaterials, it is possible to reproduce photon sphere and the scattering properties of a black hole.
 

Fig. 1 (a) Index profile of an optical black hole (b, c) ray tracing and full wave simulation
of light incident onto the photon sphere.

An index profile given in Fig. 1(a) leads to the similar phenomenon as the photon sphere in a black hole. The light rays with a specific impact parameter approach a circle asymptotically, as verified by a ray tracing in Fig. 1(b) and a full wave simulation in Fig. 1(c). Since the refractive index profile is finite, it can be realized with nano engineered composite material systems consisting of semiconductor (such as GaAs) and air.

2. Continuous index photon traps
With photonic metamaterials, we can also investigate other interesting applications. Here we propose a continous index photon traps (CIPT). In CIPT, the index profile is designed to support confined and stable photon motion, though not necessarily closed (Fig. 2). A general formulae for such a profile is given by,

 

where c(r) is an arbitrary monotonously decreasing function. The CIPT does not have an interface, or boundary, and it can eliminates completely the radiation loss, as in contrast to the well known whispering gallery mode cavity. Since CIPT is stable against perturbations, it can have a very large quality factor that is only limited by the material loss. This opens way to a completely new design towards extremely high Q cavities.

 

 

Fig. 2 FDFD simulations of bound and stable light propagation in a CIPT, a circular orbit
 with period 2p (left)  and a ‘Rosetta’ type of orbit with period 4p.
                    

Dentcho A. Genov, Shuang Zhang and Xiang Zhang, "Mimicking celestial mechanics in metamaterials" Nature Physics, Vol. 5, 687, 2009 view pdf

 

 

 
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