arXiv subjects
Publications and source records attributed to Ulf Leonhardt.
Exact time-dependent solutions of Maxwell's equations in Maxwell's fish eye show that perfect imaging is not an artifact of a drain at the image, although a drain is required for subwavelength resolution.
Imaging with a spherical mirror in empty space is compared with the case when the mirror is filled with the medium of Maxwell's fish eye. Exact time-dependent solutions of Maxwell's equations show that perfect imaging is not achievable with an electrical ideal mirror on its own, but with Maxwell's fish eye in the regime when it implements a curved geometry for full electromagnetic waves.
We demonstrate perfect imaging in Maxwell's fish eye for microwaves. Our data show that the field of a line source is imaged with subwavelength resolution over superwavelength distances, provided the field is allowed to leave through passive outlets that play the role of a detector array in imaging.
If quantum friction existed [J.B. Pendry, New J. Phys. 12, 033028 (2010)] an unlimited amount of useful energy could be extracted from the quantum vacuum and Lifshitz theory would fail. Both are unlikely to be true.
Maxwell's fish eye has been known to be a perfect lens within the validity range of ray optics since 1854. Solving Maxwell's equations we show that the fish-eye lens in three dimensions has unlimited resolution for electromagnetic waves.
Perfect imaging has been believed to rely on negative refraction, but here we show that an ordinary positively-refracting optical medium may form perfect images as well. In particular, we establish a mathematical proof that Maxwell's fish eye in two-dimensional integrated optics makes a perfect instrument with a resolution not limited by the wavelength of light. We also show how to modify the fish eye such that perfect imaging devices can be made in practice. Our method of perfect focusing may also find applications outside of optics, in acoustics, fluid mechanics or quantum physics, wherever waves obey the two-dimensional Helmholtz equation.
In the field of transformation optics, metamaterials mimic the effect of coordinate transformations on electromagnetic waves, creating the illusion that the waves are propagating through a virtual space. Transforming space by appropriately designed materials makes devices possible that have been deemed impossible. In particular, transformation optics has led to the demonstration of invisibility cloaking for microwaves, surface plasmons and infrared light. Here we report the achievement of another "impossible task". We implement, for microwaves, a device that would normally require a dielectric singularity, an infinity in the refractive index. We transmute a singularity in virtual space into a mere topological defect in a real metamaterial. In particular, we demonstrate an omnidirectional retroreflector, a device for faithfully reflecting images and for creating high visibility, from all directions. Our method is robust, potentially broadband and similar techniques could be applied for visible light.
Non-Euclidean geometry combined with transformation optics has recently led to the proposal of an invisibility cloak that avoids optical singularities and therefore can work, in principle, in a broad band of the spectrum [U. Leonhardt and T. Tyc, Science 323, 110 (2009)]. Such a cloak is perfect in the limit of geometrical optics, but not in wave optics. Here we analyze, both analytically and numerically, full wave propagation in non-Euclidean cloaking. We show that the cloaking device performs remarkably well even in a regime beyond geometrical optics where the device is comparable in size with the wavelength. In particular, the cloak is nearly perfect for a spectrum of frequencies that are related to spherical harmonics. We also show that for increasing wavenumber the device works increasingly better, approaching perfect behavior in the limit of geometrical optics.
Metamaterials are beginning to transform optics and microwave technology thanks to their versatile properties that, in many cases, can be tailored according to practical needs and desires. Although metamaterials are surely not the answer to all engineering problems, they have inspired a series of significant technological developments and also some imaginative research, because they invite researchers and inventors to dream. Imagine there were no practical limits on the electromagnetic properties of materials. What is possible? And what is not? If there are no practical limits, what are the fundamental limits? Such questions inspire taking a fresh look at the foundations of optics and at connections between optics and other areas of physics. In this article we discuss such a connection, the relationship between optics and general relativity, or, expressed more precisely, between geometrical ideas normally applied in general relativity and the propagation of light, or electromagnetic waves in general, in materials. We also discuss how this connection is applied: in invisibility devices, perfect lenses, the optical Aharonov-Bohm effect of vortices and in analogues of the event horizon.
We show how transformation media can make a superantenna that is either completely invisible or focuses incoming light into a needle-sharp beam. Our idea is based on representating three-dimensional space as a foliage of sheets and performing two-dimensional conformal maps on each sheet
The production of Hawking radiation by a single horizon is not dependent on the high-frequency dispersion relation of the radiated field. When there are two horizons, however, Corley and Jacobson have shown that superluminal dispersion leads to an amplification of the particle production in the case of bosons. The analytic theory of this "black hole laser" process is quite complicated, so we provide some numerical results in the hope of aiding understanding of this interesting phenomenon. Specifically, we consider sonic horizons in a moving fluid. The theory of elementary excitations in a Bose-Einstein condensate provides an example of "superluminal" (Bogoliubov) dispersion, so we add Bogoliubov dispersion to Unruh's equation for sound in the fluid. A white-hole/black-hole horizon pair will then display black hole lasing. Numerical analysis of the evolution of a wave packet gives a clear picture of the amplification process. By utilizing the similarity of a radiating horizon to a parametric amplifier in quantum optics we also analyze the black hole laser as a quantum-optical network.
The conversion of positive-frequency waves into negative-frequency waves at the event horizon is the mechanism at the heart of the Hawking radiation of black holes. In black-hole analogues, horizons are formed for waves propagating in a medium against the current when and where the flow exceeds the wave velocity. We report on the first direct observation of negative-frequency waves converted from positive-frequency waves in a moving medium. The measured degree of mode conversion is significantly higher than expected from theory.
The physics at the event horizon resembles the behavior of waves in moving media. Horizons are formed where the local speed of the medium exceeds the wave velocity. We use ultrashort pulses in microstructured optical fibers to demonstrate the formation of an artificial event horizon in optics. We observed a classical optical effect, the blue-shifting of light at a white-hole horizon. We also show by theoretical calculations that such a system is capable of probing the quantum effects of horizons, in particular Hawking radiation.
We explain the theory behind our fiber-optical analogue of the event horizon and present the experiment in detail.
Transformation media are at the heart of invisibility devices, perfect lenses and artificial black holes. In this paper, we consider their quantum theory. We show how transformation media map quantum electromagnetism in physical space to QED in empty flat space.
In electrical engineering metamaterials have been developed that offer unprecedented control over electromagnetic fields. Here we show that general relativity lends the theoretical tools for designing devices made of such versatile materials. Given a desired device function, the theory describes the electromagnetic properties that turn this function into fact. We consider media that facilitate space-time transformations and include negative refraction. Our theory unifies the concepts operating behind the scenes of perfect invisibility devices, perfect lenses, the optical Aharonov-Bohm effect and electromagnetic analogs of the event horizon, and may lead to further applications.
As a consequence of the wave nature of light, invisibility devices based on isotropic media cannot be perfect. The principal distortions of invisibility are due to reflections and time delays. Reflections can be made exponentially small for devices that are large in comparison with the wavelength of light. Time delays are unavoidable and will result in wave-front dislocations. This paper considers invisibility devices based on optical conformal mapping. The paper shows that the time delays do not depend on the directions and impact parameters of incident light rays, although the refractive-index profile of any conformal invisibility device is necessarily asymmetric. The distortions of images are thus uniform, which reduces the risk of detection. The paper also shows how the ideas of invisibility devices are connected to the transmutation of force, the stereographic projection and Escheresque tilings of the plane.
Invisibility devices exploit ambiguities in the inverse scattering problem of light in media. Scattering also serves as an important general tool to infer information about the structure of matter. We elucidate the nature of scattering ambiguities that arise in central potentials. We show that scattering is a tomographic projection: the integrated scattering angle is a projection of a scattering function onto the impact parameter. This function depends on the potential, but may be multi-valued, allowing for ambiguities where several potentials share the same scattering data. In addition, multivalued scattering angles also lead to ambiguities. We apply our theory to show that it is in principle possible to construct an invisibility device without infinite phase velocity of light.