Negative refraction and positive refraction are not Lorentz covariant

Refraction into a half-space occupied by a pseudochiral omega material moving at constant velocity was studied by directly implementing the Lorentz transformations of electric and magnetic fields. Numerical studies revealed that negative refraction, negative phase velocity and counterposition are not Lorentz-covariant phenomenons in general.     

Negative refraction in photonic crystals

We demonstrate that light propagation in strongly modulated 2D/3D photonic crystals (PhCs) becomes refraction-like in the vicinity of the photonic bandgap, which is contrary to the fact that light propagation in weakly modulated PhCs is very different from refraction and thus the definition of refraction index becomes meaningless. Such a crystal behaves like a material having an effective refractive index controllable by the band structure. This situation is analogous to the effective-mass approximation in electron-band theory. The propagation states having a negative effective index exhibit unusual properties, such as mirror-like imaging effect, image-transfer effect. These properties are confirmed by finite-difference time-domain simulations.     

Negative refraction and energy flow

The conditions for negative refraction are examined in a medium with complex permittivity and permeability. The direction of the wave is taken to be in the direction of the Poynting vector, and it is shown that the condition for negative refraction is that the real part of the permeability must be negative. PACS 41.20.Jb; 42.15.Dp     

Negative refraction in ferromagnet-superconductor superlattices

Negative refraction, which reverses many fundamental aspects of classical optics, can be obtained in systems with negative magnetic permeability and negative dielectric permittivity. This Letter documents an experimental realization of negative refraction at millimeter waves, finite magnetic fields, and cryogenic temperatures utilizing a multilayer stack of ferromagnetic and superconducting thin films. In the present case the superconducting YBa2Cu3O7 layers provide negative permittivity while negative permeability is achieved via ferromagnetic (La:Sr)MnO3 layers for frequencies and magnetic fields close to the ferromagnetic resonance. In these superlattices the refractive index can be switched between positive and negative regions using external magnetic field as tuning parameter.     

Negative refraction in two-dimensional photonic crystals

We present some of our recent results for negative refraction in photonic crystals. The concept of negative refraction in photonic crystals is firstly introduced. Then, the propagation of electromagnetic waves in photonic crystals is systematically studied. By the layer Korringa–Kohn–Rostoker method, the coupling efficiency between external plane waves and the Bloch waves in photonic crystals is investigated. It is found that the coupling coefficient is highly angular dependent even for an interface between air with n=1 and a photonic crystal with effective index n_eff=-1. It is also shown that, for point imaging by a photonic crystal slab, owing to the negative refraction, the influence of the surface termination on the transmission and the imaging quality is significant. Finally, we present results experimentally demonstrating negative refraction in a two-dimensional photonic crystal at optical communication wavelengths. PACS 42.70.Qs; 41.85.Ct; 42.30.Va     

Negative refraction makes a perfect lens

With a conventional lens sharpness of the image is always limited by the wavelength of light. An unconventional alternative to a lens, a slab of negative refractive index material, has the power to focus all Fourier components of a 2D image, even those that do not propagate in a radiative manner. Such "superlenses" can be realized in the microwave band with current technology. Our simulations show that a version of the lens operating at the frequency of visible light can be realized in the form of a thin slab of silver. This optical version resolves objects only a few nanometers across.     

Negative refraction of ultra-short electromagnetic pulses

We study pulse propagation across a boundary that separates an ordinary medium from a medium with simultaneously negative dielectric permittivity and magnetic permeability. Solving Maxwell’s equations with two spatial coordinates (one longitudinal, one transverse) and time we find negative refraction as the wave packet undergoes significant and unusual shape distortions. The pulse acquires and maintains a chirp as it traverses the interface, as expected, but with a sign that is opposite to the chirp attained upon traversal into a positive-index material. Both a direct calculation of the spatial derivative of the instantaneous, local phase of the pulse and a Fourier analysis of the signal reveal the same inescapable fact: that inside a negative-index material, a transmitted, forward-moving wave packet is indeed a superposition of purely negative wave vectors. The central findings of this paper are a confirmation that causality is not violated in the short-pulse regime, and that energy and group velocities never exceed the speed of light in vacuum.     

Negative refraction at various crystal interfaces

In an anisotropic positive index media the tangential components of Poynting vector S and that of wavevector k can have the opposite signs under certain conditions. The phenomenon is called as the anomalous negative refraction. The negative refraction phenomenon at planar interfaces between isotropic medium-crystal and crystal-crystal media has been analyzed. The crystals can be both uniaxial axis and biaxial axis and the azimuth of optical axis can be arbitrary. The negative refraction phenomenon under various azimuth of optical axis is analyzed. The phenomena can be very evident if the optical axis angle is arranged appropriately. The optimal conditions are obtained. For strong anisotropy crystal, the maximum incident angle that yields the negative refraction and the bending angle could be very large. For the interface of biaxial crystal the anisotropy parameter of crystal u₁ = n_z/n_x plays a dominant role in effect on negative refraction.     

Negative refraction in one-dimensional plasma photonic crystals

We have theoretically explored the negative refraction (NR) in one-dimensional plasma photonic crystals (PCs) consisting of plasma and dielectric materials. By using the transfer matrix method and Bloch theorem, we have studied the group velocity and we have obtained the NR in plasma PCs with the help of the group velocity. The results show that plasma PCs can also exhibit the NR although they have a periodically modulated positive permittivity ? and permeability μ. It is also shown that the NR in plasma PCs exhibits difference behaviour in different frequency regions, ω < ω_p and ω > ω_p, respectively. The parameter dependence of the effects is also examined and discussed.     

Negative index of refraction in optical metamaterials

A double-periodic array of pairs of parallel gold nanorods is shown to have a negative refractive index in the optical range. Such behavior results from the plasmon resonance in the pairs of nanorods for both the electric and the magnetic components of light. The refractive index is retrieved from direct phase and amplitude measurements for transmission and reflection, which are all in excellent agreement with simulations. Both experiments and simulations demonstrate that a negative refractive index n' approximately -0.3 is achieved at the optical communication wavelength of 1.5 microm using the array of nanorods. The retrieved refractive index critically depends on the phase of the transmitted wave, which emphasizes the importance of phase measurements in finding n'.     

Negative refraction in a honeycomb-lattice photonic crystal

In this paper we theoretically investigate a photonic crystal with dielectric rods in a honeycomb lattice. Two left-handed frequency regions are found in the second and third photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Subwavelength imaging by the photonic crystal flat lens are systematically studied by numerical simulations using the multiple scattering method. Different from the photonic crystals with noncircular dielectric rods in air, this structure is almost isotropic at the optimal frequency for superlensing. As a comparison, flat slab focusing is also demonstrated at other frequencies in the two left-handed regions.     

Negative refraction based on purely imaginary metamaterials

By introducing a new mechanism based on purely imaginary metamaterials (PIMs), we reveal that bidirectional negative refraction and planar focusing can be obtained using a pair of PIM slabs, overcoming the unidirectional limit in parity-time (PT)-symmetric systems. Compared with PT-symmetric systems, which require two different types of materials, the proposed negative refraction can be realized using two identical media. In addition, asymmetric excitation with bidirectional total transmission is observed in our PIM system. Therefore, a new way to realize negative refraction with properties that are unavailable in PT-symmetric systems is presented.     

Negative optical refraction in crystals with strong birefringence

The possibility of negative optical refraction of the extraordinary ray in crystals with strong birefringence is demonstrated.     

Negative refraction of complex lattices of dielectric cylinders

Some photonic crystals (PCs) consisting of complex lattices of dielectric cylinders can have an effective refraction index (neff$n_{\mathrm{eff}}$) of −1. Subwavelength imaging by a slab of a honeycomb PC of dielectric cylinders with neff=−1$n_{\mathrm{eff}}=-1$ is investigated and an open resonator with a quality factor higher than 3000 is designed with the same PC. Air–PC interfaces with low reflection are also used for the slab lens and open resonator.     

Negative refraction and dispersion phenomena in platonic clusters

We consider the problem of Gaussian beam scattering by finite arrays of pinned points, or platonic clusters, in a thin elastic plate governed by the biharmonic plate equation. Integral representations for Gaussian incident beams are constructed and numerically evaluated to demonstrate the different behaviours exhibited by these finite arrays. We show that it is possible to extend the scattering theory from infinite arrays of pinned points to these finite crystals, which exhibit the predicted behaviour well. Analytical expressions for the photonic superprism parameters p, q and r, which are measures for dispersion inside the crystal, are also derived for the pinned plate problem here. We demonstrate the existence of negative refraction, beam splitting, Rayleigh anomalies, internal reflection, and near-trapping on the first band surface, giving examples for each of these behaviours.     

十二重准晶光子结构中的负折射与成像

最近实验证明周期性的光子晶体中存在电磁波的负折射现象,并且观测到亚波长成像.然而,这些研究主要集中在周期性结构中,对非周期结构的研究还没有相关的报道.文章报道了一种新的理论和实验结果：非周期性十二重准晶光子结构同样存在负折射,并且可以实现超透镜的远场成像.具有这些特性的光子准晶可以广泛的应用于光集成器件中.     

十二重准晶光子结构中的负折射与成像

最近实验证明周期性的光子晶体中存在电磁波的负折射现象，并且观测到亚波长成像．然而，这些研究主要集中在剧期性结构中，对非周期结构的研究还没有相关的报道。文章报道了一种新的理论和实验结果：非周期性十二重准晶光子结构同样存在负折射，并且可以实现超透镜的远场成像。具有这些特性的光子准晶可以广泛的应用于光集成器件中。     

Negative refraction and left-handed properties in two-dimensional photonic crystals

We report on the negative refraction and left-handed behavior of two-dimensional photonic crystals. For the triangular two-dimensional photonic crystals there are two saddle points and a key point in the first Brillouin zone for the second band, which play important role to determine the refraction phenomena. There is no determined relation between the left-handed behavior and the negative refraction. The refraction phenomena depend on the band structure and the configuration of the incident light. For the first configuration, the first Brillouin zone can be divided into three parts. In part I there are negative refraction and left-handed behaviors. In part II there are normal refraction and left-handed behaviors. In part III there are normal refraction and right-handed behaviors. For the second configuration, the first Brillouin zone can only be divided into two parts. For these complex refraction phenomena, it is meaningless to define the phase refractive index, and it is necessary to define the effective refraction index by a Snell-like formula, and the value of the effective index is determined by the configuration and the band structure.     

Negative refraction of low‐frequency electromagnetic waves

Features of anomalous refraction of low‐frequency electromagnetic waves are investigated in all‐semiconductor nonmagnetic superlattices with a periodic array of two‐dimensional electron gas layers under quantum Hall effect conditions. We show that the structure exhibits negative refraction on the lateral surface for all angles of incidence, in the frequency region which has no limitation from the low‐frequency side, and that for such intriguing properties it requires no resonance frequency and no negative component of the permittivity tensor. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)