We present experimental scattering data at microwave frequencies on a structured metamaterial that exhibits a frequency band where the effective index of refraction (n) is negative. The material consists of a two-dimensional array of repeated unit cells of copper strips and split ring resonators on interlocking strips of standard circuit board material. By measuring the scattering angle of the transmitted beam through a prism fabricated from this material, we determine the effective n, appropriate to Snell's law. These experiments directly confirm the predictions of Maxwell's equations that n is given by the negative square root of epsilon.mu for the frequencies where both the permittivity (epsilon) and the permeability (mu) are negative. Configurations of geometrical optical designs are now possible that could not be realized by positive index materials.

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Experimental Verification of a Negative Index of Refraction

The unprecedented ability of nanometallic (that is, plasmonic) structures to concentrate light into deep-subwavelength volumes has propelled their use in a vast array of nanophotonics technologies and research endeavours. Plasmonic light concentrators can elegantly interface diffraction-limited dielectric optical components with nanophotonic structures. Passive and active plasmonic devices provide new pathways to generate, guide, modulate and detect light with structures that are similar in size to state-of-the-art electronic devices. With the ability to produce highly confined optical fields, the conventional rules for light-matter interactions need to be re-examined, and researchers are venturing into new regimes of optical physics. In this review we will discuss the basic concepts behind plasmonics-enabled light concentration and manipulation, make an attempt to capture the wide range of activities and excitement in this area, and speculate on possible future directions.

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Plasmonics for extreme light concentration and manipulation.

The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

Artificially engineered metamaterials are now demonstrating unprecedented electromagnetic properties that cannot be obtained with naturally occurring materials. In particular, they provide a route to creating materials that possess a negative refractive index and offer exciting new prospects for manipulating light. This review describes the recent progress made in creating nanostructured metamaterials with a negative index at optical wavelengths, and discusses some of the devices that could result from these new materials.

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Optical negative-index metamaterials

Optical antennas are devices that convert freely propagating optical radiation into localized energy, and vice versa. They enable the control and manipulation of optical fields at the nanometre scale, and hold promise for enhancing the performance and efficiency of photodetection, light emission and sensing. Although many of the properties and parameters of optical antennas are similar to their radiowave and microwave counterparts, they have important differences resulting from their small size and the resonant properties of metal nanostructures. This Review summarizes the physical properties of optical antennas, provides a summary of some of the most important recent developments in the field, discusses the potential applications and identifies the future challenges and opportunities.

Antennas for light

The resolution achievable by optical imaging is limited by the wavelength of the light used — the diffraction limit. Near-field scanning optical microscopy circumvents this limit by using a probe smaller than the wavelength of the incident light to map out the electromagnetic field at the sample surface, allowing a resolution well beyond the diffraction limit. Now a variant of this technique has been developed that does away with external illumination altogether. The new technique, called thermal radiation scanning tunnelling microscopy or TRSTM, makes use of the thermal infrared emissions from the sample itself. Think of it as a near-field equivalent of a night-vision camera. In standard near-field scanning optical microscopy (NSOM), a subwavelength probe acts as an optical ‘stethoscope’ to map the near field produced at the sample surface by external illumination1. This technique has been applied using visible1,2, infrared3, terahertz4 and gigahertz5,6 radiation to illuminate the sample, providing a resolution well beyond the diffraction limit. NSOM is well suited to study surface waves such as surface plasmons7 or surface-phonon polaritons8. Using an aperture NSOM with visible laser illumination, a near-field interference pattern around a corral structure has been observed9, whose features were similar to the scanning tunnelling microscope image of the electronic waves in a quantum corral10. Here we describe an infrared NSOM that operates without any external illumination: it is a near-field analogue of a night-vision camera, making use of the thermal infrared evanescent fields emitted by the surface, and behaves as an optical scanning tunnelling microscope11,12. We therefore term this instrument a ‘thermal radiation scanning tunnelling microscope’ (TRSTM). We show the first TRSTM images of thermally excited surface plasmons, and demonstrate spatial coherence effects in near-field thermal emission.

Thermal radiation scanning tunnelling microscopy

We describe methods of investigating the behavior of photonic crystals. Our approach establishes a link between the dispersion relation of the Bloch modes for an infinite crystal (which describes the intrinsic properties of the photonic crystal in the absence of an incident field) and the diffraction problem of a grating (finite photonic crystal) illuminated by an incident field. We point out the relationship between the translation operator of the first problem and the transfer matrix of the second. The eigenvalues of the transfer matrix contain information about the dispersion relation. This approach enables us to answer questions such as When does ultrarefraction occur? Can the photonic crystal simulate a homogeneous and isotropic material with low effective index? This approach also enables us to determine suitable parameters to obtain ultrarefractive or negative refraction properties and to design optical devices such as highly dispersive microprisms and ultrarefractive microlenses. Rigorous computations add a quantitative aspect and demonstrate the relevance of our approach.

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Anomalous refractive properties of photonic crystals

We describe an approach for converting reflection coefficients of any structure into colors, taking into account human color perception. This procedure is applied to the study of the colors reflected by Morpho rhetenor butterflies wings. The scales of these wings have a tree-like periodic structure which is modeled with the help of a rigorous lamellar grating electromagnetic theory. In this way, we are able to determine the colors reflected by the wing under various illumination conditions.

Morpho butterflies wings color modeled with lamellar grating theory

An electromagnetic study of the staircase approximation of arbitrary shaped gratings is conducted with three different grating theories. Numerical results on a deep aluminum sinusoidal grating show that the staircase approximation introduces sharp maxima in the local field map close to the edges of the profile. These maxima are especially pronounced in TM polarization and do not exist with the original sinusoidal profile. Their existence is not an algorithmic artifact, since they are found with different grating theories and numerical implementations. Since the number of the maxima increases with the number of the slices, a greater number of Fourier components is required to correctly represent the electromagnetic field, and thus a worsening of the convergence rate is observed. The study of the local field map provides an understanding of why methods that do not use the staircase approximation (e.g., the differential theory) converge faster than methods that use it. As a consequence, a 1% accuracy in the efficiencies of a deep sinusoidal metallic grating is obtained 30 times faster when the differential theory is used in comparison with the use of the rigorous coupled-wave theory. A theoretical analysis is proposed in the limit when the number of slices tends to infinity, which shows that even in that case the staircase approximation is not well suited to describe the real profile.

/pdf/staircase-approximation-validity-for-arbitrary-shaped-4rrki3usas.pdf

Staircase approximation validity for arbitrary-shaped gratings.

We propose an approach for the design of resonant cavities employed in magnetophotonic crystal (MPC) circulators and isolators. Starting from the analysis of a model circularly symmetric cavity, we show how to obtain a significant splitting of the eigenfrequencies of the two counterrotating cavity modes without introducing subdomains magnetized in opposite directions. Using the multiple-scattering method extended to handle uniaxial gyrotropic materials, we demonstrate numerically an MPC circulator working in a uniform external magnetic field.

Boris Gralak

Papers

Thermal radiation scanning tunnelling microscopy

Anomalous refractive properties of photonic crystals

Morpho butterflies wings color modeled with lamellar grating theory

Staircase approximation validity for arbitrary-shaped gratings.

Magneto-optical circulator designed for operation in a uniform external magnetic field