Negative refraction using plasmonic structures that are atomically flat

Broadband, all-angle negative refraction (AANR) effects and imaging with subwavelength resolution have been analyzed in a honeycomb lattice of silicon rods in air background, as well as in the inverse structure of air holes in a silicon wafer. In the rod lattice, it was possible to obtain AANR effects for transverse-magnetic (TM) polarization in the second band (TM2) with a bandwidth as large as ∼23% after optimizing the ratio of feature size to the lattice constant as 0.44 and a super-lensing effect with a binary coherent source resolution of 0.68λ. On the other hand, the hole lattice shows AANR for both TM2 (bandwidth of 14%) and TE2 (bandwidth of 15.3%) bands with an additional advantage of polarization-independent AANR of 5% bandwidth. The hole lattice also shows a super-lensing behavior, which helps in imaging with a subwavelength resolution of 0.19λ for a single-point source and 0.80λ with a binary source for TM polarization while it is 0.48λ and 0.97λ, respectively, for transverse-electric (TE) polarization. The conditions for perfect imaging have been studied, and the phenomenon of dual negative refraction for both TE and TM polarization is also discussed.

Recently, negative refraction of electromagnetic waves in photonic crystals was demonstrated experimentally and subwavelength images were observed. However, these investigations all focused on the periodic structure. Here, we report a new theoretical and experimental finding that negative refraction can appear in some transparent quasicrystalline photonic structures. The photonic quasicrystals (PQCs) exhibit an effective refractive index close to $\ensuremath{-}1$ in a certain frequency window. The index shows small spatial dispersion, consistent with the nearly homogeneous geometry of the quasicrystal. More interestingly, a superlens based on the 2D PQCs can form a non-near-field subwavelength image whose position varies with the source distance. These properties make PQCs promising for application in a range of optical devices.

Recently, negative refraction of electromagnetic waves in periodic photonic crystals has been demonstrated experimentally and sub-wavelength images observed. A theoretical and experimental investigation is reported of the electromagnetic wave transport in high-symmetry photonic quasicrystals (QCs). It is shown that negative refraction can appear in these transparent quasicrystalline photonic structures. It is interesting that highly symmetric two-dimensional photonic QCs possess a universal feature for non-near-field focus of two kinds of polarized waves (S wave and P wave). That is, the non-near-field focus for two kinds of polarized waves can be realized by using flat lenses, which consist of some high-symmetric two-dimensional photonic QCs with the same structures and parameters. In addition, some two-dimensional and three-dimensional localized states in defect-free photonic QCs have been found. It is evident that these unusual localized states can be explored by means of electron energy loss spectroscopy.

We studied a two-dimensional square-lattice photonic crystal with all-angle negative refraction at its first band. Using this photonic crystal, we designed and fabricated a flat lens functioning as a cylindrical lens by increasing the vertical dimension of the photonic crystal. Two-dimensional finite-difference time-domain simulation validated negative refraction imaging. To perform the experiment, a microwave imaging system was built based on a vector network analyzer. Field distributions were acquired by scanning the imaging plane and object plane. The experiment demonstrated negative refraction imaging in both amplitude and phase, and obtained an image with feature size, 0.77lambda0.

We present experimental demonstrations of negative refraction and focusing of ultrasonic waves in two-dimensional phononic crystals made of stainless steel rods assembled in a triangular lattice and immersed in a liquid. Negative refraction is achieved for the range of frequencies in the second band, where the directions of the wave vector and group velocity are antiparallel to each other due to circular equifrequency contours. Negative refraction is unambiguously observed using a prism-shaped crystal. By exploiting the circular equifrequency contours in the second band, focusing of the ultrasonic field emitted by a pointlike source was demonstrated using a flat phononic crystal filled with and immersed in water. During these experiments, the importance of imaging in the regime of all angle negative refraction (AANR) was established for obtaining high-quality images. The regime of AANR was achieved in a similar flat crystal, in which the liquid inside the crystal (methanol) was different from the outside medium (water). This design resulted in matching circular equifrequency contours at the frequency of $0.55\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, implying that a flat ultrasonic lens with an effective refractive index of $\ensuremath{-}1$ was realized. By imaging a subwavelength line source with this crystal, a resolution of $0.55\ensuremath{\lambda}$ was observed, which is just above the diffraction limit.

We propose a novel method to achieve tunable plasmon focusing in graphene/photonic-crystal hybrid structure exhibiting all-angle negative refraction at terahertz frequencies. A two-dimensional photonic crystal composed of a square lattice of dielectric rods is constructed on the substrate of a graphene sheet to provide the hyperbolic dispersion relations of the graphene plasmon, giving rise to the all-angle plasmonic negative refraction. Plasmon lensing induced from the negative refraction is observed. We show that the ultracompact graphene-based system can produce sub-diffraction-limited images with the resolution significant smaller than the wavelength of the incident terahertz wave. Moreover, by adjusting the Fermi energy of the graphene, the imaging performance of the proposed system can remain almost invariant for different frequencies. Our results may find applications in diverse fields such as subwavelength spatial light manipulation, biological imaging, and so forth.

Optimization design of all-angle negative refraction phononic crystals at a specified frequency

In this dissertation, they have undertaken the challenge to understand the unusual propagation properties of the photonic crystal (PC). The photonic crystal is a medium where the dielectric function is periodically modulated. These types of structures are characterized by bands and gaps. In other words, they are characterized by frequency regions where propagation is prohibited (gaps) and regions where propagation is allowed (bands). In this study they focus on two-dimensional photonic crystals, i.e., structures with periodic dielectric patterns on a plane and translational symmetry in the perpendicular direction. They start by studying a two-dimensional photonic crystal system for frequencies inside the band gap. The inclusion of a line defect introduces allowed states in the otherwise prohibited frequency spectrum. The dependence of the defect resonance state on different parameters such as size of the structure, profile of incoming source, etc., is investigated in detail. For this study, they used two popular computational methods in photonic crystal research, the Finite Difference Time Domain method (FDTD) and the Transfer Matrix Method (TMM). The results for the one-dimensional defect system are analyzed, and the two methods, FDTD and TMM, are compared. Then, they shift their attention only to periodic two-dimensional crystals, concentrate on their band properties, and study their unusual refractive behavior. Anomalous refractive phenomena in photonic crystals included cases where the beam refracts on the ''wrong'' side of the surface normal. The latter phenomenon, is known as negative refraction and was previously observed in materials where the wave vector, the electric field, and the magnetic field form a left-handed set of vectors. These materials are generally called left-handed materials (LHM) or negative index materials (NIM). They investigated the possibility that the photonic crystal behaves as a LHM, and how this behavior relates with the observed negatively refractive phenomena. They found that in the PC system, negative refraction is neither a prerequisite nor guarantees left-handed behavior. They examined carefully the condition to obtain left-handed behavior in the PC. They proposed a wedge type of experiment, in accordance with the experiment performed on the traditional LHM, to test these conditions. They found that for certain frequencies the PC shows left-handed behavior and acts in some respects like a homogeneous medium with a negative refractive index. they used the realistic PC system for this case to show how negative refraction occurs at the interface between a material with a positive and a material with a negative refractive index. Their findings indicate that the formation of the negatively refracted beam is not instantaneous and involves a transient time. With this time-dependent analysis, they were able to address previous controversial issues about negative refraction concerning causality and the speed of light limit. Finally, they attempt a systematic study of anomalous refractive phenomena that can occur at the air-PC interface. They observe cases where only a single refracted beam (in the positive or negative direction) is present, as well as cases with birefringence. they classify these different effects according to their origin and type of propagation (left-handed or not). For a complete study of the system, they also obtain expressions for the energy and group velocities, and show their equality. For cases with very low index contrast, band folding becomes an artificiality. They discuss the validity of their findings when they move to the limit of photonic crystals with a low index modulation.

We introduce a new mechanism to realize negative refraction and planar focusing using a pair of parity-time symmetric metasurfaces. In contrast to existing solutions that achieve these effects with negative-index metamaterials or phase conjugating surfaces, the proposed parity-time symmetric lens enables loss-free, all-angle negative refraction and planar focusing in free space, without relying on bulk metamaterials or nonlinear effects. This concept may represent a pivotal step towards loss-free negative refraction and highly efficient planar focusing by exploiting the largely uncharted scattering properties of parity-time symmetric systems.

In recent years, significant attention has been attracted to hyperbolic (or indefinite) materials resulting from their extraordinary optical properties, such as all-angle negative refraction. Here, tunable biaxial hyperbolic dispersion and negative refraction were found in graphite crystal. First principles were used to calculate the permittivity of graphite in [Formula: see text]-, [Formula: see text]- and [Formula: see text]-directions, the results indicate that graphite crystals exhibit indefinite dielectric constant tensor in certain frequency range. By adjusting strain, the optical properties of materials changed, and even switched from hyperbolic to elliptical materials in some frequency. This work demonstrates the feasibility of achieving high-performance tunable biaxial natural hyperbolic materials which can be used in various ways.

Summary form only given. We report our recent progress on the negative refraction and imaging properties of 2D and 3D photonic-crystal (PC) slab lens. We have employed several theoretical and numerical tools, including plane-wave expansion method, multiple-scattering method, and finite-difference time-domain technique, to analyze the negative refraction and imaging behavior of the PC slab lens. We have found that negative refraction and superlensing effect can occur in a large variety of 2D PC structures with appropriately designed geometric and physical parameters. The crystal can be made from circular, square, rectangular, and elliptical rods. The lattice can be either square or triangular lattices, or even 12-fold quasiperiodic. The composite material can be dielectric, metallic, or metallo-dielectirc. Negative refraction can happen at the lowest or higher photonic bands. Different mechanisms can contribute to the superlensing phenomenon, such as the negative refraction and self-collimation effects. We have also carried out experimental measurement on the negative refraction and imaging properties of these PC slab lens and find good agreement with the theoretical analysis.

A design of polarization beam splitter based on negative refraction in photonic crystal is proposed. The proposed structure is formed by a hexagonal lattice of embedded air holes in silicon materials and is based on 2-D photonic band structure and equi-frequency contour calculations where negative refraction is considered to be function of incident angle and thickness of slab. The designed structure exhibits oppositely signed (negative and positive) refraction for TE and TM polarization at telecom wavelength windows. The wavelength response of the designed PBS is obtained for both polarizations.

Photonic crystals are periodic dielectric structures, where the periodicity varies on the wavelength scale. Analogous to electrons in semiconductors, the photon propagation can be described using a band structure in which transmission bands are separated by bandgaps, energy ranges at which light cannot exist inside the photonic crystals. This analogy suggests that photonic crystals may be suitable to fabricate the components needed for integrated optics. As yet most of the research done on photonic crystals has been focussed on using these bandgaps. However, many novel properties of light propagating in the transmission bands may also serve this purpose. This thesis studies theoretically and experimentally the light propagation in two dimensional planar photonic crystals with the aim of creating new components for integrated optics. A theoretical model based on Fourier analysis of electromagnetic Bloch waves was developed to describe light propagation in photonic crystals. This model gives an intuitive understanding of the novel phenomena observed in the transmission bands of the photonic crystal: negative refraction, auto-collimation and super-dispersion. This new approach clarifies the fundamental physics of these phenomena enabling their advantages and disadvantages to be easily evaluated for new optical functions; particular attention is paid to auto-collimation. The influence of the structural properties of the photonic crystal (lattice type, filling factor, etc.) is also studied and has been used to create two integrated optic components: a light condenser and a wavelength demultiplexer. The theoretical predictions have been tested experimentally on two dimensional planar photonic crystals fabricated in heterostructure GaAs/AlxGa1-xAs. The fabrication of these photonic crystals was the first experimental work undertaken in this thesis. Advanced microfabrication techniques enabled the fabrication of planar photonic close to those of the state-of-the-art. The optical properties of the fabricated photonic crystals fabricated were studied using the internal light source technique. This method uses photoluminescence generated by quantum wells or quantum dots as an internal light source to probe the optical properties of the photonic crystals. Initially the experimental setup was designed to study the bandgaps. However after some modifications the transmission bands could also be investigated. Another experimental improvement made was the introduction of a technique using coupled waveguides which reduces the losses by a factor of 10 and allowed the light in the photonic crystals to be studied over long distances. Adding a spatially resolved vertical detection, enabled the analysis of the light diffracted out of the plane in order to measure the propagation losses and to map the electromagnetic field. These two modifications were used to study components for integrated optics based on photonic crystals: waveguides and auto-collimators.

Tuning of InGaAsP planar photonic crystal nanocavities by local liquid crystal infiltration

In this article, we present an experimental and numerical study of novel optical properties of two-dimensional dielectric photonic crystals (PCs) which exhibit negative refraction. We investigate two mechanisms which utilize the band structure of the PC to generate a negative effective index of refraction (neff < 0) and demonstrate the negative refraction experimentally. To the isotropic extend of neff , different PC slab structures are employed to focus the radiation of a point source. It is shown experimentally that the PC can generate an image of the source with subwavelength resolution in the vicinity of the PC interface. Using a different PC, one can also obtain a far field focusing. In the latter case, we explicitly show the flat lens behavior of the structure. These examples indicate that PC-based lenses can surpass limitations of conventional lenses and lead to novel optics applications.