Designed Negative Refraction in Photonic Crystals

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.

This work presents a comprehensive analysis of electromagnetic wave propagation inside a two-dimensional photonic crystal in a spectral region in which the crystal behaves as an effective medium to which a negative effective index of refraction can be associated. It is obtained that the main plane wave component of the Bloch mode that propagates inside the photonic crystal has its wave vector k' out of the first Brillouin zone and it is parallel to the Poynting vector ( S' ? k'> 0 ), so light propagation in these composites is different from that reported for left-handed materials despite the fact that negative refraction can take place at the interface between air and both kinds of composites. However, wave coupling at the interfaces is well explained using the reduced wave vector ( k' ) in the first Brillouin zone, which is opposed to the energy flow, and agrees well with previous works dealing with negative refraction in photonic crystals.

Dispersion and negative refraction in photonic crystals without negative index

Photonic crystals are structures that can control the propagation of light by creating periodic changes in the refractive index. These structures facilitate directing electromagnetic waves in specific directions and making objects invisible by creating a bandgap. Photonic crystals, as microscopic structures with unique optical properties, are used in the design of invisibility systems. However, the design and optimization of these structures, especially with new methods like deep learning, have not been thoroughly investigated. Utilizing deep learning techniques can be highly beneficial in this area. Therefore, this paper employs the deep neural network architecture ResNet to optimize photonic crystals. ResNet can assist designers in selecting suitable materials and determining the optimal dimensions and arrangements of photonic nanostructured crystals for invisibility by extracting complex and nonlinear features from input data. The phenomenon of negative refraction in photonic crystals and the way light propagates in the proposed invisibility were studied using FDTD simulation. The results indicated that appropriate design of photonic crystals using deep learning could contribute to the creation of efficient structures.

Summary form only given. The talk overviews the efforts to achieve negative refraction (NR) in visible and IR by systems, having negative group velocity: photonic crystals (PC) and other systems with strong spatial dispersion of dielectric function, such as gyrotropic crystals and polaritonic media. To search the NR in PCs the fluorescence of CdS and CdSe quantum dots (QD) impregnated into porous silica and polysterene opal photonic crystals have been compared for QDs of different sizes. Spatial distribution of light is visualized by confocal fluorescent microscopy for QDs emitting in blue, green and red spectral bands and compared for PCs matrices having photonic band gaps in different spectral bands. It is found that spatial distribution of fluorescence emission from single QDs and small aggregates of QD is significantly different for QD with fluorescent lines below, within and above PBG frequency in [111]direction. We discuss this different spatial fluorescent patterns in terms of negative refraction in upper photonic bands, which have negative group velocity. The light from QD in the upper band creates patterns, which can be interpreted as due to focusing by the interface between media with positive and negative refraction. We analyze the fluorescence patterns of same size QD in inverted opals, and opals with strong disordering.

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 theoretically investigate the electromagnetic properties of the multilayer graphene-dielectric composite materials based on the effective medium theory. It is found that the structure exhibits hyperbolic isofrequency wavevector dispersions at THz and far-infrared frequencies, hence thereby realizing the effective graphene-based hyperbolic metamaterials (HMM). The frequncy band of the hyperbolic dispersion can be tuned by changing the Fermi energy of graphene sheet, the thickness of the dielectric layer and the layer number of graphene sheets. Because of the hyperbolic dispersion, graphene-based HMM possesses a negative energy refraction and positive phase refraction for oblique incidence at far below the critical frequency. The highly confined bulk polariton modes are also supported. Based on the attenuated total reflection configuration, the excitation of the bulk polariton mode is studied, in addition, such properties used in the tunable optical reflection modulation are also explored.

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.

In this paper, we designed a hexagonal lattice photonic crystal (PC) which presents negative refraction behavior in the visible region. By varying the PC parameters, a graded index PC was obtained and used to focus a plane wave. Numerical calculation was adopted to demonstrate the negative refraction and focusing effect. Our calculation results demonstrated that the PC can realize focusing by negative refraction in visible region. Moreover, a broad band focusing ranging from 425 nm to 700 nm was observed with less chromatic aberration in the PC structure. The proposed structures provide an approach for designing the negative index imaging systems.

We analyze negative refraction in two-dimensional photonic crystals that are made from electro-optical active materials. Application of an electric field to the photonic crystal changes the dielectric constant of the material and consequently modifies the photonic band and dispersion properties. We have investigated focusing properties of the photonic crystal slab lens at different frequencies within the first two bands and under various magnitudes of electric field. The simulation results reveal that one can dynamically tune negative refraction by means of index-tunable photonic crystals.

Efficient tunable negative refraction photonic crystal achieved by an elliptic rod lattice with a nematic liquid crystal

In this paper, a two-dimensional(2D) hexagonal lattice annular photonic crystal is designed. The band diagram of this photonic crystal is calculated by plane wave expansion method (PWE). The negative refraction phenomenon of photonic crystal is studied by analyzing the band diagram. The finite -difference time - domain method (FDTD) is used to simulate the imaging characteristics of the point light source. We have proved that this annular photonic crystal plate can realize negative refraction imaging.

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.

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.

A layered Korringa-Kohn-Rostoker method is exploited to study the subwavelength imaging through a slab of rods-in-air photonic crystal. Both the intensity and phase spectra of transmission are investigated. The high transmission of evanescent waves arises due to the excitation of some slab-guided bound modes and the high coupling between the incident evanescent field and some bulk-guided Bloch modes. Through a study of the phase spectrum of transmission, it is shown that the self-collimation effect occurs at smaller incident angles whereas the negative refraction effect occurs at relatively larger incident angles. The existence of imaging aberrations is also explained with the phase spectrum. The focusing properties of the photonic crystal slab are mainly due to the negative-refraction effect for large incident angles, rather than the self-collimation effect.