Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability

A Metamaterial Inspired AMC Backed Dual Band Antenna for ISM and RFID Applications

This work presents the design and fabrication of a metamaterial-based stimulated dual band antenna on FR4 material (dielectric constant 4.3) to operate in Industrial, Scientific and Medical (ISM) and Radio-frequency Identification (RFID) applications. The antenna model had an overall dimension of 70 × 31 × 1.6 mm³ with etched T-slots and L-slots for dual band resonance. The main objective of this work was to enhance the gain performance characteristic at the selected dual band frequencies of 0.915 GHz and 2.45 GHz. Initially, it achieved a narrow bandwidth of 0.018 GHz with a gain of 1.53 dBi at a lower frequency, and 0.13 GHz of bandwidth featuring 4.49 dBi of gain at a higher frequency. The antenna provided an impedance bandwidth of 2% (0.905-0.923 GHz) and 5% (2.382-2.516 GHz) at two resonating frequencies. The antenna was integrated with a designed novel AMC structure to enhance the gain in CST Microwave Studio software with the finite integration method. The characteristic features of the AMC unit cell were observed at 0.915 GHz and 2.45 GHz frequencies and after antenna integration, the final prototype achieved a gain of 2.87 dBi at 0.915 GHz and 6.8 dBi at 2.45 GHz frequencies.

Achieving efficient inverse design of low-dimensional heterostructures based on a vigorous scalable multi-task learning network

A scalable multi-task learning (SMTL) model is proposed for the efficient inverse design of low-dimensional heterostructures and the prediction of their optical response. Specifically, several types of nanostructures, including single and periodic graphene-Si heterostructures consisting of n×n graphene squares (n=1∼9), 1D periodic graphene ribbons, 2D arrays of graphene squares, pure Si cubes and their periodic array counterparts, are investigated using both traditional finite element method and SMTL network, with the former providing training data (optical absorption) for the latter. There are two important algorithms implemented in SMTL model: one is the normalization mechanism that makes different parameters of different structures on the same scale, ensuring that SMTL network can deal with tasks with different dataset impartially and without bias; the other one is used to capture the impact of nanostructures' dimensions on their optical absorption and thus improve the generalization ability of SMTL. Utilizing SMTL model, we first study the absorption property of the multiple shaped nanostructures and look deeper into the impacts of n×n graphene squares and Si cuboid on the optical absorption of their heterostructures. Equally important, the multi-structure inverse design functionality of SMTL is confirmed in this context, which not only owns high accuracy, fast computational speed, and excellent generalizable ability, but also can be applied to contrive new structures with desired optical response. This work adds to the rapidly expanding field of inverse design in nanophotonics and establishes a multi-task learning framework for heterostructures and more complicated nanoparticles.

Redox-Triggered Coloration Mechanism of Electrically Tunable Colloidal Photonic Crystals

Electrically tunable colloidal photonic crystals (ETPCs) have been investigated because of several merits such as easy color tunability, no discoloration, and clear color. The coloration mechanism of ETPCs has been explained in terms of only the electric field. Herein, we report on a new mechanism: electric field plus redox reaction. Specifically, the coloration behavior of ETPCs was investigated under electrically conductive or insulated conditions using current-voltage, cyclic voltammetry, and zeta potential measurements, as well as scanning electron microscopy. Electrophoretic movement of ETPC particles toward the positive electrode was caused by the electric field due to the particles' negative surface charge. At the positive electrode, ETPC particles lost their electrons and formed a colloidal crystal structure. Finally, an ETPC transparent tube device was constructed to demonstrate the coloration mechanism.

Flat-Lens Focusing of Electron Beams in Graphene

Coupling electron beams carrying information into electronic units is fundamental in microelectronics. This requires precision manipulation of electron beams through a coupler with a good focusing ability. In graphene, the focusing of wide electron beams has been successfully demonstrated by a circular p-n junction. However, it is not favorable for information coupling since the focal length is so small that the focal spot locates inside the circular gated region, rather than in the background region. Here, we demonstrate that an array of gate-defined quantum dots, which has gradually changing lattice spacing in the direction transverse to propagation, can focus electrons outside itself, providing a possibility to make a coupler in graphene. The focusing effect can be understood as due to the gradient change of effective refractive indices, which are defined by the local energy band in a periodic potential. The strong focusing can be achieved by suitably choosing the lattice gradient and the layer number in the incident direction, offering an effective solution to precision manipulation of electron beams with wide electron energy range and high angular tolerance.

Multiple scattering of electromagnetic waves by an array of parallel gyrotropic rods

We study multiple scattering of electromagnetic waves by an array of parallel gyrotropic circular rods and show that such an array can exhibit fairly unusual scattering properties and provide, under certain conditions, a giant enhancement of the scattered field. Among the scattering patterns of such an array at its resonant frequencies, the most interesting is the distribution of the total field in the form of a perfect self-similar structure of chessboard type. The scattering characteristics of the array are found to be essentially determined by the resonant properties of its gyrotropic elements and cannot be realized for arrays of nongyrotropic rods. It is expected that the results obtained can lead to a wide variety of practical applications.

Enhanced backscattering for infrared detection using photonic crystal based flat lens

An n=-1 flat lens based on photonic crystal semiconductor technology is evaluated for infrared detection purposes. The idea consists in exploiting the backscattered waves of an incident plane wave impinging on a target placed in the focal region of a flat lens. It is shown that subwavelength detection of micronic dielectric targets can be obtained at 1.55 μm using the double focus of reflected waves induced by negative refraction. Complex relations among the intrinsic nature, the shape and size of the target, and detection efficiency are interpreted in terms of target eigenmode excitation. Reflectivity is modulated by the intrinsic mode nature, transverse, circular, or longitudinal, with an enhancement of the detection sensitivity in the case of whispering-gallery modes. It is believed that such a study paves the way to the definition of original noninvasive infrared sensors.

Second harmonic generation from metallo-dielectric multilayered structures in the plasmonic regime

We present a theoretical study on second harmonic generation from metallo-dielectric multilayered structures in the plasmonic regime. In particular we analyze the behavior of structures made of Ag (silver) and MgF2 (magnesium-fluoride) due to the straightforward procedure to grow these materials with standard sputtering or thermal evaporation techniques. A systematic study is performed which analyzes four different kinds of elementary cells--namely (Ag/MgF2)N, (MgF2/Ag)N, (Ag/MgF2/Ag)N and (MgF2/Ag/MgF2)N--as function of the number of periods (N) and the thickness of the layers. We predict the conversion efficiency to be up to three orders of magnitude greater than the conversion efficiency found in the non-plasmonic regime and we point out the best geometries to achieve these conversion efficiencies. We also underline the role played by the short-range/long-range plasmons and leaky waves in the generation process. We perform a statistical study to demonstrate the robustness of the SH process in the plasmonic regime against the inevitable variations in the thickness of the layers. Finally, we show that a proper choice of the output medium can further improve the conversion efficiency reaching an enhancement of almost five orders of magnitude with respect to the non plasmonic regime.

Image reconstruction using a photonic crystal based flat lens operating at 1.55 μm

We used an optimized photonic crystal based flat lens for target detection and image reconstruction of micrometer sized objects for an operating wavelength of 1.55 μm. Using numerical retrieval procedures inspired from tomography, the ability to detect subwavelength sized targets and to image metallic objects of complex shapes is shown. The relation between the reconstructed image quality and lens resolution is investigated.

Confinement-controlled self assembly of colloids with simultaneous isotropic and anisotropic cross-section

The phase behavior of building blocks with mushroom cap-shaped particle morphology is explored under 2D and quasi-2D confinement conditions. Fast confocal microscopy imaging of the particles sedimented in a wedge cell reveals a range of mono- and bilayer structures partially directed by the isotropic and anisotropic profiles of the particle geometry. The sequence of phases tracked with increasing confinement height includes those reported in spheres, in addition to the more complex rotator and orientation-dependent phases observed for a class of short rod-like colloids. In the later case, the major particle axis reorients with respect to the substrate. Closest packing considerations provide rationale for the observed 1Delta (hexagonal)-1Buckled-1Sides (rotator)-2square (square)-2Delta (hexagonal)-2Sides (rotator) structural transitions with height.

Linearly damped modes at gap edges of photonic crystals

It is shown that for one-dimensional dielectric photonic crystals, the Bloch modes, a vital tool in the analysis of these structures, cannot provide a complete representation of the electromagnetic field at the edges of bandgaps. On these points, the couple of Bloch modes representing the propagation on both sides of the crystal reduces to a single one, with a stationary field, and a complete representation of the field inside the crystal illuminated by a plane wave must include a linearly damped mode (LDM), the amplitude of which behaves linearly in space. The theory of transfer matrices and the use of basic properties of the field allow a precise description of the LDM from a few parameters. An extension to two-dimensional photonic crystals is proposed.

Antireflection gratings for a photonic-crystal flat lens

A dielectric structure with effective permittivity and permeability close to -1 operating for propagative waves at optical wavelengths is proposed. This structure is a two-dimensional photonic crystal with refractive index -1, coated by appropriate antireflection gratings. Numerical simulations involving a flat lens made of this optimized crystal illustrate the improvements that antireflection gratings can bring. In particular, following Veselago's proposition, this lens "can focus at a point the radiation from a point source" with negligible reflection losses. The proposed design takes into account the fabrication requirements and can be used for optical devices integrated in planar waveguides.

Superlensing properties of one-dimensional dielectric photonic crystals

We present the experimental observation of the superlensing effect in a slab of a one-dimensional photonic crystal made of tilted dielectric elements. We show that this flat lens can achieve subwavelength resolution in different frequency bands. We also demonstrate that the introduction of a proper corrugation on the lens surface can dramatically improve both the transmission and the resolution of the imaged signal.

Negative refraction, surface modes, and superlensing effect via homogenization near resonances for a finite array of split-ring resonators

We present a theoretical and numerical analysis of liquid surface waves (LSWs) localized at the boundary of a phononic crystal consisting of split-ring resonators (SRRs). We first derive the homogenized parameters of the fluid-filled structure using a three-scale asymptotic expansion in the linearized Navier-Stokes equations. In the limit when the wavelength of the LSW is much larger than the typical heterogeneity size of the phononic crystal, we show that it behaves as an artificial fluid with an anisotropic effective shear modulus and a dispersive effective-mass density. We then analyze dispersion diagrams associated with LSW propagating within an infinite array of SRR, for which eigensolutions are sought in the form of Floquet-Bloch waves. The main emphasis is given to the study of localized modes within such a periodic fluid-filled structure and to the control of low-frequency stop bands associated with resonances of SRRs. Considering a macrocell, we are able to compute the dispersion of LSW supported by a semi-infinite phononic crystal of SRRs. We find that the dispersion of this evanescent mode nearly sits within the first stop band of the doubly periodic structure. We further discover that it is linked to the frequency at which the effective-mass density of the homogenized phononic crystal becomes negative. We demonstrate that this surface mode displays the hallmarks of all-angle negative refraction and it leads to a superlensing effect. Last, we note that our homogenization results for the velocity potential can be applied mutatis mutandis to designs of electromagnetic and acoustic superlenses for transverse electric waves propagating in arrays of infinite conducting SRRs and antiplane shear waves in arrays of cracks shaped as SRRs.

Imaging with subwavelength resolution by a generalized superlens at infrared wavelengths

We demonstrate experimentally negative refraction by a photonic crystal prism and imaging of a point source by a photonic crystal slab at 1.5 microm wavelength. The photonic crystal structures were nanofabricated in a InGaAsP/InP heterostructure platform, and optical characterization was performed using a near-field scanning optical microscope. By designing a suitable lens surface termination, an image spot size of 0.12lambda2 was achieved, demonstrating superlens imaging with subwavelength resolution well below Abbe's diffraction limit (0.5lambda2).

Effective-medium properties of metamaterials: a quasimode theory

Under the generalized coherent-potential approximation, we established a "quasimode" theory to study the effective-medium properties of electromagnetic metamaterials. With this theory, we calculate the self-energy, density of states (DOS), and mean-free paths for optical modes traveling inside a metamaterial, and then determine the effective permittivity and permeability of the metamaterial by maximizing the DOS function. Compared with the traditional methods for calculating effective-medium parameters, the present approach could provide quantitative judgments on how meaningful are the obtained effective-medium parameters. As illustrations, we employed the theory to study the effective-medium properties of several examples including finite metallic wires and split ring resonators.

Focusing the electromagnetic wave with a magnetic field

We examine manipulating the electromagnetic (EM) wave with an external static magnetic field (ESMF) taking advantage of the versatility of the magnetic photonic crystal (PC). The effect of a nonuniform ESMF on the permeability of the constituent magnetic material in the PC is demonstrated to create a gradient of the effective optical index in the crystal, leading to the focusing of the EM wave, with a magnetically tunable focal length, focused waist radius, and the intensity at the focus.

Quantum interference between two orthogonal transitions of an atom in one-dimensional photonic crystals

We find that the V-type three-level Zeeman atom has the complete quantum interference when it is embedded in one-dimensional photonic crystals (1D PCs) possessing the TM-polarized complete gap. To avoid the nonradiative decay related to dissipation and the decay through surface exciton, we add two phase compensators made of ideal left-handed materials on two sides of atom, and then the total structure is equivalent to a 1D PC supporting only the radiative modes. The parameter regions (epsilon, mu) leading to the TM-polarized complete gap have been sketched out, and the influence of absorption on the quantum interference is discussed.

Optical near-field microscopy of light focusing through a photonic crystal flat lens

We report here the direct observation by using a scanning near-field microscopy technique of the light focusing through a photonic crystal flat lens designed and fabricated to operate at optical frequencies. The lens is fabricated using a III-V semiconductor slab, and we directly visualize the propagation of the electromagnetic waves by using a scanning near-field optical microscope. We directly evidence spatially, as well as spectrally, the focusing operating regime of the lens. At last, in light of the experimental scanning near-field optical microscope pictures, we discuss the lens ability to focus light at a subwavelength scale.

Experimental investigation of interface states in photonic crystal heterostructures

Optical Tamm states, a kind of interface modes, are also called Tamm plasmon-polaritons. They are experimentally observed in photonic heterostructures based on microstrip transmission lines. The position of optical Tamm states can be designed exactly under effective impedance match and effective phase shift match conditions. Our results show that the photonic band gaps can have the effect of negative-permittivity or negative-permeability media in constructing the interface modes. The simulations and experimental results agree with each other quite well.

Achieving subdiffraction imaging through bound surface states in negative refraction photonic crystals in the near-infrared range

We report the observation of imaging beyond the diffraction limit due to bound surface states in negative refraction photonic crystals. We achieve an effective negative index figure of merit [-Re(n)/Im(n)] of at least 380, approximately 125x improvement over recent efforts in the near-infrared range, with a 0.4 THz bandwidth. Supported by numerical and theoretical analyses, the observed near-field resolution is 0.47lambda, clearly smaller than the diffraction limit of 0.61lambda. Importantly, we show this subdiffraction imaging is due to the resonant excitation of surface slab modes.

Quantum interference enhancement with left-handed materials

The quantum interference between two spontaneous emission transitions, which are orthogonal, in a three-level system, can be greatly enhanced by using left-handed materials due to the focusing and phase compensation effects. The influence of the dispersion and dissipation of the materials on the quantum interference enhancement is investigated, and the enhancement of quantum interference is still significant. The quantum interference enhancement will result in a large quenching of the spontaneous emission, even if the distance between the materials and systems is larger than 10 wavelengths.

Calculation of effective permittivity, permeability, and surface impedance of negative-refraction photonic crystals

We consider the eigen-fields of a two-dimensional negative-refraction photonic crystal and obtain negative effective permittivity and negative effective permeability. Effective permittivity, permeability, and surface impedance are calculated by averaging the eigen-fields. The value of the surface impedance is shown to be location-dependent and is validated by finite-difference time-domain simulations. The unique power propagation mechanism in the photonic crystal is demonstrated through time-evolution of eigen-fields.

Evaluation and illustration of the properties of Metamaterials using field summation

The prediction and the engineering of the electromagnetic properties of metamaterials are increasingly important issues. Recently, several approaches have been proposed to compute these properties through appropriate averages of local fields within the unit cell. In particular, we proposed a Field Summation method that has been used successfully to determine either analytically or numerically the effective properties of different composites and metamaterials. But this method also provides interesting clues for understanding the behaviour of these materials. It helps chose appropriate planes to visualize the fields using electromagnetic simulation software, and understand behaviours leading to either positive or negative effective parameters, with either small or large values. It helps establish whether the materials can be adequately described by effective parameters.