Wave Vector Diagram Research Articles

Engineerable wavevector diagrams of non-Moiré geometry-based photonic crystals for beam steering applications

The wavevector diagrams or eigenfrequency contours (EFCs) (also called dispersion surfaces) are the best tools to explore the optical properties of photonic crystals (PhCs). Many optical phenomena, such as self-collimation, super-prism, negative refraction, and lensing, have been extensively explored in PhCs based on EFCs. Also, several approaches have been continuingly pursued to modulate the EFCs of PhCs for molding the flow of light. This work presents the modulated wavevector diagrams of PhCs formed by asymmetric non-Moiré (NM) patterns. The NM patterns are contours of trigonometric functions that generate attractive tiles and shapes. Employing such shapes to design a PhC tailors the dispersion of PhCs with stretching, squeezing, and shape-modulated EFCs. Based on the modulated EFCs of the proposed structures, we demonstrate the direction-dependent beam steering phenomenon. The ray tracing, full-wave electromagnetic simulations, far-field patterns, and electric field profiles corroborate the beam steering application of the modulated EFCs. We anticipate that the modulated EFCs of non-Moiré pattern-based PhCs are useful for reconfigurable wave optics and beam steering applications.

Photonic topological Lifshitz interfaces

Abstract The intrinsic geometry of wavevector diagrams describes electronic or photonic transport at a given energy level. Lifshitz transition is an intriguing example of the topological transition in wavevector diagrams, which plays a critical role in abnormal transport with enhanced magnetoresistance or superconductivity. Here, we develop the spatial analogy of the Lifshitz transition, which provides a comprehensive topological perspective on transverse-spin interface states. We establish the excitation conditions of transverse-spin interface states, which require the “Lifshitz interface” – the interface between different topologies of wavevector diagrams – along with the gap in wavevector diagrams. Based on the detailed analysis of this topological phenomenon with respect to the dimensionality and gaps of wavevector diagrams across the Lifshitz interface, we show distinct parity of transverse spins and power flows in transverse-spin modes. The unique symmetry of interface states realizing Abraham-spin-momentum locking represents the gauge induced by the Lifshitz interface, which provides a novel insight into the Abraham–Minkowski controversy.

Wave-vector analysis of plasmon-assisted distributed nonlinear photoluminescence along Au nanowires

We report a quantitative analysis of the wavevector diagram emitted by nonlinear photoluminescence generated by a tightly focused pulsed laser beam and distributed along Au nanowire via the mediation of surface plasmon polaritions. The nonlinear photoluminescence is locally excited at key locations along the nanowire in order to understand the different contributions constituting the emission pattern measured in a conjugate Fourier plane of the microscope. Polarization-resolved measurements reveal that the nanowire preferentially emits nonlinear photoluminescence polarized transverse to the long axis at close to the detection limit wavevectors with a small azimuthal spread in comparison to the signal polarized along the long axis. We utilize finite element method to simulate the observed directional scattering by using localized incoherent sources placed on the nanowire. Simulation results faithfully mimic the directional emission of the nonlinear signal emitted by the different portions of the nanowire.

Dual Doppler Effect in Wedge-Type Photonic Crystals

The dual Doppler effect, in the simultaneous occurrence of both normal and inverse Doppler effect in one moving two-dimensional wedge-type photonic crystal, is proposed. An improved finite-different time-domain algorithm is used to verify this phenomenon. The spatial Fourier Transformation has been applied to complex electrical field data to reveal the mechanism. The harmonics with negative spatial frequencies show a lagging phase evolution, while those with positive spatial frequencies show a front phase evolution. Different wedge-type photonic crystals are designed to filter out the required harmonics based on the systematic study of spatial Fourier Transformation and wave vector diagram. Our work paves a new way for Doppler cooling of atomic gases, radar deception, invisibility cloaks, microstructure dual frequency interferometer and so on.

Second Harmonic Generation of Nanoscale Phonon Wave Packets.

Phonons are often regarded as delocalized quasiparticles with certain energy and momentum. The anharmonic interaction of phonons determines macroscopic properties of the solid, such as thermal expansion or thermal conductivity, and a detailed understanding becomes increasingly important for functional nanostructures. Although phonon-phonon scattering processes depicted in simple wave-vector diagrams are the basis of theories describing these macroscopic phenomena, experiments directly accessing these coupling channels are scarce. We synthesize monochromatic acoustic phonon wave packets with only a few cycles to introduce nonlinear phononics as the acoustic counterpart to nonlinear optics. Control of the wave vector, bandwidth, and consequently spatial extent of the phonon wave packets allows us to observe nonlinear phonon interaction, in particular, second harmonic generation, in real time by wave-vector-sensitive Brillouin scattering with x-rays and optical photons.

New Acousto-Optic Regime of Interaction in Media Possessing Strong Elastic Anisotropy

We present results on theoretical and rst experimental investigation of a new regime of acousto-optic interaction existing in acoustically anisotropic medium. We de ned the new regime as semi-collinear or mixed interaction since it combined properties of the traditional non-collinear di raction and the pure collinear interaction. The peculiar phenomenon was registered in the tellurium dioxide crystal due to the extremely strong elastic anisotropy of the material. Application of a speci c cut of the crystal provided observation of the e ect in the middle infrared at the optical wavelength 3.39 μm and at the acoustic frequencies limited to 300 MHz. The observed interaction was characterized by a non-collinear propagation of incident light with respect to acoustic energy ow and simultaneously a collinear propagation of di racted radiation along the acoustic energy ow. A brief theoretical analysis of the interaction based on wave vector diagrams and two-dimensional coupled wave equations is included in the presentation. Finally, we describe in the paper, the setup and basic details of the carried out acousto-optic experiment.

Influence of Acoustic Anisotropy on Frequency Bandwidths of Bragg Diffraction in Two Orthogonally Polarized Diffraction Orders

In uence of Acoustic Anisotropy on Frequency Bandwidths of Bragg Di raction in Two Orthogonally Polarized Di raction Orders A.V. Zakharov* and V.B. Voloshinov Faculty of Physics, Lomonosov Moscow State University, GSP-2, Leninskiye Gory, 119992 Moscow, Russia This paper theoretically and experimentally examines a speci c regime of acousto-optic di raction during which an arbitrarily polarized incident light in a paratellurite crystal is scattered simultaneously into two orthogonally polarized di raction maxima. We examined acoustic energy walk-o in the crystal and its in uence on phase matching as well as on distribution of light energy between the two di raction orders. This in uence was theoretically considered by means of wave vector diagrams illustrating momentum conservation law during the photon phonon interaction. We obtained expressions for mismatch parameters in the ordinary +1 and extraordinary 1 di raction orders both depending on the walk-o angle. The obtained parameters were used in the Raman Nath system of coupled-wave equations to calculate the di racted light intensities and frequency bandwidths of di raction. We measured the bandwidths in experiments carried out in the (110) plane of paratellurite crystal at the walk-o angle equal to 54◦.

Experimental demonstration in X-band of dual-negative refraction in photonic crystals

The effect of dual-negative refraction (DNR) in a photonic crystal (PhC) is demonstrated experimentally in X-band (8–12 GHz) for the first time. The two-dimensional PhC sample is made of highly pure Al2O3 ceramic cylinders close packed in air with a triangular lattice structure. The frequency regions of DNR are predicted by the analyses of wave vector diagrams. Experiments of anomalous refraction in PhCs are carried out in a near-field scanning system to demonstrate the theory and numerical results. The experimental measurements of electric field (real part and spatial intensity) for DNR are in good agreement with the numerical simulations. This work demonstrates that the unique feature of photonic crystals can be realized experimentally in different frequency regions which are proportional to the lattice constant of the PhC. Due to the large design flexibility, we believe this result will be promising for application in the range of optical devices.

Hyperbolic metamaterial as super absorber for scattered fields generated at its surface

We show that hyperbolic metamaterials (HMs) that exhibit hyperbolic wave-vector dispersion diagrams possess two important features related to super absorption: The total power scattered by a nanosphere is (i) greatly enhanced when placed at the HM surface, compared to other material surfaces, and (ii) almost totally directed into the HM. We show that these two features are peculiar of HM interfaces, and we support them using a spectral theory study of transverse-electric and magnetic waves scattered by a subwavelength nanosphere. We analyze the nanosphere's scattered power absorbed by various substrate configurations. We also consider various nanosphere materials.

Multifunctional solid/solid phononic crystal

A two-dimensional, solid/solid phononic crystal (PC) comprised a square array of steel cylinders in epoxy is shown to perform a variety of spectral, wave vector, and phase-space functions. Over a range of operating frequencies, the PC’s elastic band structure shows uniquely shaped equifrequency contours that are only accessible to excitations of longitudinal polarization. Under this condition, the PC is shown to behave as (1) an acoustic wave collimator, (2) a defect-less wave guide, (3) a directional source for elastic waves, (4) an acoustic beam splitter, (5) a phase-control device, and (6) a k-space multiplexer. Wave vector diagrams and finite-difference time-domain simulations are employed to authenticate the above mentioned capabilities.

Mid-infrared high-frequency high-resolution reflective acousto-optic filters in mercury halides

Due to the long optical wavelengths of the mid-infrared region and to the low acoustic shear wave velocities of mercury halides, the high acoustic frequency solution of the acousto-optic wave-vector diagram can be used to design new high resolution acousto-optic filters, such as reflective AOTFs and AOPDFs, which are technically impossible to realize in the UV, visible and near-infrared regions.

One-way diffraction effects in photonic crystal gratings made of isotropic materials

The anomalous diffraction effects arising in the intrinsically isotropic photonic crystal gratings with different periods of the front-side and back-side interfaces are studied with the emphasis put on wideband one-way transmission. It is demonstrated that more than 80 percent of the incident-wave energy can be transmitted unidirectionally, i.e., with zero transmission in the opposite direction, by changing side of illumination only, while polarization always remains linear. Most but not all of the related diffraction effects can be predicted using isofrequency contours (IFCs) and wave-vector diagrams, which take into account the IFC-shape-dependent additional transmission channels that can appear due to corrugations. Three main regimes, i.e., isolation and bidirectional and unidirectional translation, can be distinguished, depending on whether the front-side corrugations affect the far field in the half space bounded by the back-side interface, and whether transmission is vanishing only at illumination from the side of one of the interfaces. The conditions providing the existence of these regimes are given and discussed in terms of the features of wave-vector diagrams. In some cases, similar regimes can appear being in contradiction with these conditions. Variation in the angle of incidence and the angle between the characteristic directions of photonic crystal and the interfaces of the corresponding noncorrugated structure allows one extending variety of situations, in which unidirectional transmission can be realized. The general condition of unidirectionality is that the zero diffraction order is not coupled to a Floquet-Bloch wave.

Multiwavelength Transmission Microcavity in SOI Planar Ridge Waveguides

A novel waveguide-based 1-D photonic crystal (PhC) microcavity that simultaneously transmits light within the 1310- and 1550-nm wavelength telecommunications bands has been realized. A novel semianalytical model based on wave-vector diagrams was developed to enable rapid optimization of the 1-D PhC with complex periodicity to be etched into an SOI ridge waveguide. Measurements of the multiwavelength transmission characteristics of the resulting complex PhC microcavity revealed transmission peaks at 1321 and 1562 nm with nearly equal transmittivity that is close to the design specification.

Collimations and negative refractions by slabs of 2D photonic crystals with periodically-aligned tube-type air holes

The FDTD method was applied to investigate the two-dimensional PhC slabs with periodically-aligned tube-type air holes. By numerical simulations, we found negative refraction behaviors by tuning the incident angle into the narrow negative-refraction angle range, and the collimation effects were analyzed by means of wave vector diagrams.

Control of self-collimated Bloch waves by partially flat equifrequency contours in photonic crystals

Self-collimation effects in photonic crystals are generally investigated by employing flat equifrequency contours. Here we report, based on a partially flat equifrequency contour inducing two different group velocity vectors, the simultaneous excitation of dual self-collimated beams and the selective excitation of either of them by varying the incident angle or the width of an input Gaussian beam. With combination of the finite-difference time-domain simulation and the Fourier analysis as well as the wave vector diagram, we analyze the refractive behaviors of these self-collimated Bloch waves.

Efficient surface plasmon field confinement in one-dimensional crystal line-defect waveguides

The authors operate a near-field optical microscope to investigate surface plasmon polariton (SPP) propagation along linear waveguides opened into one-dimensional (1D) plasmonic crystals, i.e., crystals featuring a single lattice plane orientation. They show that efficient SPP field confinement can be achieved by this type of waveguide although no band gap exists in the direction perpendicular to the waveguide axis. From computed wave-vector diagrams, they show that 1D plasmonic crystals can open a wide range of prohibited propagation directions preventing from a significant coupling of the waveguide SPP modes with the crystal Bloch modes. Finally, the authors demonstrate that the field distributions of the guided SPP modes can be qualitatively understood from simple Ewald constructions.

Negative refractive behavior of a two-dimensional negative-index photonic crystals using a wave vector diagram method

We have theoretically studied the negative refractive behavior and the focusing effect in a two-dimensional square-lattice photonic crystal made of air rods in a dielectric background. Detailed explanations are given for the effect of the negative refraction, and the imaging of the plano-concave lens is shown by the use of a wave vector diagram formalism. The typical negative refractive behavior is demonstrated by considering the Bloch mode with the wave vector inside the first Brillouin zone, because only those wave vectors inside the first Brillouin zone of multiple Brillouin zones have a definite meaning. The single propagating beam is analyzed by the use of the wave vector diagram formalism following the folding of the wave vectors. Good-quality focusing of a plane wave can be realized by using a photonic crystal plano-concave lens, while a plane wave is formed by a point source placed at the focal point. Our results are in good agreement with the experimental ones shown for a negative-index plano-concave lens by Vodo et al. [Appl. Phys. Lett. 86 (2005) 201108]. Finally, we also have shown the focusing behavior of a plane wave and a Gaussian pulse by a plano-concave lens structure with high-index modulation instead of air in the concave region.

Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects

We systematically study a collection of refractive phenomena that can possibly occur at the interface of a two-dimensional photonic crystal, with the use of the wave vector diagram formalism. Cases with a single propagating beam (in the positive or the negative direction) as well as cases with birefringence were observed. We examine carefully the conditions to obtain a single propagating beam inside the photonic crystal lattice. Our results indicate, that the presence of multiple reflected beams in the medium of incidence is neither a prerequisite nor does it imply multiple refracted beams. We characterize our results in respect to the origin of the propagating beam and the nature of propagation (left-handed or not). We identified four distinct cases that lead to a negatively refracted beam. Under these findings, the definition of phase velocity in a periodic medium is revisited and its physical interpretation discussed. To determine the ``rightness'' of propagation, we propose a wedge-type experiment. We discuss the intricate details for an appropriate wedge design for different types of cases in triangular and square structures. We extend our theoretical analysis, and examine our conclusions as one moves from the limit of photonic crystals with high index contrast between the constituent dielectrics to photonic crystals with low modulation of the refractive index. Finally, we examine the ``rightness'' of propagation in the one-dimensional multilayer medium, and obtain conditions that are different from those of two-dimensional systems.

1-D slab photonic crystal k-vector superprism demultiplexer: analysis, and design

The design of a complete demultiplexer based on the k-vector superprism in a 1-D slab photonic crystal is proposed. This design scales to resolve 32 channels spaced by 0.8 nm (100 GHz) in the C band for a dense wavelength division multiplexing system. It is shown that a prism area of 0.017 mm;2 is sufficient for the required wavelength resolution using typical silicon-on-insulator technology and that the total chip size would be 4x3 mm;2. In order to achieve this, the modest angular dispersion of a 1-D slab photonic crystal is enhanced by considerably expanding the input beam through the superprism region and employing etched mirrors to collimate and focus the light into and out of the superprism. The plane wave expansion method is used to obtain the wave vector diagram and from this we develop design equations based on conventional ray tracing. We then present an optimization approach which minimizes the prism area whilst maintaining the necessary dispersion. Finally the non-uniformity of phase velocity dispersion across the desired spectral window is addressed.

Ultracompact high-efficiency polarizing beam splitter with a hybrid photonic crystal and conventional waveguide structure.

We propose an ultracompact high-efficiency polarizing beam splitter that operates over a wide wavelength range and is based on a hybrid photonic crystal and a conventional waveguide structure. Within a small area (15 microm x 10 microm), this polarizing beam splitter separates TM- and TE-polarized modes into orthogonal output waveguides. Results of simulations with the two-dimensional finite-difference time-domain method show that 99.3% of TM-polarized light is deflected by the photonic crystal structure (with a 28.0-dB extinction ratio), whereas 99.0% of TE-polarized light propagates through the structure (with a 32.2-dB extinction ratio). Wave vector diagrams are employed to explain the operation of a polarizing beam splitter. Tolerance analysis reveals a large tolerance to fabrication errors.