Positive Index Materials Research Articles

Modulation instability in nonidentical metamaterial waveguide arrays by graph Laplacian approach

We theoretically investigate modulation instability (MI) in a nonidentical waveguide array, which is made up of positive and negative index metamaterial waveguides. The unit cell of the optical waveguide array consists of three waveguides arranged in a triangular manner. Waveguides 1 and 3 are made up of positive index material (PIM) channels and waveguide 2 is by negative index material (NIM) channels, as a result, they show different light propagation characteristics. We model this array of waveguides using a generalized nonlinear Schro¨dinger equation, replacing the Laplacian operator with the graph Laplacian. Following linear stability analysis, we will discuss MI for different values of transverse wave number, as it determines the order of the Brillouin zone. We also discuss the effect of input power on periodic MI in normal and anomalous dispersion regimes. Thus we report a comprehensive study on the MI and hence the better ways to generate and manipulate the solitons or ultra-short pulses in NIM PIM waveguide arrays.

Phase time delay caused by quantum effects in nearby plasmonic nanostructures of a one-dimensional photonic crystal

A one-dimensional photonic crystal (1DPC) incorporated with a defect layer containing a four-level double V-type quantum system adjacent to a plasmonic nanostructure is employed to investigate the Hartman effect. The study involves the interaction of two orthogonal circularly polarized laser beams with the defect layer, possessing identical frequencies but vary in phase and electric field amplitude. The defect layer exhibits quantum system adjacent to plasmonic nanostructure and field interaction phenomena like optical transparency, nonzero dispersion with zero absorption, gain without inversion, and others related effects. By manipulating the phase of the driving fields and probe detuning, the 1DPC can function as either a positive index material (PIM) or a negative index material (NIM), correlating to the normal and anomalous dispersion of the defect layer, respectively. The positive and negative Hartman effects for PIM and NIM, respectively, can be observed by adjusting the relative phase with respect to the driving fields. Our suggested approach might be used in optical memory, all-optical switching, all-optical routing, and interferometry.

An analysis of Kerr nonlinearity in negative index material and its effect on material characteristics

Optics of negative index material is known for its unconventional results. In the perspective of nonlinear optics, it has a revolutionary impact. We, thus, investigate the effect of Kerr nonlinearity on the characteristics of a representative isotropic, frequency independent negative index material by defining an intensity-dependent effective permittivity and compare it to that in positive index material. Using the intensity-dependent permittivity, responses of essential characteristic features like phase and group velocities are studied and found to exhibit unconventional behavior with incident field intensity in the negative index material. At a threshold intensity, i.e., at an intensity at which effective permittivity vanishes, the material shows features of epsilon near zero and/or near zero index materials i.e., a diverging phase velocity with zero group velocity. The study shows the prospect of altering or tailoring characteristic features of a negative index material by tuning the field intensity of the propagating wave or pulse in the material.

Engineered photonic spin Hall effect of Gaussian beam in antisymmetric parity-time metamaterials

A model of the photonic spin Hall effect (PSHE) in antisymmetric parity-time (APT) metamaterials with incidence of Gaussian beams is proposed here. We derive the displacement expression of the PSHE in APT metamaterials based on the transport properties of Gaussian beams in positive and negative refractive index materials. Furthermore, detailed discussions are provided on the APT scattering matrix, eigenstate ratio, and response near exceptional points in the case of loss or gain. In contrast to the unidirectional non-reflection in parity-time (PT) symmetric systems, the transverse shift that arises from both sides of the APT structure is consistent. By effectively adjusting the parameters of APT materials, we achieve giant displacements of the transverse shift. Finally, we present a multi-layer APT structure consisting of alternating left-handed and right-handed materials. By increasing the number of layers, Bragg oscillations can be generated, leading to an increase in resonant peaks in transverse shift. This study presents a new approach to achieving giant transverse shifts in the APT structure. This lays a theoretical foundation for the fabrication of related nano-optical devices.

Modulation instability effects of the conventional Kerr type nonlinearity on the three-core oppositely directed coupler

The present design deals with a three-core system in which two channels are made of negative index material and one made of positive index material. The nonlinear Schrodinger equation is modified by adding the Kerr-type nonlinearity and coupling coefficient terms. We derive the dispersion relation for the optical coupler under investigation in the presence of added terms. Using a linear stability analysis, we examine the modulation instability characteristic gain in both the normal and anomalous group-velocity dispersion regimes. We study the system in diversified physical parameter space to unveil many possibilities. The analytical results demonstrate that, in contrast to Shafeeque et al. (2016), some novel instability bands are produced in the normal and anomalous dispersion regimes. We observe the modulational instability (MI) occurring due to Kerr-type nonlinearity. It is also evident that MI can be controlled by varying pump power and nonlinear factors. As a result, we observe new possibilities for producing and managing the MI in three-core oppositely directed couplers with the impact of opposite directionality.

The role of septic saturation on the cross-phase instability in two-core birefringent oppositely directed PIM-NIM coupler

We examine the cross-phase modulational instability in a two-core birefringent coupler made of a positive and negative index material. The modified form of generalized nonlinear Schrödinger equation contains a nonlinear septic term, cross-phase modulation, intrapulse Raman scattering, self-steepening, and conventional type of saturation nonlinearity. We investigate normal and anomalous group-velocity dispersion regimes and cases of birefringent effects such as zero-birefringence, linear birefringence, and circular birefringence. We observe that the MI gain spectrum shows significant changes in the presence of cross-phase modulation with a nonlinear saturation effect and non-Kerr nonlinearity. In addition, the self-steepening brings out new sidebands and shifts the existing sidebands to bring them together, providing a new pathway to generate solitons or ultrashort pulses in the presence of nonlinear septic saturation. The intrapulse Raman scattering effect causes conventional and Raman bands, extending the modulational instability (MI) domain range. The saturable nonlinearity suppresses the MI gain and reduces the bandwidth of the spectrum for both normal and anomalous dispersion regimes. But, in the case of nonlinear saturation with non-Kerr nonlinearity, the MI gain spectra exhibit efficient modification in a two-core birefringent oppositely directed coupler (ODCs) with adjustable effects of SS, IRS, and cross-phase modulation. Therefore, manipulating MI and solitons in a two-core ODCs is better performed when the birefringence is linear rather than circular. Here we present how to control and generate the MI and solitons in birefringent ODCs, emphasizing the negative index material (NIM) channel.

Cloaking Property of a Plasmonic Structure in Doubly Complementary Media and Three-Sphere Inequalities with Partial Data

We investigate cloaking property of negative-index metamaterials in the time-harmonic electromagnetic setting for the so-called doubly complementary media. These are media consisting of negative-index metamaterials in a shell (plasmonic structure) and positive-index materials in its complement for which the shell is complementary to a part of the core and a part of the exterior of the core-shell structure. We show that an arbitrary object is invisible when it is placed close to a plasmonic structure of a doubly complementary medium as long as its cross section is smaller than a threshold given by the property of the plasmonic structure. To handle the loss of the compactness and of the ellipticity of the modeling Maxwell equations with sign-changing coefficients, we first obtain Cauchy's problems associated with two Maxwell systems using reflections. We then derive information from them, and combine it with the removing localized singularity technique to deal with the localized resonance. A central part of the analysis on the Cauchy's problems is to establish three-sphere inequalities with partial data for general elliptic systems, which are interesting in themselves. The proof of these inequalities first relies on an appropriate change of variables, inspired by conformal maps, and is then based on Carleman's estimates for a class of degenerate elliptic systems.

Investigating Fill Factor Effect on Brillouin Zone of Metamaterial-Based 2D Photonic Crystal

: Fill factor in the negative permittivity materials are tailored within the physically permissible limits to characterize the Brillouin zone for two-dimensional crystal under the propagation of both s and p-polarized waves. Two lowermost band-gaps are computed along with corresponding mid-band frequencies, where the plane wave expansion method is invoked for computational purposes. The rectangular geometrical shape is considered for the simulation, and all the results are calculated inside the ‘Γ’ point and ‘X’ point of the first Brillouin zone. Simulated findings depict monotonous variations of both band-gap width as well as mid-band frequency for higher negative permittivity materials, when the magnitude of fill factor is comparatively low, for both TE (Transverse Electric) and TM (Transverse Magnetic) mode of propagations. Lower negative permittivity leads to random fluctuations, which makes it unsuitable for photonic component design. Multiple forbidden regions may be observed for some specific artificial materials which can be utilized in the antenna or multi-channel filter design in higher THz region. Aims: The present paper aims to compute the shape of the first Brillouin zone from the fill factor for a two-dimensional photonic crystal structure. Background: EBG (Electromagnetic Bandgap) of a photonic crystal plays a major role in determining its candidature for optical applications, which is critically controlled by the fill factor. Therefore, it is significant to investigate the effect of F.F on the wave propagation characteristics of 2D PhC(Twodimensional photonic crystal). Objective: Investigation of metamaterial-based photonic crystal structure for electromagnetic band-gap analysis in the desired spectrum of interest as a function of fill factor inside the first Brillouin zone. Methods: Maxwell’s equations are solved using the plane wave propagation method to solve the problem, and simulation is carried out in MATLAB® software. Result: Both the first and second photonic band-gaps are simultaneously computed with a variation of refractive index differences of the constituent materials as well as with the fill factors. Results are extremely significant about the formation of narrowband and wideband filters on certain material combinations and structural designs. Conclusion: Better tenability is observed for metamaterial structure compared to conventional positive index materials, and fill factor has a great role in shaping the Brillouin zone and corresponding bandgap width.

Equivalence between positive and negative refractive index materials in electrostatic cloaks

We investigate, both theoretically and numerically, the equivalence relationship between the positive and negative refraction index dielectric materials in electrostatic invisibility cloak. We have derived an analytical formula that enables fast calculate the corresponding positive dielectric constant from the negative refraction index material. The numerical results show that the negative refraction index material can be replaced by the positive refractive index materials in the static field cloak. This offers some new viewpoints for designing new sensing systems and devices in physics, colloid science, and engineering applications.

Design and analysis of a position chirped metamaterial photonic crystal array for confinement of light pulses

In a photonic crystal (PC) array, a line defect (removal of a periodic structure) and position up-chirping (gradually decreasing lattice constant) are familiar terms to introduce light confinement and propagation due to the photonic bandgap (PBG). In this paper, we have proposed a new model for light confinement using a line defect position chirped PC array with metamaterial as a dielectric material. For comparison, we have designed and simulated for both line defect positions chirped and none position chirped PC array using normal material (refractive index +3.927) dielectric material and metamaterial (refractive index −3.927). We have used metamaterial due to the compensation of light dispersion and leakage effect because the negative refractive index makes the wave vector direction precisely opposite to the positive refractive index material. We have implemented the metamaterial positioned chirped PC array with sharp 90° bending and shown the light confinement and propagation for that structure. To support our proposed model, we have calculated the band diagram of both positive refractive index and metamaterial unit cells and verified the quantum well existence in the band diagram of metamaterial unit cell. Based on the quantum well effect, the confinement of light in metamaterial line defect position chirped PC has been explained and presented with proper finite element method (FEM) simulations. From quantum mechanics, we can comprehend that confining wave particles at the atomic level is extremely challenging because of the evanescent nature of the light wave. The novelty of this paper is that we have managed to confine the propagating of light waves by using the quantum well existence in the metamaterial dielectric for a line defect position chirped PC structure, and to the best of our knowledge, we are probably the first to introduce light confinement using a metamaterial chirped PC structure with proper FEM simulation.

Veselago lensing with Weyl metamaterials

Negative refraction is an exotic optical phenomenon that is usually observed at the interface between a positive-index material and a negative-index, or “left-handed” material. One direct application of negative refraction is the Veselago lens, a flat lens that can focus the light emitted by a point source located on one side of the negative index medium onto the opposite side. Besides negative-index materials, Veselago lensing effect has been observed with two-dimensional crystals possessing Dirac points, such as graphene for electrons. Here we observe all-angle negative refraction and Veselago imaging in three dimensions with a Type I Weyl metamaterial. Furthermore, our ideal Weyl metamaterial exhibits remarkable spin-selective transmission around the Weyl frequency that arises from its intrinsic chiral optical response. Our results show that the ideal Weyl metacrystal provides a versatile platform for lensing applications and novel photon-spin selective devices.

Tunable terahertz optical bistability and multistability in photonic metamaterial multilayers containing nonlinear dielectric slab and graphene sheet

In this study, optical bistability and multistability phenomena are numerically investigated in the terahertz frequency domain based on the quasiperiodic photonic metamaterial multilayers, in which both the regular positive index and special negative index materials are artificially arranged, according to the interesting Fibonacci sequence structure. In order to obtain the tunable bistability and multibistability behaviors, the Kerr-type nonlinear dielectric layer and graphene sheet are sandwiched between two Fibonacci quasiperiodic one-dimensional photonic crystals. Results show that the intensity-dependent hysteresis curves including bistability and multistability are thoroughly discussed by judiciously changing the systematical parameters such as the frequency of incident wave, thickness of each layer, incident angle, as well as the chemical potential of graphene which can produce strong influences on the switch-up/down threshold values and widths of hysteresis loops.

Tuning band structures of photonic multilayers with positive and negative refractive index materials according to generalized Fibonacci and Thue–Morse sequences

We investigate the photonic band structure, using the transfer-matrix method, in one-dimensional structures composed of a dispersive metamaterial A juxtaposed with a non-dispersive dielectric B according to the generalized Fibonacci and Thue–Morse sequences, which are ruled and characterized by two positive integer numbers, p and q. We present the band structures of different generations of these sequences for both TE and TM modes and discuss how they are affected by the p and q parameters and the ratio between the thicknesses of the building blocks. We obtain a new and very important analytical expression for the frequency in which the average refraction index vanishes, i.e. when the gap condition is satisfied, and we investigate, in detail, the behavior of this emergent scale insensitive gap, as a function of the thicknesses ratio, for all structures considered. For the metamaterial considered, we show that the reduced frequency for converges faster or slower to 0.41 depending on the sequence. By adjusting the p and q parameters, we can obtain a higher concentration of the pass bands inside (outside) the nA < 0 region when there are more (less) blocks A than B in the unit cell. Our results also show the presence of omnidirectional and complete band gaps, which have various practical and technological applications.

The invisibility via anomalous localized resonance of a source for electromagnetic waves

We investigate the invisibility via anomalous localized resonance of a general source in anisotropic media for electromagnetic waves. To this end, we first introduce the concept of doubly complementary media in the electromagnetic setting. These are media consisting of negative-index metamaterials in a shell and positive-index materials in its complement for which the shell is complementary to a part of the core and a part of the exterior of the core–shell structure. We then provide criteria for establishing the invisibility of a source in these media. We show that (i) a source is invisible if the power is blown up; (ii) a source is invisible if it is sufficiently close to the plasmonic shell structure, and it is visible if it is far from this plasmonic structure; (iii) if the plasmonic structure is complementary to an annulus of constant isotropic medium, there is a critical length that characterizes the cloaking phenomena, as first observed in the two-dimensional acoustic quasistatic setting by Milton and Nicorovici.

Distributed feedback lasing based on a negative-index metamaterial waveguide.

This Letter lays the foundation of a new type of distributed feedback (DFB) laser whose optical feedback is due to the evanescent coupling between an active positive-index material (PIM) waveguide and a lossy negative-index metamaterial (NIM) waveguide. Active PIM-NIM coupled-mode equations are presented and solved to characterize the dispersion relation, resonant optical gain, and lasing. The photonic bandgap of this grating-less DFB laser does not depend on a Bragg wavenumber, but depends on the difference between the wavenumbers of the PIM and NIM waveguides; controlling this wavenumber difference allows for single-mode lasing and, ultimately, single-mode broadband lasing.

Analyzing the effect of higher order nonlinearity on dispersion relation and optical multistability generation in oppositely directed coupler

We report the influence of higher order nonlinearity on dispersion relation and multistability in oppositely directed coupler with negative index material channel. The study shows that the high intensity electric field shifts the photonic bandgap down in energy. When the positive index material channel of the coupler is influenced by quintic nonlinearity the group velocity of upper branch of dispersion curve (δ–q curve) falls to zero in positive q region and the loop in the lower branch shifts to positive q region. But the minima in upper branch and loop in the lower branch are observed at negative q region when the negative index material channel is influenced by χ(5) nonlinearity. As the curvature of the dispersion relation determines the group velocity dispersion the study report the possibility for dispersion engineering in oppositely directed coupler. Also we observed that the quintic nonlinearity enhances formation of multi stable states.

Backward Third-Harmonic Pulse Generation in a One-Dimensional PIM/NIM Structure

In this work, a set of couple-mode equations for describing a backward third harmonic generation (BTHG) in a one-dimensional periodic structure of positive-index material (PIM) layers and third-order nonlinear negative-index material (NIM) layers was analysed using multiple-scale method. Due to the negative-index phase matching and band-edge field enhancement the intensities of backward third-harmonic pulsed generated from the PIM/NIM periodic structure is increased for 100 time of those generated from a single NIM medium.

Inverse design method in acoustic wave manipulation

We present here the involvement of inverse design method with the acoustic wave modulation, to simplify how we get the required material parameters and design novel acoustic devices that can perform certain prescribed operation. As an example, the acoustic cloaking will be discussed. The existing acoustic invisibility design based on coordinate transformation method needs negative index media which can be realized through complicate structures. With inverse design method, we have designed a circular cloak device with positive index materials, that successfully make a circular scatterer acoustically invisible. This inverse design method takes a significant step towards realizing practical cloaking devices and would open up new possibilities for manipulating acoustic wavefront with simplified parameter distribution and optimized properties.

Enhancement of backward third-harmonic generation in a one-dimensional PIM/NIM periodic structure

A numerical simulation is reported for backward third-harmonic generation (BTHG) in a one-dimensional periodic structure containing a stack composed of positive-index material (PIM) and negative-index material (NIM). A multiple-scale method is used to formulate a completed set of coupled-mode equations with inhomogeneous higher-order nonlinear terms for both electric and magnetic fields. The coupled equations are numerically solved to simulate output third-harmonic frequency pulses and their conversion efficiencies by a fast Fourier transform–pulse propagation method. Finally, the numerical results validate the idea that using a combination of the negative-index phase-matched condition, which is created by engineering the dispersive property of the NIM layer, and local field enhancement, which is created by arranging PIM and NIM layers in an optimal periodic fashion, yields a dramatic enhancement of BTHG conversion efficiency.

Optical signal processing in nano nonlinear Fabry-Perot resonator containing negative index material

This paper investigates the issue of signal processing in a bistable Fabry-Perot (FP) resonator. FP resonator includes two one-dimensional photonic crystals (1DPCs) containing periodic structure of positive and negative index material (PIM-NIM) considering as two semi-transparent reflectors in nano scale which sandwiched a nanocavity. The transmitted intensity versus input intensity curve is obtained using the transfer matrix method which incorporates the bistability characteristics in some convenient conditions and parameters. We consider the bright soliton as an input pulse with nearly constant frequency and by changing its amplitude we investigate the output pulse in quasi-pulse regime. Such devices can practically be used as nano signal processing systems where it is illustrated that light can be controlled absolutely by light.