Positive Index Materials Research Articles

Study on the anisotropic photonic band gaps in three-dimensional tunable photonic crystals containing the epsilon-negative materials and uniaxial materials

In this paper, the properties of anisotropic photonic band gaps (PBGs) for three-dimensional (3D) photonic crystals (PCs) composed of the anisotropic positive-index materials (the uniaxial materials) and the epsilon-negative (ENG) materials with body-centered-cubic (bcc) lattices are theoretically studied by a modified plane wave expansion (PWE) method, which are the uniaxial materials spheres inserted in the epsilon-negative materials background. The anisotropic photonic band gaps (PBGs) and one flatbands region can be achieved in first irreducible Brillouin zone. The influences of the ordinary-refractive index, extraordinary-refractive index, filling factor, the electronic plasma frequency, the dielectric constant of ENG materials and the damping factor on the properties of anisotropic PBGs for such 3D PCs are studied in detail, respectively, and some corresponding physical explanations are also given. The numerical results show that the anisotropy can open partial band gaps in such 3D PCs with bcc lattices composed of the ENG materials and uniaxial materials, and the complete PBGs can be obtained compared to the conventional 3D PCs containing the isotropic materials. The calculated results also show that the anisotropic PBGs can be manipulated by the parameters as mentioned above except for the damping factor. Introducing the uniaxial materials into 3D PCs containing the ENG materials can obtain the larger complete PBGs as such 3D PCs with high symmetry, and also provides a way to design the tunable devices.

Enhanced complete photonic band gap for three-dimensional plasma photonic crystals in pyrochlore arrangement

In this paper, the properties of complete photonic band gaps (PBGs) for three-dimensional (3D) plasma photonic crystals (PPCs) composed of the isotropic positive-index materials and non-magnetized plasma with pyrochlore lattices are theoretically investigated by a modified plane wave expansion method. The eigenvalue equations for calculating the band structure for such 3D PPCs in the first irreducible Brillouin zone (spheres with the isotropic positive-index materials inserted in the non-magnetized plasma background) are theoretically deduced. Numerical simulations show that the complete PBG and one flatbands region can be achieved. It also shows that the larger PBG can be obtained in such PPCs topology structure compared to the conventional lattices as the non-magnetized plasma density is low, such as diamond, face-centered-cubic, body-centered-cubic and simple-cubic lattices. The influences of the relative dielectric constant of spheres, the filling factor of dielectric spheres, the plasma frequency and the plasma collision frequency on the properties of complete PBG are investigated in detail, and some corresponding physical explanations are also given. The numerical results also show that the PBG can be manipulated by the parameters as mentioned above except for the plasma collision frequency. Introducing the non-magnetized plasma into 3D dielectric–air photonic crystals (PCs) can obtain the larger complete PBGs as such 3D PCs in pyrochlore arrangement.

Measurements of a Planar Nine-Way Metamaterial Power-Combined Amplifier

In this paper, measurement results of a planar nine-way metamaterial power-combined amplifier are presented. The power-divider/combiner structure is a metamaterial lens composed of positive refractive index (PRI) material with right-handed unit cells and zero refractive index (ZRI) material with left-handed unit cells. Due to its uniform isolation characteristics, the graceful degradation performance of this power-combined amplifier is shown to be independent of the amplifier failure sequence. The power combining of nine 1-W amplifiers gives an output power of 7.64 W with a combining efficiency of 85% at 1.008 GHz, and the graceful degradation characteristic of this power-combined amplifier is experimentally demonstrated.

Experimental evidence of super-resolution better than λ/105 with positive refraction

Super-resolution (SR) systems surpassing the Abbe diffraction limit have been theoretically and experimentally demonstrated using a number of different approaches and technologies: using materials with a negative refractive index, utilizing optical super-oscillation, using a resonant metalens, etc. However, recently it has been proved theoretically that in the Maxwell fish-eye lens (MFE), a device made of positive refractive index materials, the same phenomenon takes place. Moreover, using a simpler device equivalent to the MFE called the spherical geodesic waveguide (SGW), an SR of up to λ/3000 was simulated in COMSOL. Until now, only one piece of experimental evidence of SR with positive refraction has been reported (up to λ/5) for an MFE prototype working at microwave frequencies. Here, experimental results are presented for an SGW prototype showing an SR of up to λ/105. The SGW prototype consists of two concentric metallic spheres with an air space in between and two coaxial ports acting as an emitter and a receiver. The prototype has been analyzed in the range 1 GHz to 1.3 GHz.

High-frequency uniform asymptotic solution for reflected and scattered fields over half-space metamaterial

It is known that when the cylindrical wave propagates from a positive index material (PIM) to a negative index material (NIM), the backward lateral wave is excited along the interface between the PIM and the NIM over a half-space metamaterial. In this study, by using the saddle point technique, we shall derive a novel high-frequency uniform asymptotic solution for the reflected and scattered fields over a half-space metamaterial with the NIM. The validity and utility of the novel uniform asymptotic solution is confirmed by comparing with the reference solution calculated by the numerical integration of the integral representation for the reflected and scattered fields. We have also shown the physical interpretation of the uniform asymptotic solution.

ENHANCED THE COMPLETE PHOTONIC BAND GAPS FOR THREE-DIMENSIONAL PHOTONIC CRYSTALS CONSISTING OF EPSILON-NEGATIVE MATERIALS IN PYROCHLORE ARRANGEMENT

In this paper, the properties of photonic band gaps (PBGs) for three-dimensional (3D) photonic crystals (PCs) composed of isotropic positive-index materials and epsilon-negative materials with pyrochlore lattices are theoretically investigated by a modifled plane wave expansion method. The eigenvalue equations of calculating the band structures for such 3D PCs in the flrst irreducible Brillouin zone (spheres with the isotropic positive-index materials inserted in the epsilon-negative materials background) are theoretically deduced. Numerical simulations show that the PBG and a ∞atbands region can be achieved. It is also found that larger PBG can be obtained in such PCs structure than the conventional lattices, such as diamond, face-centered-cubic, body-centered-cubic and simple-cubic lattices. The in∞uences of the relative dielectric constant of spheres, fllling factor, electronic plasma frequency, dielectric constant of epsilon-negative materials and damping factor on the properties of PBG for such 3D PCs are studied in detail, respectively, and some corresponding physical explanations are also given. The calculated results also show that the PBG can be manipulated by the parameters mentioned above except for the damping factor. Introducing the epsilon-negative materials into 3D dielectric PCs can obtain the complete and larger PBG as such 3D PCs with pyrochlore lattices, and also provides a way to design the potential devices.

Controlling self-focusing of ultrashort pulses with anomalous self-steepening in nonlinear negative-index materials

Controllable and dispersive magnetic permeability in negative-index materials (NIMs) offers greatly enhanced design freedom to alter the linear and nonlinear properties. This makes it possible for us to control the propagation of ultrashort pulses at will. In this paper, we will investigate the self-focusing of ultrashort pulses associated with anomalous nonlinear self-steepening (SS) effect and anomalous space–time focus (linear SS) effect in bulk NIMs with a nonlinear electric polarization, trying to disclose some unusual behaviors different from those in naturally positive-index materials. It is found that negative SS acts to push the peak intensity toward the trailing edge of a pulse and the resulting spectrum exhibits a broad redshifted trail; however, positive SS leads to the occurrence of the opposite situation in both temporal and spectral domains, that is, the peak intensity will move toward the leading edge of the pulse by shifting the spectrum toward the blue side. In addition, compared with the case in positive-index materials (PIMs), another most notable property of NIMs is that, whether self-focusing of ultrashort pulses will occur at the leading or the trailing edge can be manipulated freely by engineering the SS effect by choosing the size of split-ring resonator circuit elements. Our analysis is performed by directly numerically solving nonlinear Schrodinger equations as well as by using the moment method, both showing consistent results. These findings demonstrate that NIMs can provide us unique opportunities unattainable in PIMs to manipulate ultrashort pulse propagation.

AntisymmetricPT-photonic structures with balanced positive- and negative-index materials

We propose a new class of synthetic optical materials in which the refractive index satisfies $n(-\bx)=-n^*(\bx)$. We term such systems antisymmetric parity-time (APT) structures. Unlike PT-symmetric systems which require balanced gain and loss, i.e. $n(-\bx)=n^*(\bx)$, APT systems consist of balanced positive and negative index materials. Despite the seemingly PT-symmetric optical potential $V(\bx)\equiv n(\bx)^2\omega^2/c^2$, APT systems are not invariant under combined PT operations due to the discontinuity of the spatial derivative of the wavefunction. We show that APT systems can display intriguing properties such as spontaneous phase transition of the scattering matrix, bidirectional invisibility, and a continuous lasing spectrum.

Theoretical model for electromagnetic wave propagation in negative index material induced by cubic-quintic nonlinearities and third-order dispersion effects

We analyze the problem of characterization of electromagnetic (EM) wave that propagates in a negative index material (NIM) and compare to the behavior that observes in a positive index material (PIM), from the conventional technique of characterization of the pulse intensity profile. Firstly, we establish the nonlinear Schrodinger equation (NLSE) and use the Drude model to obtained the NLSE terms. Secondly, we apply the collective variables technique at each frequency range and show that the stability and the light pulse intensity are significantly depending on specific normalized frequencies. We determine the specific frequency range allowing a fear characterization of the intensity profile of light pulse when the frequency increases. We illustrate the effectiveness of this EM wave stabilization by applying the indicated frequency range. This conventional technique in NIM and PIM systems where the second-order dispersion, third-order dispersion, self phase modulation (SPM) and quintic effects originated from SPM called quintic phase modulation act to provoke strong perturbations.

Properties of the defect modes in 1D lossy photonic crystals containing two types of negative-index-material defects

In this paper, the characteristic matrix method is employed to theoretically investigate the propagation of electromagnetic waves through one-dimensional defective lossy photonic crystals composed of negative-index materials (NIMs) and positive-index materials. We consider symmetric and asymmetric geometric structures with two different types of NIM defect layers at the center of the structure. The effects of polarization and the angle of incidence on the defect modes in the transmission spectra of both the structures are investigated. The results show that the number of the defect modes within the photonic band gap depends on the type of the NIM defect layer and is independent of the geometrical structure. Moreover, it is shown that the defect mode frequency increases as the angle of incidence increases. This property is also independent of the geometry of the structure. The results can lead to designing new types of narrowband and multichannel transmission filters.

Defect modes properties in periodic lossy multilayer containing negative index materials with symmetric and asymmetric geometric structures

In this paper, the characteristic matrix method is used to study the propagation of electromagnetic waves through one-dimensional lossy photonic crystals composed of negative and positive refractive index material layers with symmetric and asymmetric geometric structures with a defect layer at the center of the structure. First, the positive index material defect layer is considered, and the effects of the polarization and the angle of incidence on the defect mode in the transmission spectra of the both structures are investigated. The results show that the number of the defect modes in the transmission spectra depends on the geometry (symmetric or asymmetric) of the structure. In addition, it is shown that the defect mode frequency increases as the angle of incidence increases. This property is independent of the geometry of the structure. Then, for normal incidence, the negative index material defect layer is considered, and the properties of defect modes for both structures are investigated. The results can lead to designing new types of transmission narrow filters.

Design and Power Performance Measurement of a Planar Metamaterial Power-Combined Amplifier

In this paper, a planar nine-way metamaterial power-combined amplifier implemented with microstrip grids, lumped capacitors and inductors, and power amplifiers is presented. The power-dividing/combining structure is a metamaterial lens composed of positive refractive index (PRI) material with right-handed unit cells and zero refractive index (ZRI) material with left-handed unit cells. A semi-circular interface is between PRI and ZRI materials. The infinite wavelength phenomenon in the ZRI material attains an equal magnitude and phase distribution to have an interconnection with the collinearly aligned amplifiers as a nine-way metamaterial power-combined amplifier with its input and output ports at the two focal points of a planar PRI–ZRI–PRI lens. An output power of 7.64 W with a combining efficiency of 85% is measured at 1.008 GHz. Through the field measurement to each unit cell, the dividing/combining phenomenon is experimentally verified and shown in a good agreement with simulation results. Furthermore, the graceful degradation characteristic of this power-combined amplifier is experimentally demonstrated.

Investigating the dispersive properties of the three-dimensional photonic crystals with face-centered-cubic lattices containing epsilon-negative materials

In this paper, dispersive properties of three-dimensional (3D) photonic crystals (PCs) with face-centered-cubic (fcc) lattices composed of the isotropic positive-index materials and epsilon-negative materials are theoretically investigated based on a modified plane wave expansion (PWE) method. The eigenvalue equations of such structure (spheres with epsilon-negative materials inserted in the dielectric background) are deduced. The band structures can be obtained by solving such nonlinear eigenvalue equations. It can be obviously seen that a photonic band gap (PBG), a flat band region, and two stop band gaps (SBGs) in the Г-X and Г-L directions appear, respectively. The results show that the upper edges of flat band region cannot be tuned by any parameters except for the electronic plasma frequency. The first PBG and the first SBGs above the flat band region in the Г-X and Г-L directions for the 3D PCs can be modulated by the filling factor, relative dielectric constant and electronic plasma frequency, respectively. However, the damping factor has no effect on the locations of the first PBG and the first SBGs above the flat band region in the Г-X and Г-L directions. These results may provide theoretical instructions to design the future optoelectronic and communication devices containing epsilon-negative materials.

Omnidirectional high absorption based on an asymmetric photonic crystal composed of negative-index material and positive-index material

The absorption enhancement of photonic crystals composed of negative-index material and positive-index material is investigated in this article. It is found that whole absorption of an electromagnetic wave with weak dependence on the incident angle can be achieved in an asymmetric structure by adjusting materials and parameters. Furthermore, with the incident angle increasing to 80°, we demonstrate that the absorption for both polarizations remains over 80%. Finally, the influence of the damping factor of the Drude model is studied, and a conclusion is drawn that says the absorption is invariant with the damping factor when the ratio between the damping factor and the electronic or magnetic plasma frequency is smaller than 10−4.

Acoustic Illusion near Boundaries of Arbitrary Curved Geometry

We have proposed a scheme and presented the first experimental demonstration of acoustic illusion, by using anisotropic metamaterials to manipulate the acoustic field near boundaries of arbitrary curved geometry. Numerical simulations and experimental results show that in the presence of an illusion cloak, any object can be acoustically transformed into another object. The designed illusion cloak simply comprises positive-index anisotropic materials whose material parameters are non-singular, homogeneous and, moreover, independent of the properties of either the original object or the boundary.

Enhancement of Photonic Crystal All-Optical Diode Efficiency with a Subwavelength Layer

In this paper, the e ect of a subwavelength thin layer on all-optical diode action in a one-dimensional photonic crystal is investigated. The photonic multilayer structure is considered as (BA)(AB)C(AABB), where layers A and B are nonlinear and linear materials respectively, and C is a thin layer with positive or negative-index material. The results are shown that by introducing a thin layer with di erent optical properties the all-optical diode e ciency is controllable. In our numerical results, the transmission contrast of the structure, without the thin layer is obtained as 0.63, with a positive index material layer nearly zero and with a negative index material thin layer about 0.75.

Manipulating dispersive wave generation by anomalous self-steepening effect in metamaterials

We present a theoretical investigation of dispersive wave (DW) generation in nonlinear metamaterials (MMs). The role of the anomalous self-steepening (SS) effect, which can be either positive or negative, and the negative SS parameter can have a very large value compared to an ordinary positive-index material, in DW generation is particularly identified. It is demonstrated that the SS effect exerts a great impact on the peak power while has little effect on the frequency shift of DW. For positive third-order dispersion (TOD), the negative SS broadens the pulse spectrum and weakens the DW's peak power significantly, opposite to the case of positive SS. For negative TOD, however, the negative SS narrows the pulse spectrum and enhances the DW's peak power, also opposite to the case of positive SS. The results suggest that the DW generation in nonlinear MMs can be manipulated by SS effect to a large extent.

Broadband phase retarder based on one-dimensional photonic crystal containing mu-negative materials

The phase shift upon reflection from one-dimensional photonic crystal composed of alternating layers of mu-negative materials and positive-index materials is numerically investigated. It is found that the phase difference between TE and TM reflected waves can remain constant in a rather wide frequency range within the single-negative gap of the proposed structure. Such property can be used to design broadband phase retarder. By varying the incident angle, the phase difference of the retarder can be adjusted from 0 to π, while the working frequency range of the retarder remains almost unchanged. Moreover, by varying the scaling factor or the thickness ratio of the two constituent materials, the working frequency range of the phase retarder can be conveniently tuned.

Negative refraction induced acoustic concentrator and the effects of scattering cancellation, imaging, and mirage

We present a three-dimensional acoustic concentrator capable of significantly enhancing the sound intensity in the compressive region with scattering cancellation, imaging, and mirage effects. The concentrator shell is built by isotropic gradient negative-index materials, which together with an exterior host medium slab constructs a pair of complementary media. The enhancement factor, which can approach infinity by tuning the geometric parameters, is always much higher than that of a traditional concentrator made by positive-index materials with the same size. The acoustic scattering theory is applied to derive the pressure field distribution of the concentrator, which is consistent with the numerical full-wave simulations. The inherent acoustic impedance match at the interfaces of the shell as well as the inverse processes of ``negative refraction---progressive curvature---negative refraction'' for arbitrary sound rays can exactly cancel the scattering of the concentrator. In addition, the concentrator shell can also function as an acoustic spherical magnifying superlens, which produces a perfect image with the same shape, with bigger geometric and acoustic parameters located at a shifted position. Then some acoustic mirages are observed whereby the waves radiated from (scattered by) an object located in the center region may seem to be radiated from (scattered by) its image. Based on the mirage effect, we further propose an intriguing acoustic transformer which can transform the sound scattering pattern of one object into another object at will with arbitrary geometric, acoustic, and location parameters.

Omnidirectional band gaps in quasiperiodic photonic crystals in the THz region

In this work we calculate the emittance spectra of the electromagnetic radiation normally and obliquely incident (s- and p-polarized modes) on a one-dimensional multilayer quasiperiodic photonic structure made up by layered system of positive (SiO2) and negative (LiTaO3) refractive index materials organized in a quasiperiodic (Fibonacci-like) fashion. We model the negative refractive index material by an effective medium, whose electric permittivity ϵ(ω) is characterized by a phonon-polariton frequency dependent dielectric function, while for the magnetic permeability μ(ω) we have a Drude-like frequency-dependent function. The emittance spectra are determined by means of a well known theoretical model based on Kirchoff’s second law, together with a transfer matrix formalism. Our results shows that the omnidirectional band gaps appear in the THz regime, in well defined frequency intervals independently of the electromagnetic radiation’s polarized modes.