Negative Effective Refractive Index Research Articles

Design and analysis of wavelength tunable metamaterial reflector

This paper reports the design and performance characteristics of perfect reflector tunable metamaterial (MTM). The reported MTM parameters are optimized to achieve nearly 100 % reflection at resonance wavelength (λr) 1550 nm. The propagation characteristic of the proposed MTM structure was obtained by the finite element method (FEM). The electromagnetic parameters such as effective permittivity (εeff.), effective permeability (µeff.), and effective refractive index (ηeff.) are calculated using Nicolson-Ross-Weir (NRW) method and analysed for the 1400–1700 nm wavelength range. It has been observed that the proposed MTM structure exhibits µ-negative (MNG) metamaterial characteristics as well as a negative effective refractive index at λr. Further, it has also been shown that by varying the number of arrays of unit cells and using a mirror image of the unit cell, the operating wavelength can be easily tuned as required for different applications. The overall perfect reflectance and the tunable performance of the proposed MTM has a potential applications in the design and development of compact photonic devices such as optical resonators and antennas.

Dispersion Mapping in 3-Dimensional Core-Shell Photonic Crystal Lattices Capable of Negative Refraction in the Mid-Infrared.

Engineering of the dispersion properties of a photonic crystal (PhC) opens a new paradigm for the design and function of PhC devices. Exploiting the dispersion properties of PhCs allows control over wave propagation within a PhC. We describe the design, fabrication, and experimental observation of photonic bands for 3D PhCs capable of negative refraction in the mid-infrared. Band structure and equifrequency contours were calculated to inform the design of 3D polymer-germanium core-shell PhCs, which were fabricated using two-photon lithography direct laser writing and sputtering. We successfully characterized a polymer-Ge core-shell lattice and mapped its band structure, which we then used to calculate the PhC refraction behavior. An analysis of wave propagation revealed that this 3D core-shell PhC refracts light negatively and possesses an effective negative index of refraction in the experimentally observed region. These results suggest that architected nanolattices have the potential to serve as new optical components and devices across infrared frequencies.

SiO2-SnO2:Er3+ planar waveguides: Highly photorefractive glass-ceramics

For different applications in laser photonics and integrated optics, photorefractive materials are surely of great interest and play an important role in miniaturization of devices and fabrication of functional photonic structures such as gratings and waveguides. In this work, high photorefractivity of sol-gel derived SiO2-SnO2:Er3+ glass-ceramic planar waveguides, with negative effective refractive index change, is demonstrated. Through the photorefractivity investigation employing the UV pulsed KrF excimer laser (λ = 248 nm), the glass-ceramic planar waveguides show fast photorefractive response after a cumulative dose of only 0.3 kJ/cm2. A higher SnO2 content in the glass-ceramics leads to a greater change of saturated effective refractive index: Δneff = - (2.60 ± 0.20) x 10-3 at 1550 nm on the TE0 mode, for the 30 mol% SnO2 planar waveguides and Δneff = - (2.00 ± 0.20) x 10-3 on the 1550 nm TE0 mode, for the 20 mol% SnO2 ones. To investigate the structural modifications involved in the photorefractivity of the SiO2-SnO2:Er3+ glass-ceramics, XRD and Raman characterizations are employed. The grating fabrication by direct UV writing on the SiO2-SnO2:Er3+ glass-ceramic planar waveguide as well as an important reduction in the employed energy is demonstrated.

A tri-band left-handed meta-atom enabled designed with high effective medium ratio for microwave based applications

This paper represents a tri-band left-handed meta-atom with high effective medium ratio, which is applicable for tri-band microwave based communication applications. The proposed meta-atom consists of modified complementary split ring resonator (CSRR) with two pi shaped metal strip loaded in the inner side. It shows the behavior of negative permeability and permittivity at 2.85 GHz, 4.83 GHz, 8.39 GHz, and 11.42 GHz resonance frequencies and extracted the double negative (DNG) metamaterial properties. The designed meta-atom dimension is 0.076λ×0.076λ at lower resonance frequency. To develop and analyze the offered meta-atom, the electromagnetic (EM) simulator CST Microwave Studio and MATLAB software were used. The equivalent circuit with RLC components of the proposed metamaterial unit cell is also investigated through ADS simulator and comparing S parameter (transmission coefficients) results with CST results. Analysis and comparison have been carried out with different configurations, such as various design structures, distinct substrate, changing the gap of the splits, and various array measures. All the array configurations proved that the frequency of operation is in the S-, C-, and X-bands. The designed meta-atom has double negative regions of 2.89–2.96 GHz, 4.84–4.99 GHz, 8.42–8.49 GHz, and 11.43–12.32 GHz, with the regions of effective negative refractive index 2.85–3.09 GHz, 4.83–5.36 GHz, 8.40–8.57 GHz, and 11.40–12.55 GHz, respectively. The effective medium ratio is 13.16; this implies that the proposed miniaturized meta-atom design is efficient and compact. The scattering parameter dimension of the meta-atom promising for the microwave based applications at S-, C-, and X-bands.

A Gap Coupled Hexagonal Split Ring Resonator Based Metamaterial for S-Band and X-Band Microwave Applications

A gap coupled hexagonal split ring resonator (GCHSRR) based metamaterial is presented in this paper for S-band and X-band microwave applications with absorptance. This gap coupled hexagonal split ring resonator is the amendment of the typical split-ring resonator (SRR). Three interconnected hexagonal split ring resonators are applied with a stripline to increase the electrical length and coupling effect of the GCHSRR. SRR has an impact on the extraction of effective parameters such as permittivity, permeability and refractive index. The dimension of the proposed GCHSRR unit cell is $10\times 10$ mm 2, which is printed on low-cost FR4 material. The transmission frequency of the proposed GCHSRR unit cell ranges from 3.42 GHz to 3.73 GHz and 11.27 GHz to 11.91 GHz, which makes the metamaterial applicable for S-band and X-band microwave applications. The GCHSRR unit cell has a double negative regime of 7.92 GHz to 9.78 GHz with an effective negative refractive index regime of 6.30 GHz to 10.22 GHz and 11.97 GHz to 12.61 GHz. The effective medium ratio is 8.4, which implies the novelty of the proposed design. Moreover, the GCHSRR has high absorption peaks of 99%, 98%, and 81% at 4.27 GHz, 5.42 GHz, and 12.40 GHz, respectively. An $18\times 20$ GCHSRR array structure is also designed and studied. The effective parameters and the effective medium ratio with a high absorptance make the proposed GCHSRR based metamaterial suitable for practical microwave applications.

Possibility of negative refraction for visible light in disordered all-dielectric resonant high index metasurfaces

Effective refractive index of disordered all-dielectric metasurfaces consisting of gallium phosphide (GaP) spheres is studied by means of three-dimensional finite-difference time-domain (FDTD) simulations at the wavelength of 532 nm. It is shown that a mixture of the high index nanoparticles with sizes close to the first magnetic and electric resonances randomly dispersed on metasurface may possess negative refraction. The dependence of the metasurface effective refractive index on the nanoparticle concentration and size is constructed. The feasibility of negative refraction at large concentrations of the high index resonant spheres is demonstrated. The negative effective refractive index is exhibited only for a monolayer of GaP spheres.

Normal Doppler Frequency Shift in Negative Refractive‐Index Systems

AbstractBesides the well‐known negative refraction, a negative refractive‐index material can exhibit another two hallmark features, which are the inverse Doppler effect and backward Cherenkov radiation. The former is known as the motion‐induced frequency shift that is contrary to the normal Doppler effect, and the latter refers to the Cherenkov radiation whose cone direction is opposite to the source's motion. Here these two features are combined and the Doppler effect inside the backward Cherenkov cone is discussed. It is revealed that the Doppler effect is not always inversed but can be normal in negative refractive‐index systems. A previously un‐reported phenomenon of normal Doppler frequency shift is proposed in a regime inside the backward Cherenkov cone, when the source's velocity is two times faster than the phase velocity of light. A realistic metal–insulator–metal structure, which supports metal plasmons with an effective negative refractive index, is adopted to demonstrate the potential realization of this phenomenon.

A complementary split ring resonator based metamaterial with effective medium ratio for C-band microwave applications

A complementary split-ring resonator (CSRR) based metamaterial is designed and investigated in this paper for microwave applications with effective medium ratio. This CSRR is the modification of the conventional split-ring resonator. Three square split-ring resonators (SSRR) are interconnected with a strip line as well as two splits in three square split-ring resonators are applied to increase the electrical length and coupling effect. The CSRR has an impact on the extraction of effective permittivity, permeability, and refractive index. The dimension of the designed unit cell is 5.5 × 5.5 mm2 that is printed on FR4 material. An 18 × 20 array structure is also investigated in this paper. The unit cell has a double negative region of 6.34–7.39 GHz and 8.20–9.98 GHz with effective negative refractive index region of 4.23–7.32 GHz and 7.40–10.0 GHz. The effective medium ratio is 8.0, which implies the effectiveness and compactness of the proposed CSSR design. The compact size, effective parameters, and effective medium ratio rate represent the suitability of the proposed metamaterial for practical C band microwave applications.

Numerical study of a high negative refractive index based tunable metamaterial structure by graphene split ring resonator for far infrared frequency

We present a numerical study of a high negative effective refractive index based actively tunable squared shaped graphene split ring resonator for far infrared frequency spectrum. Graphene split ring resonator (GSRR) structure is investigated for the different cases of the split rings. Tunability of the structure is controlled by varying the different chemical potential of the graphene sheet, which can be controlled by external potential. Transmission, Reflection and Absorption parameters are investigated to check the resonance response. At each and every point of resonance, highly negative refractive index is been observed. The proposed structure is producing the multiple short as well as large band resonance band over 1 THz to 2.5 THz frequency range for the different chemical potential that varies between 0.1 eV to 0.9 eV. The study results inferred that tunable properties of the GSRR structure can help to design the various photonics device such as sensor, modulator and polarizer, etc.

Negative Luneburg lens based on the graded annular photonic crystals

Focusing by the designed negative Luneburg lens which is based on graded annular photonic crystals (GAPCs) are studied in this paper. The GAPCs are composed of ring-shaped silicon pillars in a hexagonal lattice. The gradient of refractive index is achieved by modifying the radii of inner holes. The effective negative refractive index is analyzed based on the photonic band structures and verified by the simulation of negative refraction in APCs flat lens. Numerical simulation results show that a 0.6λ focusing spot can be realized by our designed Luneburg lens and it has the potential to be utilized in photonic integrated circuits.

Multiband super-resolution imaging of graded-index photonic crystal flat lens

Multiband super-resolution imaging of point source is achieved by a graded-index photonic crystal flat lens. With the calculations of six bands in common photonic crystal (CPC) constructed with scatterers of different refractive indices, it can be found that the super-resolution imaging of point source can be realized by different physical mechanisms in three different bands. In the first band, the imaging of point source is based on far-field condition of spherical wave while in the second band, it is based on the negative effective refractive index and exhibiting higher imaging quality than that of the CPC. However, in the fifth band, the imaging of point source is mainly based on negative refraction of anisotropic equi-frequency surfaces. The novel method of employing different physical mechanisms to achieve multiband super-resolution imaging of point source is highly meaningful for the field of imaging.

Negative index and mode coupling in all-dielectric metamaterials at terahertz frequencies

We elucidate the role of the mode coupling of the Mie resonances in all-dielectric metamaterials to ensure a negative effective index at terahertz frequencies. We perform a study as a function of the lattice period and of the frequency overlapping of the modes of resonance. We show that negative effective refractive index requires sufficiently strong mode coupling and that for even more strong mode coupling, the first two modes of Mie resonances are degenerate; the effective refractive index is then undetermined. We also show that it is possible to obtain near-zero, or even null, effective index with a judicious adjustment of the mode coupling. Further, we discuss the mode coupling effect with hybridization in metamaterials.

Direct measurement of the negative Goos-Hänchen shift of single reflection in a two-dimensional photonic crystal with negative refractive index.

The negative Goos-Hänchen shift (GHS) on a two-dimensional photonic crystal with an effective negative refractive index is investigated by simulation and experiment. The measured refractive index of the fabricated photonic crystal is nearly -0.44. The difference between the Goos-Hänchen shift of the transverse electric wave GTE and that of the transverse magnetic wave GTM (DGHS) in the height direction of a silicon rod is measured at three incident angles. The result shows that DGHS is always smaller than -GTM, thus GTE<0; therefore, the negative GHS does occur on the surface of the photonic crystal with a negative refractive index.

Pencil-Beam Single-Point-Fed Dirac Leaky-Wave Antenna on a Transmission-Line Grid

Leaky-wave antennas (LWAs) are widely used as single-point-fed linear antenna arrays. The extension of LWAs to 2D implies that they can be used as single-point-fed 2D antenna arrays without requiring a complex feeding network. However, generating a pencil beam from 2D LWAs is not straightforward and due care has to be taken for the design of the LWA. On the other hand, transmission-line (TL) grids have demonstrated interesting behaviors, such as an effective negative refractive index and growing of evanescent waves. In this paper, a singlepoint-fed TL-grid 2D Dirac leaky-wave antenna (DLWA) design is proposed that generates a pencil beam at both broadside and slightly tilted angles. The TL-grid unit cell is analytically treated in light of its scattering and impedance matrices. The optimized TL-grid unit cell is shown to exhibit a closed bandgap in the dispersion relation which is also linearly varying with frequency (hence it is a DLWA). The proposed 2D DLWA design is fabricated and the experimental results are presented.

二维平板光子晶体的等效负折射率测量

二维平板光子晶体的等效负折射率测量

Broadband negative refractive index at visible range with composite materials

In this research work, composite media based on metamaterials including random distribution of spherical nanoparticles in a polymeric foam host are suggested to achieve negative effective refractive index in the visible spectrum. For this purpose structures including single, two and three layer spherical particles are investigated. Based on simulation results, media including single layer spheres (metallic and dielectric particles) and two layer nanospheres (core–shell particles consist of metallic core and dielectric shell) based on superposition of nanoparticles with different sizes and fill fractions are proposed for desired result. In this work, to obtain optimized band with negative RI media, superposition of three layer nanoparticles and doped semiconductor are designed.

Electromagnetic origins of negative refraction in coupled plasmonic waveguide metamaterials

A metamaterial composed of stacked plasmonic waveguides which support backward propagation along the layers has been shown to exhibit a nearly spherical equifrequency contour (EFC) in which the Floquet-Bloch wave vector ${\mathbf{k}}_{\mathrm{FB}}$ and Poynting vector $\mathbf{S}$ point in opposite directions everywhere on this surface. Experiments performed on this structure have also shown that polarized light beams incident from free space refract to the same side of normal over a wide range of incidence angles. Together, these observations have led researchers to describe this structure as a homogeneous medium with three-dimensionally isotropic negative refractive index; however, a close inspection of the fields throughout the structure as provided in this paper would suggest otherwise. Here, we rigorously analyze the relationship between phase and power flow within the structure by introducing a method to calculate the power flow of all Floquet-Bloch harmonics, information which cannot be obtained from either conventional analysis of EFCs or effective medium theory. Access to power flow of all harmonics enables us to demonstrate the origin of backward power (defined with respect to the direction of ${\mathbf{k}}_{\mathrm{FB}})$, and in doing so, verify the validity of the claimed three-dimensionally isotropic left-handed response and the validity of describing the medium by a simple negative effective index of refraction $n=\ensuremath{-}1$. Knowledge regarding the distribution of power flow across the harmonics can also be used to design highly efficient methods to couple light into and out of these structures. As an example, we show that tailored wave excitation can achieve coupling efficiencies of up to 96%, over 5 times greater than that achieved by normal-incidence plane-wave excitation.

Mechanism Analysis of the Inverse Doppler Effect in Two-Dimensional Photonic Crystal based on Phase Evolution

Although the inverse Doppler effect has been observed experimentally at optical frequencies in photonic crystal with negative effective refractive index, its explanation is based on phenomenological theory rather than a strict theory. Elucidating the physical mechanism underlying the inverse Doppler shift is necessary. In this article, the primary electrical field component in the photonic crystal that leads to negative refraction was extracted, and the phase evolution of the entire process when light travels through a moving photonic crystal was investigated using static and dynamic finite different time domain methods. The analysis demonstrates the validity of the use of np (the effective refractive index of the photonic crystal in the light path) in these calculations, and reveals the origin of the inverse Doppler effect in photonic crystals.

Optical Response of Silver Nanoneedles on a Mirror.

Plasmonic properties of metal nanostructures are appealing due to their potential to enhance photovoltaics or sensing performance. Our aim was to identify the plasmonic characteristics of silver nanoneedles on a reflective layer in the polarized optical response. Experimental ellipsometry results are complemented by finite-difference time-domain (FDTD) calculations. Plasmon resonances on the nanoneedles can indeed be observed in the polarized optical response. This study reveals the details of the complex antenna-like behaviour of the nanoneedles which gives an agreement between experiment and FDTD simulation. The simulations show that the plasmon resonances lead to an effective negative refractive index, originating from the negative refractive index of the nanoneedles in combination with its supporting substrate, i.e. a mirror. This original study of a complex plasmonic system by ellipsometry and FDTD has great relevance for applications, making use of intricate light matter interaction.

3次元金属マイクロコイルを装加した金属スリットアレーによるテラヘルツ波帯での負の屈折率設計

The current understanding is that the progress of terahertz technology demands highly-functional and high-performance optical devices. Materials are limited in naturally-occurring materials with positive refractive indices when conventional techniques design the devices. However, metamaterial techniques can shed light on a variety of potential applications because a refractive index including a negative one is arbitrarily controlled by various subwavelength structures. Here, inspired by novel fabrication techniques of micron-scale structures, we design a negative refractive index by a metal-slit array with three-dimensional metal microcoils in a terahertz frequency. The parallel-plate waveguide under a cutoff frequency can produce a negative permittivity, and the resonance of the sprit-ring resonators can also produce a negative permeability. An effective negative refractive index with neff = -6.9 + j1.1 is designed at 0.26 THz by an approximate analysis with periodic boundary walls, and performance with n = -3.2 at 0.30 THz is visually confirmed by a full model analysis. A time-consuming procedure in the iterative design of the full model can be drastically escaped by initial parameters which is obtained by the approximate model. The structure with the negative refractive index would be applied to many progressive devices, such as bandpass filters, superlenses, and antennas.