Negative Effective Index Research Articles

Graded flat lens with negative index for silicon photonics

We have realized a graded flat lens with negative effective index operating at telecom wavelength for Silicon Photonics. We report on its design, fabrication, and experimental characterization. This photonic device behaves as a convergent lens; it has been designed so as to be fabricated on a Silicon on Insulator platform and to operate at 1.55 μm. It consists of a graded photonic crystal whose filling factor has been varied so as to fit the profile of index of the graded index lens. Since it operates in the second band of Photonic Crystals, the effective index is negative. It has been characterized in two steps: (i) first, the output beam has been scanned by a set of waveguides and a CCD camera. (ii) Second, the focusing has been investigated by Scanning Near-field Optical Microscopy. This characterization validates the design: the focal length is about 5 μm (≃ 3λ), while the width of the focal spot is 0.87 μm (0.53 λ). This compact photonic device is at the wavelength scale (thickness = 4.4λ). Our design, based on Graded Index Optics, may be adapted to design new devices perfectly suited for Photonics applications, such as a short taper or a mode converter.

Direct Bragg Grating Inscription in Single Mode Step-Index TOPAS/ZEONEX Polymer Optical Fiber Using 520 nm Femtosecond Pulses.

We experimentally report fiber Bragg gratings (FBGs) in a single mode step-index polymer optical fiber (POF) with a core made of TOPAS and cladding made of ZEONEX using 520 nm femtosecond pulses and a point-by-point (PbP) inscription method. With different pulse energies between 9.7 nJ and 11.2 nJ, 12 FBGs are distributed along the cores of two pieces of POFs with negative averaged effective index change up to ~6 × 10−4 in the TOPAS. For POF 1 with FBGs 1–6, the highest reflectivity 45.1% is obtained with a pulse energy of 10.6 nJ. After inscription, good grating stability is reported. Thanks to the post-annealing at 125 °C for 24 h, after cooling the grating reflectivity increases by ~10%. For POF 2 with FBGs 7–12, similar FBG data are obtained showing good reproducibility. Then, the FBGs are annealed at 125 °C for 78 h, and the average reflectivity of the FBGs during the annealing process increases by ~50% compared to that before the annealing, which could be potentially applied to humidity insensitive high temperature measurement.

Magnetically Reconfigurable Unidirectional Propagation of Electromagnetic Waves by Zero-Index–Based Heterostructured Metamaterials

We present a zero-index–based heterostructured magnetic metamaterial (HSMM) composed of two arrays of ferrite rods with different radii and lattice separations, which exhibits unidirectional propagation of electromagnetic (EM) waves, and the unidirectionality is reconfigurable dependent on the bias magnetic field (BMF). By calculating the photonic band diagrams and the effective constitutive parameters, it is shown that, for the MMs with two groups of lattice separations and ferrite rod radii, the effective refractive index is switched either from effective zero index (EZI) to effective positive index (EPI) by decreasing the BMF for one MM or from EZI to effective negative index (ENI) for the other MM by increasing the BMF. As a result, two kinds of HSMMs can be constructed with the combination of either EZI and ENI or EZI and EPI, both of which can be used to implement the unidirectional transport of EM waves and exhibit reconfigurable unidirectionality by either decreasing or increasing the BMF, thus providing us with more degrees of freedom. The concept put forward in the present work can be possibly extended to the heterostructured metamaterials made of phase-change materials and realize reconfigurable EM properties in optical frequency by tuning the temperature.

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.

Negative refraction and rotons in the relativistic Bose gas

We investigate the dispersion of a classical electromagnetic field in a relativistic ideal gas of charged bosons using scalar quantum electrodynamics at finite temperature and charge density. We derive the effective electromagnetic responses and the electromagnetic propagation modes that characterize the gas as a left-handed material with negative effective index of refraction neff=−1 below the transverse plasmon frequency. In the condensed phase, we show that the longitudinal plasmon dispersion relation exhibits a roton-type local minimum that disappears at the transition temperature.

Negative refraction in relativistic electron gas

We show that a gas of relativistic electrons is a left-handed material at low frequencies by computing the effective electric permittivity and effective magnetic permeability that appear in Maxwell’s equations in terms of the responses appearing in the constitutive relations, and showing that the former are both negative below the same frequency, which coincides with the zero-momentum frequency of longitudinal plasmons. We also show, by explicit computation, that the photonic mode of the electromagnetic radiation does not dissipate energy, confirming that it propagates in the gas with the speed of light in vacuum, and that the medium is transparent to it. We then combine those results to show that the gas has a negative effective index of refraction n e f f = − 1 . We illustrate the consequences of this fact for Snell’s law, and for the reflection and transmission coefficients of the gas.

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.

Flat lens effect on seismic waves propagation in the subsoil

We show that seismic energy simulated by an artificial source that mainly propagates Rayleigh surface waves, is focused in structured soil made of a grid of holes distributed in the ground. We carry out large-scale field tests with a structured soil made of a grid consisting of cylindrical and vertical holes in the ground and a low frequency artificial source (<10 Hz). This allows the identification of a distribution of energy inside the grid, which can be interpreted as the consequence of a dynamic anisotropy akin to an effective negative refraction index. Such a flat lens reminiscent of what Veselago and Pendry envisioned for light opens avenues in seismic metamaterials to counteract partially or totally the most devastating components of seismic signals.

Spatial frequency maps of power flow in metamaterials and photonic crystals: Investigating backward-wave modes across the electromagnetic spectrum

We present spatial frequency maps of power flow in metamaterials and photonic crystals in order to provide insights into their electromagnetic responses and further our understanding of backward power in periodic structures. Since 2001, many different structures across the electromagnetic spectrum have been presented in the literature as exhibiting an isotropic negative effective index. Although these structures all exhibit circular or spherical equifrequency contours that resemble those of left-handed media, here we show through $k$-space diagrams that the distribution of power in the spatial frequency domain can vary considerably across these structures. In particular, we show that backward power arises from high-order right-handed harmonics in photonic crystals, magnetodielectric crystals, and across the layers of coupled-plasmonic-waveguide metamaterials, while arising from left-handed harmonic pairs in split-ring resonator and wire composites, plasmonic crystals, and along the layers of coupled-plasmonic-waveguide metamaterials. We also show that the fishnet structure exhibits the same left-handed harmonic pairs as the latter group. These observations allow us to categorize different metamaterials according to their spatial spectral source of backward power and identify the mechanism behind negative refraction at a given interface. Finally, we discuss how $k$-space maps of power flow can be used to explain the high or low transmittance of power into different metamaterial or photonic crystal structures.

Phase accumulation tracking algorithm for effective index retrieval of fishnet metamaterials and other resonant guided wave networks

A phase accumulation tracking (PAT) algorithm is proposed and demonstrated for the retrieval of the effective index of fishnet metamaterials (FMMs) in order to avoid the multi-branch uncertainty problem. This algorithm tracks the phase and amplitude of the dominant propagation mode across the FMM slab. The suggested PAT algorithm applies to resonant guided wave networks having only one mode that carries the light between the two slab ends, where the FMM is one example of this metamaterials sub-class. The effective index is a net effect of positive and negative accumulated phase in the alternating FMM metal and dielectric layers, with a negative effective index occurring when negative phase accumulation dominates.

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.

Accurate Circuit Modeling of Fishnet Structures for Negative-Index-Medium Applications

Metallic plates with a two-dimensional (2D) periodic distribution of sub-wavelength apertures are known to exhibit extraordinary transmission of electromagnetic waves. Stacking two or more of such plates gives place to the so-called fishnet structures, which constitute a popular way of achieving an effective negative index medium at frequencies ranging from microwaves to optics. Unfortunately, a general wideband equivalent circuit has not yet been proposed to facilitate its understanding and design. This work presents this circuit model with closed-form expressions for the circuit elements, thus making it possible to obtain the electrical response for this class of structures in a very efficient way. This procedure is much faster than alternative numerical methods at the same time that it retains a high level of accuracy when compared with some other oversimplified models. The circuit model also provides a simple rationale as well as a good physical insight in order to explain the qualitative behavior of such structures, independently of the number of stacked layers.

Optical and magneto-optical properties of plasma-magnetic metamaterials

We investigate the optical and magneto-optical properties of a tunable left-handed material (LHM) consisting of an array of plasma and ferrite layers. It has been shown that the effective refraction index of a homogeneous composite in certain frequencies is negative. It can also be seen that the magnitude of extremum of the negative effective refraction index changes with frequency, external magnetic field and the electron density of plasma layer. In addition, a theoretical calculation of the faraday optical rotation effect of the proposed metamaterial is presented. From the obtained results, we find that there is a large faraday rotation angle in the frequency range where the system shows the left-handed property. Our outcomes demonstrate the potential applications of the device for tunable perfect lenses and active magneto-optic in micro-wave devices.

Superlensing effect for surface acoustic waves in a pillar-based phononic crystal with negative refractive index

We demonstrate super resolution imaging for surface acoustic waves using a phononic structure displaying negative refractive index. This phononic structure is made of a monolithic square lattice of cylindrical pillars standing on a semi-infinite medium. The pillars act as acoustic resonator and induce a surface propagating wave with unusual dispersion. We found, under specific geometrical parameters, one propagating mode that exhibits negative refraction effect with negative effective index close to −1. Furthermore, a flat lens with finite number of pillars is designed to allow the focusing of an acoustic point source into an image with a resolution of λ3, overcoming the Rayleigh diffraction limit.

Influence of formic acid on electrical, linear and nonlinear optical properties of potassium dihydrogen phosphate (KDP) crystals

In present investigation 0.5 and 1mol% formic acid (FA) added potassium dihydrogen phosphate (KDP) crystals have been grown by a slow evaporation technique. The cell parameters of the grown crystals were determined using single crystal X-ray diffraction analysis. The presence of different functional groups has been qualitatively analyzed by the FT-IR spectral analysis. The optical transparency and optical constants were assessed employing UV–visible studies in the range of 200–900nm. The wide optical band gap of 1mol% FA added KDP has been found to be 5eV. The frequency dependent dielectric measurements were studied for pure and KDP added FA crystals. The enhanced second harmonic generation (SHG) efficiency of grown crystals was determined by a classical Kurtz–Perry powder technique. The encouraging third order nonlinear properties were examined employing a Z-scan technique using He–Ne laser, at 632.8nm. The effective negative index of refraction and high figure of merit (FOM) essential for laser stabilization were determined for grown crystals.

Analysis of Nitrides- and TCOs-Based Plasmonic Waveguides for Slow-Wave and Negative Index Sub-Wavelength Propagation

In this paper, a comparison between metal-insulator-metal (MIM) waveguides made of silver and newly emerging plasmonic materials is reported. In particular, titanium nitride (TiN) from the class of nitrides, and gallium zinc oxide (GZO) from the class of transparent conducting oxides, are proposed as alternatives to conventional metals for the more flexible exploitation of plasmonic properties. Depending on the specific application, the new choices of the plasmonic material allow for tuning of the surface plasmon resonance and may also reduce typical conductive losses. Moreover, compared to noble metals, these new plasmonic materials have the extremely important property of being compatible with the mature CMOS technology. In this paper, the specific application of MIM waveguides made of TiN and GZO for dispersion engineering (slow-wave propagation and negative effective index) is considered for the first time.

The forward-wave and backward-wave behaviors of electromagnetic waves in two-dimensional photonic crystals

The negative refractions are discussed in detail to demonstrate two different two-dimensional photonic crystal structures that undergo negative refractions associated with the backward-wave and forward-wave phenomenon, respectively. The presentation of the left-handed property of effective negative index photonic crystal is followed by a discussion of a backward flowing phase and causality. The forward-wave negative refraction occurs in photonic crystals as a result of anisotropy. This paper is based on the theoretical analysis and is illustrated with the results of finite element method simulations.

Negative Propagation Effects in Two-Dimensional Silicon Photonic Crystals

We demonstrated negative refraction effects of light propagating in two-dimensional square and hexagonal-lattice silicon photonic crystals (PhCs). The plane wave expansion method was used to solve the complex eigenvalue problems, as well as to find dispersion curves and equal-frequency contour (EFC). The finite-difference time-domain (FDTD) method was used to simulate and visualize electromagnetic wave propagation and scattering in the PhCs. Theoretical analyses and numerical simulations are presented. Two different kinds of negative refractions, namely, all-angle negative refraction (AANR) without a negative index and negative refraction with effective negative index, have been verified and compared.

Enhanced lens byεandμnear-zero metamaterial boosted by extraordinary optical transmission

In this paper we report directivity enhancement by a short-focal-length plano-concave lens engineered by stacked subwavelength hole arrays (fishnet-like stack) with an effective negative index of refraction close to zero, $n$ \ensuremath{\rightarrow} 0, that arises from \ensuremath{\varepsilon} and \ensuremath{\mu} near-zero extreme values. The plano-concave lens frequency response shows two enhancement peaks, one at the wavelength corresponding to $n$ $=$ \ensuremath{-}1 and, prominent in this configuration, another unexpected peak when $n$ \ensuremath{\rightarrow} 0 that comes as a result of the similar low values of \ensuremath{\varepsilon} and \ensuremath{\mu}. The frequency-dependent negative refractive index and beam-forming properties of the lens are supported by finite-integration-frequency- and time-domain simulations and experimental results. This near-zero metamaterial lens can find applications in terahertz and even optics since the building block, stacked extraordinary optical transmission layers, has already been reported for those regimes under the name of fishnet structure.

Enlarging the negative-index bandwidth of optical metamaterials by hybridized plasmon resonances

By exploiting the concept of internal surface plasmon polariton (I-SPP) resonances, which appear at nonsingle metallic film stacks, we have designed a metamaterial showing a negative effective index within a large frequency bandwidth. The designed structure consists of an arrangement of several fishnet layers. By properly adjusting the lattice and the thickness of the dielectric slab of the fishnet, an I-SPP mode can be excited at a certain frequency, giving rise to a negative permeability. Thus, when combining several fishnet layers, each one configured to excite an I-SPP at a slightly different frequency, the coupling among the fishnet layers will cause a plasmon hybridization effect that enables us to extend the negative-index bandwidth.