Gradient Index Devices Research Articles

Passive discrete lens for broadband elastic guided wave focusing

Elastic guided wave focusing is of great interest for applications such as vibroacoustic control, energy harvesting, or Structural Health Monitoring. Different strategies allow generation of this effect, GRadient-INdex devices in particular exploit medium with varying properties such as thickness to reproduce an adequate refractive index profile as in optics. The resulting continuous profiles have a curved geometry that can be hard to manufacture, and be difficult to integrate in a given design. The purpose of this paper is to propose a discrete design for a GRIN lens. It is composed of segments selected in number and thickness to give similar focusing effects as a continuous lens profile. The identified configuration is manufactured and bounded on an aluminium plate to evaluate the effective focusing performances. Numerical and experimental vibrometry results confirm that the proposed lens exhibits a fixed focal point over a broad frequency range. The discrete design overcomes fabrication issues encountered in continuous design, allowing for an easier integration in devices for elastic wave control.

Nanocontact Tailoring via Microlensing Enables Giant Postfabrication Mesoscopic Tuning in a Self‐Assembled Ultrasonic Metamaterial

AbstractThe ability to tune the resonant frequency of a self‐assembled ultrasonic metamaterial with mesoscale spatial resolution, after fabrication, by up to 250% is demonstrated. This tunability is achieved by the microlensing‐enabled modification of nanocontact features, wherein the metamaterial resonant elements “dig in” to the substrate. In addition to tunability exceeding prior MHz–GHz frequency ultrasonic metamaterial examples, the system presented herein can be tuned after assembly at a spatial resolution commensurate with the laser spot's diameter. It is posited that these aforementioned advantages will enable a new class of ultrasonic gradient index devices, such as ultrasonic elastic wave cloaks, that can be manufactured in a scalable manner and then rapidly tuned. Finally, it is expected that this large tunability at ultrasonic frequencies will have broader application to areas including optomechanics, acoustoplasmonics, quantum‐mechanical oscillators, and adhesion control.

Demonstration of steering acoustic waves by generalized Eaton lens

We demonstrate an acoustic generalized Eaton lens that steers an acoustic wave to a desired angle, to propose a design method for gradient-index devices using the sub-wavelength structure to shape an acoustic wave. Based on investigations on the effective parameter with several methods: the S-parameter retrieval method, Floquet-Bloch calculations, and multiple scattering theory (MST) for the cylindrical rigid rod structure, we speculate the design process to realize inhomogeneous refractive index distribution. For realization of a high effective index (∼2), the MST design inevitably fails, whereas the Floquet-Bloch calculations and S-parameter retrieval give identical results. By appropriately designing a two-dimensional array of cylindrical PMMA rods, we experimentally verify the acoustic generalized Eaton lenses for steering angles of 15° and 45°. Furthermore, the use of non-resonant metamaterials enables the proposed devices to work in the broad frequency range from 4 to 8 kHz.

Focusing, refraction, and asymmetric transmission of elastic waves in solid metamaterials with aligned parallel gaps

Gradient index (GRIN), refractive, and asymmetric transmission devices for elastic waves are designed using a solid with aligned parallel gaps. The gaps are assumed to be thin so that they can be considered as parallel cracks separating elastic plate waveguides. The plates do not interact with one another directly, only at their ends where they connect to the exterior solid. To formulate the transmission and reflection coefficients for SV- and P-waves, an analytical model is established using thin plate theory that couples the waveguide modes with the waves in the exterior body. The GRIN lens is designed by varying the thickness of the plates to achieve different flexural wave speeds. The refractive effect of SV-waves is achieved by designing the slope of the edge of the plate array, and keeping the ratio between plate length and flexural wavelength fixed. The asymmetric transmission of P-waves is achieved by sending an incident P-wave at a critical angle, at which total conversion to SV-wave occurs. An array of parallel gaps perpendicular to the propagation direction of the reflected waves stop the SV-wave but let P-waves travel through. Examples of focusing, steering, and asymmetric transmission devices are discussed.

Gradient Index Devices for the Full Control of Elastic Waves in Plates.

In this work, we present a method for the design of gradient index devices for elastic waves in plates. The method allows the design of devices to control the three fundamental modes, despite the fact that their dispersion relation is managed by different elastic constants. It is shown that by means of complex graded phononic crystals and thickness variations it is possible to independently design the three refractive indexes of these waves, allowing therefore their simultaneous control. The effective medium theory required for this purpose is presented, and the method is applied to the design of the Luneburg and Maxwell lenses as well as to the design of a flat gradient index lens. Finally, numerical simulations are used to demonstrate the performance of the method in a broadband frequency region.

3D printing: a useful tool for the fabrication of artificial electromagnetic (EM) medium

Purpose Artificial electromagnetic (EM) medium and devices are designed with integrated micro- and macro-structures depending on the EM transmittance performance, which is difficult to fabricate by the conventional processes. Three-dimensional (3D) printing provides a new solution for the delicate artificial EM medium. This paper aims to first review the applications of 3D printing in the fabrication of EM medium briefly, mainly focusing on photonic crystals, metamaterials and gradient index (GRIN) devices. Then, a new design and fabrication strategy is proposed for the EM medium based on the 3D printing process, which was verified by the implementation of a 3D 90o Eaton lens based on GRIN metamaterials. Design/methodology/approach A new design and manufacturing strategy driven by the physical (EM transmittance) performance is proposed to illustrate the realization procedures of EM medium based device with controllable micro- and macro-structures. Stereolithography-based 3D printing process is used to obtain the designed EM device, an GRIN Eaton lens. The EM transmittance of the Eaton lens was validated experimentally and by simulation. Findings A 3D 90o Eaton lens was realized based on GRIN metamaterials structure according to the proposed design and manufacturing strategy, which had the broadband (12-18 GHz) and low loss characteristic. The feasibility of 3D printing for the artificial EM medium and GRIN devices has been verified for the further real applications in the industries. Originality/value The applications of 3D printing in artificial EM medium and devices were systematically reviewed. A new design strategy driven by physical performance for the EM device was proposed and validated by the firstly 3D printed 3D Eaton lens.

Simultaneous control of the S and A Lamb modes by graded phononic crystal plates

We propose a theory of gradient index devices in plates that allow the simultaneous control of both S0 and A0 Lamb modes. This is in contrast to the existing approaches that are mainly limited to the manipulation of only the lowest A0 modes. These devices are based on phononic crystal plates, which are studied in the low frequency (homogenization) limit. We demonstrate a direct relationship between the dispersion relation of these two modes in phononic crystal plates that, together with the thickness dependence of the dispersion relation of the A0 mode, allows their simultaneous control. As a matter of illustration, a flat gradient index lens and a circular Luneburg lens are designed by means of the simultaneous variation of the inclusions' radii and the thickness of the plate. Numerical simulations show that the performance of these devices is good for the two modes in a broadband frequency region and that this approach can be used to design more advanced refractive devices for the total control of guided vibrational modes. Potential applications for the detection of small vibrations and energy harvesting devices are finally discussed.

The homogenization limit and waveguide gradient index devices demonstrated through direct visualization of THz fields

Electromagnetic homogenization approximation calculates an effective refractive index of a composite material as a weighted average of its components, and has found uses in gradient refractive index and transformation optics devices. However, the utility of the homogenization approximation is hindered by uncertainty in its range of applicability. Harnessing the capability of time-resolved imaging provided by the terahertz polaritonics platform, we determined the dispersion curves of slab waveguides with periodic arrays of holes, and we quantified the breakdown of the homogenization approximation as the period approached the terahertz wavelength and the structure approached the photonic bandgap regime. We found that if the propagation wavelength in the dielectric waveguide was at least two times as large as the Bragg condition wavelength, the homogenization approximation held independent of the detailed geometry, propagation direction, or fill fraction. This value is much less demanding than the estimate of 10:1 often assumed for homogenization. We further used the experimental capabilities to extract the effective refractive index of the photonic crystals in the homogenization approximation limit, and we used this to analyze the predictive strength of analytical formulas. These formulas enabled rapid design of a Luneburg lens and a bi-directional cloak in a waveguide platform without the need for numerical simulations. Movies of terahertz waves interacting with these structures, which were fabricated using femtosecond laser machining, reveal excellent performance. The combination of an analytical formula and confidence in the homogenization approximation will aid in fast design and prototyping of gradient index devices.

Gradient index lenses for flexural waves based on thickness variations

This work presents a method for the realization of gradient index devices for flexural waves in thin plates. Unlike recent approaches based on phononic crystals, the present approach is based on the thickness-dependence of the dispersion relation of flexural waves, which is used to create gradient index devices by means of local variations of the plate's thickness. Numerical simulations of known circularly symmetrical gradient index lenses have been performed. These simulations have been done using the multilayer multiple scattering method and the results prove their broadband efficiency and omnidirectional properties. Finally, finite element simulations employing the full three-dimensional elasticity equations also support the validity of the designed approach.

All-dielectric three-dimensional broadband Eaton lens with large refractive index range

We proposed a method to realize three-dimensional (3D) gradient index (GRIN) devices requiring large refractive index (RI) range with broadband performance. By combining non-resonant GRIN woodpile photonic crystals structure in the metamaterial regime with a compound liquid medium, a wide RI range (1–6.32) was fulfilled flexibly. As a proof-of-principle for the low-loss and non-dispersive method, a 3D Eaton lens was designed and fabricated based on 3D printing process. Full-wave simulation and experiment validated its omnidirectional wave bending effects in a broad bandwidth covering Ku band (12 GHz–18 GHz).

Spatially addressable design of gradient index structures through spatial light modulator based holographic lithography

In this paper, we present an achievable gradient refractive index in bi-continuous holographic structures that are formed through five-beam interference. We further present a theoretic approach for the realization of gradient index devices by engineering the phases of the interfering beams with a pixelated spatial light modulator. As an example, the design concept of a gradient index Luneburg lens is verified through full-wave electromagnetic simulations. These five beams with desired phases can be generated through programming gray level super-cells in a diffractive spatial light modulator. As a proof-of-concept, gradient index structures are demonstrated using synthesized and gradient phase patterns displayed in the spatial light modulator.

Integrated photonic systems based on transformation optics enabled gradient index devices

Integrated photonics is expected to play an increasingly important role in optical communications, imaging, computing and sensing with the promise for significant reduction in the cost and weight of these systems. Future advancement of this technology is critically dependent on an ability to develop compact and reliable optical components and facilitate their integration on a common substrate. Here we reveal, with the utility of the emerging transformation optics technique, that functional components composed of planar gradient index materials can be designed and readily integrated into photonic circuits. The unprecedented design flexibility of transformation optics allows for the creation of a number of novel devices, such as a light source collimator, waveguide adapters and a waveguide crossing, which have broad applications in integrated photonic chips and are compatible with current fabrication technology. Using the finite-difference time-domain method, we perform full-wave numerical simulations to demonstrate their superior optical performance and efficient integration with other components in an on-chip photonic system. These components only require spatially-varying dielectric materials with no magnetic properties, facilitating low-loss, broadband operation in an integrated photonic environment.

Metal–dielectric metamaterials for transformation-optics and gradient-index devices in the visible regime

We investigate the application of metamaterials made of dielectrics with embedded metal nanoparticles for transformation-optics and gradient-index devices. We demonstrate that the permittivity and permeability distribution required for cylindrical cloaking at optical frequencies can be obtained by a composite material made of silver spheres embedded in a PMMA host. We show that this approach can be applied also to devices with an isotropic permittivity distribution and illustrate this for the optical black hole. The key ingredient of our system is the tunability of the plasmonic interactions between the metallic nanoparticles, depending on distance and size. In addition, we discuss possible realizations of the proposed structures.

Relaxation approach for the generation of inhomogeneous distributions of uniformly sized particles

For many applications in gradient index devices and photonic crystals, it is necessary to be able to design semicrystalline distributions of particles where the lattice constant of the distribution is an arbitrary function of position. We propose a method to generate such distributions which is physically motivated by a system of interacting particles, and apply it to the design and implementation of a microwave gradient index lens. While the demonstration was preformed at microwave wavelengths, this technique would also be particularly useful for designing devices for operation at IR and visible wavelengths where the fabrication of distributions of uniformly sized holes or columns is very easy.

Gradient index metamaterial based on slot elements

We present a gradient-index (GRIN) metamaterial based on an array of annular slots. The structure allows a large variation in the effective refractive index under normal-to-plane incidence and thus enables the construction of GRIN devices consisting of only a small number of functional layers. Using full-wave simulations, we demonstrate the annular slot concept by means of a three-unit-cell thin GRIN lens for the terahertz (THz) range. In the presented realizations, we achieved an index contrast of Δn=1.5 resulting in a highly refractive flat lens which is suitable for focusing THz radiation to a spot size smaller than the wavelength.