Luneburg lens in silicon photonics

Folded Digital Meta-Lenses for on-Chip Spectrometer

In-plane diffractive optical networks based on meta-surfaces are promising for on-chip application. The design constraints of regular antenna unit place ultimate limits on the functionalities of the meta-systems. This fundamental limitation has been reflected by the large footprints of cascaded meta-surfaces. Here, we propose a digital meta-lens with a large degree of design freedom, enabling significantly improved beam focusing, collimation, and deflection capabilities. A highly dispersive and compact diffractive optical system is constructed for spectrometer via five layers of meta-lenses in a folded configuration. The device only occupies a 100 μm × 100 μm chip area on a silicon photonic platform. Sparse and continuous spectra reconstruction is achieved over a 35 nm bandwidth. Fine spectral lines separated by 0.14 nm are resolved. In addition to such a compact and high-resolution on-chip spectrometer, it is also expected to be promising for imaging, optical computing, and other applications due to the great versatility of the digital lens design.

Design of a Low-Reflection Flat Lens Antenna Based on Conformal Transformation Optics

In this paper, a wideband flat lens antenna with low reflection and good performance is presented based on conformal transformation optics (CTO). Physical space optimization is applied to eliminate singular refractive index values. Furthermore, we employ the optical path rescaling method to enhance the sub-unity refractive indices and to reduce reflection. Therefore, an implementable all-dielectric isotropic medium is obtained. The final flat lens profile comprises six layers with a constant permittivity value in each layer. Simulation results of the three-dimensional structure indicate that the designed flat lens operates in a wide frequency bandwidth. The flat lens antenna has an S₁₁ value of less than -15 dB in the frequency range of 13 to 30 GHz. The proposed lens was designed and simulated using COMSOL Multiphysics, and radiation performance results were validated using the CST Studio Suite. The simulated radiation pattern shows that the side lobe level is less than -16.5 dB in two simulation software programs, and the half-power beam width varies from 5.6° to 2.7° with increasing frequency. Moreover, the simulated antenna gain is about 28.3-35.5 dBi in the 13-30 GHz frequency range.

Acoustic waveguide based on cascaded Luneburg lens

This paper investigates the acoustic Luneburg Lens (ALL) as a design framework for guiding acoustic wave propagation. In this study, an acoustic waveguide is proposed based on the characteristics of both acoustic wave focusing and collimation of cascaded ALLs. The continuous variation of the refractive index of the ALL is achieved by using lattice unit cells with a graded filling ratio. A cascaded ALL waveguide device is fabricated based on the additive manufacturing technique. The experimental results obtained with this device are consistent with the numerical simulations and theoretical calculations.

Discretization of two-dimensional Luneburg lens based on the correctional effective medium theory

The Luneburg lens is widely applied in both the optical and microwave regimes because it offers high gain and a wide beam-scanning range. However, Luneburg lens typically suffer from low efficiency which is caused by the dielectric loss of medium employed. To address this issue, we propose herein a general method for discretization of two-dimensional Luneburg lens based on correctional effective-medium theory. In discrete Luneburg, the efficiency is not dependent on the employed medium roughly because that the main component in the lens is air, resulting into a significant improvement of efficiency. Subsequently, a systemic study of lens discretization is presented, which is validated by a discrete Luneburg lens easily fabricated by using 3D printing. In addition, a novel wave-patch reduction feature allows the discrete lens to function as well. This work presents a fundamental theory for lens discretization, which is valid not only for the Luneburg lens but also for other types of lenses. It can be applied in imaging, antennas, or phase manipulation in both the optical and microwave bands.

Metamaterial-based ultrashort multimode waveguide taper with low intermodal crosstalk

We propose and theoretically demonstrate an ultrashort multimode waveguide taper based on the all-dielectric metamaterial. Attributed to the gradient index distribution of the metamaterial, the spot sizes of the four lowest-order transverse magnetic (TM) modes can be expanded in a short distance of 6 μm with negligible mode conversions. Numerical results prove that the insertion losses of the taper are lower than 1 dB, 1.12 dB, 1.26 dB and 1.66 dB for the TM₀ - TM₃ modes, respectively, and the intermodal crosstalk values are below -15 dB for the four modes, both in the wavelength range of 1.5 μm - 1.6 μm. To the best of our knowledge, this is the first multimode waveguide taper that has low intermodal crosstalk of < -15 dB over a 100-nm bandwidth.

Structural Luneburg lens for broadband cloaking and wave guiding

In this paper, we explore the concept of structural Luneburg lens (SLL) as a design framework for performing dynamic structural tailoring to obtain a structural wave cloak and a structural waveguide. The SLL is a graded refractive index lens, which is realized by using a variable thickness structure defined in a thin plate. Due to the thickness variation of the plate, the refractive index decreases radially from the centre to the outer surface of the lens. By taking advantage of the unique capabilities of SLL for flexural wave focusing and collimation, we develop a structural wave cloak and waveguide based on SLLs. The SLL design enables the integration of functional devices into thin-walled structures while preserving the structural characteristics. Analytical, numerical, and experimental studies are carried out to characterize the performance of the SLL cloak and the SLL waveguide. The results demonstrate that these SLL devices exhibit excellent performance for structural wave cloaking and waveguiding over a broadband operating frequency range.

Silicon nitride waveguide devices based on gradient-index lenses implemented by subwavelength silicon grating metamaterials

The rapid development of photonic integrated circuits demands the design of efficient and compact waveguide devices such as waveguide tapers and crossings. Some components in the silicon nitride (SiN) waveguide platform are superior to their counterparts in the silicon waveguide platform. Designing a compact SiN waveguide taper and crossing is crucial to reduce the size of SiN photonic components. In this paper, we utilize the focusing property of the Luneburg lens to design an SiN taper connecting a 10-µm-wide waveguide to a 1-µm-wide waveguide. Three-dimensional full-wave simulations indicate that the designed 13-µm-long taper has an average transmission efficiency of 92% in the wavelength range of 1500-1600 nm. We also present an in-plane SiN waveguide crossing based on the imaging property of the square Maxwell's fisheye lens designed with quasi-conformal transformation optics. The designed waveguide crossing occupies a compact footprint of 5.65µm×5.65µm, while its average insertion loss is 0.46 dB in the bandwidth of 1500-1600 nm. To the best our knowledge, the designed SiN waveguide taper and crossing have the smallest footprints to date.

Broadband graded index Gutman lens with a wide field of view utilizing artificial dielectrics: a design methodology

A novel all-metal graded index Gutman lens is proposed. It exploits an interleaved metasurface unit-cell with glide symmetry that can provide high values of equivalent refractive index with low frequency dispersion. The result is a compact lens with broadband performance and a wide field of view up to ±70^°. The proposed lens exhibits low loss, directive beams and is an appealing candidate for space applications. The design approach introduced can be applied to other graded index lenses with circular symmetry using rectangular or circular periodic structures.

Controlling refractive index of transformation-optics devices via optical path rescaling

We present a general method of designing optical devices based on optical conformal mapping and rescaling the optical path along a given bunch of rays. It provides devices with the same functionality as those based purely on conformal mapping, but enables to manipulate the refractive index to a great extent—for instance, eliminate superluminal regions of space as well as reduce the refractive index in other regions significantly. The method is illustrated in two examples, a waveguide coupler and a plasmonic bump cloak, and numerical simulations confirm its functionality.

On-chip wavefront shaping with dielectric metasurface

Metasurfaces can be programmed for a spatial transformation of the wavefront, thus allowing parallel optical signal processing on-chip within an ultracompact dimension. On-chip metasurfaces have been implemented with two-dimensional periodic structures, however, their inherent scattering loss limits their large-scale implementation. The scattering can be minimized in single layer high-contrast transmitarray (HCTA) metasurface. Here we demonstrate a one-dimensional HCTA based lens defined on a standard silicon-on-insulator substrate, with its high transmission (<1 dB loss) maintained over a 200 nm bandwidth. Three layers of the HCTAs are cascaded for demonstrating meta-system functionalities of Fourier transformation and differentiation. The meta-system design holds potential for realizing on-chip transformation optics, mathematical operations and spectrometers, with applications in areas of imaging, sensing and quantum information processing.

Metasurfaces can be programmed for a spatial transformation of the wavefront, allowing on-chip optical signal processing. Here, the authors demonstrate a one-dimensional high-contrast transmitarray metasurface-based lens on SOI substrate and demonstrate functionalities of Fourier transformation and differentiation.

Multimode waveguide crossing based on a square Maxwell's fisheye lens

Mode-division multiplexing (MDM) is an emerging large-capacity data communication technology utilizing orthogonal guiding modes as independent data streams. One of the challenges of multimode waveguide routing in MDM systems is decreasing the mode leakage of waveguide crossings. In this article, a square Maxwell's fish-eye lens as a waveguide crossing medium based on quasiconformal transformation optics is designed and implemented on a silicon-on-insulator platform. Two approaches were taken to realize the designed lens: graded photonic crystal and varying the thickness of the silicon slab waveguide. Three-dimensional numerical simulations show that the designed multimode waveguide crossing has an ultrawide bandwidth from 1260 to 1675 nm with a compact footprint of only 3.77×3.77  μm². For the first three transverse electric modes (TE0, TE1, and TE2), the designed waveguide crossing exhibits an average insertion loss of 0.24, 0.55, and 0.45 dB; a crosstalk of less than -72, -61, and -27  dB; and a maximum return loss of 54, 53, and 30 dB, respectively. The designed waveguide crossing supports low-distortion pulse transmission with a high fidelity factor of 0.9857. Furthermore, the proposed method can be expanded to design waveguide crossings with an even higher number of supporting modes by increasing the size of the lens.

Composite Luneburg lens based on dielectric or plasmonic scatterers

We present a three-dimensional (3D) Luneburg lens design scheme that employs non-resonant spherical scatterers as inclusions in a host medium for the manipulation of electromagnetic waves. The underlying principle is that the volume fraction of the inclusion scatterers can be varied spatially so as to control the effective permittivity for the desired permittivity profile. Specifically, to achieve desired volume fraction values, simple cubic packing, hexagonal close packing and random packing methods were used for scatterer distribution. The proposed analysis features the plasmonic inclusions as a rational alternative for dielectric inclusions to produce a desired effective value of the permittivity in optics. We demonstrate the applicability of the proposed scheme by employing it to design and simulate Luneburg lens (both in microwave and optics) for beam steering applications. The design leads to polarisation independent functionality in the plane tangent to the lens and yields high antenna gain. The scheme provides a useful means to realize many disruptive applications ranging from the microwaves to optics.

Acoustic Imaging with Metamaterial Luneburg Lenses

The Luneburg lens is a spherically symmetrical gradient refractive index (GRIN) device with unique imaging properties. Its wide field-of-view (FoV) and minimal aberration have lead it to be successfully applied in microwave antennas. However, only limited realizations have been demonstrated in acoustics. Previously proposed acoustic Luneburg lenses are mostly limited to inherently two-dimensional designs at frequencies from 1 kHz to 7 kHz. In this paper, we apply a new design method for scalable and self-supporting metamaterials to demonstrate Luneburg lenses for airborne sound and ultrasonic waves. Two Luneburg lenses are fabricated: a 2.5D ultrasonic version for 40 kHz and a 3D version for 8 kHz sound. Imaging performance of the ultrasonic version is experimentally demonstrated.

Scalable variable-index elasto-optic metamaterials for macroscopic optical components and devices

Optical metamaterials with an artificial subwavelength structure offer new approaches to implement advanced optical devices. However, some of the biggest challenges associated with the development of metamaterials in the visible spectrum are the high costs and slow production speeds of the nanofabrication processes. Here, we demonstrate a macroscale (>35 mm) transformation-optics wave bender (293 mm²) and Luneburg lens (855 mm²) in the broadband white-light visible wavelength range using the concept of elasto-optic metamaterials that combines optics and solid mechanics. Our metamaterials consist of mesoscopically homogeneous chunks of bulk aerogels with superior, broadband optical transparency across the visible spectrum and an adjustable, stress-tuneable refractive index ranging from 1.43 down to nearly the free space index (∼1.074). The experimental results show that broadband light can be controlled and redirected in a volume of >10⁵λ × 10⁵λ × 10³λ, which enables natural light to be processed directly by metamaterial-based optical devices without any additional coupling components.

Acoustic wave science realized by metamaterials

Artificially structured materials with unit cells at sub-wavelength scale, known as metamaterials, have been widely used to precisely control and manipulate waves thanks to their unconventional properties which cannot be found in nature. In fact, the field of acoustic metamaterials has been much developed over the past 15 years and still keeps developing. Here, we present a topical review of metamaterials in acoustic wave science. Particular attention is given to fundamental principles of acoustic metamaterials for realizing the extraordinary acoustic properties such as negative, near-zero and approaching-infinity parameters. Realization of acoustic cloaking phenomenon which is invisible from incident sound waves is also introduced by various approaches. Finally, acoustic lenses are discussed not only for sub-diffraction imaging but also for applications based on gradient index (GRIN) lens.

Porous Silicon Gradient Refractive Index Micro-Optics

The emergence and growth of transformation optics over the past decade has revitalized interest in how a gradient refractive index (GRIN) can be used to control light propagation. Two-dimensional demonstrations with lithographically defined silicon (Si) have displayed the power of GRIN optics and also represent a promising opportunity for integrating compact optical elements within Si photonic integrated circuits. Here, we demonstrate the fabrication of three-dimensional Si-based GRIN micro-optics through the shape-defined formation of porous Si (PSi). Conventional microfabrication creates Si square microcolumns (SMCs) that can be electrochemically etched into PSi elements with nanoscale porosity along the shape-defined etching pathway, which imparts the geometry with structural birefringence. Free-space characterization of the transmitted intensity distribution through a homogeneously etched PSi SMC exhibits polarization splitting behavior resembling that of dielectric metasurfaces that require considerably more laborious fabrication. Coupled birefringence/GRIN effects are studied by way of PSi SMCs etched with a linear (increasing from edge to center) GRIN profile. The transmitted intensity distribution shows polarization-selective focusing behavior with one polarization focused to a diffraction-limited spot and the orthogonal polarization focused into two laterally displaced foci. Optical thickness-based analysis readily predicts the experimentally observed phenomena, which strongly match finite-element electromagnetic simulations.

Resonant metalenses for flexural waves in plates

The dispersion curves of a cluster of closely spaced rods supported by a thin plate are characterised by subwavelength bandgaps and slow group velocities induced by local resonance effects. A recent analytical study [Williams, Roux, Rupin, and Kuperman (2015). Phys. Rev. B 91, 104307], has shown how the slow velocity branch depends, amongst other parameters, on the height of the rods that make up the cluster. Such metamaterial, offering easy-to-tune spatial velocity gradients, is a perfect candidate for building gradient index lenses such as Luneburg, Maxwell, and 90° rotating. Here theoretical results are combined with numerical simulations to design and test metalenses for flexural waves. The lenses are obtained by tuning the height of the cluster of rods such that they provide the required refractive index profile. Snapshots and videos from three-dimensional numerical simulations in a narrow band centered at ∼4 kHz are used to analyse the performances of three types of gradient index metalens (Luneburg, Maxwell, and 90° rotating).

Superdirective dielectric nanoantennas

We introduce the novel concept of superdirective nanoantennas based on the excitation of higher-order magnetic multipole moments in subwavelength dielectric nanoparticles. Our superdirective nanoantenna is a small Si nanosphere containing a notch, and is excited by a dipole located within the notch. In addition to extraordinary directivity, this nanoantenna demonstrates efficient radiation steering at the nanoscale, resulting from the subwavelength sensitivity of the beam radiation direction to variation of the source position inside the notch. We compare our dielectric nanoantenna with a plasmonic nanoantenna of similar geometry, and reveal that the nanoantenna's high directivity in the regime of transmission is not associated with strong localization of near fields in the regime of reception. Likewise, the absence of hot spots inside the nanoantenna leads to low dissipation in the radiation regime, so that our dielectric nanoantenna has significantly smaller losses and high radiation efficiency of up to 70%.

On-chip transformation optics for multimode waveguide bends

Current optical communication systems rely almost exclusively on multimode fibres for short- and medium-haul transmissions, and are now expanding into the long-haul arena. Ultra-high bandwidth applications are the main drive for this expansion, based on the ability to spatially multiplex data channels in multimode systems. Integrated photonics, on the other hand, although largely responsible for today's telecommunications, continues to operate almost strictly in the single-mode regime. This is because multimode waveguides cannot be compactly routed on-chip without significant inter-mode coupling, which impairs their data rate and prevents the use of modal multiplexing. Here we propose a platform for on-chip multimode devices with minimal inter-mode coupling, opening up the possibilities for integrated multimode optics. Our work combines a novel theoretical approach--large-scale inverse design of transformation optics to maximize performance within fabrication constraints-with unique grayscale-lithography fabrication of an exemplary device: a low-crosstalk multimode waveguide bend.

High-efficiency broadband anomalous reflection by gradient meta-surfaces

We combine theory and experiment to demonstrate that a carefully designed gradient meta-surface supports high-efficiency anomalous reflections for near-infrared light following the generalized Snell's law, and the reflected wave becomes a bounded surface wave as the incident angle exceeds a critical value. Compared to previously fabricated gradient meta-surfaces in infrared regime, our samples work in a shorter wavelength regime with a broad bandwidth (750-900 nm), exhibit a much higher conversion efficiency (∼80%) to the anomalous reflection mode at normal incidence, and keep light polarization unchanged after the anomalous reflection. Finite-difference-time-domain (FDTD) simulations are in excellent agreement with experiments. Our findings may lead to many interesting applications, such as antireflection coating, polarization and spectral beam splitters, high-efficiency light absorbers, and surface plasmon couplers.

Recent advances in transformation optics

Within the past a few years, transformation optics has emerged as a new research area, since it provides a general methodology and design tool for manipulating electromagnetic waves in a prescribed manner. Using transformation optics, researchers have demonstrated a host of striking phenomena and devices; many of which were only thought possible in science fiction. In this paper, we review the most recent advances in transformation optics. We focus on the theory, design, fabrication and characterization of transformation devices such as the carpet cloak, "Janus" lens and plasmonic cloak at optical frequencies, which allow routing light at the nanoscale. We also provide an outlook of the challenges and future directions in this fascinating area of transformation optics.

Controlling electromagnetic scattering of a cavity by transformation media

Based on the transformation media theory, we proposed a way to control the scattering of a cavity, or trench, located on a metallic plane. Specifically, we show how is possible to design transformation medium to fill up a cavity with arbitrary cross section, which is capable of enhancing the specularly reflection wave. As the inverse problem, we also address the design of transformation medium coating, which is laid on the metallic plane, to mimic the scattering of the cavity. Based on the effective medium theory, the transformation medium for the case of a polygonal cavity can be realized by oblique layered structures, and each layered structure is consisting of two kinds of isotropic dielectrics, thus leading an ease of practical fabrication.

Two-dimensional inside-out Eaton lens: design technique and TM-polarized wave properties

In this paper we perform a theoretical and numerical study of two-dimensional inside-out Eaton lenses under transverse-magnetic-polarized excitation. We present one example design and test its performance by utilizing full-wave Maxwell solvers. With the help of the WKB approximation, we further investigate the finite-wavelength effect analytically and demonstrate one necessary condition for perfect imaging at the level of wave optics, i.e. imaging with unlimited resolution, by the lens.

Planar, flattened Luneburg lens at infrared wavelengths

Employing artificially structured metamaterials provides a means of circumventing the limits of conventional optical materials. Here, we use transformation optics (TO) combined with nanolithography to produce a planar Luneburg lens with a flat focal surface that operates at telecommunication wavelengths. Whereas previous infrared TO devices have been transformations of free-space, here we implement a transformation of an existing optical element to create a new device with the same optical characteristics but a user-defined geometry.

Design and fabrication of a metamaterial gradient index diffraction grating at infrared wavelengths

We demonstrate the design, fabrication and characterization of an artificially structured, gradient index metamaterial with a linear index variation of Δn ~ 3.0. The linear gradient profile is repeated periodically to form the equivalent of a blazed grating, with the gradient occurring across a spatial distance of 61 μm. The grating, which operates at a wavelength of 10.6 μm, is composed of non-resonant, progressively modified "I-beam" metamaterial elements and approximates a linear phase shift gradient using 61 distinguishable phase levels. The grating structure consists of four layers of lithographically patterned metallic I-beam elements separated by dielectric layers of SiO(2). The index gradient is confirmed by comparing the measured magnitudes of the -1, 0 and +1 diffracted orders to those obtained from full wave simulations incorporating all material properties of the metals and dielectrics of the structures. The large index gradient has the potential to enable compact infrared diffractive and gradient index optics, as well as more exotic transformation optical media.

Integrated Luneburg lens via ultra-strong index gradient on silicon

Gradient index structures are gaining increased importance with the constant development of Transformation Optics and metamaterials. Our ability to fabricate such devices, while limited, has already demonstrated the extensive capabilities of those designs, in the forms of invisibility devices, as well as illusion optics and super-lensing. In this paper we present a low loss, high index contrast lens that is integrated with conventional nanophotonic waveguides to provide improved tolerance in fiber-to-chip optical links for future communication networks. This demonstration represents a positive step in making the extraordinary capabilities of gradient index devices available for integrated optics.

General conformal transformation method based on Schwarz-Christoffel approach

A general conformal transformation method (CTM) is proposed to construct the conformal mapping between two irregular geometries. In order to find the material parameters corresponding to the conformal transformation between two irregular geometries, two polygons are utilized to approximate the two irregular geometries, and an intermediate geometry is used to connect the mapping relations between the two polygons. Based on these manipulations, the approximate material parameters for TE and TM waves are finally obtained by calculating the Schwarz-Christoffel (SC) mappings. To demonstrate the validity of the method, a phase modulator and a plane focal surface Luneburg lens are designed and simulated by the finite element method. The results show that the conformal transformation can be expanded to the cases that the transformed objects are with irregular geometries.