Maxwell Fish-eye Lens Research Articles

A 3D-printing metasurface-augmented half-circle Maxwell fisheye lens for millimetre-wave analogue beamforming

Abstract This article presents a 2D metasurface-augmented half-circle Maxwell fisheye lens (HMFL) designed to move its focal axis to a targeted direction with a maximum elevation angle of 45 degrees, suitable for switches and power division networks in the millimetre wave (mmWave) band. This metasurface-augmented beamformer enables consistent analogue performance across a bandwidth of 22 - 32 GHz. The proposed beamformer features a reflective metasurface consisting of 2x40 Phoenix unit cells and is integrated with a 10-dielectric zone HMFL in the diameter segment opposite the antenna source. A horn antenna feed is used for excitation in normal and oblique incidences of -15 and -30 degrees. The designed lens prototype was fabricated with 3D-printing technology and printed metasurfaces for several particular cases of focal displacement. The measurements of the proposed HMFL beamformer are presented, demonstrating a close correlation between simulated and experimental results.

Electrically tunable graded photonic crystal lens based on graphene plasmons.

Controlling the nonlinear relationship between surface plasmon polariton (SPP) mode index and chemical potential of graphene can be used in the field of active transformation optics. Here, we propose an electrically tunable 2D Graded Photonic Crystal (GPC) lens based on graphene SPP platform. Our platform comprises a graphene monolayer integrated into a back-gated structure with nano-patterned gate insulators. When the chemical potential of the graphene surface is designed to operate in the nonlinear region, the designed GPC lens can be continuously transformed between a Maxwell's fish-eye lens and a Luneburg lens by tuning the gate voltage. The range of the lens background chemical potential for allowing this transformation is systematically studied. To compensate for the significant errors inherent in the conventional effective medium theory (EMT) during the homogenization of photonic crystals (PCs), we propose a generalized effective medium theory (GEMT). The validity and accuracy of this approach are verified through comparisons with true values (based on rigorous eigenvalue solutions) and EMT values. Due to its advantages of on-site controls and easy fabrication characteristics, the proposed graphene GPC provides a new way for practical on-chip light manipulation.

Monolithically Structured van der Waals Materials for Volume-Polariton Refraction and Focusing.

Polaritons, hybrid light and matter waves, offer a platform for subwavelength on-chip light manipulation. Recent works on planar refraction and focusing of polaritons all rely on heterogeneous components with different refractive indices. A fundamental question, thus, arises whether it is possible to configure two-dimensional monolithic polariton lenses based on a single medium. Here, we design and fabricate a type of monolithic polariton lens by directly sculpting an individual hyperbolic van der Waals crystal. The in-plane polariton focusing through sculptured step-terraces is triggered by geometry-induced symmetry breaking of momentum matching in polariton refractions. We show that the monolithic polariton lenses can be robustly tuned by the rise of van der Waals terraces and their curvatures, achieving a subwavelength focusing resolution down to 10% of the free-space light wavelength. Fusing with transformation optics, monolithic polariton lenses with gradient effective refractive indices, such as Luneburg lenses and Maxwell's fisheye lenses, are expected by sculpting polaritonic structures with gradually varied depths. Our results bear potential in planar subwavelength lenses, integrated optical circuits, and photonic chips.

Wide-angle passive beam steering using 3D modified partial Maxwell fisheye lens

This study presents a broadband, 3D gradient index beam-steering lens, derived from an optimized modification of the partial Maxwell fisheye (PMFE) design, achieving a boresight gain of 23 dBi, -80° to 80° beam steering, and <10 dB gain roll-off. Utilizing fused filament fabrication (FFF) to realize its intricate geometry, the design employs a novel polar space-filling curve (PSFC) to establish a 3D varying, effective permittivity distribution. Rigorous simulations and experimental validation attest to its effectiveness, marking the first 3D implementation of a PMFE-type lens to our knowledge. This research underscores the feasibility and diverse applications of a low-cost, wide-angle passive beam-steering dielectric lens.

Super-resolution imaging based on modified Maxwell's fish-eye lens

In this paper, a modified Maxwell's fish-eye lens is proposed in order to achieve super-resolution imaging. This lens possesses elevated refractive index profile compared with the traditional Maxwell's fish-eye lens. The refractive index profile is achieved with variable thickness configuration defined in a sheet plate structure, to realise desired changes in refractive indices. The wave propagation behaviours and the full width at half maximum (FWHM) are obtained from numerical simulations and experimental studies at the focal region of the lens. Super-resolution imaging is observed in a broadband frequency scope, with the FWHM around 0.2λ from 5 to 10 kHz. This work provides a straightforward and flexible approach to the engineering of the MFEL imaging characteristics and energy distributions for related applications.

Ultrafast Excitation Exchange in a Maxwell Fish-Eye Lens.

The strong coupling of quantum emitters to a cavity mode has been of paramount importance in the development of quantum optics. Recently, also the strong coupling to more than a single mode of an electromagnetic resonator has drawn considerable interest. We investigate how this multimode strong coupling regime can be harnessed to coherently control quantum systems. Specifically, we demonstrate that a Maxwell fish-eye lens can be used to implement a pulsed excitation exchange between two distant quantum emitters. This periodic exchange is mediated by single-photon pulses and can be extended to a photon-exchange between two atomic ensembles, for which the coupling strength is enhanced collectively.

Electrically tunable graphene plasmonic lens: from Maxwell Fisheye Lens to Luneburg Lens

A graphene plasmonic lens with an electrically tunable focal length is proposed and numerically investigated. The design philosophy of the proposed tunable lens is based on the nonlinear relationship of surface plasmon polariton (SPP) wave index with respect to chemical potential of graphene. By controlling the gate voltage of graphene, the proposed lens can be continuously tuned from a Maxwell Fisheye lens to a Luneburg lens. A ray-tracing method is employed to find out the corresponding gate voltages for various focal lengths. Full-wave EM simulations using COMSOL show that excellent focusing performances can be achieved. This work offers a new way in exploiting active transformational plasmonic elements in the mid-infrared region.

Compact Sub‐Semicircular Axial Gradient Index Lens Synthesized by Metasurfaces: A Promising Solution for Miniaturized Antenna and Subwavelength Focusing Systems

AbstractWe present the design, fabrication, and experimental measurements of an Axial Gradient‐index (AGRIN) flat lens synthesized by 2D periodic metallic patches on a grounded dielectric slab, known as metasurfaces. Metasurfaces can be considered as artificial materials that possess unique characteristics, which mainly revolve around the two‐dimensional distribution of the structure. By manipulating the phase and amplitude of the near‐fields over the surface of the metasurface, specific values of the effective permittivity and permeability can be achieved, thereby regulating the overall field behavior by gaining control of the refractive index that is related to the aforementioned two material parameters. By configuring the refractive index, metasurfaces enable the manipulation of the direction in which electromagnetic waves propagate, as dictated by Snell's law. By varying the geometric dimensions of unit cells in each segment that compose the lens, the gradient refractive index profile required for our AGRIN lens can be achieved. A primary feature of this lens lies with its semicircular structure, in contrast to conventional circular ones. Its perimeter comprises a convex boundary and a straight one. In comparison to traditional circular lenses like the Luneburg lens and Maxwell fisheye lens, our proposed AGRIN lens offers the advantage of being more compact. Despite its smaller area, the AGRIN lens maintains its focusing ability. The AGRIN lens is capable of focusing over 71.75% of the energy from the incident wave onto the focal point. This efficient focusing ability, combined with its reduced size, makes the AGRIN lens highly advantageous for various applications.

E-Plane-Focused Partial Maxwell Fish-Eye Lens Antenna for Multibeam Wide-Angle Scanning

This letter presents a multi-beam wide-angle scanning antenna based on the E-plane-focused partial Maxwell fish-eye (PMFE) lens operating in Ka-band. The gradient equivalent refractive index distribution of the lens is realized by the parallel plate waveguide (PPW) partially filled with dielectric material, which can support the E-plane focus. The lens is fed by a series of rectangular waveguides arranged along the straight cut line to realize the multiple beams. To improve the impedance matching, the dielectric wedges are loaded in the interface between the feeders and the lens. The E-plane broadening of waveguide feeding ports effectively alleviates the gain drop of wide-angle scanning. The measured results of the prototype show a beam scanning range more than ±90° with the aperture efficiencies between 57% and 85.7%. The good impedance matching is also obtained in the operating band. The proposed PMFE lens antenna has the application potential in the low-cost millimeter wave (MMW) multi-beam systems.

Role played by port drains in a Maxwell fish-eye lens

The Maxwell fish-eye lens was proposed to reach super-resolution with the addition of a wave drain, and the interaction of multiple drains is theoretically predicted to improve subwavelength resolution further. In this paper, we discuss the role played by port drains in optical absolute instruments and verify by wave simulation that the coupling nature for the wave source and drain applies correctly in the picture of scanning imaging for an absolute instrument. This work has prospects for scanning near fields shaped from far-field wave propagation.

Analogy of the interior Schwarzschild metric from transformation optics.

In this paper, we make an analogy of the interior Schwarzschild metric from transformation optics (we call the method transformation cosmology). It is shown that a simple refractive index profile is sufficient to capture the behavior of the metric to bend light. There is a critical value of the ratio of the radius of the massive star to the Schwarzschild radius, which is exactly related to the condition of collapsing into a black hole. We demonstrate the light bending effect for three cases from numerical simulations as well. Especially, we find that a point source at the photon sphere will form an image inside the star approximately, and the equivalent lens is like Maxwell's fish-eye lens. This work will help us to explore the phenomena of massive stars with laboratory optical tools.

Evolution of optical vortices in gradient media and curved spaces.

Light propagation in gradient media and curved spaces induce intriguing phenomena, such as focusing and self-imaging, thus delivering a wide range of applications. However, these systems are limited to excitations without orbital angular momentum, which may produce unforeseen results. Here, we demonstrate the reconstructions (or called imaging to some extent) of optical vortices (OVs) in two-dimensional (2D) gradient media and three-dimensional (3D) curved spaces. We present the evolution of OVs in two types of generalized Maxwell fisheye (GMFE) lenses from the perspective of geometrical and wave optics, and use coherent perfect absorbers (CPAs) to better recover the OVs in the converging position. Furthermore, we also demonstrate such phenomena in two types of 3D compact closed manifolds-sphere and spindle-which are also called geodesic lenses. Surprisingly, the results we obtained in 3D curved spaces can be seen as a strong verification of the Poincaré-Hopf theorem. Our work provides a new, to the best of our knowledge, platform to investigate the evolution of OVs on curved surfaces.

A reflectionless compact elliptical half Maxwell fish-eye lens designed by transformation optics

A two-dimensional half Maxwell fish-eye lens is compressed using a linear transformation that maps a half circle to a half ellipse. The focusing property of the lens is preserved while making the device more compact. The boundary reflections, investigated for both TE and TM polarizations, were suppressed for beams directed toward the optical axis of the lens. A designed prototype provided a scanning range of ±20° with negligible reflections. The design’s functionality was verified using COMSOL multiphysics.

Ray tracing in concentric gradient-index media: optical Binet equation.

The Binet equation in mechanics describes the orbital geometry of a moving particle under a central force field. In this paper, as its counterpart in optics, we show this formula can be similarly utilized in ray tracing of a gradient-index (GRIN) medium with a concentric field. As an inference of Fermat's principle, this generalization is called the optical Binet equation (OBE). A remarkable advantage of OBE is that it can not only determine the ray trace or concentric GRIN field once one of them is given, but also derive the propagation time inside the medium. As examples, we apply OBE to rays passing through a Maxwell fish-eye lens, Luneburg lens, Eaton lens, concentrator, and hyperbolic deflector, the time delay of which can be calculated once the GRIN field or ray trace equation is solved. The results are well matched with simulations, proving it to be an effective tool in solving problems of the concentric GRIN field.

Acoustic super-resolution imaging based on solid immersion 3D Maxwell's fish-eye lens

Acoustic waves have been widely applied in communications, medical treatment, military, and other aspects. In this Letter, we explore acoustic imaging properties of three-dimensional Maxwell's fish-eye lens (3D-MFEL) with elevated refractive index profile, the analytical and numerical results show that a 3D-MFEL based on solid immersion mechanism can achieve super-resolution imaging without chromatic aberration. In addition, introducing vortex waves into the 3D-MFEL, we further explore the super-resolution imaging properties in reconstructing vortex waves. The valid combination of 3D-MFEL and solid immersion mechanism provides a meaningful way for super-resolution imaging, which also paves a way forward for future designing and manufacturing in acoustic super-imaging systems.

Solid Immersion Maxwell's Fish-Eye Lens Without Drain

Maxwell's fish-eye lens (MFEL) with positive refraction has been shown to achieve perfect imaging, but with the cost of drain assistance. This has led to ongoing heated debates about the rigor of the physics of super-resolution phenomena in MFEL. In this work, we report that a MFEL embedded in an exterior coating, inspired by the solid immersion concept, can realize super-resolution imaging without a drain. Such a solution mitigates and bypasses the corresponding criticisms and debates of the past decades. We find that the total reflection at the outer solid-immersion interface and the native perfect focusing of MFEL synthetically contribute to a super-resolution image formed in the air. Moreover, this intuitive yet simple recipe can be robustly applied to other absolute instruments, such as the general Luneburg lens and more versatile superimaging systems are anticipated. We demonstrate the imaging performance in a solid immersion general Luneburg lens both numerically and experimentally, which indirectly verifies the imaging validity of the solid immersion MFEL without a drain.

Design and analysis of Maxwell fisheye lens based beamformer

Antenna arrays and multi-antenna systems are essential in beyond 5G wireless networks for providing wireless connectivity, especially in the context of Internet-of-Everything. To facilitate this requirement, beamforming technology is emerging as a key enabling solution for adaptive on-demand wireless coverage. Despite digital beamforming being the primary choice for adaptive wireless coverage, a set of applications rely on pure analogue beamforming approaches, e.g., in point-to-multi point and physical-layer secure communication links. In this work, we present a novel scalable analogue beamforming hardware architecture that is capable of adaptive 2.5-dimensional beam steering and beam shaping to fulfil the coverage requirements. Beamformer hardware comprises of a finite size Maxwell fisheye lens used as a scalable feed network solution for a semi-circular array of monopole antennas. This unique hardware architecture enables a flexibility of using 2 to 8 antenna elements. Beamformer development stages are presented while experimental beam steering and beam shaping results show good agreement with the estimated performance.

Magnetically tunable Maxwell fisheye lens for spin waves focusing

In this paper, a Maxwell fisheye lens (MFL) for spin waves (SWs) focusing on a ferromagnetic film was presented via micromagnetic simulation. The Maxwell fisheye lens with graded refractive index distribution, achieved with gradient saturation magnetization, is designed to manipulate the wavefront of spin waves. The simulation results show that sub-wavelength focusing can be achieved by means of MFL with appropriate chosen parameters. Furthermore, simulation results also prove that the focusing properties of MFL can be tuned by external magnetic field. The MFL would be promising device for SWs focusing and wavefront manipulation.

2-D Beam-Steerable Generalized Mikaelian Lens With Unique Flat-Shape Characteristic

A novel two-dimensional (2-D) beam-steerable generalized Mikaelian lens is presented in this letter. The main difference of proposed lens with respect to conventional Luneburg, Maxwell fish-eye and Eaton lens is its unique flat-shape characteristic, which provides great advantages in designing the low-profile flat-shape lens antenna, avoiding using extremely complex conformal mapping methods. The all-dielectric low-cost lens prototype presenting desired graded permittivity profile is fabricated by 3-D printing. The measurement results at 10 GHz show 2-D beam-steering capabilities from −20° to 20° in both the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> -and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> -plane with around 18.9 dBi of realized gain with less than ∼1.2 dB variation and low-side lobe can be achieved, revealing great potentials for developing the low-profile and cost-effective lens antenna for microwave applications.

Fall-to-the-centre as a symmetry breaking transition

The attractive inverse square potential arises in a number of physical problems such as a dipole interacting with a charged wire, the Efimov effect, the Calgero-Sutherland model, near-horizon black hole physics and the optics of Maxwell fisheye lenses. Proper formulation of the inverse-square problem requires specification of a boundary condition (regulator) at the origin representing short-range physics not included in the inverse square potential and this generically breaks the Hamiltonian’s continuous scale invariance in an elementary example of a quantum anomaly. The system’s spectrum qualitatively changes at a critical value of the inverse-square coupling, and we here point out that the transition at this critical potential strength can be regarded as an example of a symmetry breaking transition. In particular, we use point particle effective field theory (PPEFT), as developed by Burgess et al [1], to characterize the renormalization group (RG) evolution of the boundary coupling under rescalings. While many studies choose boundary conditions to ensure the system is unitary, these RG methods allow us to systematically handle the richer case of nonunitary physics describing a source or sink at the origin (such as is appropriate for the charged wire or black hole applications). From this point of view the RG flow changes character at the critical inverse-square coupling, transitioning from a sub-critical regime with evolution between two real, unitary fixed points ( symmetric phase) to a super-critical regime with imaginary, dissipative fixed points ( symmetry broken phase) that represent perfect-sink and perfect-source boundary conditions, around which the flow executes limit-cycle evolution.