Mikaelian Lens Research Articles

Active encoding of flexural wave with non-diffractive Talbot effect

In this paper, a flexural Mikaelian lens in thin plate is designed by using conformation transformation. The propagation characteristics of flexural waves in the lens are investigated through rays trajectory equation, simulation analyses, and experimental tests, confirming the self-focusing properties of the Mikaelian lens. Additionally, the study explores the Talbot effect for flexural waves, revealing through simulation studies that the Talbot effect within the Mikaelian lens exhibits nearly diffraction-free properties. Building on the non-diffractive nature of the Talbot effect within the Mikaelian lens, we explore the potential for encoding flexural waves using active interference sources. The simulation and experiment results demonstrate the good performance of the designed active encoding system. This work opens up new avenues for the encoding of flexural waves, presenting promising implications for applications in communication such as structural health monitoring, wireless communication in solid media and data transmission in robotics and other areas related to flexural wave technology.

A Hybrid Lens to Realize Electrical Real‐Time Super‐Resolution Imaging

AbstractReal‐time dynamic super‐resolution focusing technology is crucial for various imaging applications. However, the diffraction limit significantly impedes the achievement of real‐time dynamic super‐resolution imaging. Prior studies within this domain, such as super‐resolution fluorescence imaging and structured illumination microscopy, heavily rely on fluorescent labels and intricate algorithms. This article proposes a novel approach to achieving real‐time dynamic super‐resolution imaging at microwave frequency by integrating the Mikaelian lens derived from conformal transformation optics with the space‐time‐coding metasurface antenna. Real‐time dynamic super‐resolution focusing with a resolution ranging from 0.3λ to 0.4λ is demonstrated at the periphery of the Mikaelian lens with a numerical aperture (NA) of 0.54. The proposed hybrid lens exhibits the capacity to discern features separated by about one‐third of a wavelength with high precision. The work offers a universal solution for achieving dynamic real‐time super‐resolution imaging electrically, which can be extended to terahertz waves, visible light, and other wave fields, such as acoustic and flexural waves.

Ultra‐Compact and Efficient Integrated Multichannel Mode Multiplexer in Silicon for Few‐Mode Fibers

AbstractSpace‐division multiplexing (SDM) is one of the key enabling technologies to increase the capacity of fiber communication systems. However, implementing SDM‐based systems using multimode fiber has been challenging with the need for compact, low‐cost, and scalable mode de/multiplexer (DE/MUX). Here a novel integrated mode MUX for few‐mode fibers (FMFs) is presented which can launch up to eight spatial and polarization channels. The new design is composed of a 2D multimode grating coupler (MMGC), highly compact spot size converters (SSCs), and adiabatic directional couplers (ADCs). Eight data lanes in FMFs can be selectively launched with integrated optical phase shifters. Experimental results reveal efficient chip‐to‐fiber coupling with peak efficiencies of −3.8, −5.5, −3.6, and −4.1 dB for LP01, LP11a, LP11b, and LP21b modes, respectively. Thanks to the use of an integrated subwavelength Mikaelian lens for mode‐independent field size conversion with loss ≤−0.25 dB, the total footprint of the MMGC and SSCs is only 35×35 µm2. The proposed design shows great potential for densely integrated photonic circuits in future SDM applications.

Effective Index Approximation Method for Graded Photonic Crystals Slabs: Precise Design of A Mikaelian Lens

Effective Index Approximation Method for Graded Photonic Crystals Slabs: Precise Design of A Mikaelian Lens

Underwater acoustic self-focusing and bending in conformal Mikaelian lens by pentamode metafluid

In this paper, we present the design of an arc-shaped Mikaelian lens using conformal transformation acoustics. We have derived the propagation trajectory equation for vertically incident rays within the lens. The ray trajectories inside the designed lens exhibit the feature of self-focusing as well as of deflection of the propagation direction. The microstructure design of the lens is realized using pentamode material unit cells, which provide the necessary property for underwater acoustic wave manipulation. The simulation results demonstrate that the designed lens has a good self- focusing effect and can deflect the propagation direction of incident waves at the same time. The pentamode conformal Mikaelian lens shows potential applications in underwater imaging, detection and communication.

Achromatic elastic metalens for high-performance confocal piezoelectric energy harvesting

In this study, we analytically, numerically, and experimentally investigated a high-performance confocal piezoelectric energy harvesting system. We achieved a significantly enhanced electrical performance through a Mikaelian lens, which achromatically focuses ambient elastic waves, resulting in the formation of a highly amplified strain energy field in the piezoelectric energy harvester. Previous studies on piezoelectric energy harvesting platforms have limitations, such as the focal position changing with operating frequencies and impedance mismatching owing to inclusions or holes. To address these problems, we utilized the self-focusing ability based on the conformal mapping theory and achromatic ability based on the Kirchhoff–Love thin plate theory to design our Mikaelian lens-based piezoelectric energy harvesting platform. The proposed platform demonstrates a remarkable elastic wave focusing ability at an identical focal position for a broad frequency range. The experimentally visualized wave fields matched well with the numerically calculated full-wave harmonic simulation results. We achieved highly amplified output power up to 1.44 mW within a broad range from 40 to 60 kHz out of the same focal point owing to confined elastic wave energy; the output power extracted at this confocal position was up to 3.76 times higher than that extracted at the lens start position. Our highly performance and broadband achromatic piezoelectric energy harvesting platform lays an attractive foundation for designing potential applications, such as wireless sensing, structural health monitoring, and biomedical devices.

Single-Pixel Scanning Near-Field Imaging With Subwavelength Resolution Using Sharp Focusing Mikaelian Lens

Obtaining sharp focusing with high resolution is of significant importance to microwave and millimeter-wave imaging and sensing. Here, we propose an all-dielectric surface focusing Mikaelian lens operating at the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> - and Ka -band, respectively, with the high-resolution focusing of theoretical full-width half-maximum (FWHM) around <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.45\lambda $ </tex-math></inline-formula> for the single-pixel scanning microwave and millimeter-wave imaging. Benefitting from easily accessible 3-D printing, the designed lens prototype with perforation and infill structure can be fabricated at a very low cost. Moreover, numerical simulations and the spatial resolution imaging experimental results demonstrate that the proposed lens prototype exhibits excellent imaging performance with a subwavelength resolution of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim 0.5\lambda $ </tex-math></inline-formula> while maintaining broadband behavior, revealing great potential for high-resolution microwave and millimeter-wave imaging applications.

Ultrabroadband and Multifunctional Achromatic Mikaelian Lens on an Elastic Plate

The emergence and development of acoustic artificial materials stimulate a large number of applications for the manipulation of ultrasonic and elastic waves. Most of the reported metasurfaces and metamaterials only work effectively at a given frequency and target a fixed functionality. Reconfigurable designs may solve this problem, to a certain extent, but require the introduction of complex active control components. Here, by integrating multiple functionalities on a conformally mapped Mikaelian lens with a hyperbolic secant refractive-index distribution, a broadband passive lens is presented and accomplished on an elastic plate. Just by adjusting the location and type of source, different regulations of flexural waves can be switched from one sort to another. Through projecting the refractive-index profile onto the thickness of the plates, the proposed Mikaelian lens is designed and fabricated. Theoretical prediction and experimental results demonstrate beam scanning at an angle of up to 120\ifmmode^\circ\else\textdegree\fi{} from 30 to 180 kHz and achromatic subwavelength focusing with a full width at half maximum of around 0.3\ensuremath{\lambda} from 30 to 120 kHz. Without using locally resonant materials or active control elements, this work provides a feasible way to construct multifunctional flexural-wave devices.

Broadband achromatic flexural wave Mikaelian lens for high resolution focusing

Conformal transformation method (CTM) has been extensively applied to control propagation of electromagnetic waves and acoustics waves due to the form-invariant property of Maxwell equations and acoustic equations. However, CTM’s application in elastic waves is rarely reported due to the governing equation of elastic waves do not have form invariant property. In this paper, through igniting evanescent waves at the interface of conformally mapped Mikaelian lens with hyperbolic secant refractive index profile, CTM is successfully used to achieve highly efficient (above 75%) broadband (30−80 kHz) achromatic high-resolution flexural wave focusing in thin plate with full width at half maximum (FWHM) around 0.2λ. The proposed Mikaelian lens is designed by linking refractive index with the thickness in plates. Simulated results agree well with theoretical prediction. This high performance for flexural wave focusing could be used for energy harvesting and medical imaging.

Near-field multiple super-resolution imaging from Mikaelian lens to generalized Maxwell’s fish-eye lens

Super-resolution imaging is vital for optical applications, such as high capacity information transmission, real-time bio-molecular imaging, and nanolithography. In recent years, technologies and methods of super-resolution imaging have attracted much attention. Different kinds of novel lenses, from the superlens to the super-oscillatory lens, have been designed and fabricated to break through the diffraction limit. However, the effect of the super-resolution imaging in these lenses is not satisfactory due to intrinsic loss, aberration, large sidebands, and so on. Moreover, these lenses also cannot realize multiple super-resolution imaging. In this research, we introduce the solid immersion mechanism to Mikaelian lens (ML) for multiple super-resolution imaging. The effect is robust and valid for broadband frequencies. Based on conformal transformation optics as a bridge linking the solid immersion ML and generalized Maxwell’s fish-eye lens (GMFEL), we also discovered the effect of multiple super-resolution imaging in the solid immersion GMFEL.

Comparative features of wave focusing by generalized Mikaelian lens with positive and negative refractive indexes

Comparative features of wave focusing by generalized Mikaelian lens with positive and negative refractive indexes

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.

Performance analysis of an all-dielectric planar Mikaelian lens antenna for 1-D beam-steering application.

This paper investigates the performance of an all-dielectric planar Mikaelian lens based on ray transfer matrices and full-wave analysis for 1-D beam-steering application. This new lens concept has its intrinsic flat shape characteristic allowing for a simple low-cost planar feed technology. To verify the design concept, a lens prototype excited by five rectangular microstrip patch antennas with perforated structure (21×24 holes) is fabricated using stereolithography (SLA) 3-D printing. The simulated and measured results of the proposed lens prototype, operating at 10 GHz, shows that the switched-beam coverage over a certain range of beam-steering angles can be obtained. The intrinsic phase error of lens resulting from comatic aberration exhibits obvious increase as the off-axis angle of beam increases, which leads to further deterioration of the corresponding radiated beam. The beam-steering capabilities from -20° to +20° with around 13.2 dBi of realized gain and side-lobe level (less than -11.5dB), and up to potential steering angles (±30°) with around 10 dBi of realized gain can be steadily achieved. Moreover, the realized gain, efficiency and side-lobe level can be further improved to get better radiation performances by using other materials with lower loss tangent. Due to its intrinsic flat shape characteristic, this lens concept could be a potential alternative to develop a low-cost, low-profile and easy-to-fabricate beam-switching array antenna for microwave communication applications.

Conformally Mapped Mikaelian Lens for Broadband Achromatic High Resolution Focusing

AbstractFocusing light into a tiny spot of high resolution is of significant importance in fields from imaging, photolithography to microwave engineering and sensing. However, most of the previous high resolution metalenses are constrained by their limited bandwidth and efficiency. In this paper, on the basis of Mikaelian lens derived from conformal transformation optics, a rectangular gradient refractive index lens with a relatively larger refractive index profile is put forward and manufactured by gradient isotropic dielectrics. Highly efficient (above 74%) broadband (7–14 GHz) achromatic high resolution focusing with full width at half maximum (FWHM) around 0.2λ as well as large numerical aperture (NA) of 2.04 has been accomplished. Measured results agree well with theoretical predictions, which makes the presented lens having a great potential to be employed in high resolution imaging systems.

Tight focusing of second-order cylindrical vector beam by Mikaelian lens

In this paper we simulated the focusing of a second-order cylindrical vector beam by Mikaelian microlens. By using FDTD-method it was shown that the gradient lens produce a region of the energy backflow near its shadow surface. Presence of a microhole in center of the lens allows localize the direct energy inside the lens material and to concentrate the the energy backflow in free space.

Analysis of Wave Focusing by Axisymmetric Mikaelian Lenses

Numerical analysis of wave focusing by axisymmetric Mikaelian lens and by its generalized version with the focus located at some distance from the surface is carried out. The analysis is based on the hybrid projection method involving projection matching of the field expansions on a spherical surface introduced in the algorithm, projection of the Maxwell's equations for the fields inside the sphere on the transverse vector spherical functions, and use of the 1-D finite element method in projection form for solving the ordinary differential equations obtained for variable coefficients of expansions as a result of the projection. The algorithm is realized for the case of a circularly polarized plane wave incident on the lens in the axial direction. A number of new numerical results obtained for the field distributions characterizing wave focusing by Mikaelian lenses of different dimensions and different relations of their parameters are presented and discussed.

Nonparaxial Mode-Size Converter Using an Ultracompact Metamaterial Mikaelian Lens

Mode-division multiplexing (MDM) is a promising approach to increase data transmission capacity by using different modes as independent data channels. Intermodal crosstalk and coherent mode interference are detrimental to the performance of an MDM system and should be avoided in the mode converters and mode expanders for MDM. The Mikaelian lens is well known to be free from spherical aberrations and is therefore an excellent candidate for focusing high order waveguide modes which have main mode field distributions located off-axis. Here we proposed an ultracompact mode-independent mode-size converter using an integrated Mikaelian lens formed by refractive index engineering using a subwavelength grating. The Mikaelian lens is fabricated on the silicon-on-insulator (SOI) platform and can be used to convert the size of high order modes at the interface between the silicon waveguide and a multimode fiber in MDM systems. We present a proof-of-concept demonstration of a low loss spot size converter for three transverse electric (TE) modes between a 14 μm wide multimode waveguide grating coupler and a 1.56 μm wide multimode silicon waveguide. The measured insertion loss of the Mikaelian lens mode size converter is 0.21 dB for TE0 mode, 0.26 dB for TE1 mode and 0.28 dB for TE2 mode. 1-dB bandwidth of all the three modes are about 60 nm. The 15 μm long Mikaelian lens has comparable experimental performance as a 450 μm long adiabatic taper.

Energy flux of a vortex field focused using a secant gradient lens

In this paper we simulated the focusing of left circular polarized beam with a second order phase vortex and a second-order cylindrical vector beam by a gradient index Mikaelian lens. It was shown numerically, that there is an area with a negative Poynting vector projection on Z axis, that can be called an area with backward energy flow. Using a cylindrical hole in the output surface of the lens and optimizing it one can obtain a negative flow, which will be situated in the maximum intensity region, unlike to previous papers, in which such backward energy flow regions were situated in a shadow area. Thereby, this lens will work as an “optical magnet”, it will attract Rayleigh particles (with diameter about 1/20 of the wavelength) to its surface.

Duplex Mikaelian and Duplex Maxwell’s Fish-Eye Lenses

In this paper, we report two new kinds of absolute optical instruments that can make stigmatically images for geometric optics in two dimensional space. One is called the duplex Mikaelian lens, which is made by splicing two half Mikaelian lenses with different periods. The other is exponential conformal transformer of duplex Mikaelian lens with the ratio of different periods of its two half Mikaelian lenses a rational number, which we call duplex Maxwell's fish eye lens. Duplex Mikaelian lenses have continuous translation symmetry with arbitrary real number, while duplex Maxwell's fish eye lenses have continuous rotational symmetry from 0 to 2*Pi. Hence each duplex Maxwell's fish eye lens corresponds to a duplex Mikaelian lens. We further demonstrate the caustic effect of geometric optics in duplex Mikaelian lenses and duplex Maxwell's fish eye lenses. In addition, we investigate the Talbot effect of wave optics in the duplex Mikaelian lens based on numeric calculations. Our findings based on splicing and exponential conformal mapping enlarge the family of absolute optical instruments.

Focusing a second-order cylindrical vector beam with a gradient index Mikaelian lens

In this paper, we numerically simulate the focusing of a second-order cylindrical vector beam with a gradient index Mikaelian lens. It is shown that the lens forms a region of the reverse energy flow near its output surface. If the lens has an on-axis micropit, the region of the direct energy flow can be confined within the lens material, whereas that of the reverse energy flow is put out in free space.