Design Of Gradient Index Lens Research Articles

Inverse design of high-NA metalens for maskless lithography

Abstract We demonstrate an axisymmetric inverse-designed metalens to improve the performance of zone-plate-array lithography (ZPAL), one of the maskless lithography approaches, that offer a new paradigm for nanoscale research and industry. First, we derive a computational upper bound for a unit-cell-based axisymmetric metalens. Then, we demonstrate a fabrication-compatible inverse-designed metalens with 85.50% transmission normalized focusing efficiency at 0.6 numerical aperture at 405 nm wavelength; a higher efficiency than a theoretical gradient index lens design (79.98%). We also demonstrate experimental validation for our axisymmetric inverse-designed metalens via electron beam lithography. Metalens-based maskless lithography may open a new way of achieving low-cost, large-area nanofabrication.

Radial GRIN Lenses Based on the Solution of a Regularized Ray Congruence Equation

We introduce a novel formulation for flat radial GRadient INdex (GRIN) lenses allowing for the optimal lens design through closed-form expressions. The validity of the proposed formulation covers a very large range of GRIN lens design parameters (focal distance, lens thickness, and maximum refractive index). The formulation is based on the derivation of a new form of nonlinear integral equation representing the equalization of all the optical ray-path lengths, denoted as regularized ray congruence (RRC) equation, and on its closed-form solution. An analytical form of aperture efficiency is given for standard feed patterns. The application of the formulas presented here allows for an instantaneous design for medium/high gain antennas with controllable total aperture efficiency till 80%. The accuracy of the formulation is tested by a full-wave analysis and compared with other formulations available in the literature. We found that the new formulation proposed here significantly reduces the phase error in a wide range of the lens parameters, thus allowing for a more efficient, accurate, and flexible design for GRIN lenses. As a proof of concept, a thin GRIN lens antenna for operation in E-band (60–90 GHz) is designed, demonstrating high aperture efficiency (63%) across a wide frequency range.

The Systematic Design of Noncommensurate Impedance Matching Tapers for Ultrawideband Gradient-Index Lens Antennas

We propose a general method for designing wideband matching tapers in inhomogeneous media where phase velocity is coupled to the taper impedance profile. Such tapers are used to match wideband gradient index (GRIN) lens antennas. To simplify fabrication tapers are often constrained to physically uniform layers wherein commensurate line theory cannot predict the frequency response. Therefore, we present a new design algorithm which derives an effective permittivity $\epsilon_{eff}$ to equalize the electrical length of commensurate and non-commensurate line tapers. The algorithm provides a systematic design method with predictable frequency response for non-commensurate line tapers. Nevertheless, there are several unavoidable nonidealities present in such discretized tapers which we discuss and provide recommendations for mitigation. The algorithm is used to design a Klopfenstein taper with return loss better than 15 dB from 8 to 78 GHz. The design is fabricated and measurements agree with simulation across the WR90, WR28, and WR12 bands. An approximate efficiency formula is proposed which predicts aperture efficiency of taper-matched lenses without the need for time-consuming full-wave simulations. Various lenses are designed and compared to highlight the advantages of Klopfenstein tapers in GRIN lens design. The results demonstrate the usefulness of the proposed design method.

Ultra-Wideband Flat Metamaterial GRIN Lenses Assisted With Additive Manufacturing Technique

This article presents the designs of ultrawideband microwave flat gradient index (GRIN) lenses, which realizes over a 108% fractional bandwidth (12-40 GHz). The frequency-independent ray optics method is employed to determine the radially varying permittivity profile of the lenses. The challenge of realizing such a radially varying profile and the limitations in dielectric material choices are overcome by two additive-manufacturing-aided approaches: 1) partially infilled dielectrics with a varied periodicity, which ensures the lens performance at the higher end of the frequency range and 2) artificially engineered dielectrics (AED) with subwavelength-scale metallic inclusions, which enables-high permittivity dielectrics and leads to benefits of thickness and mass reduction for the GRIN lenses. Measured results demonstrate that the GRIN lenses improve the gain of open-ended waveguide sources by 8.7-15.6 dB over a wide frequency range from 12 to 40 GHz, with the realized gain of up to 23.6 dBi. Both the simulation and measurements of the presented design confirm the potential of implementing the proposed GRIN lens design in high directivity and beamforming antenna applications, across an ultrawideband frequency range.

Extraordinarily transparent compact metallic metamaterials.

The design of achromatic optical components requires materials with high transparency and low dispersion. We show that although metals are highly opaque, densely packed arrays of metallic nanoparticles can be more transparent to infrared radiation than dielectrics such as germanium, even when the arrays are over 75% metal by volume. Such arrays form effective dielectrics that are virtually dispersion-free over ultra-broadband ranges of wavelengths from microns up to millimeters or more. Furthermore, the local refractive indices may be tuned by altering the size, shape, and spacing of the nanoparticles, allowing the design of gradient-index lenses that guide and focus light on the microscale. The electric field is also strongly concentrated in the gaps between the metallic nanoparticles, and the simultaneous focusing and squeezing of the electric field produces strong ‘doubly-enhanced’ hotspots which could boost measurements made using infrared spectroscopy and other non-linear processes over a broad range of frequencies.

Acoustic gradient index lens design using gradient based optimization

We demonstrate a gradient based optimization of the absolute acoustic pressure at a focal point by incrementally repositioning a set of cylindrical obstacles so that they eventually act as an effective gradient index (GRIN) lens. The gradient-based optimization algorithm maximizes the absolute pressure at the focal point by analytically evaluating its derivative with respect to the cylinder positions and then perturbatively optimizing the position of each cylinder in the GRIN lens device while taking into account acoustic multiple scattering between the cylinders. The method is presented by examples of sets of hard cylinders and sets of elastic cylindrical shells of uniform size. Designs using available cylindrical shells enable easy and realistic fabrication of acoustic GRIN lenses. Computations are performed on MATLAB using parallel optimization algorithms and a multistart optimization solver, and supplying the gradients of absolute pressure at the focal point with respect to position vectors. Providing the analytic form of the gradients enhances modeling by allowing the use of exact gradients with optimization algorithms and parallel computing. This results in reducing number of function calls and time needed to converge, and improving solution accuracy for large scale optimization problems especially at high frequencies and with a large number of scatterers.

Endoscopic fiber probe for nonlinear spectroscopic imaging

We present a compact multimodal fiber probe that enables the simultaneous recording of nonlinear imaging modalities like coherent anti-Stokes Raman scattering (CARS), second harmonic generation (SHG), and two-photon excited auto-fluorescence (TPEF) for biomedical applications. The probe is based on a gradient index lens design and a multi-core fiber supplying the excitation laser light. The multi-core fiber preserves the spatial relationship between the entrance and output; therefore, the laser scanning procedure can be shifted from the distal to the proximal end of the probe. No moving parts or electric power are required in situ. The generated sample signals can be collected in the backward (epi) direction and transferred to a detection setup with a multimode fiber integrated in the probe head. The first CARS/SHG/TPEF multimodal tissue images recorded with the introduced fiber probe will be presented.

Graphical user interfaces for teaching and design of GRIN lenses in optical interconnections

The use of graphical user interfaces (GUIs) enables the implementation of practical teaching methodologies to make the comprehension of a given subject easier. GUIs have become common tools in science and engineering education, where very often, the practical implementation of experiences in a laboratory involves much equipment and many people; they are an efficient and inexpensive solution to the lack of resources. The aim of this work is to provide primarily physics and engineering students with a series of GUIs to teach some configurations in optical communications using gradient-index (GRIN) lenses. The reported GUIs are intended to perform a complementary role in education as part of a ‘virtual lab’ to supplement theoretical and practical sessions and to reinforce the knowledge acquired by the students. In this regard, a series of GUIs to teach and research the implementation of GRIN lenses in optical communications applications (including a GRIN light deflector and a beam-size controller, a GRIN fibre lens for fibre-coupling purposes, planar interconnectors, and an anamorphic self-focusing lens to correct astigmatism in laser diodes) was designed using the environment GUIDE developed by MATLAB. Numerical examples using available commercial GRIN lens parameter values are presented.

Three-dimensional ultrathin planar lenses by acoustic metamaterials.

Acoustic lenses find applications in various areas ranging from ultrasound imaging to nondestructive testing. A compact-size and high-efficient planar acoustic lens is crucial to achieving miniaturization and integration, and should have deep implication for the acoustic field. However its realization remains challenging due to the trade-off between high refractive-index and impedance-mismatch. Here we have designed and experimentally realized the first ultrathin planar acoustic lens capable of steering the convergence of acoustic waves in three-dimensional space. A theoretical approach is developed to analytically describe the proposed metamaterial with hybrid labyrinthine units, which reveals the mechanism of coexistence of high refractive index and well-matched impedance. A hyperbolic gradient-index lens design is fabricated and characterized, which can enhance the acoustic energy by 15 dB at the focal point with very high transmission efficiency. Remarkably, the thickness of the lens is only approximately 1/6 of the operating wavelength. The lens can work within a certain frequency band for which the ratio between the bandwidth and the center frequency reaches 0.74. By tailoring the structure of the metamaterials, one can further reduce the thickness of the lens or even realize other acoustic functionalities, opening new opportunity for manipulation of low-frequency sounds with versatile potential.

An optical system incorporating gradient-index lens for confocal inspection

A differential confocal measurement system features high lateral resolution and depth-discriminated sections. In comparison with conventional lens, gradient-index lens is lighter in weight, smaller in volume and easy to couple. In order to facilitate the measurement of a small irregular surface in a limited space, a small optical inspection system is presented, which combines the high axial resolution and absolute position tracking capability of a differential confocal microscopy and the compact design of gradient-index lens, and uses gradient-index lens to obtain a small detector of 1 mm in diameter. The operating principle and construction of the measurement system are detailed. The differential design of the two detectors eliminates both the fluctuation of light source and the electronic noise from probes, and increases the axial resolution as well.

Differential confocal optical system using gradient-index lenses

Compared to conventional lenses, gradient index lenses are lighter in weight, smaller in volume, and easy to couple. To facilitate the measurement of a small irregular surface in a limited space, a small optical inspection system is presented, which combines the high axial resolution and absolute position tracking capability of differential confocal microscopy and the compact design of a gradient index lens, and uses the gradient index lens to obtain a small detector 1 mm in diam. The operating principle and construction of the measurement system are detailed, and the design of gradient index lenses is discussed. This differential confocal measurement system features high lateral resolution and depth-discriminated sections. The differential design of the two detectors eliminates both the fluctuation of light source and the electronic noise from probes, and increases the axial resolution as well. With a 1-mm-diam probe an axial resolution of 5 nm is obtained for gauge blocks less than 20 deg. In addition to its application for measurement of a small irregular surface in limited space, the sensor system proposed can be fitted onto a coordinate measuring machine for noncontact measurement of dimensions and surface roughness, and incorporated into a CNC machining center for on-line quality monitoring.

A small probe with a gradient index lens for confocal measurement

In comparison with conventional lens, gradient index lens is lighter in weight, smaller in volume and easy to couple. In order to facilitate the measurement of a small irregular surface in a limited space, a small probe is presented, which combines the compact design of gradient index lens with the high axial resolution and absolute position tracking capability of a confocal microscope. The operating principle and construction of the measurement system are detailed. The confocal measurement system features high lateral resolution and depth-discriminated sections. The effect of various factors on axial resolution, and design of key component, such as a gradient index lens, pinhole, light source and detector are discussed. Experimental results show a axial resolution of 10 nm can be obtained when a probe of 1 mm in diameter is used to detect a slope profile of less than 20°. In addition to its application for measurement of a small irregular surface in a limited space, the sensor system proposed can be fitted onto a coordinate measuring machine for non-contact measurement of dimensions and surface roughness, and incorporated into CNC machining center for on-line quality monitoring.

Third Order Aberration of Conical SELFOC Fibers+

In this paper, we have obtained explicit expressions for the third-order aberration coefficients of conical SELFOC fibers, in which, in addition to a transverse variation of refractive index, there exists a dependence of refractive index along the axis of symmetry. We have also obtained the variation of the aberration coefficients with various parameters and have shown that there exists realistic values of the parameters for which spherical aberration, coma or distortion can be made zero. The analysis should find application in the design of gradient-index lenses.