Optical lens compression via transformation optics

Machine Learning Aided Design and Optimization of Thermal Metamaterials

Artificial Intelligence (AI) has advanced material research that were previously intractable, for example, the machine learning (ML) has been able to predict some unprecedented thermal properties. In this review, we first elucidate the methodologies underpinning discriminative and generative models, as well as the paradigm of optimization approaches. Then, we present a series of case studies showcasing the application of machine learning in thermal metamaterial design. Finally, we give a brief discussion on the challenges and opportunities in this fast developing field. In particular, this review provides: (1) Optimization of thermal metamaterials using optimization algorithms to achieve specific target properties. (2) Integration of discriminative models with optimization algorithms to enhance computational efficiency. (3) Generative models for the structural design and optimization of thermal metamaterials.

Deep learning-based weak micro-defect detection on an optical lens surface with micro vision

To solve limited efficiency and reliability issues caused by current manual quality control processes in optical lens (OL) production environments, we propose an automatic micro vision-based inspection system named MVIS used to capture the surface defect images and make the OL dataset and predictive inference. Because of low resolution and recognition, OL defects are weak, due to their ambiguous morphology and micro size, making a poor detection effect for the existing method. A deep-learning algorithm for a weak micro-defect detector named ISE-YOLO is proposed, making the best for deep layers, utilizing the ISE attention mechanism module in the neck, and introducing a novel class loss function to extract richer semantics from convolution layers and learning more information. Experimental results on the OL dataset show that ISE-YOLO demonstrates a better performance, with the mean average precision, recall, and F1 score increasing by 3.62%, 6.12% and 3.07% respectively, compared to the YOLOv5. In addition, compared with YOLOv7, which is the latest version of YOLO serials, the mean average precision of ISE-YOLO is improved by 2.58%, the weight size is decreased by more than 30% and the speed is increased by 16%.

Strictly conformal transformation optics for directivity enhancement and unidirectional cloaking of a cylindrical wire antenna

Using conformal transformation optics, a cylindrical shell made of an isotropic refractive index material is designed to improve the directivity of a wire antenna while making it unidirectionally invisible. If the incident wave comes from a specific direction, it is guided around the wire. Furthermore, when an electrical current is used to excite the wire, the dielectric shell transforms the radiated wave into two lateral beams, improving directivity. The refractive index of the dielectric shell is calculated using the transformation optics recipe after establishing a closed-form conformal mapping between an annulus and a circle with a slit. The refractive index is then modified and discretized using a hexagonal lattice. Ray-tracing and full-wave simulations with COMSOL Multiphysics are used to validate the functionality of the proposed shell.

Detecting spatial chirp signals by Luneburg lens based transformation medium

Gradient refractive index (GRIN) lens-based chirp signal chirpiness detection usually relies on the fractional Fourier transform (FRFT) functionality of a quadratic GRIN lens and is limited by paraxial conditions. In this paper, a non-FRFT mechanism-based chirpiness detection GRIN lens is proposed that converts the Luneburg lens' focus capacity of input plane waves to the designed lens' focusing of input chirp waves using transformation optics, and the source chirpiness can be obtained by sweeping the illumination wavelength rather than locating the focusing pulse, consequently greatly increasing the upper limit of the chirpiness detection range. The feasibility and robustness of the method are verified through numerical simulations.

An optic to replace space and its application towards ultra-thin imaging systems

Centuries of effort to improve imaging has focused on perfecting and combining lenses to obtain better optical performance and new functionalities. The arrival of nanotechnology has brought to this effort engineered surfaces called metalenses, which promise to make imaging devices more compact. However, unaddressed by this promise is the space between the lenses, which is crucial for image formation but takes up by far the most room in imaging systems. Here, we address this issue by presenting the concept of and experimentally demonstrating an optical ‘spaceplate’, an optic that effectively propagates light for a distance that can be considerably longer than the plate thickness. Such an optic would shrink future imaging systems, opening the possibility for ultra-thin monolithic cameras. More broadly, a spaceplate can be applied to miniaturize important devices that implicitly manipulate the spatial profile of light, for example, solar concentrators, collimators for light sources, integrated optical components, and spectrometers.

The need for space between lenses in optical systems results in a trade-off between potential for miniaturisation and achieved resolution. Here, the authors demonstrate a device that propagates light longer than its thickness, a spaceplate, and can therefore replace space in optical systems.

Multiple drains in generalized Maxwell's fisheye lenses

The subwavelength imaging phenomenon in Maxwell's fisheye lens with one drain has been reported previously. In this paper, we theoretically find that coherent perfect absorbers (CPAs) perform well in generalized Maxwell's fisheye (GMFE) lenses. Such CPAs are embedded inside the GMFE lenses to absorb the incoming coherent waves. They can be served as drains and dramatically improve the resolution of images in the GMFE lenses. In particular, they can be applied to realize the subwavelength imaging. We also study the multiple imaging characteristics of GMFE lenses with several CPAs in wave optics. Full-wave simulations were performed to verify the imaging functionalities.

Ultrathin metasurface-based carpet cloak for terahertz wave

Ultrathin metasurfaces with local phase compensation deliver new schemes to cloaking devices. Here, a large-scale carpet cloak consisting of an ultrathin metasurface is demonstrated numerically and experimentally in the terahertz regime. The proposed carpet cloak is designed based on discontinuous-phase metallic resonators fabricated on a polyimide substrate, offering a wide range of reflection phase variations and an excellent wavefront manipulation along the edges of the bump. The invisibility is verified when the cloak is placed on a reflecting triangular surface (bump). The multi-step discrete phase design method would greatly simplify the design process and is probable to achieve large-dimension cloaks, for applications in radar and antenna systems as a thin, lightweight, and easy-to-fabricate solution for radio and terahertz frequencies.

Transformation-optical Fan-beam Synthesis

Gradient-index dielectric lenses are generated based on the coordinate transformation by compressing the homogeneous air spaces quasi-conformally towards and outwards the primary source. The three-dimensional modeling is then performed through revolving the prescribed transformational media 180 degrees around the focal point to reach the architecture of barrel-vaults. It is found that all these two- and three-dimensional transformation-optical designs are capable of producing fan-beams efficiently over a broad frequency range with their main lobes possessing the narrow beamwidth in one dimension and the wide beamwidth in the other, while having the great ability of the wide angular scanning. Finally, we propose to construct such four types of fan-beam lenses through multiple-layered dielectrics with non-uniformed perforations and experimentally demonstrate their excellent performances in the fan-beam synthesis.

Metamaterials and imaging

Resolution of the conventional lens is limited to half the wavelength of the light source by diffraction. In the conventional optical system, evanescent waves, which carry sub-diffraction spatial information, has exponentially decaying amplitude and therefore cannot reach to the image plane. New optical materials called metamaterials have provided new ways to overcome diffraction limit in imaging by controlling the evanescent waves. Such extraordinary electromagnetic properties can be achieved and controlled through arranging nanoscale building blocks appropriately. Here, we review metamaterial-based lenses which offer the new types of imaging components and functions. Perfect lens, superlenses, hyperlenses, metalenses, flat lenses based on metasurfaces, and non-optical lenses including acoustic hyperlens are described. Not all of them offer sub-diffraction imaging, but they provide new imaging mechanisms by controlling and manipulating the path of light. The underlying physics, design principles, recent advances, major limitations and challenges for the practical applications are discussed in this review.

Metamaterials and imaging

Resolution of the conventional lens is limited to half the wavelength of the light source by diffraction. In the conventional optical system, evanescent waves, which carry sub-diffraction spatial information, has exponentially decaying amplitude and therefore cannot reach to the image plane. New optical materials called metamaterials have provided new ways to overcome diffraction limit in imaging by controlling the evanescent waves. Such extraordinary electromagnetic properties can be achieved and controlled through arranging nanoscale building blocks appropriately. Here, we review metamaterial-based lenses which offer the new types of imaging components and functions. Perfect lens, superlenses, hyperlenses, metalenses, flat lenses based on metasurfaces, and non-optical lenses including acoustic hyperlens are described. Not all of them offer sub-diffraction imaging, but they provide new imaging mechanisms by controlling and manipulating the path of light. The underlying physics, design principles, recent advances, major limitations and challenges for the practical applications are discussed in this review.

An efficient plate heater with uniform surface temperature engineered with effective thermal materials

Extended from its electromagnetic counterpart, transformation thermodynamics applied to thermal conduction equations can map a virtual geometry into a physical thermal medium, realizing the manipulation of heat flux with almost arbitrarily desired diffusion paths, which provides unprecedented opportunities to create thermal devices unconceivable or deemed impossible before. In this work we employ this technique to design an efficient plate heater that can transiently achieve a large surface of uniform temperature powered by a small thermal source. As opposed to the traditional approach of relying on the deployment of a resistor network, our approach fully takes advantage of an advanced functional material system to guide the heat flux to achieve the desired temperature heating profile. A different set of material parameters for the transformed device has been developed, offering the parametric freedom for practical applications. As a proof of concept, the proposed devices are implemented with engineered thermal materials and show desired heating behaviors consistent with numerical simulations. Unique applications for these devices can be envisioned where stringent temperature uniformity and a compact heat source are both demanded.

Compression of a pyramidal absorber using multiple discrete coordinate transformation

The discrete coordinate transformation (DCT), as a unique technique to control the electromagnetic waves, has been applied for creating all-dielectric devices recently. To extend the applicability of this technique, we propose the concept of multiple discrete coordinate transformation, which serves to deal with more complicated geometries in the transformation domain. As an example, an all-dielectric absorber is created by compressing a pyramidal absorber to a third of its original thickness using the multiple DCT technique. The Finite-Difference Time-Domain (FDTD) method based numerical simulations demonstrate the broadband performance of the transformation absorber from 2 GHz to 20 GHz.

A versatile smart transformation optics device with auxetic elasto-electromagnetic metamaterials

Synergistic integration of electromagnetic (EM) and mechanical properties of metamaterials, a concept known as smart metamaterials, promises new applications across the spectrum, from flexible waveguides to shape-conforming cloaks. These applications became possible thanks to smart transformation optics (STO), a design methodology that utilizes coordinate transformations to control both EM wave propagation and mechanical deformation of the device. Here, we demonstrate several STO devices based on extremely auxetic (Poisson ratio −1) elasto-electromagnetic metamaterials, both of which exhibit enormous flexibility and sustain efficient operation upon a wide range of deformations. Spatial maps of microwave electric fields across these devices confirm our ability to deform carpet cloaks, bent waveguides, and potentially other quasi-conformal TO-based devices operating at 7 ~ 8 GHz. These devices are each fabricated from a single sheet of initially uniform (double-periodic) square-lattice metamaterial, which acquires the necessary distribution of effective permittivity entirely from the mechanical deformation of its boundary. By integrating transformation optics and continuum mechanics theory, we provide analytical derivations for the design of STO devices. Additionally, we clarify an important point relating to two-dimensional STO devices: the difference between plane stress and plane strain assumptions, which lead to elastic metamaterials with Poisson ratio −1 and −∞, respectively.

Transformation optics for antennas: why limit the bandwidth with metamaterials?

In the last decade, a technique termed transformation optics has been developed for the design of novel electromagnetic devices. This method defines the exact modification of magnetic and dielectric constants required, so that the electromagnetic behaviour remains invariant after a transformation to a new coordinate system. Despite the apparently infinite possibilities that this mathematical tool introduces, one restriction has repeatedly recurred since its conception: limited frequency bands of operation. Here we circumvent this problem with the proposal of a full dielectric implementation of a transformed planar hyperbolic lens which retains the same focusing properties of an original curved lens. The redesigned lens demonstrates operation with high directivity and low side lobe levels for an ultra-wide band of frequencies, spanning over three octaves. The methodology proposed in this paper can be applied to revolutionise the design of many electromagnetic devices overcoming bandwidth limitations.

Reducing physical appearance of electromagnetic sources

We propose to use the concept of transformation optics for the design of novel radiating devices. By applying transformations that compress space, and then that match it to the surrounding environment, we show how the electromagnetic appearance of radiating elements can be tailored at will. Our efficient approach allows one to realize a large aperture emission from a small aperture one. We describe transformation of the metric space and the calculation of the material parameters. Full wave simulations are performed to validate the proposed approach on different space compression shapes, factors and impedance matching. The idea paves the way to interesting applications in various domains in microwave and optical regimes, but also in acoustics.

Directive radiation from a diffuse Luneburg lens

Transformation electromagnetics has opened possibilities for designing antenna structures. Using an analytical approach, we demonstrate here how directive antenna radiation can be achieved from an omnidirectional source behind a diffuse surface. This diffuse surface has been obtained by an optical transformation of a Luneburg lens. Two different transformation approaches have been proposed (polynomial and sinusoidal), and for both cases, the resulting material properties have been simplified to ease the fabrication by using all-dielectric media. Therefore, the proposed design has no upper boundary to the operational frequency. Directive radiation has been achieved from thin diffuse structures, which demonstrates promising future possibilities for this technique.

Wide-angle scannable reflector design using conformal transformation optics

A flat reflector capable of scanning over wide angles is designed using a transformation optics approach. This reflector is derived from its virtual parabolic counterpart using a conformal coordinate transformation that determines the permittivity profile of the flat reflector. By changing the permittivity profile, the flat reflector is then capable of scanning up to 47° away from broadside while maintaining good beam characteristics across a wide frequency range. Moreover, its directivity is comparable to that of the virtual parabolic reflector, even at high scan angles. We use the Schwarz-Christoffel transformation as a versatile tool to produce perfect conformal mapping of coordinates between the virtual and flat reflectors, thereby avoiding the need to monitor the anisotropy of the material that results when employing quasi-conformal methods.

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.

Performance of a three dimensional transformation-optical-flattened Lüneburg lens

We demonstrate both the beam-forming and imaging capabilities of an X-band (8-12 GHz) operational Lüneburg lens, one side of which has been flattened via a coordinate transformation optimized using quasi-conformal transformation optics (QCTO) procedures. Our experimental investigation includes benchmark performance comparisons between the QCTO Lüneburg lens and a commensurate conventional Lüneburg lens. The QCTO Lüneburg lens is made from a metamaterial comprised of inexpensive plastic and fiberglass, and manufactured using fast and versatile numerically controlled water-jet machining. Looking forward towards the future and advanced TO designs, we discuss inevitable design trade-offs between affordable scalable manufacturing and rigorous adherence to the full TO solution, as well as possible paths to mitigate performance degradation in realizable designs.

Transformation bending device emulated by graded-index waveguide

We demonstrate that a transformation device can be emulated using a gradient-index waveguide. The effective index of the waveguide is spatially varied by tailoring a gradient thickness dielectric waveguide. Based on this technology, we demonstrate a transformation device guiding visible light around a sharp corner, with low scattering loss and reflection loss. The experimental results are in good agreement with the numerical results.

Optofluidic waveguide as a transformation optics device for lightwave bending and manipulation

Transformation optics represents a new paradigm for designing light-manipulating devices, such as cloaks and field concentrators, through the engineering of electromagnetic space using materials with spatially variable parameters. Here we analyse liquid flowing in an optofluidic waveguide as a new type of controllable transformation optics medium. We show that a laminar liquid flow in an optofluidic channel exhibits spatially variable dielectric properties that support novel wave-focussing and interference phenomena, which are distinctively different from the discrete diffraction observed in solid waveguide arrays. Our work provides new insight into the unique optical properties of optofluidic waveguides and their potential applications.

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.

Approaches to achieve broadband optical transformation devices with transmuted singularity

Many optical instruments with dielectric singularities cannot be manufactured directly. Their singularities can be transmuted through optical transformation, and equivalent physical media can be built to perform the same optical behaviors. The transformed physical media are usually anisotropic and inhomogeneous and, therefore, difficult to fabricate. In this work, several mathematical approaches are proposed to produce a transformed lens with all the elements of the material tensors to be no less than unity. This increases the ease of implementation, as natural materials may be used, which substantially widens the bandwidth of the transformed devices. Although we focus on an omnidirectional retroreflection lens as an example, the approaches developed here are universal and applicable to a wide class of devices with dielectric singularities.

A broadband zone plate lens from transformation optics

A zone plate lens utilizing a refractive instead of diffractive approach is presented for broadband operation. By utilizing transformation optics, we compress the conventional hyperbolic lens into a flat one with a few zone plates made of all-dielectric materials. Such a transformed lens maintains the broadband performance of the original lens, thus providing a superior alternative to the diffractive Fresnel element which is inherently narrow band.

Designing three-dimensional transformation optical media using quasiconformal coordinate transformations

We introduce an approach to the design of three-dimensional transformation optical (TO) media based on a generalized quasiconformal mapping approach. The generalized quasiconformal TO (QCTO) approach enables the design of media that can, in principle, be broadband and low loss, while controlling the propagation of waves with arbitrary angles of incidence and polarization. We illustrate the method in the design of a three-dimensional carpet ground plane cloak and of a flattened Luneburg lens. Ray-trace studies provide a confirmation of the performance of the QCTO media, while also revealing the limited performance of index-only versions of these devices.

Enhancing imaging systems using transformation optics

We apply the transformation optical technique to modify or improve conventional refractive and gradient index optical imaging devices. In particular, when it is known that a detector will terminate the paths of rays over some surface, more freedom is available in the transformation approach, since the wave behavior over a large portion of the domain becomes unimportant. For the analyzed configurations, quasi-conformal and conformal coordinate transformations can be used, leading to simplified constitutive parameter distributions that, in some cases, can be realized with isotropic index; index-only media can be low-loss and have broad bandwidth. We apply a coordinate transformation to flatten a Maxwell fish-eye lens, forming a near-perfect relay lens; and also flatten the focal surface associated with a conventional refractive lens, such that the system exhibits an ultra-wide field-of-view with reduced aberration.

Transformation optics and metamaterials

Underpinned by the advent of metamaterials, transformation optics offers great versatility for controlling electromagnetic waves to create materials with specially designed properties. Here we review the potential of transformation optics to create functionalities in which the optical properties can be designed almost at will. This approach can be used to engineer various optical illusion effects, such as the invisibility cloak.

Focusing light in a curved-space

We use transformation optics to demonstrate 2D silicon nanolenses, with wavelength-independent focal point. The lenses are designed and fabricated with dimensions ranging from 5.0 microm x 5.0 microm to 20 microm x 20 microm. According to numerical simulations the lenses are expected to focus light over a broad wavelength range, from 1.30 mum to 1.60 mum. Experimental results are presented from 1.52 microm to 1.61 microm.

Extreme-angle broadband metamaterial lens

For centuries, the conventional approach to lens design has been to grind the surfaces of a uniform material in such a manner as to sculpt the paths that rays of light follow as they transit through the interfaces. Refractive lenses formed by this procedure of bending the surfaces can be of extremely high quality, but are nevertheless limited by geometrical and wave aberrations that are inherent to the manner in which light refracts at the interface between two materials. Conceptually, a more natural--but usually less convenient--approach to lens design would be to vary the refractive index throughout an entire volume of space. In this manner, far greater control can be achieved over the ray trajectories. Here, we demonstrate how powerful emerging techniques in the field of transformation optics can be used to harness the flexibility of gradient index materials for imaging applications. In particular we design and experimentally demonstrate a lens that is broadband (more than a full decade bandwidth), has a field-of-view approaching 180 degrees and zero f-number. Measurements on a metamaterial implementation of the lens illustrate the practicality of transformation optics to achieve a new class of optical devices.

Conformal mappings to achieve simple material parameters for transformation optics devices

The transformation optics technique for designing novel electromagnetic and optical devices offers great control over wave behavior, but is difficult to implement primarily due to limitations in current metamaterial design and fabrication techniques. This paper demonstrates that restricting the spatial transformation to a conformal mapping can lead to much simpler material parameters for more practical implementation. As an example, a flat cylindrical-to-plane-wave conversion lens is presented and its performance validated through numerical simulations. It is shown that the lens dimensions and embedded source location can be adjusted to produce one, two, or four highly directive planar beams. Two metamaterial designs for this lens that implement the required effective medium parameters are proposed and their behavior analyzed.