Transformation optics designed general optical Luneburg lens with flattened shapes
4
Citation
16
Reference
10
Related Paper
Citation Trend
Abstract:
It is well-known that the conventional lens design suffers from the aberration, which will lead to imperfect imaging. One way to solve this problem is to use gradient index (GRIN) lenses such as Luneburg lens. However, the spherical geometry of Luneburg lens imposes difficulty for manufacturing. Also, it is desired to design the Luneburg lens with arbitrary focal length. To address these issues, in this paper, we propose to apply the transformation optics techniques to the general Luneburg lens design. In this way, the spherical lens surface will be transformed to flattened shapes, which can be practically fabricated on a flat substrate. Specifically, three-dimensional (3D) Luneburg lenses with different focal lengths will be studied. Moreover, discussion on the fabrications of proposed lens has been included. It is desired to ensure that the modified design lies within the available material properties of various polymer photoresists.Keywords:
Luneburg lens
Gradient-index optics
Transformation Optics
Simple lens
Versatile optical devices are designed from anisotropic and gradient materials based on transformation optics, which are usually hard to realize. Here, by utilizing conformal equivalence, we demonstrate that a flat gradient index optical thin-film waveguide is equivalent to a curved homogenous optical thin-film waveguide for light rays. Such a relationship provides us an alternative method to design optical devices with either an inhomogeneous medium or equivalently curved surfaces made from only a homogeneous material, leading to applications on on-chip optical devices. Moreover, we provide a prototype of the curved optical thin-film waveguide without rotational symmetry, which can serve as a concave lens. Our work gives a conformal landscape of a two-dimensional gradient refractive-index profile from the geometric optics perspective.
Transformation Optics
Luneburg lens
Gradient-index optics
Waveguide
Geometrical optics
Refractive index profile
Cite
Citations (13)
This paper presents a half-lens antenna integrated with a reflectarray. The combination of the half-lens and the reflectarray provides additional design freedom. In this work, this design freedom is used to reduce the refractive index range required to produce a planar wavefront using a half-lens, as compared to the half-Luneburg lens. Specifically, we demonstrate that the properties of a half-Luneburg lens can be mimicked with a lens that has reduced the maximum refractive index by 30% by integrating the reflectarray with the lens.
Luneburg lens
Gradient-index optics
Simple lens
Cite
Citations (2)
In this paper, a novel gradient index (GRIN) structural lens based on the concept of generalized Luneburg lens (GLL) is proposed. This lens allows for the realization of double foci and localization of energy flow between the two focal spots, thereby achieving ultralong focusing. The double-foci GRIN lens consists of two concentric circular regions with varying thickness defined in a thin plate structure. The two concentric circular regions are designed to realize continuous change of refractive indices with different profiles. Numerical simulations and experimental studies are performed to obtain the maximum displacement amplitude, full length at half maximum (FLHM), and full width at half maximum (FWHM) of the focal region of the lens. The results demonstrate that ultralong subwavelength focusing can be achieved for a broadband frequency range. In addition, our results show that the FLHM and FWHM can be tailored through the design of the focal length of the GLL. This offers a simple and flexible approach of engineering the GLL focusing characteristics and energy distributions for many applications.
Luneburg lens
Gradient-index optics
Cite
Citations (0)
This Letter presents a theory that allows graded index lenses to be mapped onto arbitrary rotationally symmetric curved surfaces. Examples of the Luneburg and Maxwell fish-eye lens are given, for numerous surfaces, always resulting in isotropic permittivity requirements. The performance of these lenses is initially illustrated with full-wave simulations utilizing a waveguide structure. A transformation of the refractive index profiles is then performed to design surface-wave lenses, where the dielectric layer is not only isotropic but also homogenous, demonstrating the applicability and ease of fabrication.
Luneburg lens
Transformation Optics
Gradient-index optics
Geometrical optics
Cite
Citations (54)
It is well-known that the conventional lens design suffers from the aberration, which will lead to imperfect imaging. One way to solve this problem is to use gradient index (GRIN) lenses such as Luneburg lens. However, the spherical geometry of Luneburg lens imposes difficulty for manufacturing. Also, it is desired to design the Luneburg lens with arbitrary focal length. To address these issues, in this paper, we propose to apply the transformation optics techniques to the general Luneburg lens design. In this way, the spherical lens surface will be transformed to flattened shapes, which can be practically fabricated on a flat substrate. Specifically, three-dimensional (3D) Luneburg lenses with different focal lengths will be studied. Moreover, discussion on the fabrications of proposed lens has been included. It is desired to ensure that the modified design lies within the available material properties of various polymer photoresists.
Luneburg lens
Gradient-index optics
Transformation Optics
Simple lens
Cite
Citations (4)
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.
Luneburg lens
Transformation Optics
Nanophotonics
Gradient-index optics
Cite
Citations (53)
Transformation Optics
Gradient-index optics
Luneburg lens
Achromatic lens
Cite
Citations (444)
Curved lenses and antennas have pivotal meaning in various applications. For example, gradient index lenses such as the Luneburg lens are used to realize perfect imaging. However, the procedure of fabricating the bended surface of these lenses and antennas is difficult and not cost effective. In order to solve this issue, in this paper, we propose to apply transformation optics techniques to re-design these curved lenses antennas. Based on the quasi-conformal mapping technique, the spherical surfaces of various Luneburg lens antennas with different focal lengths will be transformed to flattened shapes, which can be easily implemented with low cost substrates and fabrication techniques. Preliminary simulation results of the designed devices are also given in this paper.
Luneburg lens
Transformation Optics
Gradient-index optics
Conformal antenna
Cite
Citations (1)
Luneburg lens has long been developed since first being proposed in 1944. The Luneburg lens is a spherical lens generally having a gradient of decreasing refractive index radially out from its center. The focusing properties of the Luneburg lens can be achieved through an infinite number of refractive-index solutions. With the spherically symmetrical structure and gradient radial refractive index change, the Luneburg lens is an excellent candidate for all-directional beamscanning antennas. This paper presents two types of flat Luneburg lens antenna based on printed circuit board technique for beamscanning applications. The transformation optics is used to flatten the design of conventional spherical Luneburg lenses and the technology based on metamaterials is proposed to implement the gradient index lens structure.
Luneburg lens
Transformation Optics
Gradient-index optics
X-ray optics
Cite
Citations (4)
The application of thin-film Luneburg lenses to integrated optical circuits will require accurate control of their focal length to permit the necessary alignment between the various circuit elements. Of particular interest is the design of lenses for application to a silicon-based integrated optical rf spectrum analyzer. This study analyzes the sensitivity of the focal length of Luneburg lenses to thickness variation at the lens center resulting from fabrication process tolerances. It is shown that this sensitivity can be minimized by properly selecting the refractive index of the waveguide material, using a larger focal length and employing a longer optical wavelength.
Luneburg lens
Gradient-index optics
Waveguide
Cite
Citations (16)