Spherical gradient-index polymer lens with low spherical aberration

A sphere lens with a spherical gradient index (GRIN) was prepared by the modified suspension polymerization technique. GRIN spheres with quadratic- and linear-index distributions were obtained by two different methods to confirm the effect of the GRIN profile on the focusing property of the sphere lens. It was confirmed in both theory and experiment that the spherical aberration of such GRIN spheres was remarkably decreased compared with that of a homogeneous sphere.     

Single dispersive gradient-index profile for the aging human lens

We provide a single gradient-index (GRIN) profile for the crystalline lens in an updated age-dependent emmetropic-eye model. The parameters defining the GRIN profile include their variation with age and the dispersion of the refractive index in order to account for the increase in the positive-wave spherical aberration, for the constant chromatic difference in the refraction of the human eye, as well as for the decrease in the retinal-image quality with aging. In accounting for these ocular properties, the results show that first, the value of the dispersion parameters are invariant with age. Second, those parameters defining the distribution of the lens index cause the lens-center-index value to decrease slightly, and its position along the lens axis changes with age. Furthermore, these findings are in agreement with the lens paradox.     

Foundations for low-loss fiber gradient-index lens pair coupling with the self-imaging mechanism

A fiber-optic collimator that emits a Gaussian beam with its beam waist at a certain distance after the exit face of the lens is labeled a self-imaging collimator. For such a collimator, the waist of the emitted Gaussian beam and its location are partly dependent on the properties of the gradient-index (GRIN) lens. Parameters for the self-imaging collimator are formulated in terms of the parameters of a GRIN lens (e.g., pitch, core refractive index, gradient index, length) and the optical wavelength. Next, by use of the Gaussian beam approximation, a general expression for the coupling power loss between two self-imaging-type single-mode fiber (SMF) collimators is, for the first time to our knowledge, derived as a function of three types of misalignment, namely, separation, lateral offset, and angular tilt misalignment. A coupling experiment between two self-imaging collimators with changing separation distance is successfully performed and matches the proposed self-imaging mechanism coupling loss theory. In addition, using a prism, lateral offset, as well as angular tilt, misalignments are experimentally simulated for a two self-imaging collimator coupling condition by a single collimator reflective test geometry. Experimental results agree well with the proposed loss formulas for self-imaging GRIN lenses. Hence, for the first time to our knowledge, the mathematical foundations are laid for employing self-imaging-type fiber collimators in SMF-based free-space systems allowing optimal design for ultra-low-loss coupling.     

Patch-fed planar dielectric slab waveguide Luneburg lens

The design of a patch-fed planar dielectric slab waveguide Luneburg lens weighing only 45 g and operated at 27 GHz in TM₀ mode is described. The measured half-power beamwidth (HPBW) for a 10.8 lambda, 12-cm diameter lens fed by a microstrip patch placed in intimate contact with the lens rim is 6.9deg with 16.8 dB gain and 10% bandwidth for -10 dB feed return loss, lens cross-polar levels were below -20 dB. The lens is also capable of operating in the TE₀ mode with similar radiation performance to that of the TM₀ mode. Here, measured HPBW and gain is 8 and 15.5 dB at 27 GHz. Unlike other planar lens arrangements, because of its ability to handle both TM₀ and TE₀ modes the lens has the potential to deal with the circularly polarised signals, this aspect is also explored.     

Fabrication and characterization of a planar gradient-index, plasma-enhanced chemical vapor deposition lens

A thin, one-dimensional, gradient-index slab lens with a parabolic profile was designed and fabricated in fluorine-doped silica by use of plasma-enhanced chemical vapor deposition in a Helicon plasma reactor. The refractive-index profile of the fabricated lens was determined by the application of an inversion technique to the values of modal effective index measured with a prism coupler. The periodic refocusing property of the lens and the independence of the wavelength were measured with the fluorescence of a specially doped, thin polymer layer spin-coated onto the surface of the lens.     

Optical shifter for a three-dimensional image by use of a gradient-index lens array

We propose a new function of the two-dimensional lens array that is composed of many gradient-index lenses. The array forms three-dimensional (3D) images. The characteristics of the 3D images depend on the length of the gradient-index lens. Especially, if the length of the lens is an odd-integer multiple of the half period of the optical path, 3D images are pseudoscopic with a reversed depth. The two lens arrays are positioned at a suitable distance, so that orthoscopic 3D images with the correct depth are formed in front of the lens array.     

ABCD matrix of the human lens gradient-index profile: applicability of the calculation methods

The applicability of different approximate methods proposed to determine the paraxial properties of the gradient-index (GRIN) distribution resembling that of the human lens, by means of the system ABCD matrix, is tested. Thus, the parabolic-ray-path approximation has been extended to provide the ABCD matrix of a slab lens comprised of a rotationally GRIN medium. The results show that this method has good numerical stability, and it is also the easiest one in determining the Gaussian constants of the human lens GRIN profile.     

Polarisation insensitive planar dielectric slab waveguide extended hemi-elliptical lens

The authors present the performance of a patch fed planar dielectric slab waveguide extended hemi- elliptical lens antenna. The lens is constructed using polystyrene and weighs only 90 g. The maximum lens dimensions are 11 lambda times 13 lambda in the lens plane and it is 0.6 lambda thick. From 18 to 30 GHz the lens can handle both TM₀ and TE₀ signals simultaneously and at 22 GHz it can be made to generate a 1.5 dB axial ratio circularly polarised signal when fed by a linearly polarised patch antenna orientated to 38deg with respect to the horizontal. The measured gain and half-power beamwidth for TM₀ and TE₀ excitation at 28.5 GHz are 18.5 dB (aperture efficiency of 85%), 4.1deg and 18.7 dB, 4.4deg, respectively, both with a -10 dB return loss bandwidth of about 10%.     

Alternative method for measuring the full-field refractive index of a gradient-index lens with normal incidence heterodyne interferometry

A linearly/circularly polarized heterodyne light beam coming from a heterodyne light source with an electro-optic modulator in turn enters a modified Twyman-Green interferometer to measure the surface plane of a GRIN lens. Two groups of periodic sinusoidal segments recorded by a fast complementary metal-oxide semiconductor camera are modified, and their associated phases are derived with the unique technique. The data are substituted into the special equations derived from the Fresnel equations, and the refractive index can be obtained. When the processes are applied to other pixels, the full-field refractive-index distribution can be obtained similarly. Its validity is demonstrated.     

Modeling liquid-crystal gradient-index lenses

The optical properties of one-dimensional gradient-refractive-index lens arrays based on liquid crystals are studied. We find that it is quite possible, using theoretical methods, to predict angular distributions of the light emanating from such arrays when they are illuminated with collimated monochromatic light. We compare four theoretical methods in relation to experiments. The experimental data and the model, based on a combination of eikonal methods and diffraction, are in close correspondence. Features such as maximal beam width and number of extrema in the angular light distribution are discussed and explained theoretically. We also studied dispersion effects, both experimentally and theoretically, with good agreement between the two.     

Distortion in a gradient-index rod

An algebraic formula is derived for the fifth-order distortion of a GRIN-rod lens. By measuring distortion, one can then determine the coefficients of the profile formula.