Tapered gradient-index media and zone plates: Influence of off-axis illumination and finite dimension on light propagation

Abstract

The effects of off-axis illumination and finite dimension on the irradiance distribution in a hybrid system formed by a zone plate and a tapered gradient-index (GRIN) medium are investigated. Results are applied to a GRIN medium with a divergent linear taper function and a sinusoidal zone plate of amplitude to show the transverse shift and the diffractional effect.     

The effect of pressure on GRIN lenses

The changes of the optical power of Gradient Index (GRIN) lenses occurring in hydrostatic pressures of the range of 0-2 GPa are investigated. The measurements of the position of the waist of the semiconductor laser beam revealed the increase of the optical power of the lenses with increasing pressure. The use of the special plano-concave lenses insensitive to the changes of the refractive index of the pressure medium allowed to attribute the changes to the increasing index gradient in GRIN material. The effect has been explained within the frame of Mueller’s theory of photoelasticity. The findings have been then confirmed in experiments with the plano-planar and plano-convex lenses of the same materials.     

Correction of chromatic aberrations in GRIN endoscopes

A gradient-index (GRIN) endoscope can be constructed by substituting for the usual objective and relay sections suitable cylindrical index-distribution rod lenses. Currently available GRIN lenses exhibit large amounts of chromatic aberration. Axial color arises mostly from the relay lens, while lateral color is due to the objective lens. A negative lens cemented to a shortened GRIN relay lens can simultaneously correct axial and lateral chromatic aberrations with commercially available components. This correction system reduces the requirements for mechanical centration better than do color correctors that are incorporated into the ocular design. Monochromatic aberrations are also considered.     

Birefringence measurements in gradient-index rod lenses

Stress birefringence can be found in gradient-index (GRIN) materials because they contain a variation in composition. GRIN glass fabricated by ion exchange may contain stress from two different processes. These include a size difference between the exchange and the diffusing ions and a variation in the thermal-expansion coefficient across the gradient region. The optical properties of the stressed material are polarization dependent, and therefore image quality is directly affected. We examine birefringence in GRIN rod lenses that have lengths more than ten times greater than their diameters. The effects are more easily observed in long rod lenses because of the large optical path lengths.     

Single-mode fiber coupling efficiency with graded-index rod lenses

Losses are calculated for the single-mode graded-index- (GRIN-) lens coupler. The main advantage of this coupling system is large separation between fibers with small power loss. The excess loss of the GRIN-lens coupler is due primarily to the misalignments of the GRIN lenses and is most sensitive to angular tilt rather than lateral offset or end separation. The excess loss is calculated from the overlap of two differently sized or misaligned Gaussian beams. Experimental results show that this method is adequate for predicting losses that are due to misalignments of the GRIN lenses.     

Large radial graded-index polymer

A very large radial graded-index (GRIN) polymer was successfully prepared for the first time, to the best of our knowledge, by two methods: the curved mold method and the diffusion copolymerization method. Both methods gave a radial GRIN polymer with a diameter of 70 mm and a ?n value greater than 0.02. Ray tracing through these radial GRIN polymers was used to predict that such a GRIN polymer could be a promising candidate for thinner ophthalmic lenses with no spherical aberration or multifocusing characteristics.     

Pupil Effect in a GRIN Lens with Gaussian Illumination

Abstract

Using the propagator method, the quasi-geometric transmittance function and complex amplitude distribution produced by a GRIN lens are evaluated when it is illuminated by a Gaussian beam and the pupil effect is taken into account. The effective pupil is defined and derived by both quasi-geometrical optics and the exact Fresnel diffraction, which it is evaluated in a Rubinowicz representation.     

Birefringence in gradient-index rod lenses: a direct measurement method and interferometric polarization effects

Gradient-index (GRIN) media can contain stress birefringence resulting from the variation in material composition. Anisotropy in a GRIN rod lens affects ray propagation and can degrade image quality. A technique, believed to be new, for measuring birefringence in GRIN rod lenses has been developed. The change in optical path difference (OPD) for orthogonal polarizations is measured directly. With this method, effects on OPD from standard imaging aberrations are excluded. Birefringence measurements for various GRIN rod samples are presented. The data are compared with results obtained previously by use of a Twyman-Green measurement method. Also, the polarization effects on tilt fringes observed with the direct measurement method and the Twyman-Green method are presented and modeled theoretically. Tilt fringes for large birefringence test cases are also modeled.     

Birefringent properties of diametrically loaded gradient-index lenses

Gradient-index (GRIN) lenses have been widely used as collimators in various fiber-optic sensors and as optical coupling devices in components designed for optical communication systems. However, relatively little attention has been paid to the birefringent properties of GRIN lenses and the potential for using them as photoelastic sensing elements in optical transducers. Analytical and experimental results are described that were obtained for the intensity distribution produced by studying a GRIN lens by using a polariscope. The residual birefringence inherent in an unloaded lens is initially studied. The lens is then assumed to be diametrically loaded and the superposition is studied by the method of ray tracing. When the results obtained from the simulation for a Selfoc, 0.25-pitch lens are compared with experimental data, an excellent agreement is obtained. Intensity increases monotonically with load, confirming that the lens would be a good choice for the sensing element of an optical transducer designed as part of a strain or acceleration measurement system. The numerical simulation is then used to study the influence of residual stress on sensitivity.     

Studies on the light-focusing plastic rod. 15: GRIN rod prepared by photocopolymerization of a ternary monomer system

Plastic GRIN rod and fiber lenses have been fabricated by photocopolymerization of a ternary monomer system, methyl methacrylate-N-vinyl carbazole-vinyl acetate. We now propose the general mechanism for forming radial GRIN in the ternary monomer system using computer simulation. The relationship between the preparation condition and the optical characteristics was clarified. The region having quadratic-index distribution and the numerical aperture were remarkably improved by the ternary monomer system.     

Homogeneous Refracting Lenses for Integrated Optical Circuits

Abstract

Thin-film homogeneous refracting lenses have been designed and evaluated using both ray-tracing and the Huygens-Fresnel construction. Single-element lenses are shown to be unsatisfactory. Large-aperture, multielement lenses with circular or acircular boundaries are capable of near-diffraction-limited performance over field angles of several degrees.     

Application of Moments for Restoration of an Image Transmitted Through Long Multimode GRIN Fibres

Abstract

In this paper a new method of restoration of an image transmitted through a gradient-index (GRIN) fibre waveguide is considered. Instead of the difficulty in optical system mode decomposition of an output signal we suggest an easily realized moment decomposition. Compensation for the phase differences between moments instead of those between modes leads to better reconstruction of the transmitted signal at certain output planes. The numerical results of the image restoration using this method are discussed.     

Static and dynamic Fresnel zone lenses for optical interconnections

Abstract

Static and dynamic Fresnel zone lenses were fabricated in quartz glass by means of microstructuring techniques. Two types of on-axis and offaxis lenses with different focal lengths and of different apertures were designed to operate at wavelengths of 1·52 μm and 633 nm. The blazed profile of the onaxis and off-axis lenses was approximated by up to 16 and up to four discrete levels respectively. Dynamic, that is electrically switchable, lenses have been realized by filling the structured surface with liquid crystal. The optical properties of the lenses, such as the focal spot sizes and the diffraction efficiencies, were investigated. Further the switching behaviour of the dynamic lenses was studied. The design and fabrication of the static and dynamic, on-and off-axis Fresnel zone lenses as well as their optical and switching properties will be presented.     

Graded-index fiber lens proposed for ultrasmall probes used in biomedical imaging

The quality and parameters of probing optical beams are extremely important in biomedical imaging systems both for image quality and light coupling efficiency considerations. For example, the shape, size, focal position, and focal range of such beams could have a great impact on the lateral resolution, penetration depth, and signal-to-noise ratio of the image in optical coherence tomography. We present a beam profile characterization of different variations of graded-index (GRIN) fiber lenses, which were recently proposed for biomedical imaging probes. Those GRIN lens modules are made of a single mode fiber and a GRIN fiber lens with or without a fiber spacer between them. We discuss theoretical analysis methods, fabrication techniques, and measured performance compared with theory.     

Age-dependent variation of the Gradient Index profile in human crystalline lenses

PURPOSE: To reconstruct the gradient index (GRIN) profile of human crystalline lenses ex-vivo using Optical Coherence Tomography (OCT) imaging with an optimization technique and to study the dependence of the GRIN profile with age. METHODS: Cross-sectional images of nine isolated human crystalline lenses with ages ranging from 6 to 72 (post mortem time 1 to 4 days) were obtained using a custom-made OCT system. Lenses were extracted from whole cadaver globes and placed in a measurement chamber filled with preservation medium (DMEM). Lenses were imaged with the anterior surface up and then flipped over and imaged again, to obtain posterior lens surface profiles both undistorted and distorted by the refraction through the anterior crystalline lens and GRIN. The GRIN distribution of the lens was described with three variables by means of power function, with variables being the nucleus and surface index, and a power coefficient that describes the decay of the refractive index from the nucleus to the surface. An optimization method was used to search for the parameters that produced the best match of the distorted posterior surface. RESULTS: The distorted surface was simulated with accuracy around the resolution of the OCT system (under 15 μm). The reconstructed refractive index values ranged from 1.356 to 1.388 for the surface, and from 1.396 to 1.434 for the nucleus. The power coefficient ranged between 3 and 18. The power coefficient increased significantly with age, at a rate of 0.24 per year. CONCLUSION: Optical Coherence Tomography allowed optical, non-invasive measurement of the 2-D gradient index profile of the isolated human crystalline lens ex vivo. The age-dependent variation of the changes is consistent with previous data using magnetic resonance imaging, and the progressive formation of a refractive index plateau.     

Subwavelength focus of light by a planar microlens

We numerically show that using a planar gradient-index (GRIN) microlens it is possible to focus coherent light of wavelength λ into a narrow line of width 0.026 λ and length 0.182 λ. The efficiency of focusing amounts to 22%. Replacement of the GRIN lens with a photonic-crystal analogue fabricated in silicon is shown practically not to impair the lens performance. In fact, the replacement is shown to result in decreasing side-lobes in the focal spot, while increasing the efficiency up to 30%.     

Effects of Annular Pupils on Confocal Fluorescent Imaging

Abstract

For a confocal fluorescent microscope with annular lenses, the effects of varying the radii of central obstruction of the annular lenses on three, two and one-dimensional imaging have been investigated in terms of the optical transfer function. In particular, we consider the effects of the central obstruction on the signal strength for a system with either a point or finite-sized detector. The signal level as a function of the detector and the central obstruction sizes is presented for volume, planar and point objects, respectively.     

Reduction of Coupling Loss in a One-to-many Collimating System for a Wavelength Division (de)Multiplexer

In a 1 x N wavelength division (de)multiplexer, N receiving (Rx-) gradient-index-rod lenses (GRIN's) are connected to a common transmitting (Tx-) GRIN. All GRIN's are a little longer (DZ(0) for the Tx- and DZ(i) with i = 1, 2, ..., N for the Rx-GRIN's) than the quarter-pitch. To reduce the average coupling loss and the deviations, DZ(0) and DZ(i) are optimized independently (unequally) or equally by computer programming for small N, such as N = 4 and 8. For a larger N (e.g., 16), a relay GRIN is required, which is a little (DZ(r)) longer than the half-pitch. The best position of the relay GRIN is located between the seventh and the eighth Rx-GRIN's. Other parameters including DZ(0), DZ(i), and DZ(r) are all optimized. As a result the (de)multiplexer has lower losses.     

Conversion of Hermite-Gaussian and Laguerre-Gaussian beams in an astigmatic optical system. 1. Experiment

The workings of a mode converter providing energy-effective conversion of an Hermite-Gaussian beam to a Laguerre-Gaussian beam and vice versa are analyzed experimentally. The converter is an astigmatic Fourier transformer consisting of a system of two cylindrical lenses with perpendicular principal planes lying between two spherical lenses. It is shown that this device is less sensitive to the mating of the astigmatic elements. Pis’ma Zh. Tekh. Fiz. 24, 68–73 (September 12, 1998)     

Study of Anisotropy Effect in Planar Lenses for Integrated Optics

Abstract

The extraordinary-ray ray-tracing method for planar waveguides on uniaxial crystals is developed. Using the method and the extended equivalence principle, the effect of anisotropy on the performance of planar lenses is investigated in detail. The agreement between theoretical and experimental results is very good.