Gradient Refractive Index Profile Research Articles

Short focal length tunable liquid crystal lenticular lens array based on fringe field effect

AbstractA liquid crystal (LC) lenticular lens array based on fringe field effect is proposed. The gradient refractive index (GRIN) profile can be generated in the LC layer because of the fringe field between the strip‐shaped electrodes and the bottom electrode. The proposed LC lenticular lens array possesses ideal lens‐like phase profile and shortest focal length (1.199 mm) when the driving voltage is 5.4 V. The focal length can be tuned with millisecond response time by changing the driving voltage of the proposed LC lenticular lens array. The rise time τrise and decay time τdecay of the proposed LC lenticular lens array are 162 and 94 ms, respectively.

Adaptive nematic liquid crystal lens array with resistive layer

ABSTRACTWe propose an adaptive nematic liquid crystal (LC) lens array using a dielectric layer with low dielectric constant as resistive layer. With the resistive layer and periodic-arranged iridium tin oxide (ITO) electrodes, the vertical electric field across the LC layer varies linearly over the lens aperture is obtained in the voltage-on state. As a result, a centrosymmetric gradient refractive index profile within the LC layer is generated, which causes the focusing behaviour. As a result of the optimisation, a thin cell gap which greatly reduces the switching time of the LC lens array can be achieved in our design. The main advantages of the proposed LC lens array are in the comparatively low operating voltage, the flat substrate surface, the simple electrodes, and the uniform LC cell gap. The simulation results show that the focal length of the LC lens array can be tuned continuously from infinity to 3.99 mm by changing the applied voltage.

Two-Dimensional Hybrid Photonic Crystal With Graded Low-Index Using a Nonuniform Voltage

Abstract We proposed a new method for designing graded index lens using liquid crystal infiltration into annular photonic crystals. Applying an external nonuniform voltage in the transverse direction perpendicular to the direction of light propagation yields different orientation of liquid crystal molecules inside the photonic crystal unit cells. As a result, a gradient refractive index was modulated. We numerically investigate focusing properties of the designed graded index structure using plane-wave expansion and finite-difference time-domain methods. The gradient refractive index profile was adjusted by varying the nonuniform voltage excitations, which consequently altered the focal distance of the graded index structure. A wide tuning range of 1856 nm was achieved for focal distance by the proposed graded index structure. This feature can be implemented for planning a flat lens with tunable focal distance based on electro-optic effect. These achievements may have future applications in some optical devices such as near-field imaging and scanning.

Short-focus nematic liquid crystal microlens array with a dielectric layer

ABSTRACTA short-focus microlens array using dielectric layer and inhomogeneous electric field over a homogeneous nematic liquid crystal (LC) layer is proposed. The top substrate has a planar indium tin oxide (ITO) electrode which is coated on the inner surface. The bottom substrate has strip ITO electrodes which are embedded in the dielectric layers. The inhomogeneous electric field generates a required gradient refractive index profile within the LC layer which, in turn, causes the focusing effect. Due to the thinner LC layer (15 μm), the spherical aberration should be negligible. Moreover, the fabrication process of the proposed microlens array can be easily carried out because of the layer-by-layer configuration. The simulation results show that the focal length of the LC microlens can be continuously tuned from infinity to 0.988 mm with the change of applied voltage.

Refractive index redistribution with accommodation based on finite volume-constant age-dependent mechanical modeling

The human lens is considered to have a gradient refractive index (GRIN) distribution. The recently developed accommodating volume-constant age-dependent optical (AVOCADO) model can accurately describe the separate GRIN distributions in the axial and radial directions. Our study uses a finite element method to simulate the accommodation process and calculate the GRIN redistribution based on the AVOCADO model for 25-, 35- and 45-year-old lenses. The parameter p describes the steepness of the GRIN profile towards the lens periphery. The results show that axial p values increase with age. Under accommodation, the axial p value increases, while the radial p value decreases. We also use a ray tracing method to evaluate the optical performance of the lens. The aim of this paper is thus to provide an anatomically finite mechanical lens model with separate axial and radial refractive index profiles for a better understanding of accommodation at different ages.

Conformally Mapped Multifunctional Acoustic Metamaterial Lens for Spectral Sound Guiding and Talbot Effect.

We demonstrate a conformally mapped multifunctional acoustic metamaterial Mikaelian lens. Mikaelian lens is a gradient medium with a hyperbolic secant refractive index profile that can realize functions like beam self-focusing. Unlike the conventional design approaches, with a conformal transformation method, only isotropic material parameters with gradient refractive index profiles are required for the construction of such lens. To realize desired gradient index distribution, we carefully design a new type of cross-channel-shaped acoustic metamaterial, whose refractive index can be effectively modulated by simply changing the slit opening size. The distinct capabilities of the metamaterial Mikaelian lens in manipulating acoustic waves are experimentally verified with the fabricated sample. Simultaneous sound guiding and Talbot effects, which normally require respective geometrical and wave acoustic approximations, are observed in simulations and experiments. Furthermore, those effects of shaping acoustic wave propagations were validated within a relatively wide frequency range. Our study reveals how the conformal transformation method can help to bridge the ray acoustics with wave acoustics. It offers opportunities to the development of novel multifunctional acoustic devices for various applications, such as sound and particle manipulations.

Femtosecond writing of refractive index structures in multimode and multicore optical fibres

The possibility of writing fibre Bragg gratings (FBGs) in optical fibres with a complex spatial structure using femtosecond IR laser pulses is considered. In particular, selective writing of uniform FBGs in individual cores of a seven-core fibre and writing of serial and parallel FBG arrays in the core of a multimode fibre with a gradient refractive index profile are demonstrated.

Polarisation-independent blue-phase liquid crystal microlens array with different dielectric layer

ABSTRACTA fast response (sub-milliseconds) and polarisation-independent blue-phase liquid crystal (BPLC) microlens array with periodical double layer electrodes using different dielectric layers is proposed. The bottom double layer electrodes are coated with transparent and different dielectric layers to generate linearly varying electric potential from the centre to the edge, while the top planar electrode iridium tin oxide (ITO) electrode has a constant potential. As a result, gradient vertical electric fields are generated, and a gradient refractive index profile is obtained. When the applied voltage is changed, the focal length of the BPLC microlens array can be tuned from ∞ to 12.05 mm while keep a low operating voltage (~35Vrms). Besides, the driving mode (simplification driving) and fabrication process (using printing method or mold-pressing method) of the BPLC microlens array is very simple. The simulation results show that the BPLC microlens array is insensitive to the polarisation of incident light while keeping parabolic-like phase profile.

Electrochemical Fabrication of Flat, Polymer‐Embedded Porous Silicon 1D Gradient Refractive Index Microlens Arrays

Gradient refractive index (GRIN) optics has attracted considerable interest due to the ability to decouple optical performance from optical element shape. However, despite the utility of GRIN optical components, it remains challenging to fabricate arbitrary GRIN profiles and the available refractive index contrast remains small, particularly at the microscale. Here, using mathematical transformations that the authors developed, the electrochemical waveform required to electrochemically etch arrays of bulk Si microstructures into 1D porous Si (PSi) GRIN microlens arrays (MLAs) is determined. This waveform is then used to form high refractive index contrast MLAs containing precisely‐defined, arbitrary refractive index profiles. The MLAs are then embedded in a transparent optical polymer, mechanically detached from the host Si substrate, and planarized via simple polishing. Cylindrical microlenses and 1D axicons are demonstrated and characterized, and the optical behavior is found to be in agreement with theory. These MLAs could find applications in displays, photodetectors, and optical microscopy.

Broadband manipulation of refracted wavefronts by gradient acoustic metasurface with V-shape structure

We present a space folding acoustic metasurface with a V-shaped structure, which exhibits ultra-broadband and high efficiency transmission compared to previously investigated space folding metasurfaces. The proposal employs a gradient refractive index profile to redirect the refracted wave arbitrarily and an existence of air channels with direct sound propagation to improve impedance matching between the metasurface and the background medium. As expected from frequency-independent generalized Snell's law, the demonstrated acoustic metasurface can steer refracted wavefronts at will, including anomalous refraction, non-diffracting Bessel beam, sub-wavelength flat lens, and conversion of the propagating wave into the surface wave. The designed V-shape metasurface overcomes the limitation of narrowband, which may offer potential applications in medical ultrasound imaging and broadband acoustical devices.

Fully automated laser ray tracing system to measure changes in the crystalline lens GRIN profile.

Measuring the lens gradient refractive index (GRIN) accurately and reliably has proven an extremely challenging technical problem. A fully automated laser ray tracing (LRT) system was built to address this issue. The LRT system captures images of multiple laser projections before and after traversing through an ex vivo lens. These LRT images, combined with accurate measurements of the lens geometry, are used to calculate the lens GRIN profile. Mathematically, this is an ill-conditioned problem; hence, it is essential to apply biologically relevant constraints to produce a feasible solution. The lens GRIN measurements were compared with previously published data. Our GRIN retrieval algorithm produces fast and accurate measurements of the lens GRIN profile. Experiments to study the optics of physiologically perturbed lenses are the future direction of this research.

Evidence of spatially selective refractive index modification in 15GeSe_2-45As_2Se_3-40PbSe glass ceramic through correlation of structure and optical property measurements for GRIN applications

Thermally-induced nucleation and growth of secondary crystalline phases in a parent glass matrix results in the formation of a glass ceramic. Localized, spatial control of the number density and size of the crystal phases formed can yield ‘effective’ properties defined approximately by the local volume fraction of each phase present. With spatial control of crystal phase formation, the resulting optical nanocomposite exhibits gradients in physical properties including gradient refractive index (GRIN) profiles. Micro-structural changes quantified via Raman spectroscopy and X-ray diffraction have been correlated to calculated and measured refractive index modification verifying formation of an effective refractive index, neff, with the formation of nanocrystal phases created through thermal heat treatment in a multi-component chalcogenide glass. These findings have been used to define experimental laser irradiation conditions required to induce the conversion from glass to glass ceramic, verified using simulations to model the thermal profiles needed to substantiate the gradient in nanocrystal formation. Pre-nucleated glass underwent spatially varying nanocrystal growth using bandgap laser heating, where the laser beam’s thermal profile yielded a gradient in both resulting crystal phase formation and refractive index. The changes in the nanocomposite’s micro-Raman signature have been quantified and correlated to crystal phases formed, the material’s index change and the resulting GRIN profile. A flat, three-dimensional (3D) GRIN nanocomposite focusing element created through use of this approach, is demonstrated.

Porous Silicon Gradient Refractive Index Micro-Optics.

The emergence and growth of transformation optics over the past decade has revitalized interest in how a gradient refractive index (GRIN) can be used to control light propagation. Two-dimensional demonstrations with lithographically defined silicon (Si) have displayed the power of GRIN optics and also represent a promising opportunity for integrating compact optical elements within Si photonic integrated circuits. Here, we demonstrate the fabrication of three-dimensional Si-based GRIN micro-optics through the shape-defined formation of porous Si (PSi). Conventional microfabrication creates Si square microcolumns (SMCs) that can be electrochemically etched into PSi elements with nanoscale porosity along the shape-defined etching pathway, which imparts the geometry with structural birefringence. Free-space characterization of the transmitted intensity distribution through a homogeneously etched PSi SMC exhibits polarization splitting behavior resembling that of dielectric metasurfaces that require considerably more laborious fabrication. Coupled birefringence/GRIN effects are studied by way of PSi SMCs etched with a linear (increasing from edge to center) GRIN profile. The transmitted intensity distribution shows polarization-selective focusing behavior with one polarization focused to a diffraction-limited spot and the orthogonal polarization focused into two laterally displaced foci. Optical thickness-based analysis readily predicts the experimentally observed phenomena, which strongly match finite-element electromagnetic simulations.

Interfacial structure designs with impedance-matching for ideal broadband antireflections

This work focuses on the ideal broadband antireflection structure designs based on the impedance-matching and the effective medium theory. Graded refractive index profiles that satisfy the impedance-matching condition between two media result in zero reflection over the entire wavelength range. Our studies found that both the thickness of the graded refractive index layer and the refractive indices of the adjacent two media determine the dispersion properties of the graded refractive index profiles. Specifically, we case-studied the dispersion properties of the gradient refractive index profiles for silicon, GaN, and glass substrates. The effective medium theory was utilized to design interface structures that match the ideal graded refractive index profiles. The accuracy of this design approach was assessed by comparing the filling factor as a function of thickness by using effective medium theory with zeroth-order and second-order approximations. A novel interface structure with concaved-dome geometrical shape was studied as a new type of impedance-matching antireflection structure (concaved-dome impedance-matching II), which has the advantage of reduced effective feature size and thus can better match the ideal graded refractive index profiles by applying the effective medium theory more accurately. The interface reflection properties of the impedance-matching II structure were computed via a three-dimensional finite difference time domain method. The interface reflections were compared with that of a conventional flat surface, a previously proposed micro-dome structure, and a traditional impedance-matching structure (impedance-matching I), which revealed that the concaved-dome impedance-matching II structure has the best antireflection performance over a broad wavelength range and wide incidence angles.

Tunable Optical Beam Deflection Via Liquid Crystal Gradient Refractive Index Generated By Highly Resistive Polymer Film

An effective tunable optical beam deflection device based on a periodic gradient refractive index (GRIN) profile is reported, which is capable of achieving a 5 $^{\circ}$ beam deflection with an angle resolution of 0.5 $^{\circ}$ . The operation voltage is around 6 $\text{V}_{\mathrm{pp}}$ , and the maximum operation frequency is 2 kHz. The GRIN beam deflection device is induced by periodically varying liquid crystal orientations. A highly resistive and patterned polymer film with a resistivity of 11 $\text{G}\Omega/\text{sq}$ is deposited to achieve a linear potential distribution between the two addressing electrodes in every unit cell. The resulting electric field pattern across the device is sawtooth-like. Both the device fabrication and the driving interconnection circuit are very simple. The advanced materials and the techniques used in this device are also applicable to other tunable optical and photonic components (such as adaptive lenses and light intensity modulators) by adapting the electrode design and the voltage signals.

Characterization of the Effects of Hyperbaric Oxygen on the Biochemical and Optical Properties of the Bovine Lens.

To assess the morphologic, biochemical, and optical properties of bovine lenses treated with hyperbaric oxygen. Lenses were exposed to hyperbaric nitrogen (HBN) or hyperbaric oxygen (HBO) for 5 or 15 hours, lens transparency was assessed using bright field microscopy and lens morphology was visualized using confocal microscopy. Lenses were dissected into the outer cortex, inner cortex, and core, and glutathione (GSH) and malondialdehyde (MDA) measured. Gel electrophoresis and Western blotting were used to detect high molecular weight aggregates (HMW) and glutathione mixed protein disulfides (PSSG). T2-weighted MRI was used to measure lens geometry and map the water/protein ratio to allow gradient refractive index (GRIN) profiles to be calculated. Optical modeling software calculated the change in lens optical power, and an anatomically correct model of the light pathway of the bovine eye was used to determine the effects of HBN and HBO on focal length and overall image quality. Lenses were transparent and lens morphology similar between HBN- and HBO-treated lenses. At 5- and 15-hour HBO exposure, GSH and GSSG were depleted and MDA increased in the core. Glutathione mixed protein disulfides were detected in the outer and inner cortex only with no appearance of HMW. Optical changes were detectable only with 15-hour HBO treatment with a decrease in the refractive index of the core, slightly reduced lens thickness, and an increase in optimal focal length, consistent with a hyperopic shift. This system may serve as a model to study changes that occur with advanced aging rather than nuclear cataract formation per se.

Alteration in refractive index profile during accommodation based on mechanical modelling.

The lens of the eye has a gradient refractive index (GRIN). Ocular accommodation, which alters the shape of the lens in response to visual demand, causes a redistribution of the internal structure of the lens leading to a change in the GRIN profile. The nature of this redistribution and the consequence of change in the GRIN profile are not understood. A modelling approach that considers how the GRIN profile may change with accommodation needs to take into account optical and mechanical parameters and be cognisant of individual variability in the shape and size of lenses. This study models the normalised axial GRIN profile during accommodation using reduced modelling and incorporating finite element analysis to connect inhomogenous mechanical characteristics of the lens to optical performance. The results show that simulated stretching changes the length of the plateau but does not alter the cortical gradient, which supports clinical findings. There is a very small change to the accommodated and non-accommodated profiles when normalised, yet this yields measurable changes in aberrations with around 11% and almost 13% difference in spherical aberration and astigmatism respectively. The results can be used in reconstruction of the refractive index and for investigating gradual changes with age.

Liquid Gradient Refractive Index Microlens for Dynamically Adjusting the Beam Focusing

An in-plane liquid gradient index (L-GRIN) microlens is designed for dynamically adjusting the beam focusing. The ethylene glycol solution (core liquid) withde-ionized (DI) water (cladding liquid) is co-injected into the lens chamber to form a gradient refractive index profile. The influences of the diffusion coefficient, mass fraction of ethylene glycol and flow rate of liquids on the refractive index profile of L-GRIN microlens are analyzed, and the finite element method and ray tracing method are used to simulate the convection-diffusion process and beam focusing process, which is helpful for the prediction of focusing effects and manipulation of the device. It is found that not only the focal length but the focal spot of the output beam can be adjusted by the diffusion coefficient, mass fraction and flow rate of liquids. The focal length of the microlens varies from 942 to 11 μm when the mass fraction of the ethylene glycol solution varies from 0.05 to 0.4, and the focal length changes from 127.1 to 8 μm by varying the flow rate of the core liquid from 0.5 × 103 to 5 × 103 pL/s when there is no slip between the core and cladding inlet. The multiple adjustable microlens with a simple planar microfluidic structure can be used in integrated optics and lab-on-chip systems.

Modified Luneburg Lens Based on Metamaterials

We present the design, fabrication, and experimental characterization of a modified two-dimensional Luneburg lens based on bulk metamaterials. The lens is composed by a number of concentric layers. By varying the geometric dimensions of unit cells in each layer, the gradient refractive index profile required for the modified Luneburg lens can be achieved. The cylindrical waves generated from a point source at the focus point of the lens could be transformed into plane waves as desired in the microwave frequency. The proposed modified Luneburg lens can realize wide-angle beam scanning when the source moves along the circumferential direction inside the lens. Numerical and experimental results validate the performance of the modified Luneberg lens.

Porous silicon Bloch surface and sub-surface wave structure for simultaneous detection of small and large molecules.

A porous silicon (PSi) Bloch surface wave (BSW) and Bloch sub-surface wave (BSSW) composite biosensor is designed and used for the size-selective detection of both small and large molecules. The BSW/BSSW structure consists of a periodic stack of high and low refractive index PSi layers and a reduced optical thickness surface layer that gives rise to a BSW with an evanescent tail that extends above the surface to enable the detection of large surface-bound molecules. Small molecules were detected in the sensor by the BSSW, which is a large electric field intensity spatially localized to a desired region of the Bragg mirror and is generated by the implementation of a step or gradient refractive index profile within the Bragg mirror. The step and gradient BSW/BSSW sensors are designed to maximize both resonance reflectance intensity and sensitivity to large molecules. Size-selective detection of large molecules including latex nanospheres and the M13KO7 bacteriophage as well as small chemical linker molecules is reported.