Gradient Refractive Index Distribution Research Articles

Finite element method for radiative transfer in multi-dimensional graded index media based on second-order form formulation

Gradient distribution of refractive index appears commonly in gas of non-uniform temperature/pressure and water of non-uniform salinity. Efficient and accurate solution of radiative transfer in graded index media is essential for related applications. Finite element method (FEM) is a very effective tool to solve various problems governed with partial differential equations. However, FEM may suffer stability problem for solving radiative transfer in semitransparent media due to the convection-dominated property of the transfer equation. The existence of two angular derivative terms complicates the solution of radiative transfer in graded index media as compared to uniform index media. In this paper, a new stabilized FEM is proposed to solve radiative transfer in multi-dimensional graded index media, based on the second-order form transformation approach. Using the approach, a second order diffusion term is naturally introduced in the transfer equation, which ensures numerical stability, and avoids the false smearing effects as compared to the common schemes based on artificial diffusion. The performance of the presented FEM is verified with one- and two-dimensional test cases. It is demonstrated that the new FEM owns good numerical stability and accuracy, and could potentially be an effective tool to solve radiative transfer in graded index media.

A Review of 3D Printed Gradient Refractive Index Lens Antennas

Gradient index lens antennas find their application in modern wireless communication including radar systems, satellite communication, etc. They can ensure highly directional beamforming, support multibeam operations and beam steering capabilities within a wide angle of view. The development of 3D printing technologies enables the implementation of complex gradient refractive index distribution with high accuracy as well as obtaining a significant reduction in the production time and cost. This paper presents the state of the art in gradient refractive index lens antenna design using different types of additive manufacturing processes. It shows the applicability of 3D printing to a wide range of operational frequency bands from microwave to sub-THz and THz.

Broadband differential interference in a waveguide with a gradient refractive index distribution

The paper presents a model of a planar broadband differential waveguide interferometer with a gradient refractive index distribution. Its response to the change in the refractive index of the waveguide cover layer is presented. The analysis was performed for the wavelength range from 0.5um to 0.7um. The orthogonal TE0 and TM0 modes propagating in this wavelength range are considered. The influence of the coverage refractive index change on the output characteristics of the system is shown. Full Text: PDF ReferencesP. Kozma, F. Kehl, E.Ehrentreich-Forster, C. Stamm and F.F. Bier, "Integrated planar optical waveguide interferometer biosensors: A comparative review", Biosens. Bioelectron. 58, 287 (2014), CrossRef M. Kitsara, K. Misiakos, I. Raptis, and E. Makarona, "Integrated optical frequency-resolved Mach-Zehnder interferometers for label-free affinity sensing", Opt. Express 18, 8193 (2010). CrossRef K. Misiakos, I. Raptis, A. Salapatas, E. Makarona, A. Bostials, et al., "Broad-band Mach-Zehnder interferometers as high performance refractive index sensors: Theory and monolithic implementation", Opt. Express 22, 8856 (2014). CrossRef K. Misiakos, I. Raptis, E. Makarona, A. Botsialas, A. Salapatas, et al, "All-silicon monolithic Mach-Zehnder interferometer as a refractive index and bio-chemical sensor", Opt. Express 22, 26803 (2014) CrossRef K. Misiakos, E. Makarona, M. Hoekman, R. Fyrogenis, K. Tukkiniemi, et al., "All-Silicon Spectrally Resolved Interferometric Circuit for Multiplexed Diagnostics: A Monolithic Lab-on-a-Chip Integrating All Active and Passive Components", ACS Photonics 6, 1694 (2019). CrossRef E. Makarona, A. Salapatas, I. Raptis, P. Petrou, S. Kakabakos, et al., "Broadband Young interferometry for simultaneous dual polarization bioanalytics", J Opt Soc Am B 34, 1691 (2017). CrossRef K. Gut, "Broad-band difference interferometer as a refractive index sensor", Opt. Express 25, 3111 (2017), CrossRef K. Gut, "Study of a Broadband Difference Interferometer Based on Low-Cost Polymer Slab Waveguides", Nanomaterials 9, 729 (2019), CrossRef T. Pustelny, J. Ignac-Nowacka and Z. Opilski, "Optical investigations on layered metalphthalocyanine nanostructures affected by NO2 applying the surface plasmon resonance method", Opt. Appl. 34, 563 (2004). CrossRef W. Lukosz, Sensor Actuat. B-Chem. "Integrated optical chemical and direct biochemical sensors", 29, 37 (1995). CrossRef Z. Qi, S. Xia and N. Matsuda, "Spectropolarimetric interferometer based on single-mode glass waveguides", Opt. Express, 16, 2245 (2008). CrossRef K. Gut, A. Zakrzewski, T. Pustelny, "Sensitivity of Polarimetric Waveguide Interferometer for Different Wavelengths", Acta Phys. Pol. 118, 1140 (2010). CrossRef J.E. Broquin, S. Honkanen, "Integrated Photonics on Glass: A Review of the Ion-Exchange Technology Achievements", Appl.Sci. 11, 4472 (2021). CrossRef G.C. Righini, J. Linares, "Active and Quantum Integrated Photonic Elements by Ion Exchange in Glass", Appl.Sci. 11, 5222 (2021). CrossRef

Orthogonal separation of arbitrary vector beams from non-polarized light waves based on a patterned liquid-crystal photo-alignment.

An effective method for orthogonally separating arbitrary vector polarized beams from non-polarized incident light waves is proposed in this Letter. A tunable patterned spatial distribution of liquid-crystal (LC) molecules can be effectively constructed based on both the initial photo-alignment and the electrically controlled birefringence of nematic LC materials. The LC photo-alignment over a smooth surface without any common nano-grooves leads to a highly efficient light-wave transformation by inducing a desired initial arrangement of LC directors and then acquiring extraordinary light waves with the needed, or even arbitrary, spatial polarization. The vector polarized beams can be highly converged according to a microhole-patterned electrode and a gradient refractive index distribution of the LC layer, which is driven and adjusted by an applied signal voltage. Due to the intrinsic polarization sensitivity of nematic LC materials, the formed gradient refractive index appearance only corresponds to extraordinary light waves. The proposed approach provides a way to achieve the orthogonal separation of arbitrary vector beams from non-polarized light waves. Moreover, it can be further utilized to generate and obtain arbitrary vector beams, as well as to perform adaptive light-beam convergence or even the focusing of arbitrary vector beams, which is expected to advance the development of vector beam generation and manipulation, thereby stimulating potential applications.

Low-Profile Dual-Polarized Luneburg Lens Based on TE/TM Surface Wave Modes

This letter presents a novel dual-polarized two-dimensional (2-D) Luneburg lens operated at millimeter-wave band with a low-profile and planar structure. Based on a dual-mode unit cell that supports TE/TM surface wave modes with orthogonal polarizations, the proposed 2-D Luneburg lens with gradient refractive index distribution compresses the beamwidth in one dimension and achieves fan-shaped beams for both of the two polarization modes. To verify the proposed Luneburg lens, a prototype is fabricated using the printed circuit broad process with low cost, weight, and profile. The measured peak gain of H- and V-pol mode is 17.0 dBi and 17.2 dBi, respectively. Because the surface wave modes are applied to both polarizations of the proposed Luneburg lens, the electromagnetic waves transform from the lens to the air smoothly, without the need for additional radiation structures, which reduces the profile further and increases the antenna aperture.

Spatial separation of azimuthally and radially polarized beams from non-polarized light waves based on the electrically controlled birefringence effect.

Based on the electrically controlled birefringence effect in liquid crystal materials, an effective method for spatially separating azimuthally and radially polarized beams from non-polarized incident light waves is proposed. The radially polarized beam was highly converged by using a microhole-patterned electrode and a planar photo-alignment layer to shape the initial liquid-crystal radial alignment and a gradient refractive index distribution with central axial symmetry after applying a voltage signal. Due to the intrinsic polarization sensitivity of nematic liquid-crystal materials, the shaped gradient refractive index only applies to extraordinary light waves, which then converge into a spot. Thus, the azimuthally and radially polarized beams are effectively separated. The proposed method demonstrates some advantages, such as low cost, miniaturization, and easy fabrication and integration with other functional devices. Thanks to the wideband electrically controlled birefringence of liquid-crystal materials, this light-wave manipulation to spatially separate azimuthally and radially polarized beams can also be performed over a wide wavelength range.

Numerical Investigation of a Designed-Inlet Optofluidic Beam Splitter for Split-Angle and Transmission Improvement.

The beam splitter is one of the important elements in optical waveguide circuits. To improve the performance of an optofluidic beam splitter, a microchannel including a two-stage main channel with divergent side walls and two pairs of inlet channels is proposed. Besides, the height of the inlets injected with cladding fluid is set to be less than the height of other parts of the microchannel. When we inject calcium chloride solution (cladding fluid) and deionized water (core fluid) into the inlet channels, the gradient refractive index (GRIN) developed in fluids flowing through the microchannel splits the incident light beam into two beams with a larger split angle. Moreover, the designed inlets yield a GRIN distribution which increases the light collected around the middle horizontal line on the objective plane, and so enhances the transmission efficiency of the device. To demonstrate the performance of the proposed beam splitter, we use polydimethylsiloxane to fabricate the microchannel. The results obtained by simulation and experiment are compared to show the effectiveness of the device and the validity of numerical simulation. The influence of the microchannel geometry and the flow rate ratio on the performance of the proposed beam splitter is investigated.

A graded Miura-ori phononic crystals lens

As an art of paper folding, origami has inspired designs of diverse tailorable mechanical structures within physics and engineering communities. In this letter, by introducing a unilateral gradient on the Miura-ori crease pattern, we realize a gradient-index (GRIN) origami phononic crystal (PC) lens. The width distribution of a pair of adjacent panels is designed to allow the graded Miura-ori PC lens to have a refractive index variation highest at the center axis and a hyperbolic secant gradient distribution along a direction transverse to the direction of the Lamb wave propagation. The folding angle-dependent gradient refractive index distribution gradually bends and focuses the incident waves at different frequencies toward the center axis. Both numerical modeling and experimental verification are conducted to validate the focusing of the plane wave on the graded Miura-ori PC lens.

Electrically Tunable-Focusing Liquid Crystal Microlens Array with Simple Electrode

An electrically tunable-focusing liquid crystal (LC) microlens array exhibiting a wide-range tunable focal length is proposed. The lower substrate has strip indium tin oxide (ITO) electrodes, the upper substrate has periodic ITO electrodes with a certain gap coated on the inner surface., and an LC microlens is generated between the two strip electrodes. For each LC microlens, the gap between the top planar electrodes is directly above the center of the microlens. Unlike the conventional LC lens, the individual LC microlens is not coated with ITO electrodes on the central part of its upper and lower substrates, which helps to maintain the LC’s horizontal orientation. In the voltage-off state, the focal length of the microlens array is infinity because of the homogeneous LC alignment. At a given operating voltage, an ideal gradient refractive index distribution is induced over the homogeneous LC layer, which leads to the focusing effect. The simulation result shows that the focal length of the LC microlens could be gradually drawn to 0.381 mm with a change of voltage.

Double-layer liquid crystal lens array with composited dielectric layer

ABSTRACT A double-layer liquid crystal (LC) lens array with composited dielectric layer is proposed. In our design, a spatially non-uniform electric field is generated between the strip electrodes, resulting in a gradient refractive index distribution in the LC layer. Since the upper and lower parts of the LC lens array both adopt a composite dielectric layer, the operation voltage of the LC lens array is effectively reduced. In terms of LC lenslet, the double-layer design doubles the phase difference between the centre and the periphery of the LC layer, thereby reducing the focal length of the LC lens array. In addition, the shortest focal length (~1.78 mm) of the LC lens array is obtained at V = 3.3 V, and the LC lens array has a large focusing range.

Design of a gradient-index lens with a compound parabolic concentrator shape as a visible light communication receiving antenna.

We propose a design for a gradient lens that can extend the field of view and receive higher optical power for indoor visible light communication systems. The proposed structure is an axially symmetric lens with a refractive index gradient distribution in the axial direction and a slight gradient in the radial direction, and with a spherical top surface and side surface in a compound parabolic concentrator (CPC) shape. The radius of the outlet of the CPC is 3mm, and the inlet radius is 6.8mm with a 9.04mm radius of curvature. The height of the receiving system is 15.2mm, resulting in the small volume of the structure. Simulation results show that the half field of view (FOV) of the lens can reach 36.2°, while the gain is higher than that of a bare CPC. The designed receiving system has an average receiving gain ∼1.72 times larger than a bare CPC-based system, and is suitable for indoor visible light communication.

Bioinspired adaptive gradient refractive index distribution lens

Inspired by the soft, deformable human eye lens, a synthetic polymer gradient refractive index distribution (GRIN) lens with an adaptive geometry and focal power has been demonstrated via multilayer coextrusion and thermoforming of nanolayered elastomeric polymer films. A set of 30 polymer nanolayered films comprised of two thermoplastic polyurethanes having a refractive index difference of 0.05 were coextruded via forced-assembly technique. The set of 30 nanolayered polymer films exhibited transmission near 90% with each film varying in refractive index by 0.0017. An adaptive GRIN lens was fabricated from a laminated stack of the variable refractive index films with a 0.05 spherical GRIN. This lens was subsequently deformed by mechanical ring compression of the lens. Variation in the optical properties of the deformable GRIN lens was determined, including 20% variation in focal length and reduced spherical aberration. These properties were measured and compared to simulated results by placido-cone topography and ANSYS methods. The demonstration of a solid-state, dynamic focal length, GRIN lens with improved aberration correction was discussed relative to the potential future use in implantable devices.

Effect on optical properties and electrical performances of antireflective coating with gradient refractive index based on p-type amorphous SiOx thin films

The electrical performances and optical properties of p-type amorphous silicon oxide (p-SiOx) thin films with gradient refractive index are studied. The composite thin films as antireflective coatings (ARCs) are widely used in solar cells and microelectronic devices. The double-layer p-SiOx thin films are deposited by plasma-enhanced chemical vapor deposition (PECVD) system. To obtain better optical properties, the refractive index of ARCs can be adjusted by SiH4 to N2O ratio. And the electrical performances of composite thin films can be improved by adjustment of B2H6 to SiH4 ratio. The computational model is built to predict the optimized range of reflection spectra corresponding to structure of p-SiOx ARCs with gradient refractive index by finite difference time domain (FDTD) method. It shows the difference of reflection spectra with gradient refractive index distribution. The optimized reflection spectra simulated by FDTD method confirms to agree well with that measured by UV–visible spectroscopy.

Polymer Network Liquid Crystal (PNLC) Lenticular Microlens Array With No Surface Treatment

A polymer network liquid crystal (PNLC) lenticular microlens array with no surface treatment is prepared. Before polymerization, the LC and diacrylate monomers are reoriented with gradient refractive index distribution by a fringing field. After polymerization, the oriented LC is stabilized by the polymer network. The prepared PNLC lenticular microlens array is optically anisotropic. Without surface treatment, the device fabrication is simplified, and it can present almost the same optical performance as the PNLC lenticular microlens with surface treatment. Integrating with a 90 $^\circ $ twisted-nematic LC cell, the PNLC lenticular microlens array can be switched between a focusing state and non-focusing state. Such a PNLC lenticular microlens array has potential application in switchable 2D/3D displays.

Characterization and simulation on antireflective coating of amorphous silicon oxide thin films with gradient refractive index

The optical reflective properties of silicon oxide (SixOy) thin films with gradient refractive index are studied both theoretically and experimentally. The thin films are widely used in photovoltaic as antireflective coatings (ARCs). An effective finite difference time domain (FDTD) model is built to find the optimized reflection spectra corresponding to structure of SixOy ARCs with gradient refractive index. Based on the simulation analysis, it shows the variation of reflection spectra with gradient refractive index distribution. The gradient refractive index of SixOy ARCs can be obtained in adjustment of SiH4 to N2O ratio by plasma-enhanced chemical vapor deposition (PECVD) system. The optimized reflection spectra measured by UV–visible spectroscopy confirms to agree well with that simulated by FDTD method.

Transmission properties of defect modes in one-dimensional photonic crystals containing gradient refractive index defects

The gradient refractive index (GRIN) defect layer is introduced into one-dimensional photonic crystal (1D PC) to develop the optical filters needed. The transmission properties of 1D PC with GRIN defect layer were investigated based on the finite difference time domain (FDTD) method. Defect mode was obtained according to the GRIN distribution functions. With a GRIN structure in the defect layer, simulation results show that the position and width of the photonic band gap can be effectively modulated by varying the thickness and GRIN distribution functions of defect layer and the parameters of symmetrical layers. The new study provides a certain reference for photonic band gap engineering and designing the photonic-based devices.

Study of optical design of Blu-ray pickup head system with a liquid crystal element.

This paper proposes a newly developed optical design and an active compensation method for a Blu-ray pickup head system with a liquid crystal (LC) element. Different from traditional pickup lens design, this new optical design delivers performance as good as the conventional one but has more room for tolerance control, which plays a role in antishaking devices, such as portable Blu-ray players. A hole-pattern electrode and LC optics with external voltage input were employed to generate a symmetric nonuniform electrical field in the LC layer that directs LC molecules into the appropriate gradient refractive index distribution, resulting in the convergence or divergence of specific light beams. LC optics deliver fast and, most importantly, active compensation through optical design when errors occur. Simulations and tolerance analysis were conducted using Code V software, including various tolerance analyses, such as defocus, tilt, and decenter, and their related compensations. Two distinct Blu-ray pickup head system designs were examined in this study. In traditional Blu-ray pickup head system designs, the aperture stop is always set on objective lenses. In the study, the aperture stop is on the LC lens as a newly developed lens. The results revealed that an optical design with aperture stop set on the LC lens as an active compensation device successfully eliminated up to 57% of coma aberration compared with traditional optical designs so that this pickup head lens design will have more space for tolerance control.

Optically anisotropic microlens array film directly formed on a single substrate

An optically anisotropic microlens array film directly formed on a single substrate is demonstrated. UV curable diacrylate monomers are coated as a film on the substrate. Under the action of fringing field, not only the film surface is flattened by the generated dielectric force but also the monomers are reoriented to form a gradient refractive index (GRIN) distribution in the film. Via UV exposure, the GRIN distribution is fixed and the polymeric film behaves as a microlens array. The fabrication process is simple and the film offers a switchable focus through controlling the polarization direction of the incident light. Integrating with a 90° twisted-nematic liquid crystal cell, our polymeric microlens array film shows great potential for switchable 2D/3D autostereoscopic displays.

Liquid Crystal Microlens Array Using Double Lenticular Electrodes

A liquid crystal (LC) microlens array using double lenticular electrodes is proposed. Two identical substrates with a lenticular electrode on each surface are prepared. The two lenticular electrodes are placed in parallel position with a gap. When a voltage is applied across the electrodes, a periodically inhomogeneous electric field can be generated. Such an electric field can cause a homogeneous LC with a gradient refractive index distribution. Our experiment results show that the lens cell can present good focusing property. The shortest focal length (~ 1.1 mm) of the lens cell can be obtained at a low operating voltage (18 Vrms).

Influence of shape and gradient refractive index in the accommodative changes of spherical aberration in nonhuman primate crystalline lenses.

To estimate changes in surface shape and gradient refractive index (GRIN) profile in primate lenses as a function of accommodation. To quantify the contribution of surface shape and GRIN to spherical aberration changes with accommodation. Crystalline lenses from 15 cynomolgus monkeys were studied in vitro under different levels of accommodation produced by a stretching system. Lens shape was obtained from optical coherence tomography (OCT) cross-sectional images. The GRIN was reconstructed with a search algorithm using the optical path measured from OCT images and the measured back focal length. The spherical aberration of the lens was estimated as a function of accommodation using the reconstructed GRIN and a homogeneous refractive index. The lens anterior and posterior radii of curvature decreased with increasing lens power. Both surfaces exhibited negative asphericities in the unaccommodated state. The anterior surface conic constant shifted toward less negative values with accommodation, while the value of the posterior remained constant. GRIN parameters remained constant with accommodation. The lens spherical aberration with GRIN distribution was negative and higher in magnitude than that with a homogeneous equivalent refractive index (by 29% and 53% in the unaccommodated and fully accommodated states, respectively). Spherical aberration with the equivalent refractive index shifted with accommodation toward negative values (-0.070 μm/diopter [D]), but the reconstructed GRIN shifted it farther (-0.124 μm/D). When compared with the lens with the homogeneous equivalent refractive index, the reconstructed GRIN lens has more negative spherical aberration and a larger shift toward more negative values with accommodation.