Gradient Refractive Index Profile Research Articles

Terahertz refractive index control of 3D printing materials by UV exposure

Recently, significant progress has been made in the development of THz optics based on metamaterials to overcome the limited availability of suitable materials for conventional optics. Although 3D printing technology is a promising method for rapidly fabricating these subwavelength structures, the structural degree of freedom for 3D printed metamaterials is still limited by the optical properties of printing materials. In this study, we controlled the THz refractive index and extinction coefficient of the 3D printing resin by UV exposure doses during the printing process. Samples were fabricated as uniform plates under different curing conditions in printing, and their optical properties were measured in the range between 0.3 THz and 2.0 THz using THz time-domain spectroscopy (THz-TDS). The refractive index and extinction coefficient were changed from 1.65 to 1.80, and from 0.04 to 0.12, respectively, with increasing UV doses from 1 mJ/cm2, which allows resin to solidify and become printable, to 100 mJ/cm2, where the optical changes become almost saturated. The results provide insights into optimizing the fabrication process of THz devices, even those with a gradient and complex refractive index profile, by utilizing 3D printing technology for a broad range of applications.

Study of Dependence of the Energy of the Field in Weakly Conductive Fiberlight-Guide with Gradient Refractive Index Profile Without Regard to Polarization

A round-in-cross-section weakly guiding fiber optic light guide is considered. The system of Maxwellian equations for electrically conductive transparent media without due regard to polarization with an index of refraction in the case under consideration is reduced to the homogeneous Helmholtz equation, a particular solution of which is found using the Green's function. For a unimodalmode a common decision was obtained for the field and energy inside the fiber in the general case of a gradient refractive index profile depending on the radial coordinate. The concept of normalized energy is introduced as the ratio of the energy inside a fiber with gradient refractive index profile to the energy inside a fiber with a step-index profile. Since in a single-mode regime the zero-order Bessel function, which describes the field inside a step-index profile fiber, can be replaced by a Gaussoid, then, when extending this replacement to the case of a single-mode gradient fiber, as a first approximation we shall obtain a finite expression for the normalized energy for a general gradient profile. The dependences of the normalized energy on the waveguide number were obtained for each of the degrees from the first to the fourth inclusive. It is shown that in the considered approximation, the energy increases up to a certain parameter values (for the first degree – a triangle profile) or slowly decreases (other profiles), after this value the energy increases for all profiles. The results obtained will help to select a suitable single-mode fiber for practical application.

Optical coherence tomography quantifies gradient refractive index and mechanical stiffness gradient across the human lens

BackgroundAs a key element of ocular accommodation, the inherent mechanical stiffness gradient and the gradient refractive index (GRIN) of the crystalline lens determine its deformability and optical functionality. Quantifying the GRIN profile and deformation characteristics in the lens has the potential to improve the diagnosis and follow-up of lenticular disorders and guide refractive interventions in the future.MethodsHere, we present a type of optical coherence elastography able to examine the mechanical characteristics of the human crystalline lens and the GRIN distribution in vivo. The concept is demonstrated in a case series of 12 persons through lens displacement and strain measurements in an age-mixed group of human subjects in response to an external (ambient pressure modulation) and an intrinsic (micro-fluctuations of accommodation) mechanical deformation stimulus.ResultsHere we show an excellent agreement between the high-resolution strain map retrieved during steady-state micro-fluctuations and earlier reports on lens stiffness in the cortex and nucleus suggesting a 2.0 to 2.3 times stiffer cortex than the nucleus in young lenses and a 1.0 to 7.0 times stiffer nucleus than the cortex in the old lenses.ConclusionsOptical coherence tomography is suitable to quantify the internal stiffness and refractive index distribution of the crystalline lens in vivo and thus might contribute to reveal its inner working mechanism. Our methodology provides new routes for ophthalmic pre-surgical examinations and basic research.

Low loss fiber-coupled volumetric interconnects fabricated via direct laser writing

Photonic integrated circuits (PICs) are vital for high-speed data transmission. However, optical routing is limited in PICs composed of only one or a few stacked planes. Further, coupling losses must be low in deployed systems. Previously, we developed the subsurface controllable refractive index via beam exposure (SCRIBE) technique to write accurate 3D gradient refractive index (GRIN) profiles within a mesoporous silica scaffold. Here, we apply SCRIBE to fabricate low loss, broadband, polarization insensitive, fiber-coupled, single-mode volumetric interconnects that include waveguides traversing arbitrary 3D paths. By seamlessly integrating mode-matching subsurface lenses and GRIN waveguide tapers, calibrating for positional writing errors, implementing multipass exposure, automating alignment, and switching to antireflection coated fibers, we reduced the insertion loss for a fiber-PIC-fiber interconnect from 50 to 2.14 dB, or 1.47 dB, excluding the fiber array’s loss. Further, we establish an upper bound of 0.45 dB loss per coupler. We report quality factors of 27,000 and 77,000 and bending losses of 6 and 3 dB/cm for 15 and 30 µm radii microrings, respectively. We also demonstrate Bézier escalators, polarization-rotating and polarization-splitting interconnects, and a seven-channel 25 µm pitch volumetric interconnect. The SCRIBE platform presents a clear path toward realizing 3D PICs with unique functionality.

Plasma-Etched Black GaAs Nanoarrays with Gradient Refractive Index Profile for Broadband, Omnidirectional, and Polarization-Independent Antireflection.

Black GaAs nanotip arrays (NTs) with 3300 nm lengths were fabricated via self-masked plasma etching. We show, both experimentally and numerically, that these NTs, with three gradient refractive index layers, effectively suppress Fresnel reflections at the air-GaAs interface over a broad range of wavelengths. These NTs exhibit exceptional UV-Vis light absorption (up to 99%) and maintain high NIR absorption (33-60%) compared to bare GaAs. Moreover, possessing a graded layer with a low refractive index (n = 1.01 to 1.12), they achieve angular and polarization-independent antireflection properties exceeding 80° at 632.8 nm, aligning with perfect antireflective coating theory predictions. This approach is anticipated to enhance the performance of optoelectronic devices across a wide range of applications.

Optical development in the murine eye lens of accelerated senescence-prone SAMP8 and senescence-resistant SAMR1 strains

The eye lens is responsible for focusing objects at various distances onto the retina and its refractive power is determined by its surface curvature as well as its internal gradient refractive index (GRIN). The lens continues to grow with age resulting in changes to the shape and to the GRIN profile. The present study aims to investigate how the ageing process may influence lens optical development. Murine lenses of accelerated senescence-prone strain (SAMP8) aged from 4 to 50 weeks; senescence-resistant strain (SAMR1) aged from 5 to 52 weeks as well as AKR strain (served as control) aged from 6 to 70 weeks were measured using the X-ray interferometer at the SPring-8 synchrotron Japan within three consecutive years from 2020 to 2022. Three dimensional distributions of the lens GRIN were reconstructed using the measured data and the lens shapes were determined using image segmentation in MatLab. Variations in the parameters describing the lens shape and the GRIN profile with age were compared amongst three mouse strains. With advancing age, both the lens anterior and posterior surface flattens and the lens sagittal thickness increase in all three mouse strains (Anterior radius of curvature increase at 0.008 mm/week, 0.007 mm/week and 0.002 mm/week while posterior radius of curvature increase at 0.002 mm/week, 0.007 mm/week and 0.003 mm/week respectively in AKR, SAMP8 and SAMR1 lenses). Compared with the AKR strain, the SAMP8 samples demonstrate a higher rate of increase in the posterior curvature radius (0.007 mm/week) and the thickness (0.015 mm/week), whilst the SAMR1 samples show slower increases in the anterior curvature radius (0.002 mm/week) and its thickness (0.013 mm/week). There are similar age-related trends in GRIN shape in the radial direction (in all three types of murine lenses nr2 and nr6 increase with age while nr4 decrease with age consistently) but not in the axial direction amongst three mouse strains (nz1 of AKR lens decrease while of SAMP8 and SAMR1 increase with age; nz2 of all three models increase with age; nz3 of AKR lens increase while of SAMP8 and SAMR1 decrease with age). The ageing process can influence the speed of lens shape change and affect the GRIN profile mainly in the axial direction, contributing to an accelerated decline rate of the optical power in the senescence-prone strain (3.5 D/week compared to 2.3 D/week in the AKR control model) but a retardatory decrease in the senescence-resistant strain (2.1 D/week compared to the 2.3D/week in the AKR control model).

Dispersion of optical vortices in twisted elliptical-core optical fibers with torsional stresses

In this paper, the dispersion of optical vortices (OVs) with a topological charge l >= 1 in twisted elliptical fibers (TEF) with torsional stresses (TS) is studied. Analytical expressions for polarization, topological, and hybrid dispersion are derived from the spectra of vortex modes in step- and gradient-index TEFs with TS. It is shown that in strongly twisted fibers with a gradient refractive index profile, new types of dispersion appear in comparison with the case of a step-index profile. The dependence of the dispersion of OVs on the material and geometrical parameters of the fiber is studied numerically. It is established that in step-index TEFs with TS, there is a spectral region near which all types of dispersion for OVs with l >= 1 take a near zero value. It is also demonstrated that for TEFs with a gradient profile, this regime is realized for strongly twisted strongly elliptical fibers.

Compact Sub‐Semicircular Axial Gradient Index Lens Synthesized by Metasurfaces: A Promising Solution for Miniaturized Antenna and Subwavelength Focusing Systems

AbstractWe present the design, fabrication, and experimental measurements of an Axial Gradient‐index (AGRIN) flat lens synthesized by 2D periodic metallic patches on a grounded dielectric slab, known as metasurfaces. Metasurfaces can be considered as artificial materials that possess unique characteristics, which mainly revolve around the two‐dimensional distribution of the structure. By manipulating the phase and amplitude of the near‐fields over the surface of the metasurface, specific values of the effective permittivity and permeability can be achieved, thereby regulating the overall field behavior by gaining control of the refractive index that is related to the aforementioned two material parameters. By configuring the refractive index, metasurfaces enable the manipulation of the direction in which electromagnetic waves propagate, as dictated by Snell's law. By varying the geometric dimensions of unit cells in each segment that compose the lens, the gradient refractive index profile required for our AGRIN lens can be achieved. A primary feature of this lens lies with its semicircular structure, in contrast to conventional circular ones. Its perimeter comprises a convex boundary and a straight one. In comparison to traditional circular lenses like the Luneburg lens and Maxwell fisheye lens, our proposed AGRIN lens offers the advantage of being more compact. Despite its smaller area, the AGRIN lens maintains its focusing ability. The AGRIN lens is capable of focusing over 71.75% of the energy from the incident wave onto the focal point. This efficient focusing ability, combined with its reduced size, makes the AGRIN lens highly advantageous for various applications.

Obtaining a Scattering Structure by the Method of Optical Breakdown in Special Fibers

The paper describes a technique for manufacturing samples of fiber diffusers based on fibers with a gradient refractive index profile and a double cladding. Fiber diffusers can be used in medicine, for example, as sources of input radiation in photodynamic therapy or heat sources in phototherapeutic devices such as dressings or blankets. The paper describes experiments on creating quasi-periodic and non-periodic structures from microdefects inside optical fibers by means of optical breakdown and subsequent melting of the fiber core by a moving plasma spark. On the basis of experimental data, the optimal types of fibers were determined to create diffusers with the required properties. The energy characteristics of the laser diode necessary for writing structures from microdefects were estimated, and the results of measuring the parameters of microdefects were presented.

Radiation-resistant graded-index multimode optical fibers based on fluorosilicate glass

Using the MCVD-technology, radiation-resistant multimode optical fibers based on fluorosilicate glass with a gradient refractive index profile were developed. Radiation-induced attenuation (RIA) of light in the fibers was compared with the literature data on analogous fibers manufactured by the PCVD-technology. It was found out that RIA in the MCVD-fibers at the wavelength λ=1310 nm under γ-irradiation at the doses of up to 10 kGy is 1-2 dB/km (19-29%) lower than RIA in the Super RadHard fiber produced by the PCVD-technology and previously supposed to have a record-high radiation resistance. Keywords: radiation-induced attenuation of light, RIA, graded-index multimode optical fiber, radiation resistance.

Радиационно-стойкие градиентные многомодовые волоконные световоды на основе фторсиликатного стекла

Using MCVD-technology, radiation-resistant multimode optical fibers based on fluorosilicate glass with a gradient refractive index profile were developed. Radiation-induced attenuation of light (RIA) in the fibers was compared with the literature data on analoguous fibers manufactured by the PCVD-technoogy. It was found out that RIA in the MCVD-fibers at the wavelength λ=1310 nm under γ-irradiation at doses of up to 10 kGy is 1-2 dB/km (19%-29%) lower than RIA in Super RadHard fiber produced by the PCVD-technology and previously supposed to have record-high radiation resistance.

Investigation of Field and Energy in a Weakly-Conducting Optical Fiber with an Arbitrary Degree of Refractive Index Profile

Introduction. We consider a weakly conductive gradient fiber in the single-mode regime and solve the equation for the electric field in the core of this fiber in a general form in the first approximation. The aim of this study is to study the field and energy in the core of a weakly conductive gradient fiber without taking into account the polarization in the single-mode regime in the case of a power-law (generally) refractive index profile. Materials and Methods. From Maxwell’s equations for dielectric media, there was derived an equation for the field in a fiber with gradient refractive index profile. Making the appropriate substitutions, replacing the zero-order Bessel function with a Gaussian function, and making the necessary approximation of the resulting equation, we arrive at an equation that we solve by the Wentzel – Kramers – Brillouin method and obtain analytical expressions for the field and energy inside waveguide for an arbitrary degree of the refractive index. Results. There was obtained a solution of the equation for the field in fiber with a powerlaw refractive index profile. Numerical calculations were carried out. A graph of the dependence of a dimensionless quantity – “normalized” energy – on the waveguide parameter for the first five powers of the profile (n = 1, 2, 3, 4, 5) was plotted. Discussion and Conclusion. It is shown that the energy increases faster for the profile with n = 1, and after this value, the energy for the profile with n = 1 increases sharply, and for n > 1, the energy growth decreases with increasing n. The results obtained in this work can be used for creating an energy-efficient core, for carrying out a possible analysis of information transmission, and for designing waveguides taking into account specific applications.

Preparation and refractive index characterization of chalcogenide glasses with gradient refractive index

AbstractInfrared gradient refractive index (GRIN) lenses have great application value and potential in multispectral imaging systems. This study reports various chalcogenide axial GRIN glasses prepared using the hot‐pressing diffusion method. It is worth noting that the S4–S60 GRIN sample has a difference in refractive index (RI) Δn of greater than 0.3 and a diffusion depth of about 5 mm, which is the deepest diffusion depth reported in chalcogenide glass to date. In addition, the linear portion in the profile of the GRIN sample has a RI difference of 0.15 and a thickness of 1.2 mm. The effects of the temperature, concentration difference, and diffusion time on the sample diffusion process are discussed. The dispersion properties of the GRIN samples were further calculated, providing a new option for correcting chromatic aberrations in optical systems. In addition, a method for the indirect nondestructive characterization of sample RI using the Raman intensity ratio is proposed, and the reliability of the method is verified by practical experiments, which is convenient for the subsequent measurement of the GRIN profile.

Structural lens for broadband triple focusing and three-beam splitting of flexural waves

In this article, we report a lens design based on a concentric circular structure with continuous changing of thickness defined in a thin plate structure for focusing a plane wave into three spots (triple focusing) and for splitting elastic waves emanating from a point source into three collimated beams of different directions (three-beam splitting). Inspired by the principle of optical graded index triple focusing lens, the governing equations of the gradient refractive index profiles necessary for achieving such structural lens were obtained. The refractive index profiles were realized by using a lens design with two concentric circular areas of different thickness variation profiles defined in a thin plate. Analytical, numerical, and experimental studies were conducted to investigate the functionalities of the variable thickness structural lens. The results showed that the lens developed in this study were able to perform triple focusing and three-beam splitting with broadband property. Furthermore, the locations of focal points and directions of collimated beams can be engineered by changing the lens thickness profiles according to the governing equations. In addition, the proposed lens is miniature and simple design, which overcome the limitations of previous triple focusing and beam splitters.

Omnidirectional photonic band gaps in one-dimensional gradient refractive index photonic crystals considering linear and quadratic profiles

By using the transfer matrix formalism, in this work it is presented the study of the optical properties of 1D photonic structures constructed with M periods of bilayers of dielectric material and slabs with gradient refractive index (GRIN) profile of two types: linear and quadratic. By varying the profile parameters, preserving the average value of the refractive index for the GRIN slab, the results show the formation of new photonic band gaps whose bandwidths depends on the slope and the curvature of the linear and quadratic profile respectively. Also, it can be observed the formation of omnidirectional photonic bandgaps for the TE and TM polarizations, one for the linear profile and three for the quadratic one, for which their bandwidths depend linearly on the slope and the curvature of the GRIN profiles. It is expected that the presented results could be useful in the construction of optical devices based in their optical response under oblique incidence.

Algorithm for optical characterization of dielectric gradient index nanofilm by surface plasmon resonance spectroscopy

A numerical algorithm for determining the refractive index profiles of gradient nanofilms is proposed. A physical justification for the necessity of using spectroscopic measurements in surface plasmon resonance sensing in addition to angular measurements for the unambiguous reconstruction of the shape of the gradient refractive index profile is given. The proposed approach can be effective for nanofilms made of dielectric materials transparent in the IR and THz range.

Precision of Silicon Oxynitride Refractive-Index Profile Retrieval Using Optical Characterization

Layers with gradient refractive-index profile are an attractive alternative to conventional homogeneous stack coatings. However, the optical characterization and monitoring of the graded refractive-index profile is a complex issue, which has been typically solved by using a simplified model of mixed materials. Although this approach provides a solution to the problem, the precision, which can be expected from optical characterization of the refractive index gradient, remains unclear. In this work, we study optical characterization of SiO_xN_y layers deposited via reactive dual ion beam sputtering. To characterize the deposited layers, we use several methods including reflectance, and transmittance spectra at a broad range of incident angles, together with spectral ellipsometry. All the data were simultaneously fitted with a general profile of refractive index. The expected profile used in our fit was based on characterization of SiO_xN_y layers with a varying stoichiometry. By altering of the profile, we discussed sensitivity of such alternation on fit quality and we studied ambiguity of merit-function minimization. We demonstrate that while the scanning of particular parameters of the profile can be seemingly very precise, we obtain a very good agreement between the experimental data and model for a broad range of gradient shapes, where the refractive-index value on major part of the profile can differ as much as 0.02 from the mean value.

Optofluidic waveguide bending by thermal diffusion for visible light control.

Optofluidics has inspired many promising optical devices. Among them, waveguide bending is an important element for guiding light. Here, we demonstrated the thermal-diffusion liquids, acting as a natural transformation optical material in an annular structure. Compared with conventional step-index waveguide bending, this thermal one enables real-time tunable visible light bends by extreme angles, with nearly no power loss and intensity distribution. This unique light bending is because gradient refractive-index profiles caused by thermal diffusion meet the requirements by transformation optics. The work demonstrates the thermal diffusion in liquids as a natural technology to realize optofluidic gradient-index designs and has potential for tunable optical systems.

Cell compaction is not required for the development of gradient refractive index profiles in the embryonic chick lens

The development of the eye requires the co-ordinated integration of optical and neural elements to create a system with requisite optics for the given animal. The eye lens has a lamellar structure with gradually varying protein concentrations that increase towards the centre, creating a gradient refractive index or GRIN. This provides enhanced image quality compared to a homogeneous refractive index lens. The development of the GRIN during ocular embryogenesis has not been investigated previously. This study presents measurements using synchrotron X-ray Talbot interferometry and scanning electron microscopy of chick eyes from embryonic day 10: midway through embryonic development to E18: a few days before hatching. The lens GRIN profile is evident from the youngest age measured and increases in magnitude of refractive index at all points as the lens grows. The profile is parabolic along the optic axis and has two distinct regions in the equatorial plane. We postulate that these may be fundamental for the independent central and peripheral processes that contribute to the optimisation of image quality and the development of an eye that is emmetropic. The spatial distributions of the distinct GRIN profile regions match with previous measurements on different fibre cell groups in chick lenses of similar developmental stages. Results suggest that tissue compaction may not be necessary for development of the GRIN in the chick eye lens.

Conformal Landscape of a Two-Dimensional Gradient Refractive-Index Profile for Geometrical Optics

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.