Refractive Index Profile Research Articles

Semi-analytical finite ray-tracing through the quadratic symmetric GRIN lens.

The propagation of light within a gradient index (GRIN) media can be analyzed with the use of differential equations for a given non-homogenous refractive index profile. Numerical methods are often necessary to perform ray-tracing in GRIN media; however, analytical solutions exist for several types of GRIN lenses. In this paper, paraxial and non-paraxial differential equations are derived to calculate the ray path in a GRIN lens. It is shown that the paraxial equation has an analytical solution for a GRIN media with a quadratic profile within the paraxial region. The analytical solution can be obtained by using Legendre polynomials or by the Frobenius method involving a power series. Using the Legendre or Frobenius solution, one can calculate the refractive indices along the ray path. A new recursive relationship is proposed to map the trajectory of light at finite heights. To illustrate the finite ray-tracing method utilizing a non-paraxial differential equation, two lenses (with spherical and elliptical iso-indicial contours) are considered. The lenses' back focal distances, for rays entering the lenses at varying finite heights, are calculated. For each lens, its spherical aberration is estimated. The effective focal length and the shape of the principal surface are also obtained. The accuracy of the results is then compared to the numerical ray-tracing using an optical design software, Zemax OpticStudio. The predicted spherical aberration for the spherical lens differs from numerical ray-tracing by less than λ14 at the marginal zone, while the error for the effective focal length is less than λ100.

Single-shot observation of nonlinear pulse splitting in a Kerr medium.

We report single-shot, time-resolved observation of self-steepening and temporal splitting of near-infrared, 50 fs, micro-joule pulses propagating nonlinearly in flint (SF11) glass. A coherent, smooth-profiled, 60-nm-bandwidth probe pulse that propagated obliquely to the main pulse through the Kerr medium recorded a time sequence of longitudinal projections of the main pulse's induced refractive index profile in the form of a phase-shift "streak," in which frequency-domain interferometry recovered with ∼10 fs temporal resolution. A three-dimensional simulation based on a unidirectional pulse propagation equation reproduced observed pulse profiles.

Refractivity of P2O5-Al2O3-SiO2 Glass in Optical Fibers

A significant change in the refractive index profiles for the large mode area phosphoroaluminosilicate (PAS) core optical fibers was observed in comparison to that in preforms. This study shows that the refractive index of the PAS core can vary from negative (in preform) to positive (in fiber), and the difference in the refractive index between the core and preform can exceed a few thousand. By measuring a large set of fibers with different concentrations of P2O5 and Al2O3, we define the refractivity of each dopant (P2O5, Al2O3 and AlPO4 joint) after drawing fiber from the preform and discuss the possible origin of the observed refractive index variation.

The influence of refractive index profile on supercontinuum beams self-cleaning in graded index multimode fiber

We propose a theoretical scheme to improve the fundamental mode energy proportion of the supercontinuum (SC) generation in graded-index multimode fiber (GRIN-MMF). With this scheme, we conduct numerical investigations into the influence of various core refractive index profile parameters on beam-self cleaning of fundamental mode, establishing an optimal parameter range (α=2.0∼2.06). Within this range, the energy proportion of the fundamental mode gradually increases from 32% to 65% as the propagation distance. Additionally, our simulation provides the initial demonstration that the supercontinuum (SC) broadening is correlated with the distribution of core refractive indices within the graded-index multimode fiber.

Soft glass optical fiber characterization with X-ray computed microtomography

The high loss due to the presence of strong phonon resonances makes silica fibers unfit for applications in the mid-infrared spectral range. This has led to the development of specialty optical fibers, based on novel materials and manufacturing techniques. In some cases, the characterization of these new fibers by means of standard techniques may be challenging. Fiber manufacturers would strongly benefit from a tool, which is capable of checking the geometrical and optical properties of fibers (either after fiber drawing, or even in real-time, during the drawing process). Here, we propose and demonstrate that absorption contrast X-ray computed microtomography is a non-destructive technique, capable of characterizing both geometrical and optical properties of specialty optical fibers. We experimentally verified that the tomographic intensity profile in the fiber core has the same shape as the refractive index profile, which we determined via energy-dispersed X-ray spectroscopy. We tested step- and graded-index soft glass fibers, both purchased and made in-house. Owing to the presence of high atomic number elements, which provide higher X-ray cross-section, soft glasses were more suitable than silica for their characterization via X-ray computed microtomography.

Large aperture liquid crystal lens array based on integrated composite electrodes for 2D/3D switchable displays

A large aperture liquid crystal (LC) lens array based on integrated composite electrodes (ICE-LC) lens array with low operating voltages is proposed. The top substrate contains composite electrodes, while the bottom substrate contains strip electrodes. Composite electrodes are further categorized into integral plate electrode (IPE) and rectilinear-patterned electrode (RPE). Meanwhile, the strip electrodes consist of auxiliary electrodes and pixel electrodes. During the focusing mode, the electric field can easily propagate through the LC layer. Simultaneously, the voltage on auxiliary electrodes is maintained lower than that on pixel electrodes to optimize the electric field distribution. To assess the operating efficiency of the ICE-LC, an evaluation of the conventional model is taken during the simulation. Simulation results show that the ICE-LC lens array achieves the shortest focal length at a low operating voltage. The pixel electrodes operate at 4.5 Vrms, and the auxiliary electrodes at 0.9 Vrms. This configuration provides an ideal refractive index profile in a relatively thick LC layer. Additionally, this configuration enables 2D/3D switchable display, outperforming current LC lens array in the equivalent aperture.

Thermally matched chalcogenide glasses with high refractive index contrast for infrared graded‐index lenses

AbstractInfrared graded‐index (GRIN) lenses are desirable for realizing miniaturization and lightweight of infrared imaging systems. Chalcogenide glasses have excellent infrared transparency, good rheological property, and large refractive index range, making them preferred materials for infrared GRIN lenses. In this work, aiming to find thermally matched chalcogenide compositions with high refractive index contrast for preparing GRIN glasses by the stacking diffusion approach, we investigated characteristic temperature, thermal expansion coefficient and refractive index of Ge‐As‐Se and Ge‐As‐Se‐Te glasses, optimized the glass compositions, and evaluated the feasibility of preparing GRIN glass using the optimized chalcogenide glass powders. It is found that Ge20As20Se20Te40 and Ge12As22Se66 glasses have similar softening temperature (247°C vs. 249°C), reasonably difference of thermal expansion coefficient (3.8 ppm/K), and large refractive index contrast (∼.48). The glass powders with composition xGe20As20Se20Te40‐(1‐x) Ge12As22Se66 can be hot‐pressed into glass disks with good transmittance at the same temperature and pressure. Graded refractive index profile is formed near the interface between the layers after the co‐pressed glass is thermally treated. These results demonstrate the prospect of the compositions for preparing infrared GRIN glasses.

Few-mode polymer waveguide amplifier with a dual-layer coronal refractive index profile

A novel, to the best of our knowledge, few-mode waveguide amplifier with a dual-layer coronal core is first proposed. Reconfiguring the refractive index profile is adopted to equalize the modal gains pumped in a single mode. The polymer in terms of the prominent advantages of simple processing and the ease of adjusting refractive index is utilized. The waveguide supporting LP01, LP11a, and LP11b is optimized by the genetic algorithm and fabricated by accurate alignment mask. The crosstalk effect and modal profiles are characterized. The modal gains with different signal power and pumping modes are revealed. The schemes in forward and backward pumps are represented. An average gain of 11.84 dB per mode and an ultralow differential modal gain of 0.36 dB are obtained in a 0.3 cm waveguide at 1526 nm through backward pumping of the LP21b mode at 240 mW for an input signal power of 0.1 mW.

Aerosols are not spherical cows: using discrete dipole approximation to model the properties of fractal particles

ABSTRACT The optical properties of particulate-matter aerosols, within the context of exoplanet and brown dwarf atmospheres, are compared using three different models: Mie theory, modified mean field (MMF) theory, and discrete dipole approximation (DDA). Previous results have demonstrated that fractal haze particles (MMF and DDA) absorb much less long-wavelength radiation than their spherical counterparts (Mie), however it is shown here that the opposite can also be true if a more varying refractive index profile is used. Additionally, it is demonstrated that absorption/scattering cross-sections, and the asymmetry parameter, are underestimated if Mie theory is used. Although DDA can be used to obtain more accurate results, it is known to be much more computationally intensive; to avoid this, the use of low-resolution aerosol models is explored, which could dramatically speed up the process of obtaining accurate computations of optical cross-sections within a certain parameter space. The validity of DDA is probed for wavelengths of interest for observations of aerosols within exoplanet and brown dwarf atmospheres ($0.2-15~\mu$m). Finally, novel code is presented to compare the results of Mie, MMF, and DDA theories (coral: Comparison Of Radiative AnaLyses), as well as to increase and decrease the resolution of DDA shape files accordingly (spherify). Both codes can be applied to a range of other interesting astrophysical environments in addition to exoplanet atmospheres, for example dust grains within protoplanetary discs.

The intrinsic mode activation and evolution in fiber splicing based on 3D refractive index profile characterization

Fiber fusion splicing tremendously affects the modal stability, insertion loss and transmission quality of the optical fiber communication systems. Especially, in the few-mode fibers, a tiny dissatisfactory fiber splicing operation may lead to a big modal perturbation or unexpected mode coupling. In this paper, we propose a 3D refractive index profile visualization method to demonstrate the mode activation and evolution in fiber fusion splicing. A refractive index profile measuring instrument is established and applied to detect the 3D refractive index profile deformation caused by the fiber splicing. Then, based on the measured values of 3D refractive index profile, the mode activation is analyzed for fiber splicing between a single-mode fiber and a two-mode fiber with different core-offset distance. Results show that the mode begins to tremble with a core-offset of 4 μm and the high-order modes are effectively activated at the core-offset of 7 μm. The basic theoretical model and experiment results provide a profound support in almost all kinds of fiber splicing operation, mode interference construction and mode coupling modulation. Additionally, the method can be expanded to the research on fiber cleaving and bending.

3D refractive index reconstruction from phaseless coherent optical microscopy data using multiple scattering-based inverse solvers—a study

Reconstructing 3D refractive index profile of scatterers using optical microscopy measurements presents several challenges over the conventional microwave and RF domain measurement scenario. These include phaseless and polarization-insensitive measurements, small numerical aperture, as well as a Green’s function where spatial frequencies are integrated in a weighted manner such that far-field angular spectrum cannot be probed and high spatial frequencies that permit better resolution are weighed down. As a result of these factors, the non-linearity and the ill-posedness of the inverse problem are quite severe. These limitations have imposed that inverse scattering problems in the microscopy domain largely consider scalar wave approximations and neglect multiple scattering. Here, we present first inverse scattering results for optical microscopy setup where full-wave vectorial formulation and multiple scattering is incorporated. We present (a) how three popular inverse scattering solvers from microwave domain can be adapted for the present inverse problem, (b) the opportunities and challenges presented by each of these solvers, (c) a comparative insight into these solvers and contrast with the simpler Born approximation approach, and (d) potential routes to improve the performance of these solvers for the hard inverse problem of optical microscopy.

Optimization of a quantum cascade laser cavity for single-spatial-mode operation via machine learning

Neural networks, trained with the ADAM algorithm followed by a globally convergent modification to Newton’s method, are developed to predict the threshold gain of the fundamental and first higher-order modes as functions of the refractive-index profile in a quantum cascade laser cavity. The networks are used to optimize the design of a refractive-index profile that provides essentially single-spatial-mode performance in a nominally multi-moded cavity by maximizing the threshold-gain differential between the modes. The use of neural networks allows the optimization to be performed in seconds, instead of days or weeks which would be required if Maxwell’s equations were repeatedly solved to obtain the threshold gains.

Al2O3/GeO2/P2O5/F-Doped Silica Large-Mode-Area Optical Fibers for High-Power Single-Frequency Radiation Delivery

A new design of a passive optical fiber waveguide with a large mode area (LMA) and strong stimulated Brillouin scattering (SBS) suppression is proposed. The fiber core consists of two parts: a central one, doped with Al2O3 and GeO2, and a peripheral one, doped with P2O5 and F. The doping profiles form a gradient-increasing profile of the acoustic refractive index, which effectively implements the acoustic multimode SBS suppression method. Measurements of the SBS gain spectrum and SBS threshold power were carried out, showing an increase in the SBS threshold of no less than 11 dB compared to a conventional uniformly doped passive LMA fiber.

Characterization of optical waveguides in Ce3+-doped phosphate glasses formed by He+ion implantation

In this work, the Ce3+-doped phosphate glass is carried out to fabricate the planar waveguides by the 400 keV He+ ion implantation with a dose of 6.0 × 1016 ions cm−2. The dark-mode spectrum of the waveguide at a wavelength of 632.8 nm is obtained by the prism coupling technique. The SRIM 2013 software is used to analyze the energy deposition induced by the ion implantation and the RCM is employed to reconstruct the refractive index profile of the planar waveguide. The end-face coupling technique is applied to the measurement of the propagation mode image of the waveguide at 632.8 nm. The Ce3+-doped phosphate glass waveguide has the potential for an integrated optical device.

Six-wave interaction with double wavefront reversal in multimode waveguides with Kerr and thermal nonlinearities

Spatial selectivity of six-wave radiation converters, which perform double wavefront conjugation of a signal wave in long multimode waveguides with both Kerr and thermal nonlinearities, is studied. Waveguides with infinitely conductive surfaces, with a parabolic refractive index profile, were used. It is shown that the spatial structure of the first pump wave does not affect the quality of doubled wavefront conjugation in a waveguide with Kerr nonlinearity, but only slightly affects the quality of doubled wavefront conjugation in a waveguide with thermal nonlinearity. A decrease in the radius of the second Gaussian pump wave on the back face of the waveguide leads to an improvement in the quality of the doubled wavefront reversal both in the case of six-wave interaction in the Kerr and thermal nonlinearities. In a parabolic waveguide, when the zero mode of the waveguide is excited by pump waves at a constant frequency of the second pump wave, an increase in the frequency of the first pump wave worsens the quality of the double wavefront conjugation.

Bell-Shaped Refractive Index Profiles of Multimode Optical Fibers and Method for Calculating Their Optical Properties

Bell-Shaped Refractive Index Profiles of Multimode Optical Fibers and Method for Calculating Their Optical Properties

Photosensitivity and optical nonlinearity in arsenic selenide planar waveguides [Invited

We present the first experimental observation of reversible 1550 nm-induced Bragg gratings and stimulated Brillouin scattering (SBS) in a planar waveguide made of high-index chalcogenide material, arsenic triselenide (As2Se3). The temporary grating is inscribed by the two-photon absorption (TPA)-induced refractive index change along the waveguide, facilitated by the high Fresnel reflection from the chip facet. Furthermore, our SBS measurements reveal a Brillouin gain coefficient gB of 7.14 × 10−10 m/W and a frequency shift vB of 7.8 GHz. The Brillouin linewidth ΔvB is measured to be 60 MHz at an input power of 144 mW, which is four times broader compared to As2Se3 fibers. We explain the observed broadening of the linewidth that is attributed to the presence of the photorefractive effect in this platform, which induces a non-uniform refractive index profile along the length of the waveguide. The investigation of photosensitivity and optical nonlinearity in this study holds paramount importance for the realization of reconfigurable nonlinear photonic applications utilizing As2Se3 glasses.

Modal dependence of Rayleigh scattering coefficients based on the bidirectional OTDR technique

In this work, a simple method based on optical time-domain reflectometry has been implemented to compare the Rayleigh scattering coefficient of different modes of few-mode fibers. The principle of the method is first validated in the case of single-mode fibers and then applied to two weakly-coupled few-mode fibers presenting different refractive index profiles. The results are compared with those obtained by more sophisticated experiments based on the analysis of the angular distribution of light scattering.

On-chip wavefront shaping in spacing-varied waveguide arrays

Abstract The ability to manipulate light propagation sets the foundations for optical communication and information processing systems. With the ever-growing data capacity and data rate, photonic integrated circuits have attracted increasing attentions of researchers owing to their large-volume integration capacity and fast operation speed. In this work, we proposed and experimentally demonstrated a new wavefront shaping method using waveguide arrays with hyperbolic secant refractive index profiles. Through theoretically analyzing the diffraction and coherence properties, we found that a single waveguide array can perform both imaging and phase transformation, which are the two primary functions of optical lenses. We further expanded this function and fabricated the corresponding devices on a silicon nitride waveguide platform. Deterministic beam shaping, such as focusing, expansion, collimation, and steering, is successfully realized. This wavefront control method exhibits the potential for on-chip optical routing, ranging, sensing, etc., with high integration density and scalability.

Analysis of HF-Etched Uniformly Thinned Linearly Chirp Types of Refractive Index Profile Fiber Bragg Grating Sensor

Analysis of HF-Etched Uniformly Thinned Linearly Chirp Types of Refractive Index Profile Fiber Bragg Grating Sensor