Refractive Index Discontinuity Research Articles

A highly efficient, eco‐friendly method for antireflection nanostructures on poly (ethylene terephthalate)

AbstractAntireflection surfaces are widely used in optical devices (such as vehicle display, solar cells, and architectural glass) to reduce the reflection and increase transmittance. Plasma etching shows great potential in making subwavelength antireflection structures for its advantage of scalable, low‐cost, and applicable in flexible substrates. Here, we demonstrate an antireflection nanostructure by O2 plasma etching on poly (ethylene terephthalate) (PET) substrate without additional corrosive gas species or antireflective coatings. Nanopores on the surface were formed due to the different etching rates of the organic region and silica region of the surface. The solar weighted average transmittance was improved from 91.6% to 94.8% for single‐side treated PET with silica antiblocking layer. The transmission increment was attributed to the gradient refractive index of the nanostructured surface due to the elimination of step discontinuity in refractive index. The result shows a highly efficient, eco‐friendly, solvent‐free, economical, and sputtering target‐free method for reducing the reflection and increasing the transmittance of the substrates.

Low-loss grating coupler with a subwavelength structure on a thin-film lithium niobate substrate.

We demonstrated a low-loss O-band grating coupler on an x-cut thin-film lithium niobate substrate by implementing subwavelength and apodized structures. The subwavelength gratings were used to mitigate the refractive index discontinuity between the input taper and grating region, which was the first application of such a structure for grating coupler optimization on a thin-film lithium niobate substrate. The coupling efficiency was measured to be -1.99 dB/coupler at a wavelength of 1312.8 nm, which was the lowest loss among the reported lithium niobate grating couplers that do not use metal mirrors. The proposed design does not require metal mirrors or any additional material layers and can be easily fabricated with a single-step lithography and etching processes.

A collocation-based spectral element method for computing nonlinear optical waveguide

Computation of nonlinear optical waveguide needs to solve nonlinear eigenvalue/ eigenfunction problem mathematically. However, usually the refractive index profiles in the nonlinear optical waveguide are discontinuous, which makes solution of nonlinear eigenvalue/eigenfunction problem not smooth enough. In this work, we mainly discuss how to use high-order collocation-based spectral element method (SEM) to discretize such problem and propose an iterative algorithm for computing nonlinear optical waveguide with discontinuous refractive index profiles. Starting from the linear eigenvalue/eigenfunction problem, we adopt SEM to discretize it and solve the resulting discretized system with Matlab eigen solver; for the nonlinear problem, we first change the nonlinear problem into corresponding linear problems, and then solve the linear problems by usage of the iterative method. The proposed method has advantage of high-order accuracy and lower-order cost. The accuracy and efficiency of the method are tested by several one-dimensional and two-dimensional linear optical waveguide structures. Numerical results for some nonlinear optical waveguide are also presented.

Effect of crystal-photodetector interface extraction efficiency on Cerenkov photons’ detection time

Using Cerenkov photons to improve detector timing resolution in time-of-flight positron emission tomography scanners is promising since they constitute most of the signal rising edge. The main challenge in using Cerenkov light is its low yield per photoelectric interaction, which requires optimizing their complex optical transport in the detector. Monte Carlo simulations unlock information unavailable through benchtop measurements and help better understand the Cerenkov photon behavior. Although the first Cerenkov photons are emitted forward, part of the early triggering signal is lost due to poor light extraction at the crystal-photodetector interface. In addition, the electron path in the crystal, that determines the Cerenkov photon direction, is tortuous due to multiple scattering, causing the Cerenkov photons emitted after a few scatters to no longer be forward-directed. In this context, the transit time spread in the crystal, highly dependent on the detector geometry, plays a crucial role in the photon detection time. In this work, we performed optical simulations in bismuth germanium oxide using 511 keV gamma with GATE to investigate the optical photons extraction when modifying the index of refraction at the crystal-photodetector interface and the crystal aspect ratio. The mean detection time of the first, second, and third detected optical and Cerenkov photon separately was studied as a function of the total number of Cerenkov detected per event. For each configuration, we calculated the expected mean detection time using the probability of detection. Thinner crystals led to lower expected detection times due to the reduced transit time in the crystal. Reducing the refractive index discontinuity at the crystal-photodetector interface decreased all configurations expected mean detection time values. We showed that it not only improves the optical photons (scintillation and Cerenkov) detection efficiency at the photodetector face but directly ameliorates the probability of detecting the fastest one, reducing the effect of thicker materials and of losing the first detected photon information, both crucial to reduce the detector timing resolution. Thanks to their prompt emission and directionality at emission, Cerenkov photons represent the first detected optical photon in most configurations but increasing their detection efficiency is crucial to detect the fastest one.

Thermochromic Fenestration Elements Based on the Dispersion of Functionalized VO2 Nanocrystals within a Polyvinyl Butyral Laminate.

The energy required to heat, cool, and illuminate buildings continues to increase with growing urbanization, engendering a substantial global carbon footprint for the built environment. Passive modulation of the solar heat gain of buildings through the design of spectrally selective thermochromic fenestration elements holds promise for substantially alleviating energy consumed for climate control and lighting. The binary vanadium(IV) oxide VO2 manifests a robust metal-insulator transition that brings about a pronounced modulation of its near-infrared transmittance in response to thermal activation. As such, VO2 nanocrystals are potentially useful as the active elements of transparent thermochromic films and coatings. Practical applications in retrofitting existing buildings requires the design of workflows to embed thermochromic fillers within industrially viable resins. Here, we describe the dispersion of VO2 nanocrystals within a polyvinyl butyral laminate commonly used in the laminated glass industry as a result of its high optical clarity, toughness, ductility, and strong adhesion to glass. To form high-optical-clarity nanocomposite films, VO2 nanocrystals are encased in a silica shell and functionalized with 3-methacryloxypropyltrimethoxysilane, enabling excellent dispersion of the nanocrystals in PVB through the formation of siloxane linkages and miscibility of the methacrylate group with the random copolymer. Encapsulation, functionalization, and dispersion of the core-shell VO2@SiO2 nanocrystals mitigates both Mie scattering and light scattering from refractive index discontinuities. The nanocomposite laminates exhibit a 22.3% modulation of NIR transmittance with the functionalizing moiety engendering a 77% increase of visible light transmittance as compared to unfunctionalized core-shell particles. The functionalization scheme and workflow demonstrated, here, illustrates a viable approach for integrating thermochromic functionality within laminated glass used for retrofitting buildings.

Three cases of discontinuous refractive index in metamaterial study

We investigate three cases of metamaterials presented in the literature displaying refractive index with one or more discontinuities along the frequency spectrum. We reproduce the numerical simulations of these metamaterials and compare our simulations to each reported case. For each case, we perform a geometrical investigation of each metamaterial’s refractive index by mean of a numerical simulation of a prism made of the reported metamaterials upon which is incident a plane electromagnetic wave. Such investigation allows us to infirm or confirm negative refraction at resonance frequency. Finally, we carry a numerical and theoretical investigation of this discontinuity and show that, as the refractive index crosses a discontinuity, while the topology of the effective wave has changed within the metamaterial, the dynamics of the phases remain unchanged at any time at the metamaterial's boundaries.

Simultaneous Large Optical and Piezoelectric Effects Induced by Domain Reconfiguration Related to Ferroelectric Phase Transitions.

Electrical switching of ferroelectric domains and subsequent domain wall motion promotes strong piezoelectric activity, however, light scatters at refractive index discontinuities such as those found at domain wall boundaries. Thus, simultaneously achieving large piezoelectric effect and high optical transmissivity is generally deemed infeasible. Here, it is demonstrated that the ferroelectric domains in perovskite Pb(In1/2 Nb1/2 )O3 -Pb(Mg1/3 Nb2/3 )O3 -PbTiO3 domain-engineered crystals can be manipulated by electrical field and mechanical stress to reversibly and repeatably, with small hysteresis, transform the opaque polydomain structure into a highly transparent monodomain state. This control of optical properties can be achieved at very low electric fields (less than 1.5kV cm-1 ) and is accompanied by a large (>10000 pm V-1 ) piezoelectric coefficient that is superior to linear state-of-the-art materials by a factor of three or more. The coexistence of tunable optical transmissivity and high piezoelectricity paves the way for a new class of photonic devices.

Light extraction efficiency enhancement of CH3NH3PbBr3 light-emitting diodes using nanopatterned PEDOT:PSS layers

Nanopatterned poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) layers fabricated by soft-nanoimprint were applied to CH3NH3PbBr3 (MAPbBr3) light-emitting diodes to enhance light extraction. The electric field distribution of MAPbBr3 devices with different periods of the nanopatterned PEDOT:PSS was calculated using the finite-difference time-domain method, demonstrating that the 400-nm period was more effective in improving light outcoupling. By integrating the nanopatterned PEDOT:PSS layer, the external quantum efficiency of the device increased from 6.5% to 10.3%. It can be attributed to the fact that the nanopatterned structure reduced the refractive index discontinuity at the interface between MAPbBr3 and PEDOT:PSS, thereby reducing light trapping in the waveguide mode.

An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: Formulation, analysis, algorithm, and simulation

A natural medium for wave propagation comprises a coupled bounded heterogeneous region and an unbounded homogeneous free-space. Frequency-domain wave propagation models in the medium, such as the variable coefficient Helmholtz equation, include a faraway decay radiation condition (RC). It is desirable to develop algorithms that incorporate the full physics of the heterogeneous and unbounded medium wave propagation model, and avoid an approximation of the RC. In this work we first present and analyze an overlapping decomposition framework that is equivalent to the full-space heterogeneous-homogenous continuous model, governed by the Helmholtz equation with a spatially dependent refractive index and the RC. Our novel overlapping framework allows the user to choose two free boundaries, and gain the advantage of applying established high-order finite and boundary element methods (FEM and BEM) to simulate an equivalent coupled model.The coupled model comprises auxiliary interior bounded heterogeneous and exterior unbounded homogeneous Helmholtz problems. A smooth boundary can be chosen for simulating the exterior problem using a spectrally accurate BEM, and a simple boundary can be used to develop a high-order FEM for the interior problem. Thanks to the spectral accuracy of the exterior computational model, the resulting coupled system in the overlapping region is relatively very small. Using the decomposed equivalent framework, we develop a novel overlapping FEM-BEM algorithm for simulating the acoustic or electromagnetic wave propagation in two dimensions. Our FEM-BEM algorithm for the full-space model incorporates the RC exactly. Numerical experiments demonstrate the efficiency of the FEM-BEM approach for simulating smooth and non-smooth wave fields, with the latter induced by a complex heterogeneous medium and a discontinuous refractive index.

A multi-frequency iterative imaging method for discontinuous inverse medium problem

The inverse medium problem with discontinuous refractive index is a kind of challenging inverse problem. We employ the primal dual theory and fast solution of integral equations, and propose a new iterative imaging method. The selection criteria of regularization parameter is given by the method of generalized cross-validation. Based on multi-frequency measurements of the scattered field, a recursive linearization algorithm has been presented with respect to the frequency from low to high. We also discuss the initial guess selection strategy by semi-analytical approaches. Numerical experiments are presented to show the effectiveness of the proposed method.

Reconstruction method for samples with refractive index discontinuities in optical diffraction tomography

We present a reconstruction method for samples containing localized refractive index (RI) discontinuities in optical diffraction tomography. Abrupt RI changes induce regional phase perturbations and random spikes, which will be expanded and strengthened by existing tomographic algorithms, resulting in contaminated reconstructions. This method avoids the disturbance by recognition and separation of the discontinuous regions, and recombination of individually reconstructed data. Three-dimensional RI distributions of two fusion spliced optical fibers with different typical discontinuities are demonstrated, showing distinctly detailed structures of the samples as well as the positions and estimated shapes of the discontinuities.

The inverse transmission eigenvalue problem for a discontinuous refractive index

We consider the inverse spectral problem of determining a spherically symmetric and discontinuous refractive index n(r) from interior transmission eigenvalues. Using Liouville’s transform, we investigate the asymptotic properties of the solution of an auxiliary initial value problem for large wave numbers and the asymptotic behaviour of the characteristic determinants derived from the eigenfunction expansions. Next, we assume that we know all transmission eigenvalues with spherically symmetric eigenfunctions and prove under some conditions that the transformed discontinuity of the refractive index can be determined. Finally we prove that the knowledge of all transmission eigenvalues including multiplicities uniquely determines n(r), under the assumption that n(0) is known and either n(r) > 1 or 0 < n(r) < 1 by using a moment type result and applying Müntz’s theorem.

Accurate radiative transfer calculations for layered media.

Simple yet accurate results for radiative transfer in layered media with discontinuous refractive index are obtained by the method of K-integrals. These are certain weighted integrals applied to the angular intensity distribution at the refracting boundaries. The radiative intensity is expressed as the sum of the asymptotic angular intensity distribution valid in the depth of the scattering medium and a transient term valid near the boundary. Integrated boundary equations are obtained, yielding simple linear equations for the intensity coefficients, enabling the angular emission intensity and the diffuse reflectance (albedo) and transmittance of the scattering layer to be calculated without solving the radiative transfer equation directly. Examples are given of half-space, slab, interface, and double-layer calculations, and extensions to multilayer systems are indicated. The K-integral method is orders of magnitude more accurate than diffusion theory and can be applied to layered scattering media with a wide range of scattering albedos, with potential applications to biomedical and ocean optics.

Multiplexed Oil Level Meter Using a Thin Core Fiber Cladding Mode Exciter

This letter reports a multiplexed optical oil level meter using a thin core fiber (TCF) cladding mode exciter. Weak cladding mode reflection (<−75 dB) was employed to probe external refractive index discontinuity at an air-oil boundary. The insertion loss of one sensor is <3 dB. A linear relationship was evaluated between the measurement position and the absolute position during the oil-level test. System-level multiplexing capability was demonstrated and no crosstalk was found between the sensors. The system accuracy was 0.16 mm.

Multiplexed displacement fiber sensor using thin core fiber exciter.

This letter reports a multiplexed optical displacement sensor using a thin core fiber (TCF) exciter. The TCF exciter is followed by a stripped single mode optical fiber. A small section of buffer is used as the movable component along the single mode fiber. Ultra-weak cladding mode reflection (< - 75 dB) was employed to probe the refractive index discontinuity between the air and buffer coating boundary. The position change of the movable buffer segment results in a delay change of the cladding mode reflection. Thus, it is a measure of the displacement of the buffer segment with respect to the glass fiber. The insertion loss of one sensor was measured to be less than 3 dB. A linear relationship was evaluated between the measurement position and absolute position of the moving actuator. Multiplexed capability was demonstrated and no cross talk was found between the sensors.

Goos-Hänchen shift in a standing-wave-coupled electromagnetically-induced-transparency medium

The Goos-H\anchen shift of the system composed by two cavity walls and an intracavity atomic sample is presented. The atomic sample is treated as a four-level double-$\ensuremath{\Lambda}$ system, driven by the two counterpropagating coupling fields. The probe field experiences the discontinuous refractive index variation and is reflected. Moreover, under the phase-matching condition, the four-wave mixing effect based on electromagnetically induced transparency can cause effective reflection. The Goos-H\anchen shifts appear in both situations and are carefully investigated in this article. We refer to the first one with the incident and reflected light having identical wavelength as the linear Goos-H\anchen shift, and the second one with the reflection wavelength determined by the phase-matching condition as the nonlinear Goos-H\anchen shift. The differences between the two kinds of shifts, such as the incident angle range, conditions for the shift peaks, and controllability, are discussed.

Scattering of a plane electromagnetic wave by a generalized Luneburg sphere–Part 1: Ray scattering

We calculated scattering of an electromagnetic plane wave by both a radially-inhomogeneous particle and bubble, the square of whose refractive index profile is parabolic as a function of radius. Depending on the value of the two adjustable parameters of the parabola, the particle or bubble can have either a refractive index discontinuity at its surface, or the refractive index can smoothly merge into that of the exterior medium. Scattering was analyzed in ray theory, and various novel features of the scattering, including the details of the curved ray paths, transmission rainbows, and near-critical-angle scattering were apparent and were contrasted with their behavior for scattering by a homogeneous sphere.

Composite Effect of E/O Nonlinearity and Optical Echo on EPWM-OFDM Transmission in Radio Over Fiber Channel

Radio over Fiber (RoF) is a promising technology for extending broadband wireless access to indoor and outdoor dead spots. However, commonly applied intensity-modulation / direct-detection RoF transmission presents some nonlinearity and produces echo distortion. Since multiple carrier modulation signals such as Orthogonal Frequency Division Multiplexing (OFDM) are widely employed in broadband wireless systems, the above issues become more serious. The OFDM signals have high Peak-to-Average Power Ratio, which makes them more sensitive to nonlinearity. Moreover, the large delay of optical echoes that are caused by the discontinuity of refractive index at both ends of Electrical/Optical (E/O) and Optical/Electrical converters exceeds the guard time of current OFDM symbols when the length of optical fiber is long. Since the nonlinearity and echo exist simultaneously in RoF channels, their composite effect is mathematically analyzed in this paper. A RoF-echo model is proposed for the modeling of the multiple light reflections and its validity is confirmed by experiments. Then, Envelop-Pulse-Width-Modulation- (EPWM-) RoF transmission is proposed for dealing with the nonlinearity and echo in RoF channel. The performance of the EPWM-RoF scheme for OFDM signal transmission is evaluated by simulations, which reveals that the scheme improves the transmission quality in Error Vector Magnitude under the composite environment of E/O nonlinearity and optical echo.

Raman imaging of pharmaceutical materials: Refractive index effects on contrast at buried interfaces

Resolution targets composed of bilayer polydimethylsiloxane (PDMS) devices with buried polyethylene glycol (PEG) channels have been fabricated using traditional photolithographic and micromolding techniques to develop resolution targets that mimic pharmaceutical materials. Raman chemical images of the resulting PEG-in-PDMS devices composed of varying parallel line widths were investigated by imaging the PEG lines through a thin overlayer of PDMS. Additionally, a scattering agent, Al2O3, was introduced at varying concentrations to each layer of the device to explore the effects of scattering materials on Raman images. Features in the resulting chemical images of the PEG lines suggest that reflection at the PEG/PDMS interface contributes to the Raman signal. A model based on geometric optics was developed to simulate the observed image functions of the targets. The results emphasize the influence of refractive index discontinuities at the PEG/PDMS interface on the apparent size and shape of the PEG features. Such findings have an impact on interpretation of Raman images of nonabsorbing, opaque pharmaceutical samples.

Analysis of transient radiative transfer in two-dimensional scattering graded index medium with diffuse energy pulse irradiation

The natural element method (NEM) is extended to solve transient radiative transfer in two-dimensional semitransparent graded index media with energy pulse irradiation diffusely incident on the left boundary. The surfaces of the medium are diffusely reflecting and semitransparent. By using a fully implicit backward differencing scheme to discretize the transient term in the radiative transfer equation and employing the least-squares (LS) weighted residuals approach to discretize the radiative transfer equation, a LSNEM approach is devised. Firstly, LSNEM solutions to transient radiative transfer are validated by comparison with results reported in the literature. Afterward, LSNEM is employed to investigate two-dimensional transient radiative transfer in graded index medium with a refractive index discontinuity at the surfaces. Effects of the optical thickness, scattering phase function and scattering albedo on transmittance and reflectance signals are investigated. Finally, the transient radiative transfer process of the medium subject to square diffuse pulse irradiation train are investigated, and the transient behavior of the radiative energy transport inside the medium with two complex graded index distributions is analyzed.