Refractive Index Discontinuity Research Articles

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.

Short-pulsed laser transport in two-dimensional scattering media by natural element method

The natural element method (NEM) is extended to solve transient radiative transfer (TRT) in two-dimensional semitransparent media subjected to a collimated short laser irradiation. The least-squares (LS) weighted residuals approach is employed to spatially discretize the transient radiative heat transfer equation. First, for the case of the refractive index matched boundary, LSNEM solutions to TRT are validated by comparison with results reported in the literature. Effects of the incident angle on time-resolved signals of transmittance and reflectance are investigated. Afterward, the accuracy of this algorithm for the case of the refractive index mismatched boundary is studied. Finally, the LSNEM is extended to study the TRT in a two-dimensional semitransparent medium with refractive index discontinuity irradiated by the short pulse laser. The effects of scattering albedo, optical thickness, scattering phase function, and refractive index on transmittance and reflectance signals are investigated. Several interesting trends on the time-resolved signals are observed and analyzed.

Study on the sensing characteristics of a local micro-structured long period fiber grating

A simple and effective method employing a local micro-structured long period fiber grating (LMS-LPFG) for the simultaneous measurement of temperature and refractive index is proposed and investigated experimentally. The LMS-LPFG is formed by using the partial etching technique with hydrofluoric (HF) acid in a standard LPFG, in which there are discontinuities in the effective refractive index of cladding modes. Similar to the phase shift theory, a narrow passband and two stopbands are formed. The temperature and the surrounding refractive index (SRI) characteristics of the two stopbands and passband are studied. The temperature sensitivities of the two stopbands and passband are 0.05 nm/°C approximately. The SRI sensitivity of passband (−61.56 nm/RIU) is bigger than that of the two stopbands (−35.62 nm/RIU). Thus, with the sensitive matrix, we can simultaneously measure the changes of temperature and refractive index.

Confocal supercritical angle microscopy for cell membrane imaging

We demonstrate subwavelength sectioning on biological samples with a conventional confocal microscope. This optical sectioning is achieved by the phenomenon of supercritical angle fluorescence, wherein only a fluorophore next to the interface of a refractive index discontinuity can emit propagating components of radiation into the so-called forbidden angles. The simplicity of this technique allows it to be integrated with a high numerical aperture confocal scanning microscope by only a simple modification on the detection channel. Confocal-supercritical angular fluorescence microscopy would be a powerful tool to achieve high-resolution surface imaging, especially for membrane imaging in biological samples.

The lattice Boltzmann method for one-dimensional transient radiative transfer in graded index gray medium

The lattice Boltzmann method (LBM) is extended to solve transient radiative transfer in one-dimensional slab containing absorbing and scattering media with graded index subjected to a short square laser irradiation. By using a fully implicit backward differencing scheme to discretize the transient term in the radiative transfer equation, a new type of lattice structure is devised. Firstly, for the case of the refractive index matched boundary, LBM solutions to transient radiative transfer in graded index medium are validated by comparison with results reported in the literature. Afterward, LBM is employed to investigate transient radiative transfer in graded index medium with a refractive index discontinuity at the boundaries. Effects of the graded index distributions, the optical thickness, and scattering phase function on transmittance and reflectance signals are investigated, and several interesting trends on the time-resolved signals are observed and analyzed.

One-dimensional transient radiative transfer by lattice Boltzmann method

The lattice Boltzmann method (LBM) is extended to solve transient radiative transfer in one-dimensional slab containing scattering media subjected to a collimated short laser irradiation. By using a fully implicit backward differencing scheme to discretize the transient term in the radiative transfer equation, a new type of lattice structure is devised. The accuracy and computational efficiency of this algorithm are examined firstly. Afterwards, effects of the medium properties such as the extinction coefficient, the scattering albedo and the anisotropy factor, and the shapes of laser pulse on time-resolved signals of transmittance and reflectance are investigated. Results of the present method are found to compare very well with the data from the literature. For an oblique incidence, the LBM results in this paper are compared with those by Monte Carlo method generated by ourselves. In addition, transient radiative transfer in a two-Layer inhomogeneous media subjected to a short square pulse irradiation is investigated. At last, the LBM is further extended to study the transient radiative transfer in homogeneous medium with a refractive index discontinuity irradiated by the short pulse laser. Several trends on the time-resolved signals different from those for refractive index of 1 (i.e. refractive-index-matched boundary) are observed and analysed.

Analytic evaluation of diffuse fluence error in multilayer scattering media with discontinuous refractive index

A simple analytic method of estimating the error involved in using an approximate boundary condition for diffuse radiation in two adjoining scattering media with differing refractive indices is presented. The method is based on asymptotic planar fluences and enables the relative error to be readily evaluated without recourse to Monte Carlo simulation. Three examples of its application are considered: (1) evaluating the error in calculating the diffuse fluences at a boundary between two media with differing refractive index and dissimilar scattering properties, (2) the dependence of the relative error in a multilayer medium with discontinuous refractive index on the ratio of the reduced scattering coefficient to the absorption coefficient μ(s)'/μ(a), and (3) the parametric dependence of the error in the radiant flux J(s) at the surface of a three-layer medium. The error is significant for strongly forward-biased scattering media with non-negligible absorption and is cumulative in multilayered media with refractive index increments between layers.

Extension of the Kubelka–Munk theory for fluorescent turbid media to a nonopaque layer on a background

Photoluminescence is one of the processes by which photons are emitted after the absorption of incoming photons at a higher energy. But the yield and spectral band shape of the emission can be altered by the optical properties of the luminophore environment through scattering and absorption. To understand these effects on a photoluminescent turbid layer, the Kubelka–Munk model, which is a two-flux approximation of the radiative transfer equation, can be used. Compared to previous works, this translucent layer can be applied on a colored opaque background. The model takes into account the absorption, scattering, and luminescent properties of the layer and the reflection by the background, for both the light excitation and the light emission. The competition between these different optical interactions is studied; e.g., the model can predict the presence of an emission maximum by increasing the thickness of the luminescent layer on a light background. Moreover, the model is extended to two important cases: the presence of a photoluminescent background and the effect of a refractive index discontinuity.

Accuracy of three-point finite difference approximations for optical waveguides with step-wise refractive index discontinuities

AbstractA rigorous truncation error analysis of three-point finite difference approximations for optical waveguides with step-wise refractive index discontinuities is given. As the basis for the analysis we use the exact coefficients of the series that expresses the field value at a given finite difference node in terms of the field value and its derivatives at a neighbouring node. This series is applied to develop a rigorous formalism for the truncation error analysis of the three-point finite difference approximations used in the numerical modelling of light propagation in optical waveguides with step-wise discontinuities of the refractive index profile. The results show that the approximations reach O(h2) truncation error only asymptotically for sufficiently small values of the mesh size.

Arbitrary truncation order three-point finite difference method for optical waveguides with stepwise refractive index discontinuities

An exact finite difference (FD) representation of the second-order derivative on three nodes is presented and used to obtain an FD algorithm that allows achieving an arbitrary truncation order. The FD weights are calculated analytically using the series that expresses the field value at a given FD node in terms of the field value and its derivatives at a neighboring node, when a stepwise discontinuity in the refractive index distribution is present between the nodes. The results obtained confirm that the proposed algorithm is accurate, efficient, and achieves the predicted improved performance.

Wave propagation through a dielectric layer containing densely packed fibers

This paper presents the theoretical formulation for the propagation of electromagnetic wave through a dielectric layer containing a random dense distribution of fibers. The diameter of the fibers is comparable to the inter-fiber spacing and wavelength of the incident radiation, but is much smaller than the thickness of the layer. Discontinuity of refractive index across the boundaries of the dielectric layer resulted in multiple internal reflection of both the primary source wave and the scattered waves. As a result the incident waves on the fibers consist of the multiply-reflected primary waves, scattered waves from other fibers, and scattered–reflected waves from the boundaries. The effective propagation constant of the dielectric fiber layer was developed by utilizing the Effective field-Quasicrystalline approximation. The influence of the refractive index of the dielectric medium on the radiative properties of a dense fiber layer was examined by means of numerical analyses.

High-Resolution Photoacoustic Imaging of Ocular Tissues

Optical coherence tomography (OCT) and ultrasound (US) are methods widely used for diagnostic imaging of the eye. These techniques detect discontinuities in optical refractive index and acoustic impedance, respectively. Because these both relate to variations in tissue density or composition, OCT and US images share a qualitatively similar appearance. In photoacoustic imaging (PAI), short light pulses are directed at tissues, pressure is generated due to a rapid energy deposition in the tissue volume and thermoelastic expansion results in generation of broadband US. PAI thus depicts optical absorption, which is independent of the tissue characteristics imaged by OCT or US. Our aim was to demonstrate the application of PAI in ocular tissues and to do so with lateral resolution comparable to OCT. We developed two PAI assemblies, both of which used single-element US transducers and lasers sharing a common focus. The first assembly had optical and 35-MHz US axes offset by a 30° angle. The second assembly consisted of a 20-MHz ring transducer with a coaxial optics. The laser emitted 5-ns pulses at either 532 nm or 1064 nm, with spot sizes at the focus of 35 μm for the angled probe and 20 μm for the coaxial probe. We compared lateral resolution by scanning 12.5 μm diameter wire targets with pulse/echo US and PAI at each wavelength. We then imaged the anterior segment in whole ex vivo pig eyes and the choroid and ciliary body region in sectioned eyes. PAI data obtained at 1064 nm in the near infrared had higher penetration but reduced signal amplitude compared to that obtained using the 532 nm green wavelength. Images were obtained of the iris, choroid and ciliary processes. The zonules and anterior cornea and lens surfaces were seen at 532 nm. Because the laser spot size was significantly smaller than the US beamwidth at the focus, PAI images had superior resolution than those obtained using conventional US. (E-mail: rsilverman@rri-usa.org)

Rat muscle opacity decrease due to the osmosis of a simple mixture

It is known that the fibrous structure of muscle causes light scattering. This phenomenon occurs due to the refractive index discontinuities located between muscle fibers and interstitial fluid. To study the possibility of reducing light scattering inside muscle, we consider its spectral transmittance evolution during an immersion treatment with an optical clearing solution containing ethanol, glycerol, and distilled water. Our methodology consists of registering spectral transmittance of muscle samples while immersed in that solution. With the spectral data collected, we represent the transmittance evolution for some wavelengths during the treatment applied. Additionally, we study the variations that the treatment has caused on the samples regarding tissue refractive index and mass. By analyzing microscopic photographs of tissue cross section, we can also verify changes in the internal arrangement of muscle fibers caused by the immersion treatment. Due to a mathematical model that we develop, we can explain the variations observed in the studied parameters and estimate the amount of optical clearing agent that has diffused into the tissue samples during the immersion treatment. At the end of the study, we observe and explain the improvement in tissue spectral transmittance, which is approximately 65% after 20 min.

Revisiting atomic force microscopy force spectroscopy sensitivity for single molecule studies

Recently, the rapid advances in quantitative biology and polymer science have led to the atomic force microscope (AFM) being extensively employed for single-molecule force spectroscopy. Deflection sensitivity, a critical factor in single molecule force spectroscopy, is changed due to the change in bending shape of AFM cantilever when a single molecule is attached to the AFM cantilever tip. We quantitatively study this variation in the deflection sensitivity by modeling the single molecule as an AFM tip coupled spring. We further propose correction factors for the deflection sensitivity in various cases of single molecule studies. Since many single biomolecule studies are conducted in aqueous environment, we outline and include the complications induced by the refractive index discontinuity at the air-glass-liquid medium interfaces, laser spot size, and spot location on the cantilever. Finally we present correction factor charts for easy calculation of correction factors for a wide variety of stiffness of single molecules.

The Influence of Out-of-Focus Sample Regions on the Surface Specificity of Confocal Raman Microscopy

This paper considers the quantitative implications of out-of-focus regions on the lateral and depth resolution of Raman microscopy, with special regard for the surface specificity of the technique. It builds on work that has recently appeared in the literature which shows that with transparent samples, signals can originate throughout a large extended illumination volume, even though most of this region is out of focus with regard to the confocal aperture. This gives rise to weak but readily detectable spectral contributions from regions that are tens of micrometers from the point of tightest focus, an effect that is easily demonstrated if the laser is focused far above the sample surface. When we integrate the signals arising throughout this extended volume, the resulting total signal can be significant with respect to the Raman signals originating from the point of focus; this has obvious implications for surface specificity and depth resolution. Furthermore, as one moves the focal point through and above a sample surface, signals from thick transparent samples decay relatively slowly compared with thin or opaque ones, where the extended focal volume is irrelevant. This means that on moving above the surface of a thinly coated thick substrate during a confocal axial scan, the substrate-to-coating signal ratio increases dramatically, contrary to intuition. Consequently, confusing spectral artifacts arise if one focuses above the sample surface, either inadvertently when mapping an uneven sample, or deliberately in an attempt to improve surface specificity. In this work we show how a simple analytical model can predict the surface/substrate signal ratio as a function of distance above the surface. The model is validated using experimental data from monofilms and coated films. Furthermore, we show how this effect is not limited to the confocal axial profiling geometry. Similar effects are obtained when one scans laterally beyond the edge of mechanically prepared cross-sections due to an extended, out-of-focus laser field that can sample lateral regions far to the side of the optimum focus. This effect can lead to very confusing results, such as spectra from the substrate increasing in absolute intensity as one moves beyond the edge of the coating into the air. These observations, which as far as we are aware have not previously been reported, are rationalized using a simple ray-tracing description, which shows the potential for coupling light into the cross-section, which acts as a waveguide. These effects have a completely different origin than the well-known anomalies that are introduced by refraction and spherical aberration; even with a perfect, aberration-free system, the extended focal volume may cause significant degradation in depth resolution. Although the effects have been demonstrated with simple film systems, they have the potential to impact the results from Raman mapping and imaging of any samples that contain significant refractive index discontinuities, which can potentially cause refraction and waveguiding, or that have compositional depth gradients and an uneven sample surface.

Coupling effects of refractive index discontinuity, spot size and spot location on thedeflection sensitivity of optical-lever based atomic force microscopy

Atomic force microscopy (AFM) plays an essential role in nanotechnology and nanoscience.The recent advances of AFM in bionanotechnology include phase imaging of living cells anddetection of biomolecular interactions in liquid biological environments. Deflectionsensitivity is a key factor in both imaging and force measurement, which is significantlyaffected by the coupling effects of the refractive index discontinuity between air, the glasswindow and the liquid medium, and the laser spot size and spot location. The effectsof both the spot size and the spot location on the sensitivity are amplified bythe refractive index discontinuity. The coupling effects may govern a transitionof the deflection sensitivity from enhancement to degradation. It is also foundthat there is a critical value for the laser spot size, above which the deflectionsensitivity is mainly determined by the refractive index of the liquid. Experimentalresults, in agreement with theoretical predication, elucidate the coupling effects.

3-D Full-Vectorial Analysis of Strong Optical Waveguide Discontinuities Using Pade Approximants

A full-vectorial 3-D numerical method applicable to high-index contrast optical waveguide discontinuities is presented. Rigorous treatment of the longitudinal boundary condition is incorporated in the formulation. The square root of the characteristic matrix is approximated using Padeacute approximants which results in an efficient implementation. The biconjugate gradient stabilized method is utilized to iteratively calculate the reflected and transmitted fields. A preconditioner is proposed which results in reduced number of iterations. The proposed method is applied to various optical waveguide facets exhibiting strong transverse and longitudinal refractive index discontinuities. In all cases, the modal reflectivities of the fundamental TE-Like and TM-Like modes are calculated for both the full-vectorial and the semi-vectorial formulations. Significant difference in the calculated modal reflectivity is seen between the full and semi-vectorial models. The error in the power balance remains low in the full-vectorial case irrespective of the waveguide dimensions. However, in the semi-vectorial case, the error in the power balance is found to increase when the waveguide width is reduced

Inverse problem of reflection of electromagnetic waves from layered inhomogeneous plasma-like structures with refractive-index discontinuity

To reconstruct the distribution of free carriers in a layered inhomogeneous plasma-like half-space during the electromagnetic-wave reflection, we derive the Gelfrand-Levitan-Marchenko integral equation for structures with refractive-index discontinuity by the inverse problem method. Exact model solutions of the generalized equations are analyzed. The applicability limits and scope of these exact solutions for reconstruction problems are shown.

Study of ray propagation mechanisms in MultiStep index optical fibers with use in computational methods

A comprehensive analysis of the various ray propagation mechanisms that take place between the different layers of highly multimode multistep index (MSI) fibers is presented. A suitable analytical expression that allows the evaluation of the power fraction transferred from a certain layer to another one from rays undergoing either refraction or frustrated total internal reflection is provided. This expression is valid for any MSI fiber of any number of layers with a radially decreasing refractive index profile. Frustrated total internal reflection is originated as a consequence of the discontinuous refractive index profile inherent in this type of fibers, and unlike in step-index and graded-index fibers, it can also affect bound rays. Such an expression will allow determination of the remaining ray power along the fiber in each possible propagation state created as a consequence of this phenomenon. The approximations made will be of great benefit for computational purposes since they will lead to a considerable simplification in the numerical prediction of ray propagation in these fibers.