Mathematical modelling of the refractive index reconstruction through global optimization

We examine a mathematical model of non-destructive testing of planar waveguides, based on numerical solution of a nonlinear integral equation. Such problem is ill-posed, and the method of Tikhonov regularization is applied. To minimize Tikhonov functional, and find the parameters of the waveguide, we use two new optimization methods: the cutting angle method of global optimization, and the discrete gradient method of nonsmooth local optimization. We examine how the noise in the experimental data influences the solution, and how the regularization parameter has to be chosen. We show that even with significant noise in the data, the numerical solution is of high accuracy, and the method can be used to process real experimental da.ta..

Reconstruction of the refractive index profile of planar waveguides using ray tracing analysis

We propose a method for refractive index profiling based on measuring coordinates and angles of laser beams passing across the waveguide layer. Calculations are performed by solving an integral equation using new global optimization methods.

Abnormal transmittance of refractive-index-modified ZnO/organic hybrid films

The refractive index of ZnO/organic nanocomposite films was modified in the range from 1.44 to 1.55, while maintaining high visible transparency. The transparency of the nanocomposite films showed an abnormal behaviour as a function of the loading level of inorganic particles, because it did not decrease according to the Beer-Lambert law, but rather saturated to a near-constant value at high particle loading levels above 8 vol.-%. On the other hand, the refractive index of the film showed good agreement with the Bruggemann model, linearly increased as particle concentration increased. This result indicates the possibility of fabricating highly transparent nanocomposite films with controlled refractive indices.

Abnormally high optical transmittance of refractive-index modified ZnO / organic hybrid films

Hybrid films consisting of ZnO nanoparticles and organic matrices were fabricated at particle concentration levels of up to 60 wt%. The correlation between the refractive index and optical transmittance in the visible light region was investigated. The refractive index of the hybrid films was modified in a continuous manner in the range from 1.44 to 1.55. The refractive index increased linearly as a function of particle concentration. On the other hand, optical transmittance showed little change above the particle volume fraction of 0.08.

Refractive index tomography of turbid media by bifocal optical coherence refractometry

We demonstrate tomographic imaging of the refractive index of turbid media using bifocal optical coherence refractometry (BOCR). The technique, which is a variant of optical coherence tomography, is based on the measurement of the optical pathlength difference between two foci simultaneously present in a medium of interest. We describe a new method to axially shift the bifocal optical pathlength that avoids the need to physically relocate the objective lens or the sample during an axial scan, and present an experimental realization based on an adaptive liquid-crystal lens. We present experimental results, including video clips, which demonstrate refractive index tomography of a range of turbid liquid phantoms, as well as of human skin in vivo.

Planar waveguide refractive index profile reconstruction using global optimization

The approach taken here of reconstruction of the refractive index profile of planar waveguides involves solving a non-linear integral equation with Tikhonov regularization. Using global optimization with the new cutting angle and discrete gradient methods has yielded an acceptable reconstruction, even in the presence of significant noise in the data.

Measurement of the refractive index of soft contact lenses during wear

Purpose: To determine whether the refractive index (RI) of a soft contact lens can be evaluated using refractometry while the lens remains on the eye and to compare this with more traditional ex vivo RI measurements.

Methods: A slitlamp apparatus was modified to incorporate a customized Atago hand refractometer. With a double-masked study design, nine adapted symptomatic soft contact lens wearers wore a contact lens in each eye (lotrafilcon B and etafilcon A) in a randomized order. In vivo RI was determined from the relative Brix scale measurements immediately after lens insertion and after 1 and 10 hr of lens wear. Ex vivo refractometry was performed after 10 hr of lens wear for comparison. Means ± standard errors of the means are reported.

Results: In vivo RI values at baseline were 1.422 ± 0.0004 (lotrafilcon B) and 1.405 ± 0.0021 (etafilcon A); after 1 hr of lens wear, values were 1.423 ± 0.0006 and 1.408 ± 0.0007, respectively; and after 10 hr of lens wear, values were 1.424 ± 0.0004 and 1.411 ± 0.0010, respectively. Ex vivo RI values at the end of the 10 hr wearing period were 1.424 ± 0.0003 (lotrafilcon B) and 1.412 ± 0.0017 (etafilcon A). The change in in vivo RI across the day was statistically significant for the etafilcon A lens (repeated-measures analysis of variance, P<0.01) but not for the lotrafilcon B lens (P>0.05).

Conclusions: This novel adaptation of refractometry was able to measure the RI of soft contact lenses during wear (without lens removal). End of day RI measurements using in vivo and ex vivo refractometry were comparable with each other. Future work is required to determine whether this in vivo method can improve our understanding of the relationships between soft contact lens RI, hydration, on-eye lens performance, and symptomology.

Refractive indices and order parameters of two liquid crystals

Refractive indices have been measured throughout the nematic phase of 4-n-pentyl-4'cyanobiphenyl (5CB) and the smectic A and nematic phases of 4-n-octyl-4'-cyanobiphenyl (8CB). The Vuks and Neugebauer methods of calculating the order parameter are compared. Without knowledge of the molecular polarisabilities it is only possible to calculate a quantity proportional to the order parameter, and within this limitation it is found that the two methods give identical results. The order parameter is scaled using the extrapolation method suggested by Haller [14]. Using a suitable average of the refractive indices and the density data of Gannon and Faber [9], it is shown that the Lorentz-Lorenz relation is obeyed over a 2 % density range in 5CB.

An approximate numerical technique for characterizing optical pulse propagation in inhomogeneous biological tissue

An approximate numerical technique for modeling optical pulse propagation through weakly scattering biological tissue is developed by solving the photon transport equation in biological tissue that includes varying refractive index and varying scattering/absorption coefficients. The proposed technique involves first tracing the ray paths defined by the refractive index profile of the medium by solving the eikonal equation using a Runge-Kutta integration algorithm. The photon transport equation is solved only along these ray paths, minimizing the overall computational burden of the resulting algorithm. The main advantage of the current algorithm is that it enables to discretise the pulse propagation space adaptively by taking optical depth into account. Therefore, computational efficiency can be increased without compromising the accuracy of the algorithm.

Forces due to structure in a thin liquid crystal film

Measurements of the force as a function of distance between two solids separated by a liquid crystal film give information on the structure of the film. We report such measurements for two molecularly smooth surfaces of mica separated by the nematic liquid crystal 4'-n-pentyl 4-cyanobiphenyl (5CB) in both the planar and homeotropic orientations at room temperature. The force is determined by measuring the deflection of a spring supporting one of the mica pieces, while an optical technique is used to measure the film thickness to an accuracy of ± (0.1-0.2) nm. The technique also allows the refractive indices of the nematic to be measured, and hence a determination of the average density and order parameter of the liquid crystal film as a function of its thickness. Three distinct forces were measured, each reflecting a type of ordering of the liquid crystal near the mica surfaces. The first one results from elastic déformation in the liquid crystal ; it was only observed in a twisted planar sample where the 5CB molecules are oriented in different directions at the two mica surfaces. The second, measured in both the planar and homeotropic orientations, is attributed to an enhanced order parameter near the surfaces. Both of these are monotonic repulsive forces measurable below 80 nm. Finally, there is a short-range force which oscillates as a function of thickness, up to about six molecular layers, between attraction and repulsion. This results from ordering of the molecules in layers adjacent to the smooth solid surface. It is observed in both the planar and homeotropic orientations, and also in isotropic liquids.

Analytic solution for the three-layer multiple beam interferometer

We present a simple analytic solution for the condition of constructive interference for light transmitted through an interferometer incorporating three ideally transparent layers of arbitrary thickness and refractive index. We also consider the effect of adding two metallic coatings to the outer surfaces of the interferometer and give empirical expressions for the associated phase changes for silver coatings on silica, sapphire, and mica substrates. A particular application to fringes of equal chromatic order can be utilized to obtain precise measurements of the thickness of extremely thin films sandwiched between two substrates.

Tuneable optical waveguide based on dielectrophoresis and microfluidics

In this work, an array of dielectrophoretic curved microelectrodes patterned in a microfluidic channel and integrated with a multimode rib polymeric waveguide is demonstrated. The microfluidic channel is infiltrated with suspended silica (SiO2) and tungsten trioxide (WO3) nanoparticles. The optofluidic system is found to be sensitive and responds not only to the infiltration of nanoparticle suspensions in the microfluidic channel, but also to the magnitude and frequencies of dielectrophoretic forces applied on the nanoparticles. The nanoparticles can be uniformly concentrated or repelled from the region between the curved microelectrode tips forming either a dense stream of flowing nanoparticles or a region void of nanoparticles in the evanescent sensitive region of the polymeric waveguide. The concentration and repulsion of nanoparticles from this region creates a refractive index gradient in the upper cladding of the polymeric waveguide. These conditions made it possible for light to either remain guided or be scattered as a function of dielectrophoretic settings applied on the nanoparticles. The results demonstrate that we successfully developed a novel tuneable polymeric waveguide based on dielectrophoretic assembly of nanoparticles suspended in fluids.

A S-parameters-based detection method for a multilayer SPR biosensor

In this paper, S-parameters investigation of a variable incidence angle multilayer SPR biosensor is presented. Both magnitude and phase of the S-parameters are taken into account in the investigation. The work presented in this paper is the first attempt to apply S-parameters analysis to a multilayer SPR biosensor. The goal is to improve sensitivity through involving S-parameters including their phase values. In addition, further investigation is carried out to understand the relationship between the S-parameters and thickness of biomolecular layer and also the design parameters including the number of graphene layers.