Determination Of Refractive Index Profile Research Articles

Determination of Refractive Indices From the Mode Profiles of UV-Written Channel Waveguides in ${\hbox {LiNbO}}_{3}$-Crystals for Optimization of Writing Conditions

We report on a method for the simultaneous determination of refractive index profiles and mode indices from the measured near-field intensity profiles of optical waveguides. This method has been applied to UV-written single-mode optical waveguides in LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> for the optimization of the writing conditions. The results for the waveguides written with light of the wavelengths 275, 300.3, 302, and 305 nm for different writing powers and scan speeds reveal that for optimum writing conditions a maximum possible refractive index change of ~0.0026 can be achieved at a value of 632.8 nm transmitting wavelength. The computation process used in the presented technique may also become useful to extract absolute refractive index values of any slowly varying graded index waveguide.

Automatic determination of refractive index profile of fibers having regular and/or irregular transverse sections considering the refraction of light rays by the fiber

A new model, using non-destructive two- and/or multiple-beam interferometric techniques, is suggested for measuring the refractive index profile of fibers having regular and/or irregular cross-sectional shape taking into consideration the refraction of the light rays by the fiber. The proposed model is applied for three different fibers having different cross-sectional shapes and different refractive index profiles. These fibers are PPT, homogeneous fiber, with circular cross-section, graded index optical fiber of circular cross-sectional shape and Dralon fiber of irregular cross-section. To validate the proposed model it is used, firstly, to calculate the index profile for a standard PPT fiber. Secondly, the calculated results for the irregular Dralon fiber and GR-IN optical fiber are compared with that calculated using other conventional method. From this comparison, we recommend that the refraction must be taken into account to obtain accurate results especially for birefringent fibers and graded index optical fibers.

Automatic determination of refractive index profile, sectional area, and shape of fibers having regular and/or irregular transverse sections

A new method based on a mathematical model and a computer program is suggested to determine the refractive index profile of fibers having regular and/or irregular transverse sectional shape. Microinterferogram of both multiple-beam Fizeau fringes and the duplicated image from two-beam interference microscope are used for the determination of refractive index profile, cross-sectional area and shape of three different types of fibers. To confirm the suggested model, the calculated area and the shape of the transverse section of these fibers are compared with those results obtained using conventional methods.

Determination of refractive index profiles of planar buried waveguides on the basis of a set of modal propagation constants

In the work the algorithm involving the reconstruction of refractive index profiles of planar buried waveguides based on modal equation was proposed. The analysis testing the algorithm with the help of functions simulating buried profiles was carried out. Using ion-exchange technique in glass substrate, buried waveguide structures were manufactured. Propagation constants of all modes of those structures were determined by a prism coupling method with the measurements of synchronic angles. On the basis of the measured propagation constants the reconstruction of their refractive index distribution was carried out with the help of the proposed algorithm. The obtained results were compared with the results of interferometric investigations.

Determination of refractive index profile of partially and highly oriented fibers using double refracting interference microscopy

Double refracting polarizing interference microscope designed by Pluta is used with a suggested method to determine the refractive index profile and birefringence profile of partially and highly oriented fibers. The application of this method depends on using Pluta polarizing interference microscope in two positions (crossed position for the duplicated images and subtractive position for the nonduplicated image of the fiber). The mathematical representation of the suggested method is given. The refraction of the light beam inside the fibers is taken into consideration while measuring the fringe shift profile. The refractive index profiles of polypropylene fiber with draw ratio 3.5 are determined using the conventional method. The results are compared with those obtained with the suggested method and found to be in good agreement. The suggested method is applied to determine the refractive index profile of poly(aryl ether ether ketone) partially oriented fiber and poly(ethylene terephthalate) highly oriented fiber. The diffraction of He–Ne laser beam is used to determine the average diameters of these fibers. Microinterferograms are given for illustration. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 87: 2341–2347, 2003

Determination of Refractive Index Profile and Material Dispersion of Step Index Optical Fibers using Tow-beam Interferometric Method

Determination of Refractive Index Profile and Material Dispersion of Step Index Optical Fibers using Tow-beam Interferometric Method

Determination of refractive index profiles of gradient optical waveguides by ellipsometry

Ag +-Na + and K +-Na + ion-exchanged optical waveguides in soda-lime glass are characterised by ellipsometry. Refractive index profiles of the waveguides are calculated from ellipsometric multiple angle of incidence data using the Newton-Kantorovitch type iterative procedure and compared with those reconstructed by inverse WKB method. It is demonstrated that such continuous profiles with relatively small index gradient (of the order of 0.1 and 0.01), extending to few micrometers in depth, can be determined by ellipsometric measurements. A good agreement is found between results obtained by ellipsometry and by the inverse WKB method at depths above 500–600 nm, while there is a difference in the subsurface region, where ellipsometry is more sensitive to the quality of the surface. The profiles obtained by the two methods are consistent if the surface thin layer is etched.

Experimental study of copper–alkali ion exchange in glass

Copper–alkali ion exchange was performed by immersing different silicate glasses (soda-lime and BK7) in different molten eutectic salt baths (CuSO4:Na2SO4 and CuSO4:K2SO4). The obtained optical waveguides were characterized by m-lines spectroscopy for the determination of refractive index profiles, and by secondary ion mass spectrometry for the concentration profiles of the ion species involved in the exchange process. The different oxidation states of copper inside the glass structure were studied by electron paramagnetic resonance and x-ray absorption techniques. Interdiffusion copper coefficients were also determined. The Cu–alkali exchange was observed to give rise to local structural rearrangement of the atoms in the glass matrix. The Cu+ ion was found to mainly govern the exchange process, while competition between Cu–Na and K–Na exchanges occurred when a potassium sulfate bath was used. In this case, significant waveguide modal birefringence was observed.

Atomic force microscopy for the determination of refractive index profiles of optical fibers and waveguides: A quantitative study

The use of preferential etching and atomic force microscopy to measure refractive index profiles of optical fibers is investigated. Both the etch rate and the position of lateral features are shown to be independent of etch time. An elliptical core fiber was studied and the resultant profile was found to be in qualitative agreement with the preform index profile. It is shown, however, that the ellipticity of the core has changed during the drawing process. The method was extended to fluorine and germanium doped planar waveguides and the results correlated with the fabrication process.

Determination of refractive-index profiles by a combination of visible and infrared ellipsometry measurements

Model inhomogeneous silicon oxynitride films were produced by ion-beam sputtering and characterized by ellipsometry in the visible and infrared ranges. These films exhibit strong intentional gradients of the refractive index that cannot be considered linear. A discrete description of the index profile with a few layers or a continuous description with a polynomial are examined; regressions by the use of measurements in the visible only or in the total spectral range (visible and infrared) are performed. Acquisition of data in an extended range is found to be a guarantee of the reliability of the calculated index profiles.

Method of refractive index profile reconstruction from effective index of planar optical monomode waveguides: Application to potassium ion-exchanged waveguides

A simple nondestructive method for determination of refractive index profile of single-mode waveguides using the measured effective refractive indexes is proposed. The method is based on the extraction of the additional data about the waveguide profile from the investigation of its evolution with the duration of fabrication process. The profile reconstructions are carried out using an appropriate algorithm in the frames of the WKB approximation. The method is applied for few- and single-mode waveguides, obtained by K/sup +/-Na/sup +/ field assisted ion exchange. The results are corroborated with the reconstruction from the effective refractive indexes measured at a shorter wavelength, as well as with profile study by means of step-by-step etching.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On determination of refractive index profile in optical waveguides formed by ion implantation

We report a refinement of the Fermi function approximation to compute the Refractive Index Profile of optical waveguides formed by ion implantation. The computation is carried out at an exact value of the phase step at the upper boundary of a planar optical waveguide with allowances for the perturbative influence of the prism coupling element. It is shown that under real experimental conditions the method can be simplified and is applicable to the low-mode waveguides.

Determination of refractive index profile in optical waveguides formed by ion implantation

The possibility is considered of determining the refractive index profiles of optical planar waveguides, formed by ion implantation in YAG:Nd 3+ crystals, by measuring the mode spectrum of the waveguide. It is indicated that the step-index approximation is the simplest and most convenient method for calculating the average parameters of the waveguides and that the most exact description of the refractive index distribution for the waveguide of this type corresponds to using a Fermi-function approximation.

Refractive-index profile determination of single-mode fibres by far-field power measurements at 1300 nm

The refractive-index profile and dispersion data are computed from the measured far-field exit radiation pattern of the fundamental mode. Instead of Fourier-transforming the far field numerically, the near field is calculated by fitting a series of Gauss-Laguerre functions to the far field, and by further using analytical methods. The procedure is inherently insensitive against random measurement errors. We demonstrate the feasibility of this technique for the first time at a wavelength of 1300nm.

Nondestructive determination of refractive index profile of an optical fiber: backward light scattering method

A new nondestructive technique is presented for determining the refractive index profile of an optical fiber from its backscattered pattern arising from a normally incident laser beam to the fiber axis. The proposed method requires no sample preparation or index matching liquid. The principle of the method is to construct a deflection function from the measured pattern. The index profile can then be determined by the inversion of an Abel integral equation. Good agreement is obtained between the index profile determined by this technique and that measured by the near-field scanning technique.

Nondestructive determination of refractive-index profile and cross-sectional geometry of optical-fibre preform

A nondestructive method is presented to determine simultaneously the refractive-index profile and the cross-sectional geometry of a preform. In this method, a plane wave is made to impinge on the preform laterally and the power distribution of the scattered pattern is recorded. From the recorded power, the ray pathlength difference is calculated. After the preform has been rotated through 360° and the necessary data collected, a numerical inversion is performed to obtain the index profile and cross-sectional geometry.

Nondestructive determination of refractive-index profile of an optical fibre: forward light scattering method

A nondestructive technique is presented for determining the refractive-index profile of an optical fibre from its forward-scattered pattern arising from a normally incident laser beam. This method does not require any index-matching liquid and is not limited to single-mode fibres. It uses as essential information only the angular positions of the extrema in the measured pattern.

Refractive-index profile determination of optical fibers by spatial filtering

Refractive-index profile determination of optical fibers by spatial filtering

A quick method for the determination of refractive index profiles for diffused optical waveguides

An analogy between the mode equation and Schrodinger's equation has been used to show that the important parameter to study in waveguiding systems is the square of the effective index of a mode rather than the effective index itself. This method was used to interpret simply and analytically some results published earlier. The agreement with the interpretation published originally is shown to be very good. No computing is involved. A quasi-linear index profile has been observed.