Profile of refractive index

The theoretical approach is based on the solution to the mixed type linear/nonlinear generalized Schrodinger equation for spatiotemporal envelope of electrical field with account of transverse spatial derivatives and the transverse profile of refractive index. In the quasi-static approximation, this equation is reduced to the linear/nonlinear Schrodinger equation for spatiotemporal pulse envelope with temporal coordinate given as a parameter. Then the excitation problem can be formulated for a set of stationary light beams with initial amplitude distribution corresponding to temporal envelope of the initial pulse. 

Olaofe and Levine (4) investigated the scattering for concentric spheres and spherically symmetric inhomogeneous spheres with Cauchy and parabolic distributions of the radial profile of refractive index. Comparisons were with the volume-weighted refractive index... 

The fixation process (thermo, photo, y-radiation, etc.) of the gradient of concentration distribution of monomer-diffuser, and, respectively of profile of refractive index distribution. 

This approach allows one to create by gamma-irradiation of polymer films with a profile of refractive index distribution, which is a necessary condition for the creation of a profile which achieves correction of residual aberration in optical system, and the eieation of the integral optics elements, light-guides and transformers of light beams [76]. 

Some assumption is needed to relate the profile of refractive index to that of density, when the latter is neither a step-function, on the one hand, nor, on the other, a function which varies only over lengths comparable with the wavelength of the light. Thus only one imperfectly defined parameter, a thickness, can be measured, and this is typically 0 79 0 0Snm for argon at 90 K. In a mixture the adsorptions can be estimated by this technique."... 

Based on ellipsometric imaging of titania films prepared from small (-0.5nm diameter) precursors [9,10], it is likely that the elimination of porosity in the deposited film (A in Fig. 17) occurs primarily at the final stage of drying. Figures 20a and 20b show the profiles of refractive index and volume fraction solids, (j), as a function of distance from an arbitrary... 

Factors that promote creation of a gradient distribution no of copolymeric compositions include temperature, concentration, gravitation and electric field, the field of initiation, etc. Of great importance also is the search for technological regimes of formation and fixing (if necessary) of the profile of refractive index distribution obtained, which would provide materials with close to the ideal focusing distribution. 

Figure 10. Profile of refractive index for polymeric rod lens based on MMA-BzMA (4 1)...

It seems desirable to consider this approach of creation of gradient elements in more detail, because the chemical processes on which it is based are rather ordinary and quite well studied, especially for homogeneous polymer-analogous transformations, and this is not usually the case in producing materials for gradient optics. The principles of solid chlorination of PP-films that should be used for creation of thin-layer selfocs with the given profile of refractive index distribution are discussed below. 

Figure 24 shows an example of the axial profile of refractive index distribution in axial poly(chloropropylene) selfoc. 

In this Figure, the continuous curve represents a parabola branch normalized for the given n and r . Crosses mark experimental points obtained by adding the measured value of refractive index change A to the initial value n = 1.495 for the part of the PP film present. On the graph, the first ordinate shows the duration of exposure of that part of the PP film in the chlorination chamber. If a folded PP film is placed in the chamber, a profile of refractive index in the form of a parabola with both branches can be obtained. 

The present Section describes devices and methods for obtaining cylindrical polymeric objects with given radial composition gradient providing a given profile of refractive index distribution. 

The method of a eylinder preform production of an arbitrary diameter with the given radial gradual profile of refractive index distribution based on polymers, from which optical fibers ean be molded eapable of image transmission, is discussed below. 

This technology also allows the control of refractive index profiles by doping. AH vapor-phase techniques use a vapor stream of volatile haUdes such as SiCl, GeCl, BCl, or POCl, and gases such as CI2 or O2. The reactants are oxidized and deposited onto a substrate to produce a soHd glass preform which is then drawn into a fiber. The variations of the technique differ in the way the reactants are oxidized (16). 

Chomat M., Berkova D., Matejec V., Ctyroky J., Kasik I., The detection of refractive-index changes by using a sensing fiber with an inverted parabolic index profile, Proc. SPIE 3860 (1999), Boston. 

The variation of refractive index n(D) of the medium separating the mica surfaces is shown in figure 6b (for PE02), both before and after adsorption of polymer, as well as following replacement of the polymer solution by pure electrolyte after adsorption. The results show that adsorption of the PEO is essentially irreversible, and that little polymer appears to desorb either following compression/decompression cycles, or in pure solvent. The value of the adsorbance T estimated from the n(D) profiles is 4 1.5 mg m-2 for both polymers. 

The theory of a straight and uniform MNF with a circular cross-section of radius a and a step-index profile is well developed59-61. A section of an MNF is shown in Fig. 13.3 in Cartesian coordinates (pc,y,z). The distribution of refractive index along the radius r = Jx2 + y2 of such MNF is... 

Figure 3.38. Principle of the photorefractive effect By photoexcitation, charges are generated that have different mobilities, (a) The holographic irradiation intensity proHle. Due to the different diffusion and migration velocity of negative and positive charge carriers, a space-charge modulation is formed, (b) The charge density proHle. The space-charge modulation creates an electric Held that is phase shifted by 7t/2. (c) The electric field profile. The refractive index modulation follows the electric field by electrooptic response, (d) The refractive index profile.

Two main types of refractive index perturbations will be discussed here in detail. The first type is a homogeneous change in the refractive index in the whole superstrate. Fig. 13, (herein referred as to bulk refractive index change), which can be described by a change in the permittivity profile, e(x) s(x), where ... 

The first term Srh depends on the method of excitation of surface plasmons and the modulation approach used in the SPR sensor and is hereafter referred as to the instrumental contribution. Sri2 describes the sensitivity of the effective index of a surface plasmon to refractive index and is independent of the modulation method and the method of excitation of surface plasmons. The sensitivity of surface plasmon to refractive index Sri2 depends on the profile of fhe refracfive index tih and has been analyzed in Chap. 1 of this volume [ 1 ] for the two main types of refractive index changes - surface refractive index change and bulk refractive index change. 

Figure 5. Comparison of refractive index profiles of waveguides produced in the electrodiffusion processes with a predetermined value of electric field intensity for the positive value = 18.2 V/mm and E- = -9.1 V/mm for the negative value, for various durations of "+" and polarization. Waveguides produced on the first side of the substrate (a) and on the other side of the substrate (b).

Figure 6. Comparison of refractive index profiles of waveguides produced by electrodiffusion processes with fixed polarization durations C = 45 and t- = 45, for different values of electric field intensity for polarization "+" and Wave-...

The presented measurement results of refractive index profiles of waveguides produced in the electrodiffusion processes (in which there is a change of polarization direction of the applied electric field) indicate a high possibility of the use of such processes to the intended shaping of refractive index profiles of produced waveguide structures. 

Figure 13. Comparison of refractive index profiles of planar waveguides produced in soda-lime glass doped with ions Ag (a) or (b) with the refractive index profiles produced in BK-7 glass doped with ions Ag (c) or (d).

Figure 1 also shows a typical example of refractive index distribution in the GI POFA preform rod measured by an interferometric technique (10, 11), where Uq and n mean the refractive indices at the center axis and at distance r, respectively. As shown in the curve of Figure 1, the preform rod has a cladding region coming from the PMMA tube and a quadratic index profile in the core region. The normalized refractive index distribution of the GI POFA was almost the same as that of this preform rod (12),... 

Evaluation of the transverse temperature profile ( the thermal lens ) induced by laser radiation passing an absorbing (liquid) medium. Optical detection of organic compounds by the change of refractive index... 

Two pairs of refractive index profiles, D, and D, are the eigenvalues of the matrix of the ternary coefficients. In these experiments, small volumes of AV of solution, of composition ci+aci and c2+ac2 are injected into carrier solutions of composition c and C2, at time t = 0. 

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