Refractive index profile

The reconstruction algorithm proposed in this work is based on a special choice of basis flinctions to expand the unknown refractive index profile. The following set of functions is used here ... 

Whereas the OVD, PCVD, and MCVD processes build a refractive index profile layer by layer, the VAD process uses gaseous constituents in the flame to control the shape and temperature distribution across the face of the growing soot boule. 

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). 

Figure 7.11. Optical fibres, showing light trajectories for dilTerent refractive index profiles (after...

Figure 1. Optical fibre general scheme and refractive index profile.

By deriving or computing the Maxwell equation in the frame of a cylindrical geometry, it is possible to determine the modal structure for any refractive index shape. In this paragraph we are going to give a more intuitive model to determine the number of modes to be propagated. The refractive index profile allows to determine w and the numerical aperture NA = sin (3), as dehned in equation 2. The near held (hber output) and far field (diffracted beam) are related by a Fourier transform relationship Far field = TF(Near field). 

Figure 10. Tomographic representations of the refractive index profiles of telecommunications fibres prepared by plasma techniques. (Reproduced with permission from Ref. 16, Copyright 1985, IUPAC).

The simplest case of fibre structure is the step-index one, characterized by a constant circular refractive index profile in the core and polymer cladding of lower refractive index (Figure 3). The refractive indexes of the core and cladding depend on the materials used. The cores of these structures can be prepared from melts as well as from preforms without radial and azimutal variations of the refractive index. To obtain suitable mechanical... 

Different longitudinal sections in the structure may generally have very different refractive index profiles, and thus their eigenmode functions can strongly differ, too. As they have to be well-represented by the superposition of modes of other sections, the number M of considered eigenmodes needs to be sufficiently large (typically from tens to hundreds), and it means that many of these modes are evanescent in the direction of propagation (for their effective indexes, Re lV < 0). 

An example of the vectorial field distribution of the quasi-TEoo mode of a rib waveguide with a comparatively large refractive index profile is shown in Fig. 6. 

We consider two examples of waveguide junctions (Fig.l) structure A. when both waveguides have the same width and refractive index profile but possess different nonlinear properties (for simplicity, we assume that input waveguide is linear), and structure B. when both waveguides have the same refractive index profile and nonlinearity but their widths are different. 

Dealing with the (2D+T) problem of TE wave propagation, one has to take into account some additional terms responsible for light beam diffraction in the waveguide with linear refractive index profile nfc) ... 

Consider a step-index dielectric waveguide with a linear refractive index profile, ni x) = ( a < a), n i ( x > a). 

Figure 1. Refractive index profiles of H Lii jcNbOs planar waveguides ...

V.G. Pankin, V.U. PcheUcin, V.V. Shashkin, On the use of WKB method for determination of the refractive index profile in plane diffusion waveguides, Kvant. Elektron. 4, 1497-1502 (1997), in Russian. 

The effort to solve Eqs.(l) evidently depends on the refractive index profile. For isotropic media in a one-dimensional refractive index profile the modes are either transversal-electric (TE) or transversal-magnetic (TM), thus the problem to be solved is a scalar one. If additionally the profile consists of individual layers with constant refractive index, Eq.(l) simplifies to the Flelmholtz-equation, and the solution functions are well known. Thus, by taking into account the relevant boundary conditions at interfaces, semi-analytical approaches like the Transfer-Matrix-Method (TMM) can be used. For two-dimensional refractive index profiles, different approaches can be... 

If the resulting refractive index profile due to the electrode waveguide is eoded in a DLL, this gives a very efficient z-dependent refractive index update in a BPM-run. Such an approach gains attractiveness, e.g. when quite different cross sections are necessary or intended for the modelling in the thermal and the optical domain. 

C. Wachter, and K. Hehl, General treatment of slab waveguides including lossy materials and arbitrary refractive index profiles, Physica Status Solidi 102, 835-842 (1987). 

K. I. White, Practical application of the refracted-near-field technique for the measurement of optical fibre refractive index profiles. Optic and Quantum Electronics 11, 185-196 (1979). 

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.

Wang, X., Masumoto, H., Someno, Y., Hirai, T., (1998), Optical characterization of Si02-Ti02 thin films with graded refractive index profiles , J Japan Inst. Met, 62(11), 1069-1074. 

Fig. 4. Ray paths, cross section and refractive index profiles in different types of optical fibers...

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