Parabolic Refractive Index Profile Research Articles

Preparation of graded index plastic rods doped with Nd3+by interfacial-gel polymerization

A novel graded index (GI) plastic rod was prepared by interfacial-gel polymerization carried out in a poly(methyl methacrylate) (PMMA) tube with one closed end. Bromobenzene (BB) was used to obtain a graded index distribution and neodymium octanate (NOA) as a dye with Nd3+ concentrations from 60 to 700 ppm. For a polymerization system containing methyl methacrylate (MMA) as monomers, azobis-isobutyronitrile (AIBN) as an initiator, and dodecyl mercaptain as chain transfer agents, the difference of the refractive index from the center to the periphery of the rod (Δn) was found to be 0.015 at 18 wt % of BB and 60 ppm of Nd3+. Experimental results also showed that a parabolic profile of refractive index formed on the cross section of the rod and Δn increased with BB contents increasing. NOA has little effect on the profile within the given concentrations. A description for forming the GI distribution is given by the free volume theory. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67:1431–1436, 1998

Preparation of graded index plastic rods doped with Sm3+ by interfacial-gel polymerization

A novel graded index (GI) poly(methyl methacrylate) (PMMA) rod was prepared by interfacial-gel polymerization carried out in a PMMA tube with one closed end. Bromobenzene (BB), a higher refractive index molecule, was used to obtain a graded index distribution and samarium octanoate (SOA) was used as a dye with Sm3+ concentrations from 60ppm to 700ppm. For a poly-merization system containing methyl methacrylate (MMA) as monomer, azobis-isobutyronitrile (AIBN) as initiator and dodecyl mercaptan as chain transfer agent, the difference of the refractive index from the centre to the periphery of the rod (Δn) with various BB and Sm3+ contents was determined. Experimental results showed that a parabolic profile of refractive index formed on the cross-section of the rod and Δn increased with increase of BB content. SOA has little effect on the profile within the given concentrations. The GI distribution may be calculated by free volume theory. The result is identical with the experimental distribution. © 1998 SCI.

Angular momentum of the fields of a few-mode fiber. III. Optical Magnus effect, Berry phase, and topological birefringence

It is shown that, on the one hand, the evolution of the angular rotation of the lines of nodes of the CP11 mode is a manifestation of the optical Magnus effect in a few-mode fiber with a parabolic refractive index profile, and, on the other hand, the additional phase γb=±δβ21z in CV and IV vortices is the Berry topological phase, which arises as a result of the cyclic change in the orientations of the orthogonal axes of dislocations. The splitting of the propagation velocities of orthogonal circularly polarized CV+ and IV− modes in an LV vortex in a parabolic fiber is a manifestation of the phenomenon of topological birefringence of a few-mode fiber. The azimuth of the linear polarization of a vortex undergoes continuous angular rotation. In an optical fiber with a stepped index profile the CP11 mode forms circularly polarized edge dislocation over lengths which are multiples of half the beat length, and over lengths which are odd multiples of the quarter beat length it forms linearly polarized fields with a purely screw dislocation. This transformation of edge and screw dislocations can be regarded formally as conversion of the polarizational angular momentum into orbital angular momentum. The conversion of angular momentum is a reflection of the dynamical unity of the optical Magnus effect and the Berry topological phase in the fields of a few-mode fiber.

A-Axis Nd:MgO:LiNbO3 single crystal fibers with magnesium-ion indiffused cladding

A core-cladding waveguide structure for the a-axis Nd:MgO: LiNbO3 single crystal fiber with parabolic refractive index profiles was achieved by a Mg-ion indiffusion process. Propagation loss coefficient of the cladded crystal fiber was measured and is 7 times lower than the uncladded crystal fibers. Transmission modes of the 60μmlm × 45μmlm cladded crystal fiber were observed and the low order modes propagation was obtained

Dynamics of field dislocations and disclinations in a few-mode fiber. IV. Formation of an optical vortex

The physical mechanisms responsible for the formation of an optical vortex in the field of a few-mode fiber have been investigated experimentally and theoretically. In an optical fiber with a parabolic refractive index profile an optical vortex is formed as a result of interaction between circularly polarized rotating pure edge dislocations of circularly polarized even and odd CP11 modes. In a stepped-index fiber the formation of an optical vortex is also related to the simultaneous propagation of even and odd modes. The fields of these modes alter their structure over the fiber length and are not manifested by rotating edge dislocations. It has been found experimentally that a stable vortex does not alter its degree of polarization of the field at fiber lengths greater than 10 m. An unstable vortex, for which the product of the spin and the topological charge is always less than zero, periodically decays and recovers at a beat length of 0.65 m. It is noted that a stable optical vortex cannot be formed by orthogonally polarized LP11 modes. This is because an optical vortex transfers additional angular momentum like the CP11 modes whereas the LP11 modes do not transfer additional angular momentum of the field.

Planar graded-index (GRIN) PECVD lens

The authors report the design, fabrication and characterisation of a planar gradient index (GRIN) PECVD lens. The PECVD-based helicon plasma reactor was used to deposit graded layers onto a silicon wafer. Ray tracing and beam propagation methods were used to simulate the periodic refocussing of the nominally parabolic refractive index profile. Propagation characteristics were measured using a standard prism coupler and also by observing fluorescence from a specially doped thin polymer layer spun on to the top of the planar lens.

A novel method for preparing gradient index (GI) plastic rods

The initiator diffusion technique was used in this study to prepare the gradient index(GI) plastic rods, in which two kinds of initiators were used, i.e., thermal initiator and redox initiator. Experimental results showed that a GI plastic rod with a parabolic profile of refractive index was obtained by the initiator diffusion technique. The difference of the refractive index from the center to the periphery (Δn) of the plastic rods was in the range of 0.004–0.014. Δn increased with increasing temperature due to the increase of the gel effect and diffusion rates of monomers at a higher temperature. Furthermore, the GI plastic rod had substantially less defects, e.g., bubbles and opaqueness, than that prepared from interfacial-gel copolymerization.

Bilinear transformed reflectance of materials with a spatially changing refractive index

New approximate analytical expressions in integral form for the reflectance of materials with graded refractive-index profiles are presented. The reflectance of material containing a buried Gaussian refractive-index profile is simulated by these analytical expressions and compared with the reflectance computed by the matrix method. The two methods agree to within 0.7% in the root-mean-square sense. The analytical expressions, however, are 1 to 2 orders of magnitude faster to compute. The reflectance of a buried parabolic refractive-index profile is also investigated, and results from the proposed theory are compared with those from the WKB approximation. Also, in this instance it is shown that the integral formulation is superior to the WKB approximation at long wavelengths. As a practical example, the measured reflectance of semi-insulating GaAs implanted with protons is compared with theoretical calculations by use of the proposed formulas.

Interaction of light beam with its second harmonic in a square-law nonlinear guide

We discuss the role of the transverse degrees of freedom in the quadratically nonlinear interaction of two beams (second harmonic generation) in a guiding medium with a parabolic refractive index profile. Discussion of perturbative approach based on solutions of the linear inhomogeneous initial value problem is presented together with numerical results concerning a fully non-linear problem. We argue, that due to the existing self phase modulation of the pumping field the resonance (phase matching) condition cannot be described well in terms of the quasi linear model. The phase matching condition can be satisfied in a fully nonperturbative regime and coincides with the condition of good spatial overlap leading to an efficient coupling between the beams.

Propagation constant of a planar dielectric waveguide with arbitrary refractive-index variation

The calculation of a propagation constant is an interesting problem in the study of planar waveguides. We present a new method for solving the problem of a planar dielectric waveguide with arbitrary refractive-index variation for either TE or TM modes, and this method is simpler than other methods. Taking a parabolic refractive-index profile as an example, we show that high accuracy can be attained with this new method, provided that the waveguide is divided into layers of proper number and thickness.

Liquid crystal adaptive lens: beam translation and field meshing

The liquid crystal adaptive lens (LCAL) is an electrooptic device that emulates a variable focal length lens. The LCAL focuses light by creating a parabolic refractive-index profile across the aperture of a liquid crystal cell. The focal length is electronically controlled by applying appropriate voltages to the array of independent electrodes, thus grading the refractive index of the liquid crystal material across the aperture. Beam translation perpendicular to the optical beam path is described theoretically and demonstrated. This capability coupled with the LCAL's programmable focal length allows 3-D beam control. Meshing, the smoothing of the refractive index between adjacent electrodes, is a critical parameter in achieving near diffraction-limited optical performance. Using two planar electrodes and a ground plane immersed in an isotropic dielectric as a model, a steady-state dc theoretical computer simulation is compared with experiment. Improvements in the liquid crystal cell design demonstrate improved performance over previous LCALs. A larger number of electrodes creates an image without spatial aliasing within the aperture.

GaPAlxGa1−xP heterostructure edge coupling waveguides for hybrid integrated optic devices

AbstractIn this paper we present the performance of GaPAlxGa1−xP heterostructure waveguides for integrated optic hybrid devices. The waveguide layer is graded with a parabolic refractive index profile for the light emission of a DHGaAs semiconductor laser. The waveguide heterostructure performed allows to couple at it edge crossection semiconductor laser or photodetector as well as fix or solder them on the same substrate on which the heterostructure layers were deposited.The heterostructure layers were grown by liquid phase epitaxy and the heterostructure waveguide was performed by means of etching technics specially developed for this purpose.Both, the growth procedure, as well as the etching technics are described. The results achieved are shown in curves and photographs, taken on a scanning microscope.

Depolarization of radiation in an ideal multimode graded-index waveguide

A calculation is reported of the reduction in the degree of linear polarization of a beam on increase in the length of a waveguide with a parabolic refractive-index profile when the propagation in this waveguide is accompanied by a Rytov rotation of the plane of polarization. It is shown that the degree of circular polarization remains constant.

MgO:LiNbO_3 single-crystal fiber with magnesium-ion in-diffused cladding

A Mg-ion in-diffusion process was applied to form an optical guiding structure in LiNbO(3) single-crystal fibers. A parabolic refractive-index profile was formed in a 56-microm-diameter, c-axis MgO:LiNbO(3) fiber, yielding quasi-single-mode (two modes) propagation.

Calculation of the parameters of a laser beam transmitted by a focusing rod

Expressions are derived for relating the parameters of a laser beam at the entry and exit of a focusing rod with a parabolic refractive index profile. The derivation is made by using the framework of paraxial geometric optics and by modeling a laser beam by a ray packet equivalent in results to the Kogelnik model.

Measurement of instability of the optical length of waveguides due to bending and heating

The results are presented of an experimental investigation of the instability of the optical length of waveguides having rectangular and parabolic refractive index profiles, when they are subjected to bending and heating.

Mode excitation in circularly symmetric graded-index optical fibers by focused gaussian beams

Abstract Field distributions and propagation constants of modes in weakly guiding circularly symmetric optical waveguides having arbitrary radial refractive index distribution are determinable from a variational analysis, which uses the solution of the scalar wave equation for the infinitely extended parabolic refractive index profile as a reference (Laguerre-Gaussian functions). The power coupling coefficients of the power, which is transferred from a focused Gaussian beam to an LPvp-mode, depend on frequency and on four normalized launching parameters. Once the field-describing matrix equation has been solved numerically, closed-form expressions are obtained. The condition for optimal matching of the fundamental mode is given, and it is found that the maximum power excitation coefficient may be close to 100% even for substantially disturbed profiles.

Propagation of Hermite–Gaussian beams in spatially curved optical waveguides having a parabolic refractive index profile

It is found that for a certain value of the parameter w, which characterizes the effective beam width, paraxial Hermite–Gaussian beams propagate along certain trajectories without changing their structure in a spatially curved waveguide having a parabolic refractive index profile. It is shown that in the case of a Gaussian intensity distribution at the entry to the waveguide and arbitrary w, the beam also propagates along a particular trajectory but the beam width varies periodically along the waveguide axis.

Propagation of Gaussian beams in piano-curved optical waveguides with a parabolic refractive index profile

An analysis is made of the propagation of paraxial Gaussian beams in optical waveguides arbitrarily curved in one plane and having a parabolic refractive index profile. The propagation function is derived for this case and by analyzing this function, it is shown that the center of the beam moves along a specific trajectory. Moreover, the Gaussian intensity distribution with a periodically varying parameter characterizing the beam width is conserved along the trajectory in the transverse cross section of the beam.

Analysis of an inhomogeneous symmetric cladded slab optical waveguide

A detailed analysis of a symmetric cladded slab waveguide having a parabolic refractive-index profile in the core is carried out. Two techniques, one based on the step-index approximation and the other on the WKB approximation, are used to obtain the dispersion curves and the field plots for both the even and odd TE and TM-modes. An example of the practical relevance of the structure studied is given.