Parabolic Index Profile Research Articles

AN EXPLICIT CALCULATION OF THE DISPERSIVE AND NONLINEAR FREQUENCY CHIRPS FOR FEMTOSECOND OPTICAL PULSES OF THE HIGH DISPERSIVE CUBIC AND CUBIC–QUINTIC NONLINEAR SCHRÖDINGER EQUATIONS

The cancellation of the dispersive and nonlinear phase components on the optical pulses of a nonlinear Schrödinger equation in the presence of fourth order dispersion and a parabolic refractive index profile is explicitly demonstrated when hyperbolic function pulses are injected. With the help of the split step Fourier method we obtain the frequency chirp associated with GVD and SPM phenomena. Its mutual compensation leads to the analytical exact soliton solutions of the high dispersive cubic and cubic quintic nonlinear Schrödinger equations.

Preparation and Characterization of Rhodamine B-Doped Gradient-Refractive-Index Plastic Rods

The gradient-refractive-index (GRIN) plastic rods with a dopant of rhodamine B (RB) dye in DMSO, prepared by the method of swollen-gel polymerization, were used in preparing a light-pump rod. The high refractive monomer benzyl methacrylate (BzMA) and low refractive monomer methyl methacrylate (MMA) were used in this investigation. 2,2-Azoisobutyronitrile (AIBN) was used as the thermal initiator. The dependence of the optical properties of the GRIN rod on initiator concentration, swelling time, and feed composition weight ratio was investigated. The parabolic refractive index profile of the plastic rod prepared in this investigation was evaluated. Effects of dopant concentration, launched pumping power, and rod length on the light pumping efficiencies were all investigated. The pumping efficiency was estimated by using a Nd:YAG laser at 532 nm wavelength as a pumping source and a dye laser at 610 nm wavelength as a signal source.

The optical Magnus effect in a fibre with a confined parabolic refractive index profile

On the basis of numerical simulation of the propagation of the circular polarized light through an optical fibre with a confined parabolic refractive index profile, the features of the optical Magnus effect are demonstrated.

A comprehensive ray approach for teaching intermodal dispersion of a parabolic index profile fiber

A simple and comprehensive ray approach for teaching intermodal dispersion of a parabolic index fiber is proposed. The result is the same as that by using the conventional approach. Because the approach here only uses the ray concepts with very simple mathematics, it can be easily understood by sophomore students. A simple perturbation idea adopted in this paper makes the calculation easier and the distinction between the concepts of near axial and far-axial rays makes the solution have more physical significance.

Graded-Index Polymer Optical Fiber with High Thermal Stability of Bandwidth

The development of the perfluorinated (PF) polymer based graded-index polymer optical fiber (GI POF) for high-speed data communication is described. It was experimentally confirmed that gigabit data transmission for 500–1000 m at 1.3 µm wavelength was achieved by the low-loss PF polymer based GI POF. The thermal stability of poly (methyl methacrylate) PMMA based GI POF is discussed. We selected several kinds of dopants that can maintain a high glass transition temperature (Tg) of the GI POF core. By using the newly selected dopants, we succeeded in maintaining the parabolic refractive index profile of GI POF with no degradation even at 85 to 90°C for more than 5000 h.

Characterization of graded refractive index silicon oxynitride thin films by spectroscopic ellipsometry

Layers with a continuous variation in the optical index with thickness were characterized by spectroscopic ellipsometry. These oxynitride films were grown by electron cyclotron resonance plasma-enhanced chemical vapor deposition using silane as a silicon precursor and oxygen and nitrogen as plasma gases. Specific linear and parabolic index profiles were fabricated by computer-controlled gas flow. Reduction of ellipsometry data measured ex situ on these films was performed with polynomial analysis. The validity of this approach was checked by a depth analysis via chemical etching. An investigation of the limits of the method is presented.

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.

Estimation of dispersion parameters involving the Petermann II spot size using a Gaussian-type approximation in single-mode graded-index fibers

Based on a recently prescribed simple and novel approxima- tion of the fundamental mode, we present analytic expressions for the Petermann II spot size, suitable for evaluating the dispersion parameters of single-mode graded-index fibers. With these expressions, we calcu- late the group delay dispersion factor and also the normalized wave- guide dispersion coefficient. On comparison, our formulation is shown to be superior to the Gaussian approximation and predicts the parameters identically with the exact numerical techniques for step and parabolic index profiles. © 1997 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(97)01509-2)

Fabrication and characterization of graded refractive index silicon oxynitride thin films

Oxynitride films with continuous variations of the optical index with thickness were grown by electron cyclotron resonance plasma-enhanced chemical vapor deposition using silane as a silicon precursor and oxygen and nitrogen as plasma gases. Specific linear and parabolic index profiles were fabricated by computerized-control gas flow. These gradient index layers were characterized by spectroscopic ellipsometry. The data reduction was performed by polynomial analysis. The validity of the ellipsometric results was also verified by performing an in-depth analysis via the chemical etching of the gradient index layers.

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

Scattering losses from dielectric apertures in vertical-cavity lasers

In vertical-cavity lasers (VCLs) employing oxide or airgap apertures, the lasing mode typically travels unguided throughout most of the structure. For the aperture to exactly compensate for the diffraction of the mode in these regions, it would need to have a parabolic lateral index profile (i.e. that of an ideal thin lens). Although nonparabolic aperture shapes will partially compensate diffraction losses, some light will be scattered out of the mode. These scattering losses increase as the aperture size is reduced and will limit the performance of the smallest devices. We analyze these losses first using a semianalytic approach which allows us to frame the problem in terms of two parameters of the structure: the Fresnel number and the effective optical path length across the aperture. We compare the estimate with experimental results and with an iterative numerical calculation of the actual mode and losses. Lastly, we compare the loss reduction with different amounts of tapering that provide a better approximation to the ideal parabolic lens.

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.

Desired concentration-dependent ion exchange for micro-optic lenses

The required concentration-dependent diffusion coefficients for both ideal one-dimensional and ideal radial gradient-index profiles are determined. The modified quasi-chemical diffusion model is used to relate the diffusion coefficient to optimum glass composition. Adding aluminum to sodium silicate glasses facilitates the approach to the desired concentration dependence of the diffusion coefficient for silver-sodium ion exchange. A parabolic one-dimensional index profile is fabricated in one of the glasses. It deviates from ideal values by less than 2%.

Generalized effective index series solution analysis of waveguide structures with positionally varying refractive index profiles

The use of a generalized series solution technique for analyzing semiconductor integrated-optic waveguide devices is presented. This technique can be employed to obtain TE and TM modes for any slab-waveguide structure with an arbitrary index variation, as long as the square of the index in each layer can be fitted to a polynomial function of position. The method is applied to a slab waveguide with a parabolic index profile, an AlGaAs heterostructure electrooptic phase modulator, heterostructure ridge-waveguide structures with sloped sidewalls, and an InGaAs-AlGaAs graded-index separate-confinement-heterojunction quantum-well structure.

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.

Thermally controlled lateral beam shift and beam steering in semiconductor lasers

We demonstrate a thermally controlled, offset-gain and index-guiding (OGIG) structure, which permits continuous control of output beam position and direction from a semiconductor laser. The gain and index guiding axes in this structure are parallel but transversely offset. For parabolic gain and index profiles the resulting modes will be Hermite-Gaussian modes with complex-valued spot sizes and tilted wavefronts such that the beam emerges from the end face at a tunable angle with respect to the facet normal. An experimental demonstration of thermally controlled mode displacement and beam steering by as much as 15/spl deg/ is obtained by applying asymmetric heating to a semiconductor laser using a microstripe heater. >

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.

Control of Mode Structure in Active or Passive Graded-index Waveguides with Large-scale Periodic Longitudinal Inhomogeneities

Abstract The mode structure of both active and passive graded-index waveguides with a parabolic-index profile and large-scale (in comparison with wavelength) periodic variations of the profile in the longitudinal direction is investigated analytically in the paraxial approximation of the scalar wave equation. Quasimode solutions which periodically reconstruct themselves up to some phase factor characterizing quasi-propagation constants are investigated in detail using a quantum-theoretical formalism. The possibility of effective control of the quasi-mode structure in such waveguides is shown and possible practical applications to different waveguide components and lasers are discussed. The spontaneous emission K factor for the quasi-modes in active and passive periodic waveguides is also evaluated.

Pulse propagation in a nonlinear optical fibre of parabolic index profile by direct numerical solution of the Gel'fand—Levitan integral equations

The evolution of an optical pulse in a graded-index (parabolic profile) single-mode nonlinear optical fibre is treated by means of differential equation techniques. Using a slowly varying envelope approximation and an averaging method over the transverse direction, a differential equation of the nonlinear Schrodinger type is obtained for the unknown envelope function of the electric field. The inverse scattering method is then applied, leading to the equivalent system of Gel'fand-Levitan-Marchenko coupled integral equations. A new iterative solution to these equations is presented. As an example, numerical results for a hyperbolic secant initial pulse profile of variable amplitude are obtained and the behaviour of both the soliton and the radiation part of the solution is examined. Finally, in the special case of reflectionless potentials, the well known analytical single and double solitons are recovered.

Reductive perturbation analysis of short pulse propagation in a nonlinear dielectric slab: the role of material dispersion in bright-to-dark solution transitions

The pulse propagation in a lossless nonlinear dielectric slab of parabolic index profile with material dispersion is analyzed with the reductive perturbation method. The cases of temporally and spatially short optical pulses, with respect to the respective effectiveness of the nonlinearity are both considered. The evolution equations are given explicitly for the practical single mode case. Envelope solitons are obtained through the nonlinear Schroedinger equation which results in the third order of the perturbation scheme. The lower-order soliton solutions are derived analytically along with the conditions for sustaining bright or dark solitons (the latter cannot be excited if resonance effects in the material dispersion are absent).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>