Linear Refractive Index Profile Research Articles

Graded-index Ge-As-Se-Te chalcogenide glass for compact infrared imaging system

The use of graded-index (GRIN) lenses in infrared imaging systems is an effective way to reduce system volume. Chalcogenide glass has been considered an ideal matrix material to produce infrared GRIN lenes because of its excellent rheological property and large refractive index (RI) tunability. Herein, an axial GRIN Ge-As-Se-Te chalcogenide glass with large RI contrast (Δn) was designed and prepared. The GRIN glass was obtained by hot-pressing 11 stacked glass disks with gradually changing RIs and thermally treating them. The glass compositions of the disks were designed according to (1-x) (Ge20As20Se20Te40)-xGe12As22Se66, where x = 0–1. It was found that these glasses had similar glass transition temperatures of 194∼199 °C, and excellent anti-crystallization performance. The RI (at 10 μm) of the glass dropped approximately linearly from 3.050 to 2.566 as x increased from 0 to 1. More than 1.2 mm diffusion depth was observed on hot-pressed two-layer glass preforms after only 24-h heat treatment. A GRIN glass with a thickness of ∼4.3 mm and linear RI profile was achieved by treating a hot-pressed eleven-layer glass preform for 24 h. The obtained GRIN glass showed good transmittance in the 3–12 μm wavelength range. These results indicate good prospects of the GRIN Ge-As-Se-Te glass for infrared imaging.

Design of diode laser using slab coupled optical waveguide with graded refractive index structure

Thickness and refractive index of slab layer have major effects in the electro-optical characteristics of slab coupled optical waveguide diode lasers. In this research, ordinary step refractive index profile was replaced by a broadened waveguide with linear graded refractive index profile and optimized doping. The results show such design can significantly improve the power conversion efficiency (PCE). According to these results, by using the asymmetric barrier in the sides of active region, the threshold current decreases and slop efficiency (SE) increases. The PCE and SE in the proposed structure are respectively 12% and 0.21 W/A higher than those in conventional step profile.

The numerical analysis of E-polarizied electromagnetic wave reflections from inhomogeneous dielectric layer

The work is devoted to the electromagnetic analysis of metamaterial based on a dielectric layer having inhomogeneous atoms distribution along the transverse coordinate. The paper considers the solution of a two-point boundary value problem of the plane linearly polarized electromagnetic wave reflection from an inhomogeneous dielectric layer. High-speed algorithm of electromagnetic wave reflection and transmission characteristics calculating based on solving a two-point boundary value problem is proposed. The frequency dependences of the reflection coefficients modulus are calculated for different real part of the complex permittivity inhomogeneous profiles at various incidence angles. It is shown that in the region of the lower normalized frequency range a dielectric layer with a parabolic profile has less reflection than a dielectric layer with a linear refractive index profile.

Refractive index profile tailoring of multimode optical fibers for the spatial and spectral shaping of parametric sidebands

We introduce the concept of spatial and spectral control of nonlinear parametric sidebands in multimode optical fibers by tailoring their linear refractive index profile. In all cases, the pump experiences Kerr self-cleaning, leading to a bell-shaped profile close to the fundamental mode. Geometric parametric instability, owing to quasi-phase-matching from the grating generated via the Kerr effect by pump self-imaging, leads to frequency multicasting of beam self-cleaning across a wideband array of sidebands. Our experiments show that introducing a gaussian dip in the refractive index profile of a graded index fiber permits to dramatically change the spatial content of spectral sidebands into higher-order modes. This is due to the breaking of oscillation synchronism among fundamental and higher-order modes. Hence modal-four-wave mixing prevails over geometric parametric instability as the main sideband generation mechanism. Observations agree well with theoretical predictions based on a perturbative analysis, and with full numerical solutions of the (3D + 1) nonlinear Schrodinger equation.

Effects of refractive index mismatch on SRS and CARS microscopy.

An inhomogeneous linear refractive index profile, such as that occurring in biological tissues, is shown to significantly alter stimulated Raman scattering (SRS) and coherent anti-Stokes Raman scattering (CARS) microscopy images. Our finite-difference time-domain simulations show that near-field enhancement and microlensing can lead to an increase of an object's perceived molecular density by a factor of nine and changes in its perceived position by 0.4 μm up to 1.0 μm. Thus the assumption that SRS scales linearly and CARS quadratically with density does not always hold. Furthermore, the inhomogeneous linear index can cause false CARS and AM-SRS signals, even for a homogeneous nonlinear susceptibility.

Surface antireflection properties of GaN nanostructures with various effective refractive index profiles.

GaN nanostructures with various effective refractive index profiles (Linear, Cubic, and Quintic functions) were numerically studied as broadband omnidirectional antireflection structures for concentrator photovoltaics by using three-dimensional finite difference time domain (3D-FDTD) method. Effective medium theory was used to design the surface structures corresponding to different refractive index profiles. Surface antireflection properties were calculated and analyzed for incident light with wavelength, polarization and angle dependences. The surface antireflection properties of GaN nanostructures based on six-sided pyramid with both uniform and non-uniform patterns were also investigated. Results indicate a significant dependence of the surface antireflection on the refractive index profiles of surface nanostructures as well as their pattern uniformity. The GaN nanostructures with linear refractive index profile show the best performance to be used as broadband omnidirectional antireflection structures.

Manipulation of light beam propagation in one-dimensional photonic lattices with linear refractive index profile

We use Bloch oscillations to demonstrate potential light beam propagation control in photonic lattices with linear refractive index change in transverse direction. It is qualitatively investigated how composite photonic lattice systems with varied values of refractive index gradient and nonlinearity strength along the propagation direction can be used to perform different functions, such as beam splitting and switching, in future components of all-optical networks. Additionally, we demonstrate the robustness of Bloch oscillations to nonlinearity and disorder in the proposed setup.

TLM Z-transform method modelling of Lossy Grin MTM with different refractive index profiles

In this paper, a numerical three-dimensional (3D) model of electromagnetic lefthanded metamaterials (LH MTM) is applied for the modelling of composite right-left handed (RH/LH) structures with a graded refractive index profile commonly named GRIN MTM. The core of this model is Transmission Line Matrix (TLM) Z-transform method that incorporates the Drude function to account for dispersive LH MTM properties in the time-domain. Lossy GRIN slabs with abrupt, hyperbolic tangent, cosine, and linear refractive index profiles have been considered. The accuracy, efficiency and stability of the proposed approach are verified using analytical solution.

SOLITON STEERING IN A RAMP WAVEGUIDE WITH NONLOCAL NONLINEARITY

We present an analytical and numerical investigation of a spatial soliton propagating in a waveguide with ramp linear refractive index profile (ramp waveguide) and nonlocal nonlinearity. It is shown analytically by equivalent particle approach and numerically by implicit Crank-Nicolson scheme that in a ramp waveguide with local nonlinearity, the soliton experiences negative acceleration along the waveguide where its refractive index decreases linearly. On the other hand, if the soliton propagates in a uniform medium with nonlocal nonlinear response then it will experience a self-bending in the positive direction where the bending level depends on the soliton amplitude as well as on the strength of nonlocality. By combining these two effects, rich dynamics of soliton can be achieved. In this case, the soliton may oscillate inside the waveguide, move to the left or to the right part of the waveguide or even be trapped. Such soliton steering can be controlled by the soliton amplitude or by its initial position.

Influence of the refractive index core profile on modal scattering of terminated two-dimensional waveguides

We examine the influence of the refractive index core profile on the modal scattering of abruptly terminated slab waveguides. The analysis is based on the integral equation method with accelerating parameters, while for the field description in the waveguide core, an appropriate Lanczos-Fourier expansion is employed. The electric-field distribution on the terminal plane, the reflection and transformation coefficient of the TE guided modes, and the far-field radiation pattern are computed. Numerical results are presented for slab waveguides with step, linear, and parabolic refractive index profiles of the core. Finally, several approximate analytical solutions are derived to study the problem in question and to explain the results obtained.

Mode dispersion and delay characteristics of optical waveguides using equivalent TL circuits

A new analysis leading to an exact and efficient algorithm is presented for calculating directly and without numerical differentiation the mode dispersion characteristics of cylindrical dielectric waveguides of arbitrary refractive-index profile. The new algorithm is based on the equivalent transmission-line (T-L) technique. From Maxwell's equations, we derive an equivalent T-L circuit for a cylindrical dielectric waveguide. Based on the TL-circuit model we derive exact analytic formulas for a recursive algorithm which allows direct calculation of mode delay and dispersion. We demonstrate this technique by calculating the fundamental mode dispersion for step, triangular, and linear chirp optical fiber refractive index profiles. The accuracy of the numerical results is also examined. The proposed algorithm computes dispersion directly from the propagation constant without the need for curve fitting and subsequent successive numerical differentiation. It is exact, rapidly convergent, and it results in savings for both storage memory and computing time.

Break up of bound-N-spatial-soliton in a ramp waveguide

We present an analytical and numerical investigation of the propagation of spatial solitons in a nonlinear waveguide with ramp linear refractive index profile (ramp waveguide). For the propagation of a single soliton beam in a ramp waveguide, the particle theory shows that the soliton beam follows a parabolic curve in the region where the linear refractive index increases and a straight line outside the waveguide. The acceleration of the soliton depends on the beam intensity: higher amplitude solitons experience higher acceleration. Numerical calculations using an implicit Crank-Nicolson scheme confirm the result of the particle theory. Combining these propagation properties with the theory about bound-N-soliton, we study the break up of such a bound-N-soliton in a ramp waveguide. In a ramp waveguide, a bound-N-soliton will always be splitted into N independent solitons with the higher amplitude soliton emitted first. The amplitude of the separated solitons after break up are calculated using the soliton theory as if the solitons are independent. Numerical simulations show that the results agree quite well with this theoretical prediction, indicating that the interaction during break up has only little influence.

Electromagnetic scattering by refractive index variations over a rough conducting surface

This paper presents a numerical method for calculating the scattered field when a vertically polarized Gaussian beam is incident on a flat or slightly rough conducting surface at a grazing angle and the refractive index of the propagation medium has a profile which is not constant. The method is a solution to the parabolic approximation of the full wave equation. The results presented are taken for a linear and log-linear refractive index profile.

ON THE SWING EFFECT OF SPATIAL INHOMOGENEOUS NLS SOLITONS

In this paper, we consider the propagation of a spatial soliton in a waveguide with triangular linear refractive index profile. We propose a model that is obtained by starting with a small perturbation of the constant linear refractive index in the displacement vector of the Maxwell equation, and then deriving the NLS equation for this case. Using this model it is shown, both analytically and numerically, that the soliton beam oscillates inside the waveguide. This is as expected, but differs from the model found in the literature in which the inhomogeneity is introduced directly in the standard NLS equation. Finally, the proposed model is used to study the breakup of bound N-soliton in a triangular waveguide.

Design and preparation of a 33-layer optical reflection filter of TiO2–SiO2 system

Multilayer optical reflection filters with several kinds of graded refractive index profiles were designed. The effects of the number of layers of multilayer films and grading functions of refractive index profiles on the optical filter characteristics were examined by using simulation. A 33-layer optical reflection filter with a linear refractive index profile was found to be optimal in terms of both optical performance and manufacture. The designed 33-layer TiO2–SiO2 reflection filter was fabricated by helicon plasma sputtering. The optical performance of the prepared multilayer film agreed well with that of the designed filter. The measured transmittance spectrum exhibited a sharp cutoff stop band around a central wavelength of 1340 nm and a wide pass region with high transmittance of about 90%. The reflectance of the stop band was greater than 99.0% in the wavelength region from 1208 to 1518 nm.

Dispersion characteristics of an optical fiber having linear chirp refractive index profile

We analyze the dispersion characteristics of an optical fiber having linear chirp type refractive index profile. The chirp type profile is general in nature and by controlling the profile parameters, one can obtain a wide range of profiles from simple step index to complex multiple cladded type. The problem is treated as an optimization problem in the profile parameter space. It is shown that a variety of dispersion characteristics can be realized with proper optimization of the profile parameters. Linear finite element method (LFEM) is employed for computing the modal fields and propagation constants. Tolerance analysis of the fiber dispersion characteristics and bending loss calculation are also carried out.

Letter refractive index variation measurements of fluids using common-path Zeeman interferometry

A common-path Zeeman interferometry technique has been deveioped and applied for the measurements of refractive index gradients of the fluids to an accuracy of Δn=9.4 × 10−9. The Zeeman interferometry technique has over 100 times better resolution than the other interferometry techniques. A linear refractive index profile of the solution at the interface of the growing L-arginine phosphate crystal from solution was measured successfully using a scanning Zeeman interferometry technique.

Fabrication of Optically Inhomogeneous Titanium Dioxide Films by Ion Assisted Deposition Method. Structures and Properties of Inhomogeneous Films.

It is well known that titanium dioxide films, deposited by conventional electron beam gun, are homogeneous. Controlling acceleration voltage and current applied to the ion gun continuously during ion assisted deposition by additional Kaufman type ion gun, large degree of intentionally produced inhomogeneous titanium dioxide films are obtained. There exist both types of positively and negatively inhomogeneous films. These optical properties and relationships among their film structures are investigated by the terms of surface topology by surface profilometer and cross-sectional view by scanning electron microscope. Positively inhomogeneous films show a linear refractive index change along film thickness, but the negatively inhomogeneous films possess nonlinear nature and still need to find the appropriate deposition condition, which gives a linear refractive index profile. For this purpose, the films are further characterized by an ellipsometer. Finally the results are compared with those obtained from the macroscopic structure model for the inhomogeneous films.

Determination of radar coverage diagrams in complex environments using closed form ray tracing

In the present work, radio ray tracing equations are derived for linear refractive index profiles. The solution is obtained in closed form without approximations. Wave front reconstruction is proposed to infer wave parameters for a large number of points from few ray traces. A computer program to evaluate radar coverage diagrams was developed utilizing a closed form solution in a complex troposphere consisting of several linear refractive index profile layers in conjunction with complex topography. The computer program is expected to be highly superior in speed compared to similar programs due to the use of wave front reconstruction and closed form ray tracing.

Manufacturing tolerances for silver-sodium ion-exchange planar optical waveguides

The variation of effective refractive index due to the manufacturing process is studied for silver-sodium-ion-exchanged slab waveguides, and the results are related to a theoretical model which is derived from the linear refractive index profile. The consequences of the observed variability are considered for the fibre-film directional coupler and the three-dimensional silver-sodium ion-exchanged waveguide.