Graded-index Optical Waveguides Research Articles

A hybrid variational method for beam propagation and interaction in a graded-index nonlinear waveguide

The hybrid variational method can be used to simplify multidimensional numerical simulations. We examine the applicability of this method to study the nonlinear propagation of a single beam and the interference of two spatial soliton beams in a graded-index optical waveguide governed by a two-dimensional nonlinear Schrodinger equation. We classified three distinct regimes of the dynamics that emerge during single Gaussian beam propagation, corresponding to beam decay, breather formation, and self-focusing. When two spatial soliton beams were set up to interfere in the waveguide, we identified the boundary where the nonlinear interaction during the interference led to excitation or self-focusing. These quite involved dynamics were used to test the predictive power of our variational models by comparing them with direct numerical simulations, obtaining good agreement.

Configurational entropy of optical bright similariton in tapered graded-index waveguide

Configurational Entropy (CE) consists of a family of entropic measures of information used to describe the shape complexity of spatially-localized functions with respect to a set of parameters. We obtain the Differential Configurational Entropy (DCE) for similariton waves traveling in tapered graded-index optical waveguides modeled by a generalized nonlinear Schrödinger equation. It is found that for similariton's widths lying within a certain range, DCE attains minimum saturation values as the nonlinear wave evolves along the effective propagation variable ζ(t). In particular, saturation is achieved earlier for lower values of the width, which we show correspond to global minima of the DCE. Such low entropic values lead to minimum dispersion of momentum modes as the similariton waves propagate along tapered graded-index waveguides, and should be of importance in guiding their design.

Ultrasonically Steerable Graded-Index Optical Waveguides for Deep Tissue Light Delivery: Theory and Applications.

Graded-index (GRIN) fibers have been used as implantable optical waveguides to guide light and relay images through the depth of the tissue. We have recently shown that non-invasive ultrasound can generate refractive index gradients within the tissue that form virtual GRIN lenses for imaging and photostimulation deep into the tissue. Here we present the theory behind this idea by analyzing the coupled acoustic-photonic system that models the interaction of light with the ultrasonically modulated medium. We will discuss how changing the parameters of ultrasound will change the confinement and guiding of light within the modulated medium. We will also demonstrate that using a custom-designed cylindrical ultrasonic array, the pressure interference can be controlled to sculpt complex patterns of light in the medium, such as dipole and quadrupole shapes, suitable for multisite imaging. Finally, we will discuss experimental results corroborating the theoretical predictions to generate single and multisite in situ virtual lenses that can be used for fluorescent imaging of mouse brain tissue that expresses green fluorescent protein (GFP).

Photonic potential for TM waves.

We discuss the effective photonic potential for TM waves in inhomogeneous isotropic media. The model provides an easy and intuitive comprehension of form birefringence, paving the way for a new approach on the design of graded-index optical waveguides on nanometric scales. We investigate the application to nanophotonic devices, including integrated nanoscale wave plates and slot waveguides.

Utilizing multimode interference effects in integrated graded-index optical waveguides for efficient power splitting

PurposeFor the realization of optical waveguide components, needed for photonic integrated circuits, multimode-interference based (MMI-based) devices are an excellent component class for the realization of low loss optical splitters. A promising approach to the manufacturing of these components is their embedding in thin glass sheets by ion-exchange diffusion processes, which has not yet been extensively studied. This study aims to significantly enhance the modeling of the diffusion process to support manufacturing of graded-index, MMI-based optical splitters.Design/methodology/approachThe methods of design and analysis of MMI-based components are based on a step-index refractive index profile. In this work, fundamental correlations between the properties of the manufacturing ion-exchange process and the characteristics of the graded-index, MMI-based components are established. The refractive index profile is calculated with a proprietary solver based on the finite element method. Any further investigation with respect to parameter influence is based on the beam propagation method, specifically a finite difference based, semi-vectorial, wide-angle beam propagation algorithm. The influence of the parameters of the self-imaging effect is investigated. On this basis, different approaches for efficient power splitting with graded-index, MMI-based waveguide components are evaluated.FindingsEasy approximations – mostly linear – can be found to model the dependencies of the investigated parameters. The resulting graded-index splitters are characterized by their low excess and insertion loss.Originality/valueThese findings are the first step in the direction of the semi-analytical modeling of the respective waveguide components to reduce the numerical effort.

Optical solitons in media with focusing and defocusing saturable nonlinearity and a parity-time-symmetric external potential.

We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time ([Formula: see text])-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave propagation in graded-index optical waveguides with balanced gain and loss. We find both fundamental and multipole solitons for both focusing and defocusing signs of the saturable nonlinearity in such [Formula: see text]-symmetric waveguides. The dependence of the propagation constant on the soliton's power is presented for different strengths of the nonlinearity saturation, S The stability of fundamental, dipole, tripole and quadrupole solitons is investigated by means of the linear-stability analysis and direct numerical simulations of the corresponding (1+1)-dimensional nonlinear Schrödinger-type equation. The results show that the instability of the stationary solutions can be mitigated or completely suppressed, increasing the value of SThis article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

An efficient method based on FIR filtering and fourier transform for solving the eigen-problems in optoelectronic devices

This paper presents a highly efficient method based on finite impulse response filtering and Fourier transform techniques to solve the eigen-problems, especially with smoothly varying inhomogeneous-core, such as solving optical eigen modes in graded-index optical waveguides and electronic eigen states in intermixed quantum wells. This type of structure is normally less efficient to be dealt with in space domain directly, but bears with a narrow spectrum in spatial frequency domain. Simulation examples show that the computation cost of the proposed method is approximately at least one order of magnitude smaller than that of the conventional finite difference method solved by the most efficient multiple relatively robust representations method.

Vector Laguerre-Gauss beams with polarization-orbital angular momentum entanglement in a graded-index medium.

It is shown that the vector-vortex Laguerre-Gauss modes with polarization-orbital angular momentum (OAM) entanglement are the vector solutions of the Maxwell equations in a graded-index medium. Focusing of linearly and circularly polarized vortex light beams with nonzero azimuthal and radial indices in a cylindrical graded-index waveguide is investigated. The wave shape variation with distance taking into account the spin-orbit and nonparaxial effects is analyzed. The effect of long-term periodic revival of wave packets due to mode interference in a graded-index cylindrical optical waveguide is demonstrated. High efficiency transfer of a strongly focused spot through an optical waveguide over large distances takes place with a period of revival.

Spin-dependent transverse force on a vortex light beam in an inhomogeneous medium

Spin-dependent effects on vortex light beams propagating in an inhomogeneous medium are demonstrated by solving the full three-component field Maxwell equations using the perturbation analysis. It is found that the hybrid Laguerre–Gauss modes with polarization-orbital angular momentum (OAM) entanglement are the vector solutions of the Maxwell equations in a graded-index medium. Focusing of linearly and circularly polarized vortex light beams in a cylindrical graded-index medium is investigated. It is shown that the vortex light beam undergoes an additional transverse force acting differently on circular polarized beams with opposite handedness. The wave shape variation with distance taking into account the spin–orbit and nonparaxial effects is analyzed. Effect of long-term periodical revival of wave packets due to mode interference in a graded-index cylindrical optical waveguide is demonstrated.

Modified Airy Function Method Applied to Optical Waveguides and Quantum Tunneling: A Critical Analysis

The validity of applying the Modified Airy Function (MAF) method to the problems of graded-index optical waveguides and graded potential barrier analysis was critically examined. In the former case, the method yielded very accurate results from the derived eigenvalue equations. In the latter case, however, the same method produced results that deviated significantly from exact numerical results for barriers with a smooth peak. The causes of the discrepancies were investigated in detail.

Accurate interchannel pitch control in graded-index circular-core polymer parallel optical waveguide using the Mosquito method

We successfully fabricate polymer optical waveguides with graded-index (GI) circular cores whose diameter and interchannel pitch are accurately controlled using the Mosquito method: GI-core waveguides with 250-, 125- and 62.5-μm pitches are successfully obtained. The Mosquito method utilizing a microdispenser is a very simple technique for fabricating GI-circular-core polymer optical waveguides. The accurately controlled pitch is confirmed by a high connectivity with a commercially available multimode fiber (MMF) ribbon with a 125-μm pitch. Furthermore, by inserting the waveguide between two 12-channel MMF ribbons, we experimentally demonstrate 11.3 Gbps × 12 Ch. parallel signal transmission through a GI-core waveguide with a 125-μm pitch for the first time to the best of our knowledge.

Fabrication of defocus graded-index optical waveguide for evanescent wave optical amplifier

This is the first report on an evanescent wave optical amplifier with a plastic waveguide that can amplify a CW signal transmitted by a plastic optical fiber. The waveguide with a concave refractive index distribution was fabricated by an interfacial-gel polymerization technique. Since the waveguide increases the number of reflections at the boundary surface of the waveguide and the laser dye solution, the enhancement of amplification efficiency can be realized. The function of the fabricated waveguide was confirmed by calculations and experiments. The obtained results indicate that the fabricated fiber generated a larger evanescent field than the waveguide without a refractive index distribution.

Spin-orbit and tensor interactions of light in inhomogeneous isotropic media

Propagation of polarized vortex light beams in a rotationally symmetric graded-index optical waveguide is investigated by solving analytically the three-component field Maxwell's equations. An operator approach to calculate the average values describing the propagating beams is developed. Polarization-dependent transmission associated with spin-orbit interaction for left- and right-handed circularly polarized Gauss-Laguerre light beams is shown.

TE Mode Mixing Dynamics in Curved Multimode Optical Waveguides

AbstractPropagation of light through curved graded index optical waveguides supporting an arbitrary high number of modes is investigated. The discussion is restricted to optical wave fields which are well confined within the core region and losses through radiation are neglected. Using coupled mode theory formalism, two new forms for the propagation kernel for the transverse electric (TE) wave as it travels along a curved two-dimensional waveguide are presented. One form, involving the notion of “bend” modes, is shown to be attractive from a computational point of view as it allows an efficient numerical evaluation of the optical field for sharply bent waveguides.

Refractive-index profiling of single-mode graded-index optical planar waveguides by the inverse Wentzel-Kramers-Brillouin method with improved accuracy

We demonstrate with examples a technique of improving the accuracy of the inverse Wentzel-Kramers-Brillouin (WKB) method for refractive-index profiling of single-mode graded-index optical planar waveguides.

Tunable fractional Fourier transformer for ballistic electrons

We show that a two-dimensional electron gas in a magnetic field can act as a tunable fractional Fourier transformer for the wave function of ballistic electrons traveling in the direction of the magnetic field. The degree of fractionality of this device, a graded-index electron waveguide, can be controlled through the magnetic field. This unique feature is not encountered in graded-index optical waveguides.

A ray tracing approach to model wave propagation in highly multimode graded index optical waveguides

A ray tracing approach to model wave propagation in highly multimode graded index optical waveguides

Scanning probe microscope

Graded-index optical channel waveguides like Ti-indiffused LiNbO3 waveguides have been modelled by effective refractive index profile along the lateral direction, discretising the profile and then using the matrix method. This effective-index-based matrix method, which was earlier used to compute the modal propagation constants of Ti:LiNbO3 channel waveguides and directional couplers [Fib. Integrat. Opt. 17 (1998) 139] and the bending loss [J. Opt. Commun. 155 (1998) 125], has been established in this paper as a computationally fast, analytical method to compute electric field and modal intensity profiles in single and coupled waveguides. In order to handle coupled waveguides consisting of three waveguides, the concept of overlap integral has been used to analyse power coupling to the middle waveguide for applications in power splitting. Some of the computed intensity profiles have been compared with experimental data obtained by the authors. Although computation has been performed only for TE and TM polarisations, the method has the inherent capability of handling arbitrary polarisation.

Graded-index mid-infrared planar optical waveguides made from silver halides

Since the index of refraction of AgCl(x)Br(1-x) (x<1) is higher than that of AgCl, by diffusing Br(-) ions into AgCl it was possible to control the index and thus obtain planar waveguides made from silver chlorobromide (AgClBr) on a AgCl substrate. Silver halides are transparent in the mid IR, and it was therefore possible to characterize the waveguides by transmission of 10.6-mum CO(2)-laser radiation through them. In a typical case, the thickness was optically measured and was found to be 65mum , and the propagation loss was 16 dB/cm. The output-beam profile distribution was determined experimentally and found to be well correlated with a numerical analysis simulation based on a ray-tracing model of the eikonal equation. Planar waveguides that are transparent in the mid IR will likely be useful in numerous applications.

Simple algebraic recursion formulas for calculation of propagation characteristics of graded-index waveguides

Using the perturbation method with the aid of the hypervirial theorem and Hellmann–Feynman theorem in quantum mechanics, simple algebraic recursion formulas for calculating propagation constants of graded-index planar optical waveguides in successive orders of approximation are derived. Algebraic formulas for calculation of the modal field functions are also presented. Numerical results for typical graded-index waveguides (Gaussian, exponential, complementary error function and symmetric Epstein profiles) demonstrate that the present method can be applied to an accurate calculation of the propagation characteristics to an arbitrary order of perturbation approximation.