Nonautonomous Dark Solitons and Rogue Waves in a Graded-Index Grating Waveguide

We analytically present a family of nonautonomous dark solitons and rogue waves in a planar graded-index grating waveguide with an additional long-period grating.The dark solitons whose dynamics described by the explicit expressions such as the valley,background and wave central position are investigated.We find that dark soliton's depth and the long-period grating have effects on soliton's wave central position;the gain or loss term affects directly both the background and valley of the soliton.For rogue waves,it is reported that one can modulate the distribution of the light intensity by adjusting the parameters of the long-period grating.Additionally,more rogue waves with different evolution behaviors in this special waveguide are demonstrated clearly.     

Nonautonomous Vortices in (2+1)-Dimensional Graded-Index Waveguide

With the help of self-similarity transformation, we construct and study the nonautonomous vortices with different topological charges inside a planar graded-index nonlinear waveguide, analytically, and numerically. Although these vortices are approximate, they can reflect the real properties of self-similar optical beam during a short-term propagation. Existence of these autonomous vortices require delicate balances between the system parameters such as diffraction, nonlinearity, gain, and external potential. We are concerned with some special but interesting situations, and discussing the changes of the height, width, energy, and central position of the vortices as the increase of propagation distance. Moreover, we are also interested in the azimuthal modulational instability of the system, and comparing our prediction for the modulational instability growth rates to numerical results.     

Propagation of p-polarized waves in a linearly graded index film surrounded by negative index materials

The theory of step-index waveguides is well-established. Most practical slab waveguide structures have a graded-index profile. The basic properties of graded-index planar waveguide structures are similar to those of step-index waveguides with subtle differences. The most common types of graded-index slab waveguides are linearly and exponentially graded-index profiles. We here treat linearly graded-index slab waveguide. In this work, a three-layer waveguide structure with linearly graded-index film is considered. We assume three structures: the first structure comprises a left-handed material (LHM) cladding, the second structure contains a LHM substrate layer and the third has a LHM cladding and substrate. Closed-form expressions for electric and magnetic fields and the characteristic equation are derived. The three normalized parameters: the asymmetry coefficient (a), the normalized film thickness (V) and the normalized guide index (b) are used to study the dispersion properties of the proposed slab waveguide structure.     

A geometrical optics treatment of differential mode delay

We consider the problem of expressing the index of the refraction profile of a graded-index fibre or planar waveguide in terms of the results of differential mode delay measurements. We develop a perturbative solution to this problem within the context of geometrical optics by assuming that only meridional rays contribute experimentally.     

A numerical investigation of the mode coupling among the local normal modes of sinusoidally modulated parabolic graded-index planar waveguides

We employ the propagating beam method (PBM) to study mode coupling in the framework of the local normal modes of planar, two-dimensional, graded-index optical waveguides. In particular, we examine the effects of periodic radial deformations along the axis of a parabolic, graded-index, waveguide and compare our results to those of perturbation theory. This comparison allows us to establish the accuracy of the PBM and to generate an improved version of a frequently cited PBM formalism based on the full scalar wave equation rather than the Fresnel approximation.     

Nonlinear planar waveguides with gracled-index core: power series solution

Abstact Solutions are presented for a class of nonlinear, planar waveguides with graded-index linear film and nonlinear cladding and/or substrate. The solutions are based on a powerseries expansion for the field in the core and, for several interesting examples, can be expressed explicitly - without the need to solve any eigenvalue equation. For more general problems, the solution can be described in a form that is directly analogous to that for the asymmetric step-index waveguide. Some interesting differences between the mocles of the step-and graded-index waveguides are illustrated.     

Cutoff behaviour of graded-index slab waveguides

The cutoff behaviour of graded-index planar waveguides is analysed in terms of the normalized waveguide parameters by using the multilayer technique and the WKB approach. The results show a very high degree of accuracy when checked against exact known values for exponential and hyperbolic index profiles. A set of universal plots showing the general features is given for the cutoff values of both fundamental and first-order modes. The TM polarization is also studied by comparison with the TE one.     

Improved implanted,planar buried heterostructure lasers through enhanced optical confinement

We fabricated and tested implanted, planar-buried heterostructure, graded-index, separate confinement heterostructure (IPBH-GRINSCH) lasers in various waveguide geometries. These devices were also numerically simulated with a two-dimensional waveguide model. We report improved laser performance that results from a reduced overlap of the optical field with the absorbing regions produced by residual implant damage.     

反WKB方法的改进

改进了用于确定渐变平面波导折射率分布的反WKB方法。这种渐变折射率分布是从在WKB近似的条件下得到的本征方程用数值方法求得的。用改进的反WKB方法计算3种(指数、高斯和阶跃函数)折射率分布，结果验证了该方法的有效性。先用最小二乘法拟合测量得到的有效折射率。进而求出有效折射率函数，再利用改进的算法分布计算出各自的折射率分布。计算结果同精确值吻合得很好。计算出的波导表明折射率同精确值的绝对误差约为0．1%。     

Analysis of non-linear multilayer waveguides with Kerr-like permittivities

This paper presents a semi-analytical method for calculating the dispersion relationships for stationary non-linear TE waves guided by general multilayer waveguides with Kerr-like permittivities. The non-linear wave equations are solved rigorously for each layer, and the mode index and field distribution are systematically determined so as to satisfy the boundary conditions at all interfaces. To verify the validity of the present method, a non-linear graded-index waveguide is approximated by a number of step layers and the resultant multilayer waveguide is analysed numerically. The convergence properties of mode index and total power flow are presented, and these are compared with direct solutions of the non-linear wave equation by the numerical integration method. The dispersion relationships for a non-linear multiple-quantum-well waveguide have also been investigated under two simple permittivity models. The present method is useful for the analysis of non-linear graded-index waveguides in addition to non-linear multilayer waveguides such as the multiple-quantum-well structure.     

WKB approximation for optical modes in a periodic planar waveguide

The application of the WKB method to a periodic dielectric graded-index waveguide is presented. Its justification is then verified by calculating the complex effective index of a graded-index waveguide operating in the basic TE₀ mode with three radiating diffraction orders.     

Breathing and beating dynamics of Gaussian beam in planar graded-index absorbing nonlinear waveguides

The spatial dynamics of laser beams in absorbing planar waveguides with a parabolic index profile in a saturable or cubic-quintic medium are calculated using the “collective variable approach” technique. In the absence of losses, we construct diagrams which define regions of self-focusing and self-diffractive beam propagation for both types of media. It is found that propagating pulses exhibit an oscillatory pattern, similar to breathing behavior in homogeneous media. If the incident pulse spatial profile and the center of the index profile are not aligned, the pulse oscillates around the index origin with a “beat” frequency that depends on the graded index. Both the breathing and the beat frequencies are also calculated for other graded-index profiles, such as those with additional higher-power terms, and are found to be extremely sensitive to the index profile. In media with linear and nonlinear absorption, we demonstrate the difference between the breathing behavior in graded-index and homogeneous waveguides.     

An interferometric method for refractive index profiling of planar gradient index waveguides

In this paper, we present an interferometric method to determine the refractive index profile in graded-index planar waveguides. To begin, part of the soda-lime glass substrate surface was coated with aluminum and then was immersed in molten AgNO₃ to fabricate a planar waveguide on the uncoated part of the surface. After the ion exchange, the coating was removed. Then, the sample was polished obliquely along the boundary between the ion-exchanged and non-ion-exchanged regions, to form a wedge. Thereafter, it was placed inside a Mach–Zehnder interferometer. The fringe pattern was analyzed using the well-known Fourier method and the refractive index profile was determined. The sample preparation, data analysis and experimental results are presented.     

Simplified universal dispersion curves for channel waveguides

Simplified universal dispersion curves for graded-index diffused channel waveguides have been obtained with the new normalized WKB equation using the effective index method. It is shown that, similarly to planar guides, the propagation constant of all the guided modes of a particular channel can be obtained by two parameters, called the normalized mode orders. The dispersion relations between the propagation constant and the normalized mode order of the channel have been obtained for a number of profile shapes and waveguide dimensions.     

Mode Structure and the Envelope of a High-Power Pulse in a Nonsymmetric Graded-Index Waveguide Layer

Radiophysics and Quantum Electronics - We consider a weakly nonlinear process of propagation of a modulated pulse with high-frequency filling in a plane graded-index waveguide layer. The transverse...     

平面交叉玻璃波导型微透镜阵列光学性能研究

介绍了平面交叉玻璃光波导型半球形微透镜阵列的制作方法.利用积分形式的光线方程式讨论了半球形微透镜的光学特性,得到了半球形微透镜的光线轨迹方程式和焦距表示式,理论结果与实验数据是一致的.     

Hidden features of the soliton adaptation law to external potentials: Optical and matter-wave 3D nonautonomous soliton bullets

We show that the law of the soliton adaptation to varying-in-time external potentials indicates conclusively the way for solitonlike bullets generation in three-dimensional nonautonomous nonlinear and dispersive systems. It turns out that the generation of matter-wave soliton bullets can be realized if periodic variations of non-linearity and confining sign-reversal varying-in-time harmonic oscillator potential are opposite in phases so that peaks of nonlinearity inside the atomic cloud coincide in time with repulsive character of trapping potential during reversal periodic transformations from cigar-shaped to ball-shaped trapping structures. In nonlinear optical applications, periodic graded-index nonlinear structures with alternating waveguiding and antiwaveguiding segments can be used to simulate complicated processes of matter-wave soliton bullets generation.     

Dynamic trapping of light in modulated waveguide lattices

A discrete analogue of the dynamic (Kapitza) trapping effect, known for classical and quantum particles in rapidly oscillating potentials, is proposed for light waves in modulated graded-index waveguide lattices. In particular, it is shown that, while a graded-index potential in a nonmodulated waveguide lattice can confine light at either normal or Bragg angle incidence, periodic modulation of the potential in the longitudinal direction enables one to trap optical beams at both normal and Bragg incidence angles.     

Waveguiding properties of optical vortex solitons

An optical vortex soliton induces a graded-index waveguide over an extended propagation distance in a self-defocusing nonlinear optical medium. Using numerical techniques, we determine the waveguide dispersion and optimal size of the guided beam.     

Anti-resonant reflecting photonic crystal waveguide (ARRPCW): modeling and design

In this paper, we apply an antiresonant reflecting layer concept in photonic crystal based waveguides. We have proposed a thin core ARRPCW with linear waveguide carved in it and hence calculated the transmission spectra for various length of waveguide and have shown that the longer waveguides in ARRPCW yields transmission with significantly high quality factor. Comparison of the transmission characteristics of normal conventional planar ARROW-B waveguides & ARRPCW has also been reported. The 2D FDTD numerical modeling reveals improved transmission for various lengths of planar ARROW and ARRPCW with low losses in long waveguides. Transmittance and quality factor are also calculated to confirm superior performance of the proposed design of ARROW based photonic crystal waveguide.