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.     

WKB analysis of guided and semileaky modes in graded-index anisotropic optical waveguides

WKB analysis of graded-index anisotropic optical waveguides is briefly presented. The angular dependencies of the propagation characteristics of both guided and semileaky modes are calculated numerically for the out-diffused and in-diffused LiNbO₃ waveguides with parabolic index profile. The results for the out-diffused waveguide are compared with those obtained from the rigorous theory and the applicability of the WKG method is discussed for semileaky mode loss calculations. The angular dependence of the propagation constants of a TiO₂-diffused LiNbO₃ waveguide is demonstrated experimentally, too.     

离子交换玻璃波导1×8多模干涉光功分器的研制

利用三维有限差分光束传输法 ( 3 D-FDBPM)对渐变折射率波导中自镜象效应进行分析与模拟 ,在此基础上 ,利用 K+ -Na+ 离子交换在国产 K9光学玻璃上制作了 1× 8多模干涉( MMI)光功分器 ,测试表明 ,该器件初步实现了光均分功能 .     

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.     

The dynamics of nonautonomous soliton inside planar graded-index waveguide with distributed coefficients

We present a series of exact nonautonomous solitons inside the planar graded-index waveguide amplifier with Kerr nonlinearity by Darboux transformation. Especially, properties of the nonautonomous soliton such as typical width, peak intensity and trajectory of wave center are analytically investigated. We also study the trajectory of wave's center with different conditions in detail. Solitons in planar waveguide without graded-index are also demonstrated.     

Multiple wavelength electroluminescence and laser generation in p-i-n resonant tunneling heterostructures

We report a design and electroluminescence (EL) investigation of a p-i-n resonant tunneling device based on an Al_0.4Ga_0.6As/GaAs graded-index waveguide heterostructure. The intrinsic region of the structure consists of a quantum well (QW) surrounded by multiple barrier energy filters providing simultaneous resonant occupation of electron and heavy-hole second excited subbands in the QW. Several peaks are observed in the EL spectra, confirming occupation of the excited subbands. The EL efficiency displays a resonant behavior accompanied by an S-shaped negative differential resistance region in the voltage–current characteristic. Current bistability is demonstrated, leading to bistability in the EL and laser generation spectra.     

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.     

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.     

局域波导模展开方法求解梯度型折射率光纤

将阶跃折射率光纤作为一个理想波导,以这个理想波导纤芯一包层的界面为界将横向平面分成两个区域,然后用局域波导模展开方法以及耦会波理论计算了梯度折射率光纤模式场和传播常数.     

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...     

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.     

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.     

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.     

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.     

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.     

Snake—Modulation Dynamics of an Optical—Terahertz Soliton in a Graded-Index Waveguide

A nonlinear stage of the effect of snake and modulation instabilities on the dynamics of an optical—terahertz soliton in a quadratically nonlinear graded-index waveguide has been studied theoretically. It has been shown that both instabilities are of fundamental importance and cannot be separated from each other. If the carrier frequency of the optical component is in the region of an anomalous dispersion of the group velocity, these instabilities are developed in a blow-up regime, leading to the self-focusing of the soliton. In the case of the normal dispersion of the group velocity, the mutual effect of the waveguide and snake—modulation dynamics results in the formation of a stable spatiotemporal soliton.

     

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.     

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.     

Optical-field profiles in InxGa1−xN -MQW laser structures

In this paper, we calculated the optical fields for In_xGa_1−xN-multiquantum well (MQW) laser structures. Two different optical cavities are compared, the conventional step separate confinement heterostructure (Step) and a graded-index (GRIN) structure with a parabolic variation of the Al content in the Al_xGa_1−xN guide layers. A comparison is made regarding the confinement factor, near- and far-field patterns. An anomalous behavior for the confinement factor is observed in the structure, and it can be eliminated by choosing an appropriated combination of the layer’s thicknesses forming the waveguide. For Al_xGa_1−xN, an improved expression for the refractive index is presented, which shows better agreement with experimental data than previously reported expressions.     

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%。