Network analysis of eigenvalue problem for multilayer dielectric waveguide consisting of arbitrary number of layers

In this paper, the eigenvalue problem of a multilayer dielectric waveguide consisting of arbitrary number of layers is solved by the microwave network method. A general program with the function of computer graphics has been developed for analyzing the dispersion characteristics and the electromagnetic field distributions of an N layer dielectric waveguide. As examples of practical applications of the program, first, the dispersions and field patterns for the planar waveguides with refractive index of parabolic and exponential profiles are analyzed. Secondly, the procedure of mode conversion and mode separation in dielectric branching waveguides is vividly demonstrated through analyzing the field distributions of asymmetric multilayer dielectric structures and the general rules of mode conversion are discussed. The examples show that the present method possesses the advantages of versatility, rapidity, simplicity and accuracy.     

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.     

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.     

New method for calculating the spectra and radiation losses of leaky waves in multilayer optical waveguides

The efficiency of a new method for calculating the spectrum and attenuation coefficient of leaky electromagnetic modes is demonstrated with multilayer planar optical waveguides the guiding properties of which are determined by antiresonant reflection from the multilayer cladding (antiresonant reflecting optical waveguides) rather than by total internal reflection from the core-cladding interface as in standard optical waveguides. The new method applies to calculation of both electromagnetic modes in dielectric waveguides and electron quantum states in multibarrier semiconductor heterostructures. The characteristics of multilayer waveguides calculated by the new method are compared with published data obtained from a complex dispersion relation by the transfer matrix method. As an example, the wavelength dependence of the radiation losses for the first TE mode of a planar optical waveguide containing 52 pairs of layers is calculated.     

The study of multilayer planar optical waveguide structure with nonlinear cladding

A novel method for analyzing the multilayer and multibranch optical waveguides with nonlinear cladding is presented. This method can also be used to analyze the multiple-quantum-well (MQW) waveguide structure. Numerical simulation results show that our analyses are reasonable.     

多层线型分割法分析渐变型平板介质波导

提出了一种求解渐变折射率平板光波导的传播常数和场强分布的数值计算方法,计算了几类典型的渐变折射率波导的传播常数数值,并与其它方法进行了比较,结果表明,该方法计算的精度极高,速度较快,有实用价值.     

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.     

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.     

Measurements of refractive index profiles of proton－exchanged LiNbO_3 waveguidesusing TE－TM mode conversion

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A New Type of Terahertz Waveguides

A new type of THz waveguides, which employs a solid polyethylene rod as the core and polyethylene tubes in a periodic array of square lattice as the cladding, is proposed. Optical properties of this new THz waveguide, especially in dispersion, confinement loss and single mode property, are investigated in detail with the plane wave expansion method and the beam propagation method. Numerical results demonstrate that the new THz waveguide can reach not only low dispersion but also low confinement loss at single mode propagation. Therefore, the square lattice structure is a better candidate as THz waveguides than the triangular ones.     

Propagation of soliton waves in nonlinear dielectric slab waveguides of parabolic index of refraction

The pulse propagation in a non-linear slab waveguide of parabolic index of refraction is treated by using differential equation techniques. A graded index dielectric slab waveguide free of material dispersion with a cubic order non-linearity is considered. The electromagnetic wave inside the waveguide is described in terms of a non-linear equation. Slowly varying envelope function representation is employed to develop a non-linear partial differential equation for the unknown envelope function of the electric field. An averaging method over the transverse direction is applied to reduce the unknown envelope function non-linear differential equation into a form resembling the well known non-linear Schrödinger differential equation. This equation is solved by applying the Inverse Scattering Method. The N-soliton solution is developed and presented explicitly for the practical case of the single mode dielectric slab waveguide. Numerical results presenting single and double soliton propagation are also given.     

K-Na离子交换单模平面波导的制备及其表征

通过K-Na离子交换技术制备了多模玻璃平面波导.采用棱镜耦合技术测量了波导的有效折射率,用IWKB方法拟合得到K-Na离子交换波导的折射率分布符合高斯分布,由色散曲线得到单模波导的制备条件(即扩散深度范围),从而得出单模波导的离子交换时间范围,制备出单模波导,并通过求解WKB色散方程得出单模波导的表面折射率.用普通数码相机,通过对离子交换平面玻璃光波导传输线进行数字成像,根据传输线上的光强分布拟合出光强传输衰减曲线,计算出单模波导的传输损耗大约为0.4 dB/cm.     

Covariant dispersion relations and evolution tensor operators for optical waveguides

The operation approach is applied to solve the Maxwell equations for a sequence of circular layers the permittivity and permeability tensors of which depend on the radial coordinate. This makes it possible to extend the well-known method of stratification for cylindrical structures. Operator dispersion relations for graded-index and multilayer step-index isotropic circular fibers are derived. Numerical solutions to the dispersion relation for a multilayer waveguide with a periodically varying permittivity of the layers are obtained.     

Generation of stable self-similar wave packets in inhomogeneous optical waveguides with a traveling refractive index wave

The specific features of the dynamics of wave packets in inhomogeneous optical waveguides with a traveling refractive index wave and a parabolic dependence of the refractive index on the transverse coordinates of the waveguide have been investigated. It has been shown that stable self-similar pulses of short (picoand subpicosecond) duration with a high total pulse energy and a large mode area can be generated in the corresponding waveguides. It has also been demonstrated that the self-similar regime of propagation of durationpreserving wave packets can be achieved, in particular, with the normal dispersion of the active optical waveguide used in the work.     

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.     

Propagation characteristics of highly elliptical core optical waveguides: a perturbation approach

A simple first-order perturbation approach to study the propagation characteristics of highly elliptical core waveguides is presented. The unperturbed index profile is taken to be a pseudo-rectangular core waveguide for which exact scalar wave modes are known. The method is used to obtain the various propagation characteristics of elliptical core, single mode waveguides. Results for various propagation characteristics obtained by the present analysis agree very well with those reported by other authors obtained by accurate numerical techniques.     

Exciton-induced enhancement of optical waveguide confinement in (Zn,Cd)(Se,S) quantum well laser heterostructures

Room-temperature waveguide properties have been studied experimentally in ZnSe-based multiple-quantum-well laser structures. The spectra of waveguide transmission show distinct spectral features associated with heavy- and light-hole quantum well excitons. Refractive index dispersion in the multiple-quantum-well region is derived from interference spectra measured in short waveguide samples. The refractive index increases with approaching the exciton resonances, resulting in perfect confinement and low losses of the fundamental TE waveguide mode in a narrow spectral region below the heavy-hole exciton resonance energy. The spectra of laser generation have been measured under the conditions of optical pumping, showing the position of the lasing line to correlate with the spectral region of the waveguide transparency.     

Propagation-mode near-field method for measuring optical waveguides of graded index profile: some considerations on TM-modes

A new set of formulae is developed for profiling refractive index of optical waveguides using the propagation-mode near-field method. Effects of graded-index profile on wave equations for TM-modes are taken into account. Anisotropic waveguides are also studied.     

Influences of supercell termination and lateral row number on the determination of slow light properties of photonic crystal waveguides

We systematically analyze the effects of the use of an inaccurate supercell termination and an insufficient supercell size of plane-wave expansion method on the dispersion and the slow light properties of the photonic crystal waveguides. The inattentive use of supercells of photonic crystal waveguides appeared in the literature is found to be yielding errors in the dispersion and slow light characteristics of the fundamental guided mode of photonic crystal waveguides. In addition, extra modes appear in the photonic band gap of the photonic crystal waveguide due to inaccurate supercell termination. By examining the field distribution of the modes, the extra modes can be determined and removed from the band diagram. The dispersion, group index and bandwidth characteristics are observed to be less affecting from inaccurate supercell termination as the number of rows adjacent to the waveguide increases. Moreover, the dispersion and the group index-frequency curves of the fundamental guided mode of correctly terminated supercells are found to be converging as the lateral row number along the line-defect is increased.     

Forward and backward wave propagation in multilayer planar waveguide using metamaterials layer

In this study, an efficient method is discussed to analyze the multilayer planar waveguides with double negative guided (DNG) and double positive material as guiding film. Here, among various lossless multilayer planar waveguide structures, only three layer and five layer structures are discussed. For these structures, guided dispersion characteristic, along with electric field distribution of TM modes are numerically analyzed and compared. This analysis enables an effective comparison of guided modal properties of various modes and results in a better understanding of the multilayer planar waveguide with DNG as guiding film.