Method of integral equation in the theory of weak-guiding inhomogeneous optical waveguides

A method of integral equation is stated and applied in the analysis of the characteristic and noncharacteristic modes in 3D weak-guiding inhomogeneous optical waveguides. The dispersion curves for the modes of diffused channel waveguides are studied near the critical conditions in absorbing media. The accuracy of recovering the permittivity profile in a channel waveguide from the far-field radiation of the fundamental mode is estimated.     

(Al)GaAs/AlGaAs周期光波导中的等幅基模

本文应用周期介质光波导的模场分布函数和特征方程分析了(Al)GaAs/AlGaAs周期光波导中结构参量及介质折射率对模场分布形状的影响,研究了波导中形成等幅基模的条件,讨论了相应参量的优化选择。     

用科尔-霍普夫变换法求非均匀光波导导模本征方程的严格解

采用科尔-霍普夫(Cole-Hopf)变换法，将渐变折射率波导导模的本征值方程变换为里卡提(Riccati)方程，通过较简洁的数学演算导出导模的传播常量与模场分布的解析解，给出了平方律分布、对称爱泼斯坦(Epstein)分布、爱泼斯坦层的平板波导与平方律分布圆光纤4种折射率分布的计算公式。     

求复折射率波导本征值的打靶法

给出了求一维缓变复折射率波导本征值的打靶法，它是对求一维实折射率波导本征值的打靶法的推广，利用它可以分析增益或损耗对ＴＥ和ＴＭ模式的影响，并给出了计算实例。     

Femtosecond laser fabrication of tubular waveguides in poly(methyl methacrylate)

Femtosecond laser direct writing is employed for the fabrication of buried tubular waveguides in bulk poly(methyl methacrylate). A novel technique using selective chemical etching is presented to resolve the two-dimensional refractive-index profile of the fabrication structures. End-to-end coupling in the waveguides reveals a near-field intensity distribution that results from the superimposition of several propagating modes with different azimuthal symmetries. Mode analysis of the tubular waveguides is performed using the finite-difference method, and the possible propagating mode profiles are compared with the experimental data.     

Lognormal Modes of Dielectric Optical Waveguides

It is shown that, at a critical point where the effective refractive index of a mode coincides with the bulk index of a cladding region, optical waveguide modes exhibiting a lognormal feature are supportable for a hyperlongrange refractive-index profile. As a typical example of waveguides that support lognormal modes a parabolic-index core surrounded by a depressed-index cladding is presented.     

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.     

He^＋离子注入LiNbO3晶体波导的制备及其性能研究

报道了液氮温度下Ｈｅ＾＋离子注入ＬｉＮｂＯ３波导的制备，采用棱镜耦合法测量了波导退火前后导模的有效折射率，计算了波导层折射率的分布和晶体中Ｈｅ＾＋离子的射程分布和损伤分布，两者吻合得较好。     

基于等效衰减矢方法的非均匀光波导色散方程

利用转换矩阵理论和等效衰减矢的概念，以此为根据分析了任意折射率分布平板波导的模式传输特性，导出了意义明确的非均匀平板波导的色散方程的严格的解析解，并指出了ＷＫＢ法的局限性，数值计算的结果表明本文所得公式的结果和严格的数值解非常接近，表明本文所得的公式是严格的。     

Optical planar waveguides in Yb³⁺-doped phosphate glasses produced by He⁺ ion implantation

Optical planar waveguides in Yb 3+-doped phosphate glasses are fabricated by implanting triple-energy helium ions. The guiding modes and the near-field intensity distribution are measured by using the prism-coupling method and the end-face coupling setup with a He-Ne laser at 633 nm The intensity calculation method (ICM) is used to reconstruct the refractive index profile of the waveguide. The absorption and the fluorescence investigations reveal that the glass bulk features are well preserved in the active volumes of the waveguides, suggesting the fabricated structures for possible applications as waveguide lasers.     

Birefringence of (Al)GaAs/AlGaAs multiplequantum well optical waveguides

Ｂｉｒｅｆｒｉｎｇｅｎｃｅｏｆ（Ａｌ）ＧａＡｓ／ＡｌＧａＡｓｍｕｌｔｉｐｌｅｑｕａｎｔｕｍｗｅｌｌｏｐｔｉｃａｌｗａｖｅｇｕｉｄｅｓ￥ＭＡＣｈｕｎｓｈｅｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＥｌｅｃｔｒｏｎｉｃＥｎｇｉｎｅｅｒｉｎｇ，ＮａｔｉｏｎａｌＩｎｔｅ...     

Mode analysis of realistic optical waveguide structures and microstructured holey fibers by modal field evolution

In this article, we describe a useful technique for calculating modes of practical optical waveguides having two-dimensional arbitrary transverse refractive index profile. The method uses a finite difference platform for evaluating Helmholtz's equation in scalar and semivectorial forms through a field evolution algorithm. The method is straightforward, easy to handle and does not involve any complex analysis or matrix formulation. We tested the accuracy of our analysis approach by applying it on a large number of realistic waveguide problems having known results or results available in the literature. The formulation has facilitated us to study the modal properties, viz., field distribution, birefringence, dispersion and mode effective area, of a variety of practical two-dimensional structures namely, planar structure, coupler, semiconductor optical waveguides, optical fibers and arbitrary profile microstructured fibers which are uniquely important in photonics and guided-wave devices. The algorithm will therefore be very useful in designing and studying any arbitrary-structure waveguides, and to explore new geometry and properties.     

Unusual bound modes in asymmetrically graded planar waveguides

 We show analytically that for certain asymmetrically graded-index planar waveguides at the cutoff point where the effective refractive index of a mode coincides with the index of the substrate, there exist unusual bound modes. We have calculated the refractive-index profile that makes these modes possible. Received: 20 July 1996     

A variational mode expansion mode solver

A variational approach for the semivectorial modal analysis of dielectric waveguides with arbitrary piecewise constant rectangular 2D cross-sections is developed. It is based on a representation of a mode profile as a superposition of modes of constituting slab waveguides times some unknown continuous coefficient functions, defined on the entire coordinate axis. The propagation constant and the lateral functions are found from a variational principle. It appears that this method with one or two modes in the expansion preserves the computational efficiency of the “standard” effective index method while providing more accurate estimates for propagation constants, and well-defined continuous approximations for mode profiles. By including a larger number of suitable trial fields, the present approach can also serve as a technique for rigorous semivectorial mode analysis.     

Analysis of arbitrary index profile planar optical waveguides and multilayer nonlinear structures: a simple finite difference algorithm

we present here a simple numerical method to obtain the mode effective indices as well as field distributions of modes of any arbitrary profile planar optical waveguide. The method is based on the solutions of scalar and semivectorial Helmoltz’s equation by finite difference algorithm and devised with a field convergence technique. This approach is quite general and can be applied straightforwardly to calculate the guided as well as quasi- or leaky modes of any arbitrary planar structure without the need to solve any eigenvalue equation or any complex matrix formalism. Besides providing the ease of application, the algorithm is particularly useful for waveguides with any graded index profile or with irregular multilayered structure and multilayered waveguides with a localised arbitrary nonlinear film. The performance of our method is verified against typical problems with analytical solutions or having results known otherwise, and is shown to yield results with good accuracy.     

Near-stoichiometric Ti:LiNbO3 strip waveguide with varied substrate refractive index in waveguide layer

We report the near-stoichiometric Ti:LiNbO3 strip waveguides fabricated by vapour transport equilibration (VTE) at 1060 C for 12 h and co-diffusion of 4-8 μm wide, 115-nm thick Ti-strips. Optical studies show that these waveguides are monomode at 1.5 μm and have losses of 1.3 and 1.1 dB/cm for the TM and TE modes, respectively. In the waveguide width/depth direction, the mode field follows a Gauss/Hermite-Gauss profile. A secondary ion mass spectrometry study reveals that the Ti profile follows a sum of two error functions along the width direction and a complementary error function in the depth direction. Micro-Raman analysis shows that the Li-composition in the depth direction also follows a complementary error function. The mean Li/Nb ratio in the waveguide layer is about 0.98. The inhomogeneous Li-composition profile results in a varied substrate index in the guiding layer, and the refractive index profile in the guiding layer is given.     

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.     

Dielectric waveguide model for guided surface polaritons

Although surface polariton modes supported by finite-width interfaces can guide electromagnetic energy in three dimensions, we demonstrate for the first time to our knowledge that such modes can be modeled by the solutions of two-dimensional dielectric slab waveguides. An approximate model is derived by a ray-optics interpretation that is consistent with previous investigations of the Fresnel relations for surface polariton reflection. This model is compared with modal solutions for metal stripe waveguides obtained by full vectorial magnetic-field finite-difference methods. The field-symmetric modes of such waveguides are shown to be in agreement with the normalized dispersion relationship for analogous TE modes of dielectric slab waveguides. Lateral confinement is investigated by comparison of power-density profiles, and implications for the diffraction limit of guided polariton modes are discussed.     

Vectorial wave-matching mode analysis of integrated optical waveguides

For mode fields of integrated optical waveguides with piecewise constant and rectangular permittivity profile, Maxwell's equations reduce to the two-dimensional Helmholtz wave equation, supplemented by continuity requirements on the boundaries between different media. Two basic components of the mode field are expanded into factorizing harmonic or exponential functions, separately on each rectangular region. We determine approximations for guided modes and propagation constants by means of a minimization procedure based on a least squares expression for the mismatch in the continuity requirements. Results for the hybrid mode fields of typical sample waveguides classify this approach as competitive with and superior to alternative methods for vectorial mode analysis, although some open questions remain.