Modal Solutions of Active Dielectric Waveguides by Approximate Methods

Approximate methods are used to obtain the modal properties of stripe-contact semiconductor injection lasers using a planar three-layer waveguide model. The central active layer has a dielectric constant that varies smoothly along the direction parallel to the heterojunction boundaries. The complex dielectric constant under the stripe contact is dependent on the gain and approaches a constant value at large lateral distances. The two methods are compared in terms of their modal propagation constants. An application of the effective index method facilitates a physical understanding of dielectric waveguide modes as well as providing an efficient calculation procedure.     

Propagation Properties of a Modified Slot Surface Plasmonic Waveguide

In this paper, we present a modified slot surface plasmonic waveguide formed by metallic rod, core dielectric layer, and metallic film on the substrate. Using the finite-difference frequency-domain method, modal field distribution are analyzed firstly. Results show that the fundamental mode could be well confined in the space between the metal rod and the metal film. The dependence of modal field distribution, effective index, and propagation length of the fundamental plasmonic mode without gain on dielectric constant of the core layer, geometrical parameters, and working wavelengths are analyzed and discussed. A kind of available gain dielectric medium was used for the core dielectric layer to extend the propagation length. Results show that the propagation length can be extended observably with the help of the gain dielectric medium. Finally, effect of the thickness of the core dielectric layer on modal field distribution, effective index, and propagation length are analyzed and discussed. Since the modal field distribution, effective index, and propagation length can be controlled by adjusting the geometrical parameters, dielectric constant and gain of the core layer and working wavelengths of the waveguide, this kind of surface plasmonic waveguide can be applied to the field of photonic device integration and sensors.      

Amplification properties of Er/sup 3+/-doped photonic crystal fibers

The amplification properties of different photonic crystal fibers have been studied by means of a full vector finite-element modal formulation combined with a population and propagation rate equation solver. A honeycomb as well as a cobweb photonic crystal fiber have been considered. The consequences of the defect dimension and the dopant radius on the field intensity distribution as well as the overlap integrals have been analyzed. Results demonstrate that a proper photonic crystal fiber design can be usefully exploited in order to obtain active fibers with superior characteristics compared to standard step index ones. In particular, photonic crystal fibers open up the possibility of a gain medium with highly flexible geometric, dispersion, and amplifying characteristics.     

Dispersion characteristics of an optical fiber having linear chirprefractive index profile

We analyze the dispersion characteristics of an optical fiber having linear chirp type refractive index profile. The chirp type profile is general in nature and by controlling the profile parameters, one can obtain a wide range of profiles from simple step index to complex multiple cladded type. The problem is treated as an optimization problem in the profile parameter space. It is shown that a variety of dispersion characteristics can be realized with proper optimization of the profile parameters. Linear finite element method (LFEM) is employed for computing the modal fields and propagation constants. Tolerance analysis of the fiber dispersion characteristics and bending loss calculation are also carried out     

增益玻璃波导光场的数值模拟

在采用BPM法的基础上分析了玻璃波导中场的分布,提出了考虑增益后的光场数值模拟计算方法;比较了加入增益因子前后光场的变化,讨论了抽运功率、掺铒浓度及步长的变化对光场的影响,得到了场分布图.     

Analysis of end-pumped and electrooptically tuned Nd,Ti,MgO:LiNbO3 microchip waveguide lasers

An end-pumped and electrooptically tuned Nd,Ti,MgO:LiNbO₃ microchip waveguide laser is studied by using the self-consistent model and the conformal mapping method. The complex atomic susceptibility is used to describe the laser gain and pump absorption by applying the fast Fourier transform beam propagation method (FFT-BPM) for simulation. Using the conformal mapping method, the index change distributions in the waveguide, caused by the applied electric field, were evaluated. The optimal configuration for the microchip waveguide laser with various cavity lengths was designed. The output performances of the end-pumped and electrooptically tuned Nd,Ti,MgO:LiNbO₃ microchip waveguide lasers were simulated and investigated     

Correction to the analysis of dielectric guides by transversemagnetic field finite element penalty function method with extensions

Recently a method to obtain the propagation constants of lossless dielectric waveguides using the Helmholtz equation with the finite element method and penalty function method was presented. The advantage of using this approach is that only one final eigenvalue matrix needs to be solved for only two components of the H-fields. We have determine that the results were obtained using an eigenvalue solver that did not account for the asymmetry in the final eigenvalue matrix. In this paper, we present the results of the same cases simulated using the correct eigenvalue solver, and the results obtained are in good agreement with previously published ones. We also show by simulation of appropriate cases, a high penalty factor is correlated to highly coupled modes, while weakly coupled modes may be correlated to small penalty factors. Finally, we have extended the penalty function method to include the complex case without the use of the perturbation method. The gain results obtained for a channel waveguide are in good agreement with previously published ones     

Loss/gain characterization of optical waveguides

Finite element analysis employing the vector H-field formulation, with the aid of the perturbation technique, is used to calculate modal loss or gain for several different types of optical waveguides. Further, the complex propagation constant of an optical waveguide is obtained from the solution of the complex transcendental equation and the use of the effective index approach. Results obtained by both methods for different optical waveguides are found to be in good agreement for a wide range of gain/loss values. The accuracy limit for modal loss or gain calculation using the perturbation technique is also examined     

Multilayer waveguides: efficient numerical analysis of generalstructures

An efficient numerical method for accurately determining the real and/or complex propagation constants of guided modes and leaky waves in general multilayer waveguides is presented. The method is applicable to any lossless and/or lossy (dielectric, semiconductor, metallic) waveguide structure. The method is based on the argument principle theorem and is capable of extracting all of the zeros of any analytic function in the complex plane. It is applied to solving the multilayer waveguide dispersion equation derived from the well known thin-film transfer matrix theory. Excellent agreement is found with seven previously published results and with results from two limiting cases where the propagating constants can be obtained analytically     

Virtual boundary method for the analysis of elliptically cross-sectional photonic-crystal fibers with elliptical pores

This paper introduces a new semianalytical method for the analysis of propagation characteristics of elliptically cross-sectional photonic-crystal fibers (PCFs) with elliptical pores. This method known as a virtual boundary method (VBM) is based on the equivalency between an actual PCF and a three-layered, transversely inhomogeneous waveguide. The complicated refractive-index profile of the PCF is written as a double Fourier series, and an approximate separable wave equation is found in an elliptical coordinate system for the longitudinal field components. The exact solution to the derived equation is expressed in terms of higher order transcendental functions, such as regular and irregular Coulomb-wave functions and Mathieu functions. After having expressed all the field components, boundary conditions are imposed on the boundaries, and then, a transcendental equation for the propagation constant is derived, which is solved numerically. The validity of the method is ensured by comparing various quantities, such as effective indexes, modal birefringences, and electromagnetic field distributions, with those from an accurate full-vector finite-element method (FEM) simulator, showing relatively good agreement between the results. The method correctly confirms some of the unique PCFs' properties, such as strong localization of light within the fiber and enhancement of modal birefringence as a function of the topology of hole arrangement.     

Computation of full-vector modes for bending waveguide using cylindrical perfectly matched layers

A new full-vector approach to calculate leaky modes on three-dimensional bending waveguides is developed and demonstrated with the help of the cylindrical perfectly matched layer (CPML) numerical boundary conditions. By utilizing the complex coordinate stretching technique in the cylindrical system, a new set of full-vector wave equations for the bending waveguide structures are derived for the perfectly matched layer regions. Numerical solutions by the finite-difference schemes for the new wave equations are shown to yield highly accurate complex propagation constants (e.g., the bending-induced phase shifts and leakage losses) and modal field patterns, due primarily to the effective CPML.     

A Simple Numerical Method for Studying the Propagation Characteristics of Single-Mode Graded-Index Planar Optical Waveguides

A simple numerical method based on the Runge-Kutta method is presented to compute the propagation constant, the modal field, and the cutoff wavelength corresponding to the fundamental TE/sub 0/ and TM/sub 0/ modes of a planar optical waveguide with an arbitrary refractive index profile. The method is much simpler and requires less computational effort than the earlier reported numerical methods. We have also used the technique for an estimation of the effect of the /spl nabla/epsilon term in TM modes.     

Planar optical waveguides with arbitrary index profile: an accuratemethod of analysis

We present here an improvement of the existing modified Airy function (MAF) method. The results of our study show that the improvement gives extremely accurate propagation constants and also the modal fields for planar waveguides with arbitrary index profile     

Guided Mode Characteristics of Metal-Clad Planar Optical Waveguides Produced by Diffusion (Short Paper)

Analytical and numerical results for the guided mode characteristics of metal-clad planar waveguides produced by diffusion are developed. Values of the complex propagation constants are obtained numerically and are shown to be in good agreement with the analytical results. These give insight into how waveguide and material parameters determine the loss. Since the profile of the waveguide represents the variation of the refractive index of the diffused-channel waveguide with the depth dimension, the results obtained can be used to reduce the dimensionality of the diffused-channel waveguide and facilitate the application of the effective-index method.     

Analysis of multilayered dielectric waveguides: variationaltreatment

A fast and near exact modal analysis is presented to obtain the propagation constants and electric field profiles for dielectric multilayered channel (rib) waveguides. Calculations are performed for a particular channel configuration and found to be in excellent agreement with those obtained using the finite difference method     

Optical Channel Waveguides in $hbox {KTiOPO}_{4}$ Crystal Produced by Proton Implantation

We reported on, to our knowledge the first time, the channel waveguide formation in KTiOPO₄ crystal by the implantation of protons with a special designed photoresist mask. The 2-D refractive index profile was constructed according to the measured dark-mode spectroscopy (for longitudinally planar configuration) as well as the shape of the channel waveguide cross section. Based on this index distribution, the modal profile was calculated through a numerical simulation, which showed reasonable agreement with the near-field light intensity distribution of the guided mode that was obtained by an end-coupling method. After annealing at 200deg C for 30 min in air, propagation loss of the channel waveguides was determined to be as low as ~2.9 dB/cm at wavelength of 632.8 nm.     

铒镱共掺波导放大器的增益特性

在忽略放大自发辐射(ASE)及均匀掺杂和稳态的情况下,在初始能量转移效率的基础上从速率方程和传输方程出发,推导出了用于分析铒镱共掺波导放大器(EYCDWA)的新公式.利用这些公式分析了泵浦光功率、信号光功率、掺杂浓度、波导长度对放大器增益特性的影响,并与单掺铒波导放大器(EDWA)进行了比较,得到了一些具有实用价值的模拟结果.     

Analysis of end-pumped Nd:Ti:LiNbO3 microchip waveguideFabry-Perot lasers

A self-consistent analysis of end-pumped Nd:Ti:LiNbO₃ microchip waveguide lasers based on the fast Fourier transform beam propagation method (FFT-BPM) has been proposed. The algorithm of the model allows one to describe the laser gain and pump absorption in terms of the complex atomic susceptibility for the case of the Nd³⁺ ions. Considering the interference effects between the forward and backward light waves, the population inversion longitudinal and transversal spatial effects can be simulated. The laser characteristics of the Nd:Ti:LiNbO₃ waveguide laser correlate well with the experimental data and theoretical results. The design rules for the optimized microchip laser are also developed by using the proposed model     

Gain saturation effects in supermodes of phase-locked semiconductor laser arrays

A basic modal analysis that includes gain saturation effects in phase-locked semiconductor laser arrays is presented. For a particular supermode operation, different lasers in the array emit different amounts of light, and hence their (waveguide) propagation constants are modified differently. Solving the lasers' rate equations self-consistently with the coupled-mode wave equations seems to provide an answer that is in much better agreement with experimental results than the result using only the coupled-mode analysis.     

Full vectorial finite-element solution of nonlinear bistable optical waveguides

The accurate computation of the propagation constants and field distributions of different modes in nonlinear optical dielectric waveguides is addressed in this paper. Using the vector finite-element formulation of the beam propagation method, combined with the imaginary distance propagation technique, both linear and nonlinear modes can be accurately calculated. The proposed technique is applied to obtain the fundamental TE nonlinear mode of a strip-loaded waveguide, and the excellent agreement seen with published results shows its high numerical precision.