Analysis Of Optical Waveguides Research Articles

Numerically efficient full-vectorial rational Chebyshev pseudo-spectral modal analysis for optical Waveguides

In this paper, an efficient full-vectorial modal analysis based on the rational Chebyshev pseudo-spectral method (V-RCPSM) is introduced to analyze 3 dimensional (3D) structures that are invariant along one spatial variable. Such structures are essential in silicon photonics and plasmonics applications where permittivity profiles with high-index contrast need precise treatment of the interface boundary conditions. Besides, such structures are open in general. Hence, good domain truncation is important. Our method handles these challenges via hybrid usage of the domain decomposition technique where the electromagnetic field is expanded in terms of Chebyshev functions in homogeneous regions, while the rational Chebyshev functions are used for semi-infinite homogeneous domains. The boundary conditions are rigorously imposed along the interfaces, a step that maintains the known exponential convergence rate of Chebyshev functions. Chebyshev functions have the ability to capture the correct rapid variation of the electromagnetic fields at the interfaces of the high-index-contrast waveguides using only a few basis functions; a critical feature for accurate mode computation. To show the accuracy and efficiency of our new approach, we studied rib and plasmonic waveguides and compared the results with those obtained using other full-vectorial approaches such as the finite elements method (FEM). Our developed approach has achieved a huge reduction in computational resources over the FEM.

Analysis of optical channel waveguides composed of bianisotropic materials with a strong magnetoelectric effect using a transmission-line formulation

Optical modes in channel waveguides composed of lossy bianisotropic magnetoelectric (ME) materials have been theoretically investigated here. In this study, a semi-analytical method based on the Fourier expansion technique, a well-known transmission-line formulation, is generalized to ME materials in a general case. Using this method, the dispersion diagram, including both phase and attenuation constants, and the field profile of the guided modes in channel waveguides such as rib waveguides are obtained. The presence of ME materials changes the polarization of guided modes in the structure. In all stages of the analysis, the numerical results are calculated and compared with those generated by commercial electromagnetic solvers to verify the computational efficiency and accuracy of the proposed method.

Design, Fabrication and Validation of Mixed Order Distributed Feed-Back Organic Diode Laser Cavity

In the context of the quest for the organic laser diode, we address a key challenge to design and fabricate high-quality factor cavities compatible with electrical excitation of organic semiconductors. More precisely, we present the design of DFB micro-cavities for integration in organic laser diodes and their validation under optical pumping. To design high-quality factor mixed-order DFB micro-cavities, we consider the half- and quarter-wavelength multilayered system and use the optical waveguide analysis to quantify the effective indices of the high and low indices, and the matrix transfer method to calculate the reflectances. Matrices of DFB micro-cavities made from different doses and different grating periods were fabricated. We then identified those showing laser emission under optical pumping as an indication of optimal matching of their resonance wavelength with respect to the electroluminescence peak of the organic gain material. Potential applications of organic laser diodes deal with light communication, spectroscopy, sensors, and other applications where heterogenous integration is important.

Optical waveguide analysis using alternative direction implicit (ADI) method in combination with successive over-relaxation (SOR) algorithm

Optical waveguide analysis using alternative direction implicit (ADI) method in combination with successive over-relaxation (SOR) algorithm

Modal analysis of planar waveguides by the immersed interface method

Modal analysis of optical waveguides is a basic task in the design of advanced waveguide devices and optical circuits. How to deal with the problem of electromagnetic heterogeneous interface and absorption boundary condition are two major difficulties in implementing efficient numerical analysis of optical waveguides. Existing high-order accurate finite-difference modal analysis methods do not take into consideration the absorption boundary problem, which, thus, makes it difficult to accurately simulate leakage and radiation modes. Based on the immersed interface method and perfectly matched layer absorption boundary condition, a finite-difference method with the second- and fourth-order accuracy is proposed in this work. By using this method, the single-interface plasmonic waveguide mode, planar symmetric waveguide mode, and one-dimensional photonic crystal waveguide mode are analyzed. Numerico-experimental results show that the convergence rate of the second- and fourth-order algorithm are consistent with the anticipated order of the guided mode, leakage mode and radiation mode. The second-order algorithm provides an ultimate accuracy of about <inline-formula><tex-math id="M5">\begin{document}$10^{-9}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230595_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230595_M5.png"/></alternatives></inline-formula> for the relative error of effective refractive index, when the normalized step size is <inline-formula><tex-math id="M6">\begin{document}$10^{-4}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230595_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230595_M6.png"/></alternatives></inline-formula>. The fourth-order algorithm provides an ultimate accuracy of about <inline-formula><tex-math id="M7">\begin{document}$10^{-10}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230595_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230595_M7.png"/></alternatives></inline-formula> for the relative error of effective refractive index, when the normalized step size is <inline-formula><tex-math id="M8">\begin{document}$10^{-3}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230595_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230595_M8.png"/></alternatives></inline-formula>. Through the study of field distribution of guided mode and cladding mode in a one-dimensional photonic crystal waveguide, we show that the continuity of the field of transverse electric mode and its first derivative across the interface, and the continuity of the field of transverse magnetic mode and the discontinuity of its first derivative across interface, can be analyzed accurately. The method proposed in this paper can be used to calculate any mode for any refractive index profile, only by using the value of refractive index, independent of the specific functional representation of modal fields. The method provides a simple and efficient tool for implementing the modal analysis of step-index planar waveguides.

Full-Vector Mode Solver for Nonlinear Optical Waveguides Using Meshfree Finite Cloud Method

A full-vector mode solver based on the meshfree (MF) finite cloud method (FCM) is developed for analysis of nonlinear optical waveguide. Self-consistent solutions are approximated through a simple iterative scheme after the nonlinear eigenvalue matrix equation derived using the quadratic basis function as well as the MF shape function. The proposed mode solver can significantly reduce the computational requirements since major parts of formulations are tackled analytically. Results for two numerical examples are presented and compared with those from the well-known finite element method (FEM) and FEM-based imaginary-distance beam propagation method (FEM-IDBPM), respectively, showing the validity and utility of the proposed method.

Unified Coupled-Mode Theory for Geometric and Material Perturbations in Optical Waveguides

Coupled-mode theory is a powerful tool to understand and control the effects of deployment and fabrication imperfections on optical waveguides. Although it provides many advantages compared to the finite element method, it still lacks the ability to treat geometric and material perturbations when they act simultaneously on the waveguide. This work fills this gap, providing a novel framework for a unified treatment of geometric and material perturbations in the coupled-mode analysis. The proposed approach consists of, first, applying the theory of transformation optics to convert geometric deformation into material perturbations and, second, studying the obtained waveguide by using a custom-developed coupled-mode theory able to deal with perturbations of both the permittivity and the permeability tensor. The framework is applied to three examples: a solid-core fiber affected by intrinsic perturbations, a bent solid-core fiber, and an elliptical hollow-core fiber. Results are validated against simulations based on the finite element method and compared with the standard coupled-mode theory most suitable for each specific example; they show that the proposed unified coupled-mode theory performs consistently better than standard theories, confirming it as a general and accurate tool for the design and analysis of optical waveguides.

Improved Full-Vectorial Meshfree Mode Solver for Step-Index Optical Waveguides With Arbitrary Dielectric Interfaces

A novel improved full-vectorial meshfree finite cloud mode solver is constructed for analysis of step-index optical waveguides with arbitrary interfaces, where the waveguide interfaces can be tilted towards the global coordinate axes or can even be curved. In order to obtain rigorous formulations capable of dealing with tilted and curved interfaces, the local coordinate transformations along with the curvilinear mapping technique are introduced to the approximation of spatial derivatives at interpolated nodes, respectively. In the improved finite cloud scheme, a simple modification to the meshfree kernel shape function is proposed to enforce the Kronecker delta property, significantly improving the computational efficiency. The computational accuracy is also greatly improved since a novel scheme is proposed to carefully treat field values in the vicinity of material interfaces. Numerical results for the fundamental and high-order modes of a rectangular rib waveguide, an equilateral triangular core waveguide, a trapezoidal rib waveguide and a circular optical fiber are presented and compared with those from the conventional mesh-based methods, which shows the validity and utility of the proposed method.

Volume Integral Equations Combined with Orthogonality of Modes for Analysis of Two-Dimensional Optical Slab Waveguide

Volume Integral Equations Combined with Orthogonality of Modes for Analysis of Two-Dimensional Optical Slab Waveguide

Boundary Integral Equations Combined with Orthogonality of Modes for Analysis of Two-Dimensional Optical Slab Waveguide: Single Mode Waveguide

Boundary Integral Equations Combined with Orthogonality of Modes for Analysis of Two-Dimensional Optical Slab Waveguide: Single Mode Waveguide

Efficient topology optimization of optical waveguide using finite element method based on slowly varying envelope approximation

Abstract We propose a novel finite element method (FEM) for efficient optical waveguide analysis to improve the computational efficiency in inverse design of optical waveguide devices. In our formulation, applying slowly varying envelope approximation (SVEA) to FEM, an electromagnetic field expression is split into a slowly varying complex envelope amplitude and a steady-state oscillating term. Then, field profile can be obtained by just solving the slowly varying complex envelope amplitude and the number of unknown variables along the propagation direction can be greatly reduced. The proposed method can achieve efficient optical waveguide analysis. Furthermore, by employing this analysis method in the inverse design of optical waveguide devices, automatic optimization of device structure can be carried out with reasonable computational costs.

Designing Optical Waveguides: Myth and Reality

In this paper, a review of numerical methods for design and analysis of nano/micro-sized optical waveguides is carried out. Besides discussing various types of optical waveguides, design of few structures is also presented using FDTD, BPM, and FEM algorithms. Subsequently, few optical devices based upon integration of more than one optical waveguide have also been revealed. Modal effective index analysis and its impact on waveguide designing/signal propagation has also been brought into consideration. Optical waveguides characterization has been carried out by computing second-order and higher order dispersion characteristics, which is vital for information interchange and other nonlinear phenomena. It is anticipated that this effort will help readers in understanding the requirement (subsequently selection) of tools for the design and analysis of optical waveguides.

Computational design & analysis of GeSe2-As2Se3-PbSe based rib waveguide for mid-infrared supercontinuum generation

We report computational modelling and numerical analysis of rib optical waveguide composed of chalcogenide GeSe2-As2Se3-PbSe and MgF2 glasses for mid infrared supercontinuum generation. Employing finite element method, we analyse the influence of geometrical parameters on waveguide dispersion & nonlinearity and perform dispersion engineering to minimize dispersion effects. Later, we analyse the influence of laser operating conditions on spectral broadening. Our simulations report a waveguide featuring zero dispersion wavelength at 2680 nm and 3310 nm in the mid infrared region, 1.4–7.6 μm spectral broadening when pumped at 3.1 μm wavelength with 85 fs pulses at peak power of 5.2 kW in a 10 mm long waveguide and nonlinearity of 991 W−1 km−1 making it suitable for mid infrared nonlinear applications.

Mode characteristic analysis of optical waveguides based on graphene-coated elliptical dielectric nanowire

In this paper, an elliptical dielectric graphene-coated nanowire optical waveguide is designed. In the elliptical cylinder coordinate system, the dispersion equation is obtained by using the separation variable method with the Mathieu functions. The effective refractive indexes and the field distributions are obtained from the dispersion equation by using the numerical method, then the propagation lengths are obtained. The influence of the operating wavelength, structure parameters and the Fermi energy of graphene on the mode characteristics are investigated. What is more, the figure of merit of the first five modes are calculated too. The influence of the operating wavelength and the graphene Fermi energy on the mode characteristics of circular nanowires and that of elliptical nanowires are compared. The results show that as the operating wavelength increases from 4.3 <inline-formula><tex-math id="M4">\begin{document}${\text{μ}}{\rm{m}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20182090_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20182090_M4.png"/></alternatives></inline-formula> to 8.8 <inline-formula><tex-math id="M5">\begin{document}${\text{μ}}{\rm{m}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20182090_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20182090_M5.png"/></alternatives></inline-formula>, the real part of the effective refractive index decreases monotonically, the propagation lengths of the fundamental mode and the 1st order modes increase, and the 2nd order modes first increase and then decrease. When changing the elliptical nanowire structure parameters—the length of semi-major axis and semi-minor axis, there are slight influence on the mode characteristics of the fundamental mode and the 1st order modes, but greater influence on those of the 2nd order modes. As the Fermi energy of graphene increases from 0.45 eV to 0.72 eV, in the first five modes, the real part of the effective refractive index decreases, the propagation lengths of the fundamental mode and the 1st order modes increase, the propagation lengths of the 2nd order modes decrease. In addition, the propagation length approaches to 2 <inline-formula><tex-math id="M6">\begin{document}${\text{μ}}{\rm{m}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20182090_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20182090_M6.png"/></alternatives></inline-formula> approximately. When the semi-minor axis <i>b</i> = 100 nm and ​<inline-formula><tex-math id="M7">\begin{document}${E_{\rm F}} \;{\rm{ = 0}}{\rm{.5}}\;{\rm{eV}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20182090_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20182090_M7.png"/></alternatives></inline-formula>, the curves of the circular nanowire (<i>a</i> = 100 nm) and the elliptical nanowire (<i>a </i>= 140 nm), the real part of the effective refractive index and propagation length with the operating wavelength and the Fermi energy of graphene are compared. Then, the advantages of elliptical nanowire over the circular nanowire are verified. The results of the separation variable method are in good agreement with the results of the finite element method. This work can provide a theoretical basis for the design, fabrication and application of optical waveguides based on graphene-coated elliptical dielectric nanowires.

基于光波导技术的水中六价铬离子痕量检测

基于光波导技术的水中六价铬离子痕量检测

Efficient rational Chebyshev pseudo-spectral method with domain decomposition for optical waveguides modal analysis.

We propose an accurate and computationally efficient rational Chebyshev multi-domain pseudo-spectral method (RC-MDPSM) for modal analysis of optical waveguides. For the first time, we introduce rational Chebyshev basis functions to efficiently handle semi-infinite computational subdomains. In addition, the efficiency of these basis functions is enhanced by employing an optimized algebraic map; thus, eliminating the use of PML-like absorbing boundary conditions. For leaky modes, we derived a leaky modes boundary condition at the guide-substrate interface providing an efficient technique to accurately model leaky modes with very small refractive index imaginary part. The efficiency and numerical precision of our technique are demonstrated through the analysis of high-index contrast dielectric and plasmonic waveguides, and the highly-leaky ARROW structure; where finding ARROW leaky modes using our technique clearly reflects its robustness.

Analysis of compound coupled-resonator optical waveguide by coupled-mode theory

We theoretically investigate the dispersion relations of the compound coupled-resonator optical waveguides (CCROWs) in time domain by using the coupled-mode method. As a result, the dispersion relation and the group velocity are obtained. Unlike in the coupled-resonator optical waveguide, the field vibration in the CCROW splits. We also design CCROW in photonic crystals and demonstrate the optical properties by using finite-difference time-domain method, and an excellent agreement has been found with the theoretical analysis.

Polarization dispersion characteristics analysis of optical rib waveguides in organic/polymer photonic devices

An efficient and high-precision single parameter variational effective index method is proposed to investigate the polarization dispersion characteristics of polymer optical rib waveguides. The transverse distribution of the effective refractive index of the waveguide is calculated by using effective index method (EI), and the distribution of optical field is approximately expressed as piecewise functions in each sub-region. The optical field with high precision is obtained by variational effective index method (VEI), and the effective index of polymer rib waveguide is computed by scalar variational formula taking the improved piecewise functions as the accurate optical field distribution. Based on the vector wave equation that governs the guided modes, the effective index is modified by perturbation method (PM) to obtain more accurate dispersion characteristics. The dispersion characteristics and transverse field distributions of the fundamental and higher order modes are analyzed in polymer multimode rib waveguides with different structure parameters and dimensions. The method has advantages such as high precision, low calculation cost and high efficiency, which provides an analytical method for the fabrication of polymeric electro-optic devices.

A simple and exact method to analyze optical waveguide with graded index profile

A simple analytical method is proposed to obtain the exact propagation constant and distribution of electric field intensity of optical waveguides with graded refractive index profile. The method is based on the Wenzel-Kramers-Brillouin (WKB) solution, variational method, modified eigen-equations and discretized scalar wave equation for planar optical waveguide. The expressions of the distribution of electric field intensity based on the conventional WKB method, which diverge around the turning point, have been demonstrated to be very exact in the region beyond the turning point where the refractive index profile varies slowly. The proposed method uses the conventional WKB method to calculate the values of electric field intensity at two adjacent positions beyond the turning point and then the electric field intensity profile for the whole region is obtained by making use of the two calculated values. Two simple and explicit formulas are deduced from the discretized scalar wave equation, which provide a relationship among the values of electric field intensity at three adjacent positions. If the effective refractive index of optical waveguide and the refractive index profile for the whole region are known, we can obtain the value of electric field intensity at any position according to the corresponding values at the adjacent positions by using the two formulas aforementioned. By using the two values calculated by WKB method, the electric field intensity profile for the whole region can be determined through the iterative use of the two formulas. The accuracy of the electric field intensity profile determined by the proposed method is greatly dependent on the accuracy of the applied value of the effective refractive index. To achieve exact propagation constant and distribution of electric field intensity, the variational method and modified eigen-equations are employed in the proposed method. Variational method is a very useful method to improve the accuracy of the propagation constant in the analysis of optical waveguide with step-asymmetrical graded refractive index profile. By combining the traditional variational method and calculation of electric field intensity profile by the proposed method, the improved variational method is presented to obtain the exact propagation constant of optical waveguide. The value of propagation constant calculated by WKB method and the corresponding electric intensity field profile determined by the proposed method are chosen as the initial trial value and trial function in the variational method. Propagation constant and the corresponding electric field intensity profile with better accuracy can be achieved by the variational calculation and then are regarded as the new trial value and trial function. By the iterative use of the variational method and calculation of electric field intensity profile by the proposed method at finite times, quite accurate results are obtained. The modified eigen-equations in combination with the proposed method is another approach to calculating accurate propagation constants of optical waveguides with both the step-asymmetrical and symmetrical graded index profile. In comparison with other published methods, the proposed method has the advantages of the simplicity and considerable accuracy.

Optical Waveguide Theory by the Finite Element Method

Recent progress in research on the finite element method (FEM) for optical waveguide design and analysis is reviewed, focusing on the author's works. After briefly reviewing fundamentals of FEM such as a theoretical framework, a conventional nodal element, a newly developed edge element to eliminate nonphysical, spurious solutions, and a perfectly matched layer to avoid undesirable reflections from computational window edges, various FEM techniques for a guided-mode analysis, a beam propagation analysis, and a waveguide discontinuity analysis are described. Some design examples are introduced, including current research activities on multi-core fibers.