Search

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A full-vectorial meshfree finite cloud mode solver is presented, for the first time, for the analysis of optical waveguides with full anisotropic permittivity tensors, where the interface can be regular or irregular. The computational window are divided along the dielectric interfaces into appropriate number of clouds with homogeneous refractive index profiles and then patched by using the continuity conditions of the longitudinal field components among clouds. Present formulations yield a nonlinear eigenvalue matrix equation, and it is solved using an efficient iterative scheme after transforming the matrix equation to a standard linear eigenvalue equation, in which the convergent solutions can be achieved after performing only four iterations. The proposed method employs an unconstrained interior node distribution scheme as well as a novel scheme for dealing with dielectric interfaces, in which two extra rows of nodes are added on either side of the interfaces, significantly improving computational accuracy and efficiency. Comparing results for a nematic liquid crystal core channel waveguide and an E7-nematic-liquid crystal waveguide in silicon V-groove with the finite-difference frequency-domain method and pseudospectral-based eigenvalue method highlight the proposed method versatility, efficiency and accuracy. [ABSTRACT FROM AUTHOR]

By using a meshless finite cloud method, a full-vector mode solver in terms of transverse-magnetic-field components for optical dielectric waveguide bends is developed in a local cylindrical coordinate system. To construct the interpolation function, both the point collocation and the fixed reproducing kernel technique are utilized, and then with the help of the continuity conditions of the longitudinal field components and the perfectly matched layer absorbing boundary conditions, a standard matrix eigenvalue is obtained. Compared with the conventional meshed numerical techniques, the distributions of solution points of the present meshless method can be applied to the area of complexity in a completely free manner. Consequently, excellent convergence with high accuracy can be realized. Moreover, the present method can be applied to both the uniform and non-uniform nodal distributions, thus the computational procedure is relatively flexible. To validate the proposed method, both fundamental and high-order leaky modes for a typical rib bending waveguide are analyzed and their modal field distributions and corresponding effective refractive indexes are presented. Results are in good agreement with those published earlier, showing the effectiveness of the present method. [ABSTRACT FROM AUTHOR]

An ultracompact polarization beam splitter based on silicon nitride-on-silicon platform is proposed and analyzed, where the two polarized modes are guided in two separated layers independently, almost no affecting each other. By using subwavelength grating structure in bottom silicon layer, the injected TE mode undergoes a strong coupling from input port to adjacent waveguide and then outputs from a bending waveguide. As to the injected TM mode, it is directly transmitted along the above silicon nitride layer. Moreover, the adjacent waveguide in bottom layer is cut by a right angle at one corner to further enhance the device performance. Results show that a coupling length of only 2.7~\mu \textm is achieved with an insertion loss of 0.22 dB (0.2 dB), an extinction ratio of 27.05 dB (25.73 dB), and a reflection loss of −26.94 dB (−37.79 dB) for TE (TM) mode at 1.55~\mu \textm . In addition, fabrication tolerances and field evolution are also presented. [ABSTRACT FROM PUBLISHER]

A silicon-based ultracompact TE-pass/TM-stop power divider is proposed and analyzed in detail. By using subwavelength grating (SWG) structures, for injected TE mode, a twofold image in a SWG multimode waveguide is formed and then equally divided into two output channels. As to the injected TM mode, it is radiated into the claddings with the help of three segmented hybrid plasmonic horizontal slot waveguides (HPHSWs), located above the bottom strip and SWG waveguides. Consequently, both equal-power splitting and polarization selection can be realized in the present single device, beneficial to realization of dense integration in photonic-integrated circuits. Moreover, to enhance the device performance, tapered HPHSWs above the SWG structure are used. Results show that a compact device of 4.25 μm in total length is achieved with an insertion loss (IL) of 0.28 dB (TE), an extinction ratio (ER) of 19.73 dB, and a reflection loss of −28.13 dB (−19.69 dB) for TE (TM) mode. The bandwidth is up to 118 nm when the ER is over 15 dB and IL is below 0.4 dB. In addition, fabrication tolerances to the structural parameters are investigated detail and field evolution along the propagation distance through the proposed device is also presented. [ABSTRACT FROM PUBLISHER]

An ultracompact and broadband polarization beam splitter (PBS) is proposed by using an asymmetrical directional coupler composed of a hybrid plasmonic waveguide (HPW) and a regular silicon wire (RSW). By properly choosing the structural parameters, transverse-magnetic (TM) mode is cutoff for the RSW and phase-matching condition is only satisfied for transverse-electric (TE) mode. As a result, the input TM-mode in HPW directly passes through, while the input TE-mode in the same HPW is coupled into the RSW. Consequently, the two polarized modes can be effectively separated. Moreover, the present PBS shows fabrication-friendly design and its length can be significantly reduced, since the gap between the HPW and RSW can be shortened to zero. From the results, a ~2.6- \mu \textm -long PBS with a coupling length of 0.1~\mu \textm is achieved and its bandwidth is ~120 nm with a polarization extinction ratio over 14 dB, and an insertion loss below 1 dB for both polarizations. In addition, fabrication tolerances to the key structural parameters are analyzed in detail and field evolution through the designed PBS is also presented. [ABSTRACT FROM AUTHOR]

An efficient reflective beam propagation method (R-BPM) based on the multi-domain pseudospectral method for optical waveguides is developed. By imposing the lateral boundary conditions through a weighting technique, a transverse characteristic operator like that in the finite-difference method (FDM) is constructed so that the R-BPM techniques for FDM are available. The present method can accurately deal with the reflection problems with the number of sampling points greatly less than that of FDM, significantly reducing the computational requirements. Results from several numerical examples show the validity and utility of the present method. [ABSTRACT FROM PUBLISHER]

An ultracompact and broadband strip-to-slot mode converter based on subwavelength grating (SWG) structures is proposed and analyzed, where an SWG multimode waveguide combined with two SWG-wire tapered transitions at its both ends is used to connect the input strip and output slot waveguides. In this SWG multimode waveguide, a twofold image can be easily formed based on the symmetric interference for the central input, and then this image can be further converted into the output slot mode due to similarity of their field distributions. Based on this mechanism, we optimize the structural parameters and obtain a device length of \sim 4.3~\mu \textm (SWG multimode waveguide length is only 1.4 \mu \textm ) with an insertion loss (IL) and a reflection loss (RL) below 0.36 and −20 dB, respectively, in an ultra-wide wavelength range covering the O, E, S, C, L , and U bands ( \text IL=0.19 dB and \text RL=-28.72 dB at 1.55 \mu \textm ). [ABSTRACT FROM PUBLISHER]

An ultracompact and polarization-insensitive silicon-based strip-to-slot power splitter based on multimode interference is proposed, where an inverse-tapered subwavelength grating (SWG) structure is embedded in the center of the multimode waveguide and two strip-to-slot mode converters are integrated at the end. With the optimized SWG structure, the length of the multimode waveguide is reduced by nearly half against without such a structure and polarization-insensitive transmission can be achieved. Tapered and cut-right-angled waveguides are also introduced to enhance the performance. Simulation results show that a length of 1.92 \mu \textm for the multimode region with an insertion loss of 0.39 dB (polarization-dependent loss (PDL) = 0), the reflection losses of −30.51 dB (transverse-electric mode) and −33.62 dB (transverse-magnetic mode) are obtained at 1.55 \mu \textm , and the bandwidth can be enlarged to $\sim 105$ nm for a \textrm {PDL}<0.1 dB. In addition, fabrication tolerances and mode-field evolution are also presented. [ABSTRACT FROM PUBLISHER]

An efficient semi-vectorial bidirectional beam propagation method (Bi-BPM) based on the complex Denman–Beavers iterative (C-DBI) scheme for three-dimensional (3-D) optical waveguide structures is constructed. Beside merely calculating the transition operators by the C-DBI scheme, like our previous paper, a new approximation for the bidirectional propagators by using the combination of Padé approximants and C-DBI scheme is proposed and developed. Such a treatment can be capable of correctly dealing with the evanescent waves generated in the transition processes, greatly improving the stability and accuracy of the Bi-BPM. Moreover, the efficiency of the present Bi-BPM can be also improved since the operators calculated by the C-DBI scheme can be simultaneously utilized for both processes of the Bi-BPM. In addition, the biconjugate gradient stabilized method is utilized to solve the resulting linear systems, further improving the efficiency. Numerical results from both single and multiple longitudinal discontinuity examples show that the present method can deal with evanescent waves properly with the accuracy comparable to that of the existing well-established methods. [ABSTRACT FROM PUBLISHER]

A new algorithm for the wide-angle beam propagation method (BPM) is proposed, where the propagation propagator in the Helmholtz equation is approximated by the Denman–Beavers iterative scheme. By rotating the propagator into the complex plane, the generally concerned problem, incorrect evolution of the evanescent waves, in the conventional BPM is well solved, greatly improving the computational stability and convergent behaviors. Numerical results from several typical tests show that the present approach has reasonable efficiency and high accuracy with the convergence rate faster than the widely used Padé-based BPM. [ABSTRACT FROM PUBLISHER]

A compact silicon-based polarization splitter (PS) is proposed using a three-guide directional coupler composed of a silicon nanowire in the center and two horizontal/vertical hybrid-plasmonic waveguides (HPWs) at outer sides. Utilizing the evanescent coupling, the injected TE/TM modes in the central silicon nanowire can be only coupled to the horizontal/vertical HPWs, leading to the separation of input polarizations. Moreover, to improve the extinction ratio (ER), an S-bend connecting with the vertical HPW is employed. Results show that a coupling length of 6.5 (4.5) \mu \textm is achieved at the wavelength of 1.55~\mu \textm with ER and insertion loss of $\sim 18.9$ (15.2) dB and $\sim 0.44$ (0.89) dB for TE (TM) mode, and the bandwidths can cover the entire C-band for both polarizations. In addition, fabrication tolerances to the structural parameters are presented and field evolution through the designed PS is also demonstrated. [ABSTRACT FROM PUBLISHER]

Abstract: A silicon-based horizontal multiple-slotted waveguide with slanted sidewalls is analyzed by using a full-vectorial mode solver based on the finite element method. The results show that the mode classification of the present waveguide structures is different from that of the conventional ones (e.g., typical rib waveguides, optical fibers), both symmetric and anti-symmetric fundamental (and higher-order) quasi-TE and quasi-TM modes exist due to the strong coupling of high-index silicon layers. The field distributions, effective indexes, and optical field confinement factors, both in quasi-TE and quasi-TM modes, as functions of the top width and sidewalls angle of the waveguides, and the refractive index and thickness of the slots are investigated in detail, where the single-mode regime, non-birefringence condition, and maximum optical confinement factor are obtained. From the numerical results, a single-mode waveguide structure for fundamental symmetric quasi-TM modes with the power confinement factor of 80% and the normalized power density of 120μm−2 is achieved. [Copyright &y& Elsevier]

Abstract: The characteristics of the directional couplers based on the horizontal multiple-slotted waveguides with slanted sidewalls are analyzed in detail by using a mode solver based on the full-vectorial finite element method with perfectly matched layers absorbing boundary conditions. The coupling length of the directional coupler as functions of the structural parameters including waveguide spacing, sidewalls angle, the thickness and refractive index of the slot regions, both in quasi-TE and quasi-TM modes, is obtained. The effective indexes and the field distributions of the even and odd modes also are presented. The numerical results show that polarization-independent directional couplers can be realized by properly choosing structural and material parameters. [Copyright &y& Elsevier]

Abstract: A full-vectorial mode solver in terms of the transverse magnetic field components for optical waveguides with transverse anisotropy is described by using the multidomain spectral collocation method based on Chebyshev polynomials. The waveguide cross section surrounded by the perfectly matched layers is divided into suitable number of homogeneous rectangles, and then connected with by imposing the continuities of the longitudinal field components at the dielectric interfaces shared by the adjacent rectangles, resulting in a generalized matrix eigenvalue problem. To validate the established method, results of an anisotropic square waveguide and a magnetooptic rib waveguide are presented and compared with those from the full-vectorial finite difference method, full-vectorial beam propagation method, and the experimental data. [Copyright &y& Elsevier]

Abstract: A full-vectorial (FV) analysis of optical dielectric waveguide bends by using finite difference (FD) method in terms of magnetic field components is developed in a local cylindrical coordinate system. The perfectly matched layer absorbing boundary conditions via the complex coordinate stretching technique are incorporated into the FV wave equations for effectively demonstrating the leaky nature of waveguide bends, and a six-point FD scheme is constructed to approximate the cross-coupling terms for improving the convergent behavior. The leaky modes of a typical rib waveguide bend are calculated and the complex propagation constants and the field patterns for TE- and TM-like modes are obtained. Solutions are good agreement with those from the film mode matching method, which shows the validity and utility of the established method. [Copyright &y& Elsevier]

Abstract: The mapped Galerkin method in solving the full-vector and quasi-vector wave equations in terms of transverse magnetic fields (H-formulation) for optical waveguides with step-index profiles is described. By transforming the whole x–y space onto a unit square and using two-dimensional Fourier series expansion, the modal distributions and propagation constants for optical waveguides are obtained in the absence of boundary truncation. Results for step-index circular fiber, buried rectangular waveguide, and optical rib waveguide are presented. Solutions are good agreed with exact solutions and numerical results by using vector nonlinear iterative method, Fourier operator transform method, and vector beam propagation method. [Copyright &y& Elsevier]

A new approach for solving the optical waveguide discontinuity problems is proposed, where the field‐based operator techniques are employed. Instead of using Padé approximation, the square roots of the characteristic matrices are approximated by the Denman‐Beavers iterative scheme with a branch‐cut rotation in the complex plane. Numerical results show that the present scheme is more accurate and stable than the widely used Padé approximation. [ABSTRACT FROM AUTHOR]