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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]

We have proposed an ultracompact mode-division (de)multiplexer ((de)MDMUX) based on an asymmetrical directional coupler (ADC) with SiO 2 top cladding, where a taper-etched silicon wire and a hybrid plasmonic waveguide (HPW) are used. By carefully selecting the structural dimensions, TE 0 mode from the input port 1 (I 1) is gradually coupled into the wide multimode waveguide (MMW) and then transformed to TE 1 mode while that from the input port 2 (I 2) just passes through the bar branch and outputs directly, forming an efficient two-mode (de)multiplexer. With the aid of the HPW as well as the taper-etched wire, coupling length is reduced and fabrication tolerance is enlarged to some extent. From the results, such device has a total length of only 17. 1 μ m with a short coupling length of 4. 1 μ m , and it provides a low crosstalk (CT) of -25.6 (-27.7) dB and a low insertion loss (IL) of 0.51 (0.04) dB at the wavelength of 1. 55 μ m when TE 0 mode is input in the I 1 (I 2). [ABSTRACT FROM AUTHOR]

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 3-D semivectorial horizontally wide-angle beam-propagation method (WA-BPM) based on the alternating direction implicit (ADI) scheme is proposed, where only the paraxial term in the vertical direction is considered. The present formulation reduces the splitting error to the second order and shows good compatibility with previously developed WA-BPMs. A block matrix decomposition process and a simulation window-cutting scheme are utilized to further improve the efficiency of the WA-BPM. Then, by applying Padé approximation to the resulting operator, an efficient ADI scheme that can be solved by the Thomas algorithm is constructed. Alternatively, the resulting operator can be approximated by the Denman–Beavers iterative scheme, leading to an ADI scheme with faster convergence rate and reasonable efficiency. Results from several numerical examples show the effectiveness of the present WA-BPM. [ABSTRACT FROM PUBLISHER]

A full‐vectorial mode solver in terms of the transverse‐magnetic field components for bending waveguides with curved dielectric interfaces is developed by using multidomain pseudospectral method based on the Chebyshev polynomials basis functions. A curvilinear coordinate transformation is used to map a subdomain with curved boundary onto a unit square. The perfectly matched layers absorption boundary conditions are incorporated into the present method for effectively demonstrating the leaky nature of the bending waveguides. A bending step‐index optical fibre with high index contrast is considered as a numerical example to validate the established method. [ABSTRACT FROM AUTHOR]

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: A compact wavelength demultiplexer is designed for the operation at 1.30 and 1.55μm wavelengths using the three-dimensional semi-vectorial beam propagation method. The parabolically tapered multimode interference (MMI) coupler based on the deep-etched SiO2/SiON rib waveguide is introduced into the present demultiplexer for reducing the length. The numerical results show that a MMI section of 330.0μm in length, which is only 76% length of a straight MMI coupler, is achieved with the contrasts of 42.3 and 39.2dB in quasi-TE mode, and 38.4 and 37.8dB in quasi-TM mode at wavelengths 1.30 and 1.55μm, respectively and the insertion losses below 0.2dB. The modified finite difference scheme is applied to approximate the resulting equations along the transverse directions, in which the discontinuities of the derivatives of magnetic field components H y and H x along the vertical and horizontal interfaces, respectively, are involved. [Copyright &y& Elsevier]

Abstract: A modified full-vectorial finite-difference beam propagation method based on H-fields in solving the guided-modes for optical waveguides with step-index profiles is described. The propagation is split into two substeps. In the first substep, the field propagates in the absence of the cross-coupling terms, and then they are evaluated and double used in the second substep. An improved six-point finite-difference scheme is constructed to approximate the cross-coupling terms along the transverse directions. By using the imaginary-distance procedure, the field patterns and the normalized propagation constants of the fundamental modes for a buried rectangular waveguide and rib waveguide are presented, and the hybrid nature of the full-vectorial guided-modes is demonstrated. Solutions are in good agreement with the benchmark results from film mode matching method, which tests the validity and utility of the present 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]

An ultracompact mode-order converting power splitter using a multimode interference (MMI) coupler with subwavelength gratings (SWGs) is proposed for mid-infrared (MIR) wavelength. Two symmetric oblique SWG-wires are embedded in the central input-region that is connected with the input waveguide. As a result, the input TE 0 mode is evenly coupled from the input waveguide into the MMI coupler due to the adiabatical mode evolution, and then two desired TE 1 modes are formed via self-imaging effect and further guided into the two output channels. Additionally, tapered structures and straight SWG wires are introduced into the two output channels to better obtain the required phase difference for the improvement of converting efficiency. Consequently, both TE 0 -to-TE 1 mode-order converting and power splitting, for the first time, are attained simultaneously in the present single device. Moreover, TE 0 -to-TE 2 power splitting can be readily achieved by flexibly changing the dimensions of the proposed device. Results show that a compact device length of 7 μ m with an insertion loss (IL) of 0.41 dB, a conversion efficiency (CE) of 99% and a crosstalk (CT) of -19.77 dB is obtained at the wavelength of 2 μ m; its bandwidth can be enlarged to 220 nm for IL < 0.79 dB and CE> 91%. Besides, fabrication tolerances are addressed and mode propagation profiles are illustrated. • Power splitting and mode-order conversion simultaneously in an individual component. • The total length of the proposed device power is only 7 microns. • The operating bandwidth can be enlarged to 220 nm. • The fabrication tolerances are large enough for fabrication. • The proposed device has the advantages of flexibility and expansibility. [ABSTRACT FROM AUTHOR]

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]

A compact and polarization-independent three-guide power splitter using subwavelength gratings (SWGs) on the SOI platform is proposed and analyzed in detail, where the SWG structures are located at both sides of the central input waveguide and the inner sides of the two outside waveguides. The introduced SWG structures can effectively enhance the coupling strength for TE mode, while that for TM mode is hardly affected. Consequently, by carefully choosing the structural parameters, the input TE mode can be evenly coupled from the central input waveguide to the outside waveguides, with the same coupling length for TM mode, thus a polarization-independent power splitter is realized. Results show that a compact power splitter of 8.5 μ m in coupling length is achieved with an insertion loss (IL) of 0.1 dB (0.085 dB) and reflection loss (RL) of −39 dB (−46 dB) for TE (TM) mode at the wavelength of 1. 55 μ m , and the operation bandwidth is up to 170 nm (from 1.48 to 1. 65 μ m) when IL <0.8 dB, RL <−20 dB and splitting ratio (SR) ∼ 1.001 for both polarizations. In addition, fabrication tolerances to the key structural parameters are presented and field evolution through the device is illustrated [ABSTRACT FROM AUTHOR]

A compact silicon-based polarization beam splitter (PBS) using directional couplers assisted with subwavelength grating (SWG) is proposed and analyzed in detail, where a conventional directional coupler at the input/output end and an SWG coupler in the middle together with SWG-based transitions between them are used. The introduced SWG structures can significantly improve the coupling strength for TE mode, whereas that for TM mode is hardly affected. Subsequently, by carefully choosing structural dimensions, the total coupling length for TM mode can be exactly twice that of TE mode, thus the two polarization states can be effectively separated so that a PBS is realized. Results show that a PBS with a coupling length of 10 μm is achieved, and the extinction ratio, insertion loss, and reflection loss are 23.38/31.78, 0.136/0.104, and −22.03 / − 26.91 dB, respectively, for TE/TM mode. In addition, fabrication tolerance to the key structural parameters and field evolution through the present device are both presented. [ABSTRACT FROM AUTHOR]

A compact polarization converter for silicon-based slot waveguides is proposed, in which a metal strip of silver (Ag) with a right-angled cross section located at the upper-right corner of the slot waveguide is embedded in its upper claddings. Owing to the characteristics of the introduced asymmetric hybrid plasmonic waveguide, the modal hybridness is highly enhanced and the optimal optical axis rotation angle, 45°, is realized by optimizing the location and size of the Ag, resulting in high polarization conversion efficiency (PCE). Numerical results show that a polarization converter of 15.2 μm in length, operating at a wavelength of 1.55 μm for TM-to-TE conversion, is achieved, where the PCE and insertion loss are 96.9% and 0.7 dB, respectively, and bandwidth with PCE >92% is ∼67 nm (from 1524 to 1591 nm), covering the entire C-band. Moreover, fabrication tolerances to the structural parameters and field evolution along the propagation distance are investigated. [ABSTRACT FROM AUTHOR]

A compact crossing scheme for a silicon-based slot-to-strip (or vice versa) waveguide is proposed and analyzed by using a finite-difference time-domain method, where a strip–multimode waveguide (SMW) crossing is used at the center and two logarithmically tapered slot-to-strip mode converters are incorporated into the ports with slot waveguides. For the input ports with slot waveguides and output ports with strip waveguides, the guided modes are efficiently transformed through the mode converter, and then enter into the SMW, where the fields converge at the center of the intersection due to the self-imaging effect. Hence, the size of the input beam is much smaller than the width of the SMW at the crossing center, leading to significant reductions of both crosstalk and radiation loss. The numerical results show that a slot-to-strip waveguide crossing operating at a wavelength of 1.55??m can be achieved with insertion loss, crosstalk, and reflection of 0.134/0.182, ?36.18/?38.6, and ?35.8/?42.02?dB for input ports with slot/strip waveguides, respectively. [ABSTRACT FROM PUBLISHER]

A compact silicon-based slot-waveguide crossing composed of a slot-to-strip mode converter (at each port) and an orthogonal strip multimode waveguide (SMW) is proposed and designed using a finite difference time domain method. With the mode converter based on logarithmically transitional tapers, the guided modes of the input slot waveguide are efficiently transformed to those of a strip one, and then enter into the SMW, where the fields converge at the centre of the intersection due to the self-imaging effect. As a result, the size of the input beam is much smaller than the width of the SMW at the crossing centre, leading to significant reductions in the crosstalk and radiation loss. The numerical results show that a slot-waveguide crossing operating at a wavelength of 1.55 µm with insertion loss, crosstalk and reflection of 0.131 dB, −37.44 dB and −35.47 dB, respectively, is achieved. Moreover, the fabrication tolerances to the structural parameters are investigated in detail. And the evolution of the injected field along the propagation distance through the slot-waveguide crossing is also demonstrated. [ABSTRACT FROM AUTHOR]

• The rectangular grooves are shallowly etched on the MMI waveguide to introduce the refractive-index perturbations on the MMI waveguide eigenmodes, leading to an effective refractive-index manipulation of the eigenmodes. • The refractive-index perturbation scheme provides a simple and scalable method to manipulate the four beat lengths of the two wavelengths at TE- or TM-polarization in a single waveguide via self-imaging effect, leading to a compact footprint. • The present refractive-index perturbation scheme realizes, for the first time, NIR/MIR wavelength demultiplexing and polarization independence simultaneously in an individual device. • A compact and polarization-independent wavelength diplexer for 1.31/2 μm is also realized by flexibly changing the dimensions, showing the flexibility and extensibility of our refractive-index perturbation scheme. Faced with the rapid growth of internet traffic demand, which has posed a huge challenge to the current fiber-based communications systems, expanding the telecommunications bands from traditional near-infrared (NIR) region to mid-infrared (MIR) region is emerging as an attractive solution. And on-chip wavelength division multiplexing (WDM) application for NIR/MIR wavelengths is an essential element in future optical telecommunication systems. Here, we propose a compact silicon-based polarization-independent wavelength diplexer for the NIR/MIR wavelengths of 1.55/2 μm, where multiple rectangular grooves are shallowly etched on the silicon MMI waveguide for introducing the refractive-index perturbations on the MMI waveguide eigenmodes. And this refractive-index perturbation scheme provides a simple and scalable method to manipulate the four beat lengths of the two wavelengths at TE- or TM-polarization in a single waveguide via self-imaging effect, leading to a compact footprint. By optimizing the structural parameters, both NIR/MIR wavelength demultiplexing and polarization independence, for the first time, are obtained simultaneously in the present single device. From the results, the proposed diplexer is only 21.6 μm in length, and shows a wide bandwidth of ∼ 100/120 nm around the wavelength of 1.55/2 μm for insertion loss (IL) < 1 dB and extinction ratio (ER) > 15 dB. Moreover, we also realize a compact and polarization-independent wavelength diplexer for 1.31/2 μm by flexibly changing the dimensions, showing the flexibility and extensibility of our refractive-index perturbation scheme. Besides, fabrication tolerances are analyzed and mode propagation profiles are also demonstrated. [ABSTRACT FROM AUTHOR]

The article presents a reply on the research on the design of a compact silicon-based slot-waveguide through orthogonal strip multimode waveguide.