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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]

The characteristics of directional couplers and power splitters based on three-guide optical couplers in slot waveguide structures are analyzed in detail by a three-dimensional full-vectorial beam propagation method. The numerical results show the achievement of a compact three-guide directional coupler operating as polarization independent with a length of 58.0 [micro]m and having almost evenly spaced propagation constants of the three lowest order modes for quasi-TE and quasi-TM modes. Thus, a high coupling efficiency from one outside waveguide to the other outside waveguide is demonstrated and is over 99.5% for both polarization states. For a three-guide power splitter, multiple sets of waveguide parameters for achieving polarization-independent operation are presented. Tolerances to operating wavelength and structural parameters are also analyzed, and the evolution of the injected field along the propagation distance through the proposed devices is demonstrated. OCIS codes: 130.3120, 230.7380, 130.2790, 250.5300.

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 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]

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]

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]

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 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: 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]

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]

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

A compact polarization splitter based on the directional coupler in horizontal multiple-slotted waveguide (HMSW) structures is proposed and designed by using a modified three-dimensional full-vectorial beam propagation method with perfectly matched layer absorbing boundary conditions. The results show that the birefringence of the HMSW is stronger than that of the single-slotted waveguide, leading to a reduction in length for the present device. Moreover, the HMSW can also enhance the optical confinement inside the slot regions. The coupling length of the directional coupler composed of two-parallel HMSWs as functions of the waveguide parameters are analyzed, and a compact device of 238.0 µm in length is achieved with the crosstalks of -27.9 and -35.6 dB for quasi-transverse-electric and quasi-transverse-magnetic modes, respectively. In addition, the evolution of the injected field along the propagation distance through the polarization splitter 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]

We present a compact TM polarizer with high polarization extinction ratio (PER), low loss, and suppressed reflection over an ultra-wide bandwidth on a 220 nm silicon-on-insulator (SOI) platform. The device utilizes a contra-mode conversion Bragg grating (CMC-BG) with strong polarization dependence embedded in a multimode waveguide. Through a sophisticated grating design incorporating tailored chirping and apodization profiles to match modal properties, we have achieved, by simulation, a compact device footprint of 34.72 × 1.22 µm 2 and an ultra-wide bandwidth of 346 nm with PER > 40 dB and an insertion loss (IL) < 1 dB, a 5-fold increase over our previous design. Particularly notable is the polarizer's ability to suppress reflection to <-15 dB across an extended bandwidth exceeding 450 nm. Experimental measurements confirm the excellent performance of the fabricated TM polarizer, with IL < 1.2 dB (0.5 dB) and PER > 30 dB over a bandwidth of 336 nm (268 nm).

We present what we believe is the first report on a polarization-insensitive 3 × 3 silicon star-crossing utilizing a composite subwavelength metamaterial waveguide structure. Two different types of subwavelength grating metamaterials (nanohole grating and fan-shaped bent subwavelength grating) are respectively used to address diffraction issues in the crossing region and mode interference issues caused by a compact non-adiabatic design. This approach results in a device with an ultra-compact footprint of 12.68 × 10.98 µm 2 on a standard 220 nm silicon-on-insulator (SOI) platform. Simulation results show low insertion loss (IL) values of <0.2 dB/0.3 dB and suppressed cross talk (CT) levels of <-27.2 dB/-23.6 dB for TE/TM polarizations across a wavelength range of 100 nm (1500-1600 nm). Experimental measurements of the fabricated devices confirm outstanding performance, with IL values of <0.35 dB/0.4 dB and CT levels of <-31.5 dB/-28.6 dB for TE/TM polarization in the C-band.

On-chip Bragg gratings with high reflectivities have been found to have widespread applications in filters, resonators, and semiconductor lasers. However, achieving strong Bragg reflections with flat response across a broad bandwidth on the popular 220 nm silicon-on-insulator (SOI) platform still remains a challenge. In this paper, such a high performance device is proposed and fabricated, which is based on a slot waveguide with gratings etched on the inner sidewalls of the slot. By manipulating the local field in the slot region using a chirped and tapered grating-based mode transition, the device achieves a flat response with ultra-high reflection and low transmission for the TE mode across a broad operating bandwidth. Leveraging the ultra-high birefringence of the SOI waveguide, the device functions both as a TE slot waveguide reflector and a TM pass polarizer. Simulation results demonstrate that the device exhibits an ultra-high rejection of more than 50 dB and a reflectivity exceeding 0.99 for the TE mode across a 91 nm wavelength range, while maintaining a high transmittance of larger than 0.98 for the TM mode. Experimental results validate that the device performance is consistent with the simulation results. A fabricated device based on such a gratings exhibits a low insertion loss (<0.8 dB) and high polarization extinction ratio (>30 dB) over 100 nm bandwidth (1484 nm-1584 nm), demonstrating that the performance of the present design is competitive with that of the state-of-the-art SOI Bragg gratings.