Solutions of the full- and quasi-vector wave equations based on H-field for optical waveguides by using mapped Galerkin method

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.     

A Modified full-vectorial finite-difference beam propagation method based on H-fields for optical waveguides with step-index profiles

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.     

Impact of misfit dislocations on wavefront distortion in Si/SiGe/Si optical waveguides

Silicon-rich SiGe alloys represent a promising platform for the development of large-area single-mode optical waveguides to be integrated in silicon-based optical circuits. We find that SiGe layers epitaxially grown on Si successfully guide radiation with a 1.55 μm wavelength, but, beyond a critical core thickness, their optical properties are strongly affected by the clustering of misfit dislocations at the interface between Si and SiGe, leading to a significant perturbation of the local refractive index. Transmission electron microscopy and micro-Raman spectroscopy, together with finite-element simulations, provide a complete analysis of the impact of dislocations on optical propagation.     

Reconstruction of extraordinary refractive index profile of O ion-implanted LiNbO3 single-mode channel waveguide based on beam propagation method and image processing

A method bases on beam propagation method and image processing is brought forward to reconstruct the extraordinary refractive index profile of the ion-implanted single-mode channel waveguide in lithium niobate. Channel waveguide is formed by O²⁺ ion implantation at three energies of (3.0, 3.6 and 4.5 MeV) and respective doses of (1.8, 2.2 and 4.8) × 10¹⁴ ions/cm² in vacuum at room temperature. Only one enhanced-index mode is observed for extraordinary light at 1539 nm by prism-coupling method. TRIM’98 code is used to simulate the damage profile in channel waveguide. The modes pattern of TE and TM are measured by use of end-face coupling method.     

Design of a wavelength demultiplexer based on a parabolically tapered multimode interference coupler

A compact wavelength demultiplexer is designed for the operation at 1.30 and 1.55 μm 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 330.0 μm in length, which is only 76% length of a straight MMI coupler, is achieved with the contrasts of 42.3 and 39.2 dB in quasi-TE mode, and 38.4 and 37.8 dB in quasi-TM mode at wavelengths 1.30 and 1.55 μm, respectively and the insertion losses below 0.2 dB. 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.     

Tunable optical switch based on two orthogonal line defect waveguides

The transmission characteristics of a 2-dimensional (2D) square lattice photonic crystal waveguide (PCW) with an additional perpendicular line defect are investigated by the plane wave expansion method (PWM) and the finite difference time domain (FDTD) method. From simulation results and theoretical analysis, it is found that changing the refractive index of the dielectric columns in the additional line defect can effectively adjust the light transmission through the PCW. The working mechanism can be boiled down to either the excitation of a single defect mode or the contra-directional coupling of the two defect modes. And this mechanism can be used to design other tunable optical devices.     

Analysis of symmetric and asymmetric nanoscale slab slot waveguides

Nanoscale slab slot waveguides provide for high optical confinement and have found abundant applications in silicon photonics. After developing an analytical mode solver for general asymmetric slot waveguides, the confinement performance of symmetric as well as asymmetric geometries was systematically analyzed and compared. For symmetric structures, 2D confinement optimization by varying both low-index slot and high-index slab width revealed a detailed saturation trend of the confinement factor with the increase of the studied width. Furthermore, simple design rules on how to choose the slot and slab width for achieving optimal confinement was obtained. For asymmetric structures, we demonstrated that the confinement performance was always lower than the 2D optimized confinement of the symmetric structures providing the two high-index slab layers and the two cladding layers have same refractive indices, respectively. In addition, the sensitivity of the confinement to the degree of asymmetry was studied, and we found that the fabrication tolerance on the material and structural parameters may be reasonably large for symmetric structures designed at optimal confinement.     

Reconstruction of extraordinary refractive index profiles of optical planar waveguides with single or double modes fabricated by O ion implantation into lithium niobate

A method named intensity calculation method (ICM), which is based on beam propagation method (BPM) and image processing, was carried out to reconstruct the extraordinary refractive index profile (RIP) of single-mode planar waveguide in lithium niobate (LiNbO₃), which was fabricated by multi-energy megaelectron-volt (MeV) O²⁺ ion implantation. In addition, it has been proved reasonable that the alternation of extraordinary refractive index induced by ion implantation into LiNbO₃ is mainly due to the degradation of polarization and reduction of material physical density. As a result, the possible extraordinary RIP of the double-mode planar waveguide could be reconstructed using BPM according to such a hypothesis and the calculated guiding mode values. The end-fire coupling and m-line arrangements were carried out to obtain the near-field modal patterns and dark-mode spectra of waveguides, respectively.     

Optimal design for a flat-top AWG demultiplexer by using a fast calculation method based on a Gaussian beam approximation

Passband broadening of an AWG (array waveguide grating) demultiplexer with an MMI (multimode interference) coupler connected at the end of a tapered input waveguide is considered. An explicit formula based on the field propagation of an approximate Hermit-Gaussian beam is used to calculate quickly and reliably the spectral response of the AWG demultiplexer. The widths of the input waveguide, the output waveguides and the MMI coupler are optimized. The optimal design is verified with the experimental measurement.     

Low-loss, compact waveguiding with TE mode in metal/dielectric waveguides for planar lightwave circuit

We propose a low-loss metal/dielectric waveguide for compact planar lightwave circuit. The basic waveguide structure is a metal-defined high-index-contrast strip waveguide based on silicon/silica. As the guide is designed for TE single mode waveguiding, extremely low propagation loss (e.g. <0.04 dB/cm), very low bend loss (e.g. 0.0043 dB/90°-turn) and small waveguide pitch of zero-crosstalk are theoretically achievable, and can be further improved by compromising with component size and density. Examples of multi-bends and device integration are demonstrated with numerical simulations. The proposal is compatible with silicon technology and appealing for development of silicon-based planar lightwave circuit.     

Vector modes of rectangular-core dielectric waveguides: An improved perturbation approach

We present an improved analysis to obtain vector modes of a rectangular-core waveguide (RCW) structure whose dielectric constant profile is separable in x and y coordinates. Using this analysis, a perturbation method is then developed to obtain vector modes of a practical RCW. The propagation constants so obtained for a fully-buried and a ridge RCW structure using the present analysis are found to be in better agreement with reported numerical values than the ones obtained with an earlier reported perturbation approach [Kumar et al., Opt. Lett. 8 (1983) 63].     

Optimization of signal-to-noise ratio in integrated planar optical interconnects packages

The signal-to-noise ratio (SNR) of integrated planar optical (IPO) board-to-board interconnections system is analyzed. The SNR is derived as a function of separation between the boards, beam spot size, optical system efficiency, receiver thermal noise, thickness of the substrate, and the angle of propagation of the beam. Based on the analyses and the results obtained it is shown that the design of optical interconnects system can be optimized for maximum SNR using at least one parameter, namely, angle of propagation.     

Design and simulation of a novel 32 × 32 photonic bandgap power switch based on SOI waveguide

In this paper, we propose a novel 32 × 32 photonic bandgap (PBG) power switch based on silicon-on-insulator (SOI) substrate. The 32 × 32 PBG power switch merges the design concept of PBG structure and multimode interference (MMI) structure. With controlling the voltages of 256 blocks for changing the refractive index, we can demonstrate that the light propagation direction can be switched to the assigned output port as a 32 × 32 power switch. According to the simulations, the power switching control tables are searched and selected for successful switching. The size of our designed 32 × 32 PBG switch can be reduced to 252 × 6040 μm which is much smaller than the conventional opto-electronic switches.     

Full-vectorial analysis of optical waveguides by the finite difference method based on polynomial interpolation

Based on the polynomial interpolation, a new finite difference (FD) method in solving the full-vectorial guided-modes for step-index optical waveguides is proposed. The discontinuities of the normal components of the electric field across abrupt dielectric interfaces are considered in the absence of the limitations of scalar and semivectorial approximation, and the present FD scheme can be applied to both uniform and non-uniform mesh grids. The modal propagation constants and field distributions for buried rectangular waveguides and optical rib waveguides are presented. The hybrid nature of the vectorial modes is demonstrated and the singular behaviours of the minor field components in the corners are observed. Moreover, solutions are in good agreement with those published early, which tests the validity of the present approach.     

Measurement of small chirp-parameter for Mach-Zehnder-type optical modulator

A new measurement method of chirp-parameters is proposed for electro-optic (EO) intensity modulators with the Mach-Zehnder (MZ) waveguide interferometer. This method is suitably applied for the measurement of the small chirp with operation at a specific RF-frequency. To determine the chirp-parameter, optical spectrum components of the modulated light are observed with varying the relative optical phase difference between the two arms of the MZ waveguide interferometer. The chirp-parameter of 0.17, which is a value small enough for EO intensity modulation, was successfully measured by the experiment.     

Comparison of the electro-optic coefficient r33 in well-defined phases of proton exchanged LiNbO3 waveguides

The electro-optic coefficient, r₃₃, of proton exchanged LiNbO₃ waveguides has been measured in well-defined phases of the exchanged layer. Namely, in two low index-jump α-phases, i.e. unannealed soft-exchanged (SPE) and annealed (APE) guides, and in two high index-jump phases, i.e. β₁ guides and, for comparison, ordinary proton exchanged (PE) guides (having a mixture of phases). The following values have been obtained (in pm/V): 22.1±0.6 for SPE; 20.9±0.7 for APE; 0.33±0.01 for β₁; and 0.76±0.04 for PE. Differences between these values are discussed in terms of the structure of the phase involved. Received: 18 May 2001 / Revised version: 22 August 2001 / Published online: 30 October 2001     

Optimal design of multimode interference couplers using an improved self-imaging theory

Self-imaging theory is widely accepted as a good method in designing 1 × N multimode interference (MMI) couplers, but it is also true that self-imaging theory is not suitable for low-contrast structures. An improved self-imaging theory is proposed in this paper for the optimal design of low-contrast 1 × N MMI couplers. The average effective width of MMI waveguide and the average effective propagation constant of MMI waveguide are used as the basis to modify the conventional self-imaging theory. A direct calculation of the average effective width of low-contrast MMIs is presented. We use this approach in the optimal design of a 1 × 4 silica MMI coupler, and the results show that the improved self-imaging theory is more accurate than conventional self-imaging theory for low-contrast structures, the results also show that if the material parameters and the width of an MMI waveguide are fixed, the average effective width of the MMI waveguide will increase with the decrease of the height of the core layer.     

An improved ray approximation method to design the single-mode 3-D optical waveguide

A novel method is developed to analyze a single-mode 3-D optical waveguide based on the ray-approximation method, which we call the improved ray approximation method. The effect of the optical parameters (wavelength, refractive-index and refractive-index difference) on the optimum design is investigated for a strong single-mode 3-D optical waveguide. This is simple and effective for the optimum design of the optical waveguide using the method. This will be helpful for the design of waveguide devices.     

Analysis and optimization of an InGaAsP/InP waveguide variable optical attenuator

An InGaAsP/InP waveguide variable optical attenuator (VOA) is proposed in this paper. The device consists of straight input and output waveguides and an S-bend waveguide. An electrode is deposited on a portion of the waveguide to form an active region so that its refractive index can be modified by a current injection, resulting in the variation of the transmitted optical power. The beam propagation method is employed in the numerical simulation and the device structure is optimized using a genetic algorithm. The optimized VOA has a low excess loss (<1 dB) and a large dynamic range of about 40 dB.     

Compensation of beam walk-off in hollow metal waveguides

Hollow metal waveguides feature well collimated beams and small losses across air gaps. This enables introduction of multiple optical beam splitters, or taps, along the waveguide to multicast signals from a source to multiple receivers. The splitters need to be of sufficient thickness to provide mechanical integrity and ease of handling. As a result, passing through the thickness leads to a beam walk-off. Walk-off dependence on the splitter thickness and its effect on the system optical efficiency are investigated. Two methods to compensate the walk-off are described: by offsetting the outgoing waveguide, and by introducing an additional symmetric optical element to shift the beam back to the original optical path. Both methods have been shown to effectively mitigate the walk-off effects.