Finite-difference Mode Solver Research Articles

Modal analysis of silicon-on-insulator based rib waveguide using fully vectorial finite-difference mode solver

In order to interface optical integrated devices with external sources, an understanding of the modal characteristics of the optical waveguide is essential. The finite difference approach is utilized in this work to analyse a rib waveguide based on a silicon-on-insulator platform. A silicon device layer with thickness of 220 nm and a buried oxide with thickness of 2000 nm are considered. It is important to study the modal field distribution and parameters of the waveguide. The simulation results on the behaviour of modal parameters show that both effective refractive index and group index decrease with wavelength. The effective refractive index of the guided mode increases with rib width and slab thickness. It is also observed that energy is more confined in a deeply etched waveguide than in a shallow etched waveguide. Additionally, it is noted that the effective mode area and full-width half maximum increase with rib width and slab thickness.

Theoretical analysis of tuning property of the graphene integrated excessively tilted fiber grating for sensitivity enhancement

The graphene integrated optical fiber devices show many excellent characteristics, especially their tunable optical properties. Here we investigate thoroughly the influence of the tuning property of the graphene on the resonance and sensing performance of the excessively tilted fiber grating (Ex-TFG) operating around the dispersion tuning point. An improved piecewise discretization method for the finite-difference mode solver combined with coupling mode theory is presented to explore the general variation rule of mode characteristics and polarization-dependent resonances corresponding to polarized TE/TM0,m and HE/EHv,m modes of the graphene integrated Ex-TFG. The results reveal that both p-polarized and s-polarized modes and their resonances are greatly influenced by the tunable graphene. On this basis, the sensitivity enhancement of the graphene coated Ex-TFG is explored in detail. It is shown that the sensing performance of both polarized cases can be greatly improved by tuning the chemical potential. In particular, the graphene induces a greater influence on both resonance wavelength and resonance strength of the s-polarized mode, but the p-polarized one has a higher sensitivity. We believe that these unique tuning properties make the graphene integrated Ex-TFG devices ideal for the telecommunication and sensing applications, such as tunable fiber modulators and biochemical sensors.

Efficient design of polymer micro-ring resonator filters based on coupled mode theory and finite difference mode solver

Polymer photonics have been identified as a strong candidate technology for producing low-cost optical devices. In this paper, we provide a time efficient framework for designing polymer micro-ring devices based on Coupled Mode Theory (CMT) and a Finite Difference Mode Solver. We benchmark two alternative methods for modeling the coupling regions of the micro-ring filter in 3D. We deduce that compared to full blown finite difference time domain simulations, CMT can provide accurate results in just a small fraction of time. The proposed model allows the study of bending losses on the spectral properties of the device, that can be otherwise modelled using time demanding FDTD or less accurate simplified analytical expressions.

Optimization of the Local Evanescent Array-Coupled Optoelectronic Sensing Chip for Enhanced, Portable, Real-Time Sensing

Performance of the local evanescent array coupled (LEAC) biosensor is optimized by modifying the CMOS-compatible fabrication scheme and fine-tuning waveguide parameters based on simulation results of a full-vector finite difference mode solver. To enable in situ, real-time detection, an index-matched upper cladding reference region is patterned onto the waveguide. The reference region is followed by a sensing region exposed to the analyte, which is delivered via a flow cell. An on-chip, continuous photodetector array is implemented, which enables the fabrication of an optically smooth lower cladding/core interface, removing the need for chemical-mechanical polishing. As close mode-matching between reference and sensing regions increases the optical power launched into the sensing region, different mixtures of oils (n=1.4680-1.4722) were used as a proof of concept for real-time refractive index measurements. The ~ 1-cm2 LEAC chip, which exploits three independent sensing mechanisms, is demonstrated to have a static sensitivity of 4.6×10-6 RIU and a real-time (2s resolution) sensitivity of 4.1×10-5 RIU.

Experimental Assessment of the Accuracy of an Advanced Photonic-Bandgap-Fiber Model

From scanning-electron microscope images of the cross section of a photonic-bandgap fiber (NKT Photonics' HC-1550-02) we developed a realistic model for its permittivity profile that includes all observable structural deformations in the core and in the first two rows of cladding holes. Using this more accurate index profile in our C++ full-vectorial finite-difference mode solver, we numerically studied this fiber's modal dispersion, along with the intensity profile, group index spectrum, and group-velocity dispersion spectrum of its fundamental mode. Comparisons between these predictions and their experimental counterparts measured in the fiber show good quantitative agreement for all these characteristics. On the other hand, when these structural deformations are purposely not included in the permittivity profile, the predicted and measured characteristics generally poorly match. The study demonstrates that first, accurate simultaneous predictions of several key modal characteristics of hollow-core fibers can be obtained numerically, and that although small, the aforementioned index-profile perturbations must be included in order to obtain sufficient accuracy.

Study of an Electro-Optic Polymer Modulator

In order to characterize electro-optic polymer modulators, a full-vectorial finite-difference mode solver has been developed to solve Maxwell's equation for an optical waveguide, and a finite-element method has been employed to analyze a microwave electrode. A systematic and detailed discussion has been presented to describe and design a modulator about performance parameters: <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$V_{\pi}L,\Delta fL, N_{m}, \alpha_{c}$</tex></formula> , and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$z_{c}$</tex></formula> with all the necessary design parameters: optical waveguide (width and height), electrode (width and height), and thickness of cladding layer. We can see that most of the results are interesting, even very different from general opinions, for example, one can observe that <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$V_{\pi}L$</tex></formula> is not always reduced with an increased width of optical waveguide. These will be helpful for an optimized design of a modulator.

High sensitive fiber strain sensor using suspended-core fibers

A novel fiber strain sensor is proposed, based on the two-mode interference of a suspended-core fiber. A fullvectorial finite difference mode solver is employed as the numerical tool for characterizing the proposed strain sensor. The numerical results show that the proposed strain sensor has an estimated sensitivity of 0.05 rad/(m·μɛ), higher than that of the strain sensors using conventional multimode fibers, while the temperature sensitivity of the proposed sensor is relatively low.

Finite-Difference Mode Solver for Curved Waveguides With Angled and Curved Dielectric Interfaces

A finite-difference scheme for accurately analyzing step-index dielectric waveguides with angled and curved dielectric interfaces has been proposed by Chiang Here, this formulation is generalized to take into account a possible curvature of the entire waveguide along the propagation direction, and it is shown how Perfectly Matched Layers can be incorporated in order to accurately compute the bending or curvature loss of dielectric waveguides with step-index profiles of arbitrary shape. Furthermore, the formulation of the interface equations that relate the fields and their derivatives on both sides of a dielectric interface has been simplified, so that their implementation no longer requires any further explicit conversions between coordinate systems.

First-Principles Full-Vectorial Eigenfrequency Computations for Axially Symmetric Resonators

Starting from the time-harmonic Maxwell's equations in cylindrical coordinates, we derive and solve the finite-difference (FD) eigenvalue equations for determining vector modes of axially symmetric resonator structures such as disks, rings, spheres and toroids. Contrary to the most existing implementations, our FD scheme is readily adapted for both eigenmode and eigenfrequency calculations. An excellent match of the FD solutions with the analytically calculated mode indices of a microsphere resonator provides a numerical confirmation of the mode-solver accuracy. The comparison of the presented FD technique with the finite-element method highlights the relative strengths of both techniques and advances the FD mode-solver as an important tool for cylindrical resonator design.

Design and characterization of microring reflectors with a waveguide crossing

We present a novel design of a wavelength-selective reflector using a microring resonator integrated with a low-loss, low-crosstalk waveguide crossing. Functioning as a reflective notch filter, it can be used for optical communications and for sensor applications. The device is simulated using the transfer-matrix method combined with a two-dimensional finite-difference mode solver and is fabricated by a CMOS-compatible silicon-on-insulator technology. The measurement shows an extinction ratio greater than 25 dB and a resonance-wavelength temperature dependence of 0.09 nm/K.

Classification of the Core Modes of Hollow-Core Photonic-Bandgap Fibers

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Using a new full-vectorial finite-difference mode solver utilizing a hexagonal Yee's cell, we calculated the dispersion diagram of a slightly multimode (16 modes) air-core photonic-bandgap fiber (PBF) and the electric-field profiles of all of its core modes. Careful comparison shows striking similarities between these properties and those of the hybrid modes of a conventional step-index fiber, in terms of the modes' field profiles, the modes' degeneracy, the order in which the modes mode cut off in the wavelength space, and the maximum number of modes. Based on these similarities, we propose for the first time a systematic nomenclature for the modes of a PBF, namely hybrid HE and EH modes and of quasi-TE and quasi-TM modes. Other small but relevant similarities and differences between the modes of these two types of fibers are also discussed. </para>

Long-range surface plasmon polariton waveguides embedded in fluorinated polymer

Low-attenuation waveguides based on the propagation of long-range surface plasmon polaritons (LRSPPs) along thin Au stripes embedded in low absorption perfluorocyclobutane (PFCB) polymer are presented. A new low in propagation loss of <2.0 dB/cm was achieved for a 4 microm wide waveguide by optimizing the cladding material and fabrication process. The coupling efficiency between the LRSPP waveguide and the optical fiber is studied theoretically and experimentally for different widths of Au stripes and various cladding thicknesses. Lower coupling loss is found when the cladding thickness is close to the mode diameter of the butt-coupled fiber. Based on the 2D distribution of SPP modes calculated by a finite-difference mode solver, a symmetric structure of multilayer claddings with different refractive indices is proposed to optimize device insertion loss.

Characterization of bent large-mode-area photonic crystal fiber

In this paper, the characteristics of bent large-mode-area photonic crystal fibers are investigated comprehensively by using a finite difference mode solver with perfectly matched layers. Numerical results show that in bent large-mode-area photonic crystal fibers, the mode-field distributions are deformed and the effective mode area and the width of the guided region are reduced. The propagation character of bent photonic crystal fibers is determined by normalized propagation number and normalized bend radius. Meanwhile, the bending loss oscillation is observed and the position of the first loss peak is obtained in bent large-mode-area photonic crystal fibers.

Inverse design of dispersion compensating optical fiber using topology optimization

We present a new numerical method for designing dispersion compensating optical fibers. The method is based on the solving of the Helmholtz wave equation with a finite-difference modesolver and uses topology optimization combined with a regularization filter for the design of the refractive index profile. We illustrate the applicability of the proposed method through numerical examples and, furthermore, address the problem of keeping the optimized design single moded by including a singlemode constraint in the optimization problem.

Improved full-vectorial finite-difference mode solver for optical waveguides with step-index profiles

A general relation considering an interface condition between a sampled point and its nearby points in the finite-difference analysis of optical waveguides, is derived. Our formulation is a full-vectorial one, and the interface can be oblique to the global coordinate axes or even can have curvature. Using the derived formulation, optical waveguide structures with arbitrary step-index profiles can be dealt with. The validity of the proposed method is examined by comparing the numerical calculation with the analytical solution of a step-index optical fiber. The method is also applied to the analysis of fused fiber-optic couplers and compared with prior analysis using the surface integral equation method.

Sidelobe Suppression of Vertical Coupler Filter with an X-Crossing Configuration

An antiresonant reflecting optical waveguide (ARROW) type vertical coupler filter exhibiting low sidelobe charateristics is demonstrated. The sidelobe level of the filter has been suppressed by using an X-crossing arrangement to provide strength apodization along the device. The main sidelobe of the fabricated filter is measured to be less than -17 dB with the central wavelength in the 1.55 µm region. An analysis procedure which combines the coupled mode theory with the finite difference mode solver is also presented to efficiently calculate the vertical coupler filter response.