Semivectorial Beam Propagation Method Research Articles

Sensitivity improvement in Si3N4 tapered waveguides for compact refractive index sensors

Optical waveguide sensors have been widely used in biosensing applications. However, ensuring an improvement in the sensitivity and detection limit of these sensors with low fabrication complexity and high integration capacity is essential for them to stand out among new sensing technologies. In this context, a refractive index (RI) sensor based on intensity detection is proposed and numerically simulated in this work. The sensor is composed of a non-complex structure based on a silicon nitride (Si3N4) tapered waveguide on a silicon substrate, which is integrated with a sensing window. The tapered waveguide design aims to enlarge the interaction area of the evanescent field, increasing significantly the device sensitivity. In order to verify the sensor performance and provide a high fidelity numerical simulation, it is employed a 3D semi-vectorial beam propagation method (BPM). Both bulk and surface maximum sensitivity is computed and the values of 1701%/RIU and 1.74%/nm are obtained, respectively. These results suggest that the proposed sensor is compact, structurally simple, and provides better performance than complex sensors presented in the literature.

Analysis of Mode Competition in Resonant Leaky-Wave Coupled Phase-Locked Arrays of Mid-IR Quantum Cascade Lasers

A numerical model is developed for a phase-locked array of quantum cascade lasers. The population density is derived from rate equations. The temperature distribution for stationary generation is produced by ohmic heating. It is shown that the results of above-threshold operation modeling by the semi-vectorial beam propagation method are in good agreement with the modal analysis provided by the vectorial-COMSOL solver supplemented with the Rigrod’s model estimations. The wall-plug efficiency and the limits of the single-mode lasing are found. Thermal lensing is shown to be the main reason limiting the single-spatial-mode power under CW-operating conditions.

Generalized modelling for the design of guided-wave optical directional couplers

In this Letter we propose a rigorous and generalized approach for the design of integrated optical bent directional couplers (DCs) based on the coupled mode theory and super mode theory. The full vectorial finite-element method is used for the calculation of effective indices of optical modes propagating into the waveguides constituting the DCs. The flexibility and robustness of this general modelling approach is demonstrated by simulating several directional coupling configurations, as those based on cosine S-bend and double arc bent waveguides. Furthermore, some numerical results have been validated by comparison with the three-dimensional semi-vectorial beam propagation method.

Design of a fiber polarizer based on an asymmetric dual-core photonic crystal fiber

We propose a novel optical polarizer based on an asymmetric dual-core photonic crystal fiber (PCF) with triangular lattice air-holes. The fiber is designed as that the effective indices of modes in the two cores are matched at one polarized state but mismatched at another polarized state. As a result, one of the polarization states is coupled to the other core and transferred into a high-order mode. The transmission properties of the polarizer are investigated by the semi-vectorial beam propagation method (SV-BPM). Numerical results demonstrate that a device length of 11.3 mm shows extinction ratio as low as −20 dB with bandwidth as great as 80 nm ranging from 1.51 m to 1.59 m.

Frequency Response of Silicon-Clad Proton-Exchanged Channel Waveguides

The annealed proton-exchanged (APE) process has emerged as an important technique for the fabrication of low-loss optical waveguides in LiNbO3. The propagation characteristics of a silicon-clad X- and Z-cut APE channel optical waveguide are investigated by the semi-vectorial beam propagation method (BPM). Numerical results for several different waveguide structures indicate that the attenuation of channel dielectric waveguides clad with silicon behaves as a damped periodic oscillation with increasing silicon thickness. Results also show that the attenuation of the propagating mode is highly dependent on wavelength. Moreover, this loss characteristic can be controlled by waveguide parameters such as the thickness of silicon-clad and buffer layer. As a result, the silicon-clad proton-exchanged optical waveguides can be used as optical frequency filters.

Ultra-Long Compact Optical Polymeric Array Waveguide True-Time-Delay Line Devices

New types of UV curable polymeric ultra-long array waveguide true-time-delay (TTD) lines for wideband phased array antennas (PAA) are designed and fabricated using direct UV photolithography process. The unique feature of the approach consists of different 1 × N waveguide splitters, low-loss S-bend cosine waveguide connectors, and 180° array bend waveguides with a constant spacing difference ¿R between adjacent waveguides. The delay time increments are measured from 1.4 ns to 6.6 ps. 1 × 2, 1 × 4, 1 × 8 polymeric star coupler devices are also successfully prepared. The bend loss of different curved waveguides is calculated and analyzed by the 3-D semivectorial beam propagation method (BPM). The optimized structural properties of the UV curable polymeric waveguides and fabrication procedures are demonstrated. The near-infrared field guided-mode patterns of the devices are obtained. The new technique can be well suited for realizing absence of "beam squint" in the antenna pattern as its frequency is switched from L(1-2.6 GHz) to X(8-12 GHz) band.

Optical matching layer structures in evanescent coupling photodiodes at a wavelength of 1.55 μm: physics, design and simulation

We have studied the optical matching layers (OMLs) and external quantum efficiency in the evanescent coupling photodiodes (ECPDs) integrating a diluted waveguide as a fibre-to-waveguide coupler, by using the semi-vectorial beam propagation method (BPM). The physical basis of OML has been identified, thereby a general designing rule of OML is developed in such a kind of photodiode. In addition, the external quantum efficiency and the polarization sensitivity versus the absorption and coupling length are analysed. With an optical matching layer, the absorption medium with a length of 30 μm could absorb 90% of the incident light at 1.55 μm wavelength, thus the total absorption increases more than 7 times over that of the photodiode without any optical matching layer.

Determination of wave propagation properties for multilayered dielectric waveguide by semivectorial beam propagation method with Douglas scheme

AbstractAn improved parabolic‐equation‐based numerical method with Douglas scheme is developed for modeling the new 3D multilayered dielectric transmission waveguides. Unlike the traditional one, such waveguides are constructed by putting the multilayered dielectric cladding with step indices property on a silicon substrate. The propagation properties of widely used polarization‐maintaining waveguides and antiresonant reflecting dielectric waveguide are investigated by this method as examples. The discussion on the numerical dispersion and radiation loss property is also included to validate this improved beam propagation method (or BPM). © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 2521–2524, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23725

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 SiO 2/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.

Semi-vectorial analysis of a compact wavelength demultiplexer based on the tapered multimode interference coupler

Based on a parabolically tapered multimode interference (MMI) coupler with a deep-etched SiO2/SiON rib waveguide, a compact wavelength demultiplexer operating at 1.30 and 1.55µm wavelengths is proposed and analysed by using three-dimensional semi-vectorial finite-difference beam propagation method (3D-SV-FD-BPM). The 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 1.55 µm, respectively, and the insertion losses below 0.2dB at both wavelengths and in both polarization states. The alternating direction implicit algorithm with the Crank–Nicholson scheme is applied to the discretization of the 3D-SV-FD-BPM formulation along the longitudinal direction. Moreover, a modified FD scheme is constructed to approximate the resulting equations along the transverse directions, in which the discontinuities of the derivatives of magnetic field components Hy and Hx along the vertical and horizontal interfaces, respectively, are involved.

Design and simulation of a novel arrayed-waveguide grating

A novel arrayed-waveguide grating (AWG) based on unbent waveguides is proposed. Two graded-index planar waveguides (GISLAB) are used as input and output planar waveguides, respectively, and the arrayed waveguides are replaced by unbent waveguides, which are photosensitive waveguides exposed to UV light twice. Next, the 2-D semivectorial beam propagation method is adopted to simulate the light transmitting process in the device, and the simulation shows that this device and the design are feasible.

Theoretical Performance Analysis of an Integrated Optic Filter Made of Glass Waveguides and POLICRYPS Holographic Gratings

We present the theoretical study and the simulation of the optical field propagation in a guided wave tuneable optical filter using a composite material grating. A numerical analysis of the optical propagation has been performed by using a 3D semivectorial BPM (Beam Propagation Method) based software and the results have been compared with a matrix-transfer approach based on the effective index method. The dependency of the filter response on the index modulation depth (Δn), the length and the thickness of the grating have been also analyzed. Performance of chirped and apodized gratings were also studied. The optical filter reflection and transmission spectral responses in terms of full width at half maximum (FWHM) have been calculated.

Experimental evaluation of curved polymer waveguides with air trenches and offsets

Excess waveguide bend loss can be minimized through the use of offsets and air trenches. Offsets, used for reducing the junction loss between straight and curved waveguides, and air trenches, which prevent bend radiation loss, were simulated by a three-dimensional, semivectorial beam propagation method. Low loss polymer waveguide bend structures, employing both offsets and trenches, were fabricated. A reduction of the 180° bend insertion loss from 17.7to3.0dB with a bending radius (BR) of 1.5mm is experimentally confirmed at λ=1.55μm. BR ranging from 5to0.5mm are evaluated with decent match when compared with simulation results. The polarization dependent loss is BR dependent with a maximum value of 0.4dB when the BR is reduced to 0.5mm. The experimental results confirm that the joint use of air trenches and junction offsets is effective in reducing the bend radii of low index contrast polymer waveguides in planar lightwave circuits.

Bilevel mode converter between a silicon nanowire waveguide and a larger waveguide

A bilevel mode converter is analyzed for providing low-loss coupling between the small fundamental mode of a silicon nanowire waveguide and the larger mode of a conventional silicon-on-insulator (SOI) rib waveguide. The bilevel converter can also be used to improve the coupling efficiency between a lensed fiber and a silicon nanowire waveguide. The mode converter consists of two tapers formed at different levels. The top taper comprises a parabolic and sine taper, which is optimized to improve the mode conversion efficiency. Numerical analyses are given by using a three-dimensional semivectorial beam propagation method. The design has good tolerance against misalignment of the two masks needed for the double etch.

Polarization splitter/combiner in high index contrast Bragg reflector waveguides

Novel designs of polarization devices based on Bragg reflector waveguides in a high index contrast silicon-on-insulator (SOI) platform have been proposed. Brewster angle condition is incorporated in the periodic structures. Numerical simulations with a 3D semivectorial beam propagation method demonstrate the device performance as TE mode polarizer with high TE to TM extinction ratio and TE/TM mode polarization splitter and combiner with high polarization splitting efficiency.

Analysis of polarization properties of lateral antiresonant reflecting optical waveguides

Polarization properties of lateral antiresonant reflecting optical waveguides (ARROWs) with many periods have been investigated in a high index contrast material based on silicon-on-insulator platform. Two designs, one based on grazing incidence and a second one incorporating Brewster angle condition, with depressed and non-depressed index cores are compared. The numerical simulations with a 3D semi-vectorial beam propagation method presented demonstrate that depressed and non-depressed index core in the two analyzed designs have very different polarization properties. With non-depressed index core TE and TM polarization modes are efficiently supported, whereas with the depressed index core both designs perform well as TE mode polarizers with a TE to TM extinction ratio of better than 22 dB/mm. Attenuation properties have also been studied for different number of periods in the ARROW design.

Fast semivectorial non‐linear finite‐difference beam‐propagation method

AbstractIn this paper a new semivectorial finite‐difference beam‐propagation method (FD‐BPM) technique for the analysis of nonlinear optical devices is presented. The proposed technique relies on the application of the Runge–Kutta method to perform each propagation step; it is easier to use than the Crank–Nicholson‐based FDBPM method and exhibits better numerical performance. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 73–77, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11288

General properties of N x M self-images in a strongly confined rectangular waveguide.

General properties of N x M self-images in a strongly confined rectangular waveguide are given. Analytical formulas are derived for the positions, amplitudes, and phases of the N x M images at the end of multimode interference section. The formulas are verified with numerical simulation of a three-dimensional semivectorial beam propagation method.

Characterisation of low-loss waveguide bends with offset-optimisation for compact photonic integrated circuits

Use of a semivectorial finite element-based beam propagation method is benchmarked with the results available by using alternative numerical methods to analyse compact optical bends in photonic integrated circuits. It is also shown that the incorporation of the perfectly matched layers boundary condition is a superior approach for the treatment of high radiation loss from compact bends to the more common use of the absorbing boundary conditions. The least squares boundary residual method is employed to calculate the lateral offset necessary to maximise the transmission and simultaneously to minimise the reflection coefficients at the straight-to-bend waveguide interfaces. Using these efficient numerical techniques, the radiation loss, transition loss and the required waveguide offset to maximise the transmission and reduce the reflection are calculated.

Analyzing the polarization dependence in optical spot-size converter by using a semivectorial finite-element beam propagation method

This paper describes a semivectorial wide-angle finite-element beam propagation method (FE-BPM) that uses the Pade approximation and that can allow efficient and accurate analyzes of the polarization dependence in arbitrary step-index optical waveguide devices. It also reports the use of this method to analyze the polarization dependence of coupling loss between a semiconductor tapered-waveguide spot-size converter and a single-mode optical fiber. It is shown that semiconductor spot-size converters having cores with a small cross-section provide low-loss and polarization-insensitive coupling to flat-end fibers. A low-loss (far less than 1 dB) and completely polarization-insensitive spot-size converter can be made using a lightly n-doped InP substrate for the tapered waveguide. These spot-size converters are consequently potentially useful for making polarization-insensitive semiconductor optical devices such as optical amplifier gate switches.