Three-dimensional Beam Propagation Method Research Articles

Suppression of modal crosstalk in laser-direct-writing weakly-guiding bending multimode waveguides

Space division multiplexing (SDM) techniques based on few-mode or multicore fibers have attracted great interest to enhance the capacity of optical networks, for which laser direct writing (LDW) is a promising approach to realize compact spatial multiplexer/demultiplexer (MUX/DEMUX). However, the modal crosstalk induced by bending multimode waveguide in LDW spatial MUXs/DEMUXs may have significant influence on the overall performance of a weakly-coupled SDM system supporting independent spatial channels. In this paper, we firstly analyze the bend-induced mode coupling behaviors for linearly-polarized (LP) modes in circularly-symmetric-step-index weakly-guiding bending multimode waveguides (WGBMW) and show that LP01 and LP11 modes will have the strongest mode coupling. Then we propose an optimal design of 90°-bend and S-bend using hybrid Euler-Circular (HEC) bend, where the length of Euler bend is optimized to be the beat length of LP01 and LP11 modes to suppress their mode coupling. Numerical simulations based on conformal mapping model and three-dimensional Beam Propagation Method are performed. The simulation results show that the optimal HEC bend can significantly suppress the mode crosstalk and loss. The crosstalk of LP01 and LP11 modes for the optimal HEC bend is below −60 dB, whereas the value for the circular bend is about −23 dB. This work provides a better understanding of bend-induced mode coupling in WGBMWs and is beneficial for the practical design of LDW devices.

Design of Silicon TE0/TE1 Mode Router Using Mach-Zehnder and Multimode Interferometers


 
 
 This paper proposes a new design of two-mode three-port optical mode router for mode division multiplexing systems. The device consists of a Mach-Zehnder interferometer (MZI) and a multimode interferometer (MMI), which utilizes silicon material for photonic integrated circuits (PIC). By setting appropriate values for the two butterfly-shaped phase shifters (PSs) at MZI and MMI, the input mode, either transverse electric (TE) modes TE0 or TE1, can be routed to the desired output among the three output ports. The device is designed and optimized via three-dimensional beam propagation method (3D BPM). The proposed device achieves very low insertion loss and small cross-talk, which are less than 0.4 dB and -24.5 dB, respectively, over the whole C band.
 
 

Design of polarization beam splitter based on dual-core photonic crystal fiber with three layers of elliptical air holes

A polarization beam splitter (PBS) based on dual-core photonic crystal fiber (DC-PCF) with three layers of elliptical air holes is proposed. The full-vector finite element method is used to investigate the coupling and propagation characteristics of the PBS, and the three-dimensional beam propagation method is used to demonstrate the evolutions of the x-pol and y-pol light fields in cores A and B of the DC-PCF. In this design, the elliptical air holes are introduced to enhance the birefringence of the DC-PCF. The simulation results show that, with the proposed PBS, the complete beam splitting can be achieved at wavelength 1.55 μm when the fiber length is 254 μm. Moreover, when the extinction ratio is less than −20 dB, the bandwidth of the PBS can be up to 48 nm, covering the whole C-band. It is believed that the proposed PBS will be a promising candidate in laser and sensor systems.

Design of a visible light photonic chip for Haar transform based optical compression

An optical chip has been designed and simulated using low contrast optical waveguide structures with the aim of investigating all-optical data compression in the visible spectrum. The chip comprises optical circuits for digital compression at wavelength λ = 532 nm (green light) based on the optical Haar transform (HT). Each circuit contains one or more 2-point HT building block(s), based on multimode interference (MMI) structures, which enables HT operation on the input signal pairs. Each of the two Outputs of each building block represents the sum and subtraction of the input signals. Compression can be achieved only by considering the sum signal and eliminating the subtraction signal. Higher order HT and, as a result, a higher rate of compression has been realized in the chip by implementing HT on the sum signals obtained from the first step compression. Simulation results obtained by three-dimensional beam propagation method (3D-BPM) show that designed circuits in the chip have an excellent capability for the realization of all-optical compression in the visible spectrum based on Haar transform.

Manufacturing Tolerance Analysis of Deep-Ridged 90° Hybrid Based on InP 4 × 4 MMI

An optical 90° hybrid based on an InGaAsP/InP deep-ridged 4 × 4 multimode interference (MMI) coupler is proposed and fabricated. Manufacturing tolerances on structural parameters of the 90° hybrid including multimode waveguide width and length, waveguide core thickness, and refractive index are analyzed over the whole C-band using a three-dimensional beam propagation method (3D BPM). The simulation results show that the 90° hybrid is insensitive to the interference length with a deviation of 10 μm. However, the width fluctuations produce far stronger performance variations than length fluctuations. The common-mode rejection ratios (CMRRs) are always above 40 dB, and the phase error (PE) is always below 2.5° with the fluctuations of the refractive index by 0.01 and the thickness by 0.1 μm of the core layer. The fabricated device exhibited a quadrature phase response with a high common-mode rejection ratio of more than 25 dB and a small phase error of less than 5° from 1545 nm to 1560 nm.

Three-mode multiplexed device based on tilted- branch bus structure using silicon waveguide

We propose a new design of a silicon chip for (de)multiplexing three optical modes based on a tilted-branch bus structure using silicon waveguide. Input lights at fundamental, first-order, and second-order modes in three-dimensional space are simultaneously demultiplexed and converted to three fundamental modes at three individual output ports. The device is designed and optimized via numerical simulation using three-dimensional beam propagation method (3D-BPM).Successful three-mode demultiplexing can be achieved over 150 nm wavelength band of telecom winodws with insertion loss smaller than 1.45 dB and crosstalk below -16 dB. The proposed device also features with a small footprint (8 μm × 950 μm) and a large fabrication tolerance against chip-size variations while maintaining the desired optical performance.

Three-mode multiplexer and demultiplexer utilizing trident and multimode couplers

In this paper, a simultaneous three-mode silicon (de)multiplexer using a trident coupler and a 3 × 3 multimode interference (MMI) is presented. The fundamental (TE0), first-order (TE1), and second-order (TE2) modes at the input are successfully demultiplexed and converted to three uniform fundamental modes (TE0) at the output ports. The device is designed and optimized by numerical simulation using three-dimensional beam propagation method together with effective index method. The three-mode (de)multiplexing is achieved over the whole C-band with small insertion loss (<0.9 dB) and crosstalk (<−17 dB). The proposed device also features with a small footprint (5μm × 400μm) and a large fabrication tolerance against chip-size variations while maintaining the desired optical performance.

All-Optical Half Adder Based on a 2x2 Multimode Interference Coupler

In this paper, an all-optical logic gate based on 2x2 (MMI) multimode interference coupler is theoretically designed and simulated using three-dimensional beam propagation method (3D-BPM) and effective index method (EIM) to analyze and evaluate the performance of the device. The proposed device is used to convert phase information of input optical signals to amplitude at the output ports of MMI. With this mechanism, the device can operates as a logical half adder. Simulation results show that the optical half adder archives with insertion loss and extinction ratio from ON to OFF logic–level below 0.7 dB and over 40 dB, respectively. Furthermore, wide bandwidth of 100nm is also an advantage of this devices. Therefore, it can be applied to all optical signal processing in next generation optical networks as well as in photonics integrated circuits.

Highly uniform and polarization-independent Y-branch with mode filter based on deeply etched silica-on-silicon waveguide

A slight misalignment between an optical fiber and a Y-branch would excite high-order modes and subsequently induce a snaking behavior of the input light, which would dramatically deteriorate the device performance. Here, a highly uniform and polarization-independent Y-branch based on deeply etched silica-on-silicon (SoS) waveguide is proposed, optimized, fabricated, and characterized, in which a mode filter with the quadratic-spline boundary is inserted to suppress the high-order modes. The proposed Y-branch is optimized by using three-dimensional full-vectorial finite difference beam propagation method. The experimental results show that the proposed Y-branch is with an ultra-low nonlinearity over a broad bandwidth from 1250 nm to 1620 nm, a low polarization dependent loss of less than 0.2 dB, and an ultra-low relative power difference of less than 0.04.

Optical lattice generation using vertically embedded multimode-interference square-core polymer waveguides on a silicon chip.

We demonstrate two-dimensional optical lattice generation at 1064nm wavelength using vertically embedded multimode-interference (MMI) square-core polymer waveguides on a silicon chip. We demonstrate tuning of the effective waveguide length by longitudinally offsetting the waveguide input end-face from the input beam waist. Our measurement results of the waveguides with different cross-sectional dimensions at different effective waveguide lengths exhibit lattice patterns spanning from 4 × 4 to 10 × 10 arrays at the waveguide output end-face. Our theoretical analysis reveals that the offset causes additional mode-dependent phase changes. Our numerical modeling results using the three-dimensional beam-propagation method are consistent with our experimental results and theory.

Design of an InGaAsP/InP compact integrated optical depolarizer

In this paper, we propose and demonstrate two integrated optics InGaAsP/InP depolarizer circuits. The first one is based on the Lyot depolarizer configuration, while the second one is based on the Mach-Zehnder configuration. Detailed simulation, using three-dimensional full vectorial beam propagation method, shows that a high-index contrast material allows the design of a compact polarization insensitive depolarizer. For the first design, an output degree of polarization (DOP) less than 0.1 is obtained for light sources with spectral widths larger than 25nm, while for the second one, output DOP less than 0.06 is obtained for light sources with spectral widths larger than 40nm.

Calculation of coupling length for spatial waveguides using planar waveguides

A simple method to calculate the coupling length of the spatial waveguides is presented in this paper. Spatial waveguides with same center–center separation space and different center–center vertical and horizontal distances are studied using the field matching method. The analysis results indicate that the coupling length strongly depends on the center–center separation space. Therefore, the coupling length of spatial waveguides can be calculated using the existing formula for planar waveguides. The proposed method is verified using the three-dimensional full-vector beam propagation method.

Three-Dimensional Finite-Element Time-Domain Beam Propagation Method and Its Application to 1-D Photonic Crystal-Coupled Resonator Optical Waveguide

A 3-D finite-element time-domain beam propagation method is described for the first time, to the best of our knowledge, for the analysis of transmission characteristics of any kind of photonic structures. In order to avoid nonphysical reflections from computational window edges, the perfectly matched layer boundary condition is introduced. Furthermore, the present method can treat wideband optical pulses owing to the use of Pade approximation. The validity of this method is verified by numerical simulations of a photonic crystal cavity and a microring resonator. In addition, in order to demonstrate the usefulness of the developed method, a taper waveguide for a highly efficient connection between a straight waveguide and a 1-D photonic crystal-coupled resonator optical waveguide is designed.

The design and error analysis of 90° hybrid based on InP 4×4 MMI

A 90° hybrid based on InGaAsP/InP deep-ridge 4×4 Multi-Mode Interference (MMI) structure is designed. Three-dimensional beam propagation method (3-D BPM) is used in the simulation and error tolerance investigation process. The calculated common-mode rejection ratio (CMRR) and phase deviation are larger than 30dB and smaller than 1.4° within 1530–1565nm, respectively. Error tolerance of refractive index, thickness of core layer, waveguide width and length of MMI are analyzed. The designed hybrid is fabricated in the laboratory and measured in the coupling test platform. The test results show that CMRR of the hybrid is almost greater than 10dB in the wavelength from 1530 to 1565nm. The estimated phase deviation of the hybrid is less than 12° within 1533–1548nm and even larger in other wavelengths. The performance degradation is explained well by the error-tolerance analysis.

A High Extinction Ratio Polarization Beam Splitter With MMI Couplers on InP Substrate

A high extinction ratio (ER) polarization beam splitter with three different multimode interference couplers on InP substrate was designed by a three-dimensional beam propagation method. Simulations show that the polarization ER (PER) is over 34 dB and internal loss is $ . The effects of the width of the input port on the performance of the device are discussed in detail.

A good performance 3-dB splitter based on coupling-weighted and velocity-tapered waveguides

A coupling-weighted and velocity-tapered 3-dB splitter with a symmetric triple-mode evolution structure weighted by the Blackman function is analytically and numerically investigated for C+L-band passive optical network applications. The splitter is analyzed by the coupled-mode theory and simulated by the use of three-dimensional finite-difference beam propagation method. It is found that the power uniformity, wavelength dependent loss, excess loss and polarization dependent loss of the proposed 3-dB splitter in the whole C+L-band are better than 2.49×10−3dB, 0.018dB, 0.14dB, and 0.004dB, respectively. It is evident that the 3-dB splitter can achieve the good performances for C+L-band passive optical network applications.

A triplexer based on cascaded $$2\times 2$$ 2 × 2 butterfly MMI couplers using silicon waveguides

An ultra-compact triplexer is designed by mean of the construction of \(2\times 2\) generalized interference–multimode interference (GI–MMI) couplers. In order to reduce the device length these couplers are formed into linear butterfly shape. Firstly, a butterfly \(2\times 2\) MMI coupler is designed to separate the wavelength 1,490 nm into one port and wavelengths 1,310 and 1,550 nm into an another port. Then another one is used to drop wavelengths of 1,310 and 1,550 nm to output ports individually. Numerical simulations with three-dimensional beam propagation method and effective index method are utilized to design and optimize the operation of the proposed triplexer.

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.

A design of triplexer based on a 2×2 butterfly MMI coupler and a directional coupler using silicon waveguides

A novel ultra-compact triplexer is designed by basing it on a combination of a 2×2 generalized interference-multimode interference (GI-MMI) coupler. The MMI is formed into linear butterfly shape and a directional coupler using silicon rib waveguides. Firstly, the 2×2 MMI coupler is designed to separate the wavelength 1490nm into one port and wavelengths of 1310nm and 1550nm into another port. Then a directional coupler is used to drop wavelengths of 1310nm and 1550nm to output ports individually. Numerical simulations with three-dimensional Beam Propagation Method (BPM) are utilized to design and optimize the operation of the proposed triplexer.

Engineering the Lateral Optical Guiding in Gallium Nitride-Based Vertical-Cavity Surface-Emitting Laser Cavities to Reach the Lowest Threshold Gain

In order to improve the current injection in GaN-based blue vertical-cavity surface-emitting lasers (VCSELs) a dielectric aperture is generally used in combination with an indium–tin-oxide (ITO) layer on the top intracavity p-contact layer. The most straightforward way to realize this introduces a depression of the structure near the optical axis and we show, by using a two-dimensional (2D) effective index method and a three-dimensional (3D) coupled-cavity beam propagation method, that this typically results in optically anti-guided structures with associated high optical losses and thus very high threshold gains. Remarkably, the threshold gain reduces with increased negative guiding, which is due to improved lateral confinement and reduction of lateral leakage. Still, moderately positively guided designs should be preferred to avoid the detrimental effect of lateral leakage and high diffraction loss. To ensure positive index guiding, we propose to planarize the structure or introduce an elevation near the optical axis by additional processing, with an associated reduction in threshold material gain from 6000 to 2000 cm-1 for the studied structures.