Finite Difference Beam Propagation Research Articles

The design and analysis of a CMOS-compatible silicon photonic ON–OFF switch based on a mode-coupling mechanism

A directional-coupler-based 1 $$\times$$ 1 silicon-on-insulator photonic ON–OFF switch with a complementary metal–oxide–semiconductor (CMOS)-compatible driving voltage is proposed in this paper. The directional coupling of the switch is accomplished by a carrier injection method with the help of a P-i-N diode phase shifter. The advantage of using the directional coupler as a switch is its smaller layout requirement, which makes it more suitable for use in integrated photonic applications. The ON–OFF switch has potential applications in programmable photonic switch fabrics, where the OFF-state behavior is used to prevent the input from being propagated to the output. The proposed switch offers a wide range of cross power-coupling coefficient $$(\kappa ^2)$$ values, ranging from 0 to 0.3 for the ON-state and from 0.79 to 1 for the OFF-state. The finite-difference beam propagation and two-dimensional (2D) finite-difference time-domain methods are used for photonic simulations. The results are compared analytically using the coupled mode theory with the help of the MATLAB software package.

Femtosecond Laser-inscribed Non-volatile Integrated Optical Switch in Fused Silica based on Microfluidics-controlled Total Internal Reflection

We demonstrate a non-volatile optical power switch, fabricated by femtosecond laser inscription in a fused silica substrate, with switching operation based on microfluidics-controlled total internal reflection. The switch consists of crossed waveguides and a rectangular, high aspect ratio microfluidic channel, located at the waveguide crossing. The switching between total internal reflection and transmission at the channel wall is determined by the refractive index of the medium inside the channel. Femtosecond laser inscription allows for co-integration of low-loss optical waveguides and channels with smooth sidewalls and thus the fabrication of low insertion loss switches that are broadband and show low polarization dependent losses. The measured total internal reflection loss of the fabricated switch is about 1.5 dB at the wavelength 1550 nm. The loss due to transmission through the channel filled with refractive index matching liquid is about 0.5 dB. Detailed finite difference time domain and beam propagation method simulations of the switch's performance indicate that the losses can be further reduced by optimizing its geometry, together with further adjusting the inscription parameters.

Design of reversible sequential circuits using electro-optic effect of lithium-niobate-based Mach–Zehnder interferometers

In recent years, it has been shown that reversible logic can play an important role in power optimization for computer design. The various reversible logic gates such as Feynman, Fredkin, Peres, and Toffoli gates have been discussed by researchers, but very little work has been done on reversible sequential circuits. Design of reversible sequential circuits using lithium-niobate-based Mach–Zehnder interferometers is proposed. Here, flip-flops are designed with the help of basic reversible logic gates such as Feynman, Fredkin, and Peres gates. Theoretical descriptions along with mathematical formulation of the devices are provided. The devices are also analyzed through finite difference-beam propagation method and MATLAB® simulation.

Design of an optical 4-bit binary to BCD converter using electro–optic effect of lithium niobate based Mach–Zehnder interferometers

Binary to Binary coded decimal (BCD) converter is a basic building block for BCD processing. The last few decades have witnessed exponential rise in applications of binary coded data processing in the field of optical computing thus there is an eventual increase in demand of acceptable hardware platform for the same. Keeping this as an approach a novel design exploiting the preeminent feature of Mach–Zehnder Interferometer (MZI) is presented in this paper. Here, an optical 4-bit binary to binary coded decimal (BCD) converter utilizing the electro–optic effect of lithium niobate based MZI has been demonstrated. It exhibits the property of switching the optical signal from one port to the other, when a certain appropriate voltage is applied to its electrodes. The projected scheme is implemented using the combinations of cascaded electro–optic (EO) switches. Theoretical description along with mathematical formulation of the device is provided and the operation is analyzed through finite difference-Beam propagation method (FD-BPM). The fabrication techniques to develop the device are also discussed.

Guided-Mode-Leaky-Mode-Guided-Mode Fiber Interferometer and Its High Sensitivity Refractive Index Sensing Technology.

A cascaded symmetrical dual-taper Mach-Zehnder interferometer structure based on guided-mode and leaky-mode interference is proposed in this paper. Firstly, the interference spectrum characteristics of interferometer has been analyzed by the Finite Difference-Beam Propagation Method (FD-BPM). When the diameter of taper waist is 20 μm–30 μm, dual-taper length is 1 mm and taper distance is 4 cm–6 cm, the spectral contrast is higher, which is suitable for sensing. Secondly, experimental research on refractive index sensitivity is carried out. A refractive index sensitivity of 62.78 nm/RIU (refractive index unit) can achieved in the RI range of 1.3333–1.3792 (0%~25% NaCl solution), when the sensor structure parameters meet the following conditions: diameter of taper waist is 24 μm, dual-taper length is 837 μm and taper distance is 5.5 cm. The spectrum contrast is 0.8 and measurement resolution is 1.6 × 10−5 RIU. The simulation analysis is highly consistent with experimental results. Research shows that the sensor has promising application in low RI fields where high-precision measurement is required due to its high sensitivity and stability.

Characterization of Strongly Coupled Si-Wire Waveguides for High-Density Optical WDM and Sensing Applications

This paper presents theoretical and experimental study of ultra-compact Si-wire Optical Directional Couplers (ODCs) on Silicon-on-Insulator wafer for optical signal processing. The presence of the controllable evanescent light strongly confined in the region bounded by the Si nano-wires has a large impact on the optical power coupling between waveguides. The characteristics of coupling length and power transmission in ODCs based on separation, wavelength, light field propagation distance and geometry of waveguides are described in detail by the coupled mode theory, 3-D finite-difference time-domain analysis and beam propagation method, and are confirmed by experiments. The exponential dependency of coupling length on the separation of coupled waveguides and wavelength shows interesting high-sensitivity optical sensing, switching and multiplexing properties. Custom spectral properties can be achieved by the configuration of coupled nano-wire waveguides based on their separation and lengths. We show that optimization of ODCs based on the physics of the coupled waveguides will lead to short optical devices which can be integrated as building blocks within high-density photonic circuits with the desired spectral characteristics. In the end, two new systems based on Mach-Zehnder structure and Micro-Ring Resonators are proposed in which ODCs are implemented as embedded tunable devices resulting in more functional optical sensing and signal processing devices.

Design and Analysis of Taper Structure for Light Coupling into Photonic Crystal Waveguides Fabricated by Si-Ion Implantation

In this paper, we designed and analyzed an efficient taper structure to couple light into and out of photonic crystal waveguides (PhCWs) fabricated by Si-ion implantation and electron beam lithography. The coupling structure employs the gentle refractive-index distribution produced in the SiO2layer by Si-ion implantation. A taper structure is designed for effective coupling of transverse electric (TE) polarized light (λ = 1.55 μm) into a submicron size PhCW consisting of triangular lattice of air holes (lattice constant,a= 0.666 μm, radius of air holes,r= 0.232 μm, waveguide width, W1 ~ 0.7 μm). The influence of the taper length on the transmission characteristics is investigated. Efficiency in excess of 95% is demonstrated using the finite-difference time-domain and beam propagation methods. This is important for their practical applications in photonic integrated circuits.

A Christiansen filter realized with a cylindrical lens

A type of Christiansen filter that takes the form of a cylindrical lens is proposed. This kindof Christiansen filter has a pass band narrower than the traditional one, with more meansof control of its performance; it could approximate arbitrary functions over a frequencyrange of interest. An inverse scattering theory for the synthesis of such a filter is developedand a systematic design technique is established. A desired, prescribed response can betailored by properly configuring the lens of the filter. A Gaussian filter centered at225 nm with a full width at half maximum of 1 nm is synthesized and is numericallymodeled on a computer using the finite difference beam propagation method.The simulation results confirm the feasibility of the proposed Christiansen filter.

Equivalent rectangle approximation-staircase concatenation method for wedge shaped fiber

Wedge shaped fiber (WSF) is the key component to acquire high coupling efficiency between input/output ports of planar lightwave circuit chips and fiber arrays. It is very important to analyze the mode spot and the mode field evolution of the lightwave propagating in WSF using numerical simulation tools. A three_dimensional equivalent rectangle approximation-staircase concatenation method (ERA-SCM) is proposed to fractionize the wedged tip of WSF along the propagating direction and introduce rectangular waveguide approximation so that effective index of the segmentations is obtained and SCM analysis model is established. Lightwave propagation and mode field evolution is analyzed by ERA-SCM and compared with finite difference-beam propagation method (FD-BPM), showing that the former is more precise to solve mode field evolution for asymmetric fiber and waveguide structures. The measurement of the output optical spot verifies the ERA-SCM simulation error is within 1.9%, while that for FD-BPM method is 4.5%. Thus, ERA-SCM is an effective method for analyzing asymmetric fiber and waveguide structures.

Analytical model of spatial four-waveguide coupler

Analytical model of spatial four-guide coupler is presented by utilizing Marcatili's principle, where the spatial four-guide coupler can be described by two perpendicular five-layer slab waveguides. The common expressions to calculate the effective indices and the mode field distributions are shown in this paper. Introducing perturbation corrections to take the effect of the distinct regions into account, more accurate results can be obtained. The effective refractive indices and coupling lengths of specific examples are investigated to verify the feasibility of the analytical model by comparing with the numerical approaches such as finite difference (FD) numerical calculation and beam propagation method (BPM).

An improved three-dimensional full-vectorial finite-difference imaginary-distance beam propagation method

A modified alternating direction implicit approach is proposed to discretize the three-dimensional full-vectorial beam propagation method (3D-FV-BPM) formulation along the longitudinal direction. The cross-coupling terms (CCTs) are neglected at the first sub-step, and then double used at the second substep. The order of two substeps is reversed for each transverse electric field component so that the CCTs are always expressed in an implicit form, thus the calculation is efficient and stable. Based on the multinomial inter-polation, a universal finite difference scheme with a high accuracy is developed to ap-proximate the 3D-FV-BPM formulation along the transverse directions, in which the dis-continuities of the normal components of the electric field across the abrupt dielectric in-terfaces are taken into account and can be applied to both uniform and non-uniform grids. The corresponding imaginary-distance procedure is first applied to a buried rectangular and a GaAs-based deeply-etched rib waveguide. The field patterns and the normalized propagation constants of the fundamental and the first order modes are presented and the hybrid nature of the full-vectorial guided-modes is demonstrated, which shows the validity and utility of the present approach. Then the modal characteristics of the deeply- and shallow-etched rib waveguides based on the InGaAsp/InGaAsP strained multiple quantum wells in InP substrate are investigated in detail. The results are necessary for modeling and the design of the planar lightwave circuits or photonic integrated circuits based on these waveguides.

The Design of Single Mode Large Cross-section Glass-based Waveguides for Photonic Integrated Circuits

This paper presents our recent simulation results and novel designs of single mode large cross-section glass-based waveguides for photonic integrated circuits (PICs). Simulations were performed using an in-house Finite Difference (FD) based mode solver and the FD Beam propagation Method (FD-BPM). Our simulation results show that this innovative technology could provide a simplified means to couple optical energy efficiently between optical components in a single chip. This would provide the base for the future large-scale integration of optical components in PICs. The novel idea of using single mode large cross-section glass-based waveguides as an optical integration platform is an evolutionary innovative solution for the monolithic integration of optical components, in which the glass-based structures act both as waveguides and as an optical bench for integration. This allows easy and efficient optical coupling between optical components and optical fibres, removing costly and tedious alignment problems and considerably reducing optical coupling losses in PICs. We expect that the glass-based waveguide PICs technology will enable the emergence of a new generation of compact, reliable, high speed, and multifunctional devices.

Theoretical and experimental study on multimode optical fiber grating

The characteristics of multimode optical fiber Bragg grating (MMFBG) are studied theoretically and experimentally. For the first time the analysis of MMFBG based on a novel quasi-three-dimensional (Q-3D) finite-difference time-domain beam propagation method (Q-FDTD-BPM) is described through separating the angle component of vector field solution from the cylindrical coordinate so that several discrete two-dimensional (2D) equations are obtained, which simplify the 3D equations. And then these equations are developed using an alternating-direction implicit method and generalized Douglas scheme, which achieves higher accuracy than the regular FD scheme. All of the 2D solutions for the field intensities are also added with different power coefficients for different angle mode order numbers to obtain 3D field distributions in MMFBG. The presented method has been demonstrated as suitable simulation tool for analyzing MMFBG. In addition, based on the hydrogen-loaded and phase mask techniques, a series of Bragg grating have been written into the silicon multimode optical fiber loaded hydrogen for a month, and the spectrums for that have been measured, which obtain good results approximate to the results in the experiment. Group delay/differentiate group delay spectrums are obtained using Agilent 81910A Photonic All-Parameter Analyzer.

Simulations on an SOI grating-based optical add/drop multiplexer

With a suitable design of a silicon-on-insulator (SOI) grating in an optical add/drop multiplexer (OADM), a wavelength-selectable OADM is described. We study the characteristics of the designed SOI OADM and simulate the relationship of the electron and hole concentrations including the temperature effect by using integrated system engineering-technology computer aided design. The voltages for the light wavelength switching are evaluated and are best set below V/sub p/=0.8 V and above V/sub n/=-0.8 V for OADM operation. The light propagation and spectral response are also illustrated in finite-difference time-domain beam propagation method (FDTD-BPM) simulations.

Evanescent field characterisation of tapered optical fibre sensors in liquid environments using near field scanning optical microscopy and atomic force microscopy

Near field scanning optical microscopy (NSOM) is used to measure the evanescent field surrounding a biconically tapered optical fibre sensor in air, water and dimethyl sulfoxide solution. These measurements are found to be in good agreement with those theoretically predicted using the finite difference-beam propagation method in combination with refractive and atomic force microscope measurements, demonstrating the validity of the model described for a number of environments.

Finite-difference time-domain beam propagation method for analysis of three-dimensional optical waveguides

A three-dimensional time-domain beam propagation method has been developed using an alternating-direction implicit method that can be solved by the standard Thomas algorithm. The presented method achieves second-order accuracy not only in space but also in time and has the advantage of allowing a larger time step than that in the conventional finite-difference time-domain method. The effectiveness of the present method is demonstrated through the analysis of pulse propagation in an optical fibre with a facet.

Simulation of light propagation in optical linear and nonlinear resist layers by finite difference beam propagation and other methods

This article presents a new method for the calculation of light propagation in resist layers and compares it with scaled defocus and transfer matrix algorithms. Our method is not restricted to homogeneous resist and substrate layers. For the first time, a simulation of focus drilling is presented.

A joint finite-difference and FFT full vectorial beam propagation scheme

A full vectorial beam propagation scheme is developed and it is applied on 3-dimensional waveguide structures. The formulation is based on the coupled wave equations for the transverse electric field. Each propagation step is performed by utilizing both the FFT and a finite-difference implementation. Under this perspective the offered advantages of FFT and finite-differences are exploited within a single propagation step resulting in a joint propagation scheme. The scheme is applied on a step-index circular fiber where analytical solutions are readily available for cross-checking. Moreover, the dependence of the phase constant on the reference refractive index is discussed. The polarized modes and the effective mode indices are derived in the case of rib waveguides by performing propagation along imaginary distance. Further, the rib waveguide coupler is examined and the energy transfer is simulated. >