Time-domain Beam Propagation Method Research Articles

Optimal Design of Photonic Devices Using Time-Domain Beam Propagation Method

In this paper, we introduce shape and topology optimal design approach making use of a time-domain beam propagation method (TD-BPM) for optical waveguide devices. The design approach is based on sensitivity analysis to density parameters, and the sensitivity is computed by an adjoint variable method (AVM). We describe how to compute the sensitivity in the case of using the standard BPM which is a frequency domain method, then adapt it to the case of using the TD-BPM. As a numerical design example, a reflector is optimized using our design approach with the TD-BPM, and we study on its advantage over the case of using frequency domain techniques.

Recursive implicit time domain technique for modeling dispersive materials

Short pulse propagation inside a frequency-dependent Debye medium is studied by developing an algorithm for the solution of wave equation using recursive time-domain beam propagation method. Being an implicit and recursive technique, it is compared with other existing similar techniques, such as recursive finite difference time domain and time domain beam propagation method. The developed technique avoids matrix inversion though a considerable numerical dispersion is observed. The numerical dispersion is assessed and superseded through an empirical relation. The prominent benefit of this technique is that it is stable for multi-pole Debye medium even at high time steps with relaxed mesh-grid.

Dispersive optical power splitter: assessment through time domain techniques

A comparative study has been performed between the finite difference time domain technique and the time domain beam propagation method (TD-BPM) while assessing the ultra short pulsed beam propagation inside dispersive power splitter. The dispersive GaAs material, used in the device, is modeled by Lorentzian dispersion relation that satisfies the refractive index of the material at a certain wavelength and shows a strong dispersion over a wide wavelength range. A smarter moving window technique is needed to be applied rather than at pulse’s group velocity for the TD-BPM, especially for bifurcated opto-electronic devices at the ultra short pulse.

Smoothed finite element method for time dependent analysis of quantum resonance devices

In this paper, a new finite element method (FEM) is introduced to study the time-dependent wave nature of the electron in quantum resonance devices. Unlike the well-known FEM, the new method smooths the wave function derivatives over the edges. In this sense, the new method is termed “smoothed FEM” where an “inter-element” matrix is formed to smooth the derivatives over the edges. For the electron’s wave function propagation in time, the presented method exploits the time domain beam propagation method (TD-BPM). Based only on first order elements, our suggested SFETD-BPM has high accuracy levels comparable to second-order conventional FEM elements; thanks to the element smoothing. The proposed method numerical performance is tested through the analysis of a quantum resonance cavity and a quantum resonant tunneling device. It is clearly demonstrated that the presented method is not only accurate but also more time efficient than the conventional FEM approach.

Design considerations for quasi-phase-matching in doubly resonant lithium niobate hexagonal micro-resonators

Fabrication capabilities of high optical quality hexagonal superstructures by chemical etching of inverted ferroelectric domains in lithium niobate platform suggests a route for efficient implementation of compact hexagonal microcavities. Such nonlinear optical hexagonal micro-resonators are proposed as a platform for second harmonic generation (SHG) by the combined mechanisms of total internal reflection (TIR) and quasi-phase-matching (QPM). The proposed scheme for SHG via TIR-QPM in a hexagonal microcavity can improve the efficiency and also the compactness of SHG devices compared to traditional linear-type based devices. A simple theoretical model based on six-bounce trajectory and phase matching conditions was capable for obtaining the optimal cavity size. Furthermore numerical simulation results based on finite difference time domain beam propagation method analysis confirmed the solutions obtained by demonstrating resonant operation of the microcavity for the second harmonic wave produced by TIR-QPM. Design aspects, optimization issues and characteristics of the proposed nonlinear device are presented.

Modeling femtosecond pulses in optical power splitter using time domain techniques

In this paper, time domain beam propagation method (TD-BPM) has been developed and implemented for analyzing short and ultra short pulse interaction inside optical power splitter. The results obtained by the technique has been compared to that of the finite difference time domain (FDTD) technique. The TD-BPM is as effective and stable on the properly designed device as on waveguide and directional coupler. Proper design of the device ensures minimum radiation loss enhancing the output power. Moreover, the TD-BPM provides complete visualization of the pulse in course of its propagation as the technique updates the spatiotemporal pulsed window with propagation step, unlike the FDTD where finely gridded device is updated with time. Being an implicit technique, it is free from Courant–Friedrich–Levy constraint and infinitesimal gridding.

Efficient smoothed finite element time domain analysis for photonic devices.

In this paper, a new finite element method (FEM) is proposed to analyse time domain wave propagation in photonic devices. Dissimilar to conventional FEM, efficient "inter-element" matrices are accurately formed through smoothing the field derivatives across element boundaries. In this sense, the new approach is termed "smoothed FEM" (SFETD). For time domain analysis, the propagation is made via the time domain beam propagation method (TD-BPM). Relying on first order elements, our suggested SFETD-BPM enjoys accuracy levels comparable to second-order conventional FEM; thanks to the element smoothing. The proposed method numerical performance is tested through applicating on analysis of a single mode slab waveguide, optical grating structure, and photonic crystal cavity. It is clearly demonstrated that our method is not only accurate but also more computationally efficient (far few run time, and memory requirements) than the conventional FEM approach. The SFETD-BPM is also extended to deal with the very challenging problem of dispersive materials. The material dispersion is smartly utilized to enhance the quality factor of photonic crystal cavity.

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.

Time-Domain BPM Technique for Modeling Ultra Short Pulse Propagation in Dispersive Optical Structures: Analysis and Assessment

In this work, the time-domain beam propagation method (TD-BPM) has been extended to model ultra-short optical pulse propagation in structures containing material dispersion. The method uses Pade approximant to solve the one-way non-paraxial wave equation. The TD-BPM is implemented and analyzed using several iterative numerical techniques to model the propagation of ultra-short pulses in optical waveguide structures containing Lorentz material dispersion. Systematic accuracy and efficiency assessment, compared to the FDTD, showed that the longitudinal and the temporal steps sizes can be a number of order of magnitude larger than the FDTD step sizes. It is concluded that the TD-BPM is suited for long dispersive dielectric structures interaction of short and ultra-short pulse propagation.

Analysis of femtosecond pulsed beam propagation in dispersive directional coupler

An analysis of ultrashort-pulse interaction inside directional coupler structures having dispersive material is conveyed using the well-known finite difference time domain (FDTD) technique and time domain beam propagation method (TD-BPM). The implicit TD-BPM uses a higher-order non-paraxial equation suitable for femtosecond pulse. The result obtained by the one-way technique is verified with that of the widely used FDTD. A rigorous study is conveyed in order to distinguish material dispersion from intermodal dispersion. The analysis reveals that material dispersion causes energy loss in the device, in addition to extra pulse broadening and splitting that occur to a low extent in the case of intermodal dispersion.

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.

An adaptive algorithm for strongly chirped pulses propagating in optical fibers

Chirp, especially strong chirp, can be used to control the pulses in optical fibers, but it makes numerical simulation difficult by using the time-domain beam propagation method (TD-BPM) because of more sampling data requirements. In this paper, we present a modified beam propagation method (M-BPM) to efficiently simulate the propagation of strongly chirped pulses along an optical fiber. The validity of the M-BPM is demonstrated both theoretically and numerically. Numerical simulations show that the number of samples in time necessary to simulate the chirped pulse propagation by the TD-BPM varies linearly with the initial chirp parameter, but that of the M-BPM is the same one would need to simulate the propagation of the envelope without the initial chirp. In addition, the closer the propagation distance is to the temporal focal length, the more efficient the M-BPM comparing with the TD-BPM is.

Stable Time-Domain Beam Propagation Method for Modeling Ultrashort Pulse Propagation in Dispersive Optical Structures

In this letter, the time-domain beam propagation method has been formulated and verified to model ultrashort optical pulse propagation in structures containing material dispersion. The nonparaxial time-domain wave equation was used to march the pulsed beams using Pade approximant technique. The method has been tested using three different Lorentzian dispersive profiles. It has been observed that the new technique is very stable, accurate, and efficient in modeling ultrashort pulse propagation in long dispersive optical structures.

Efficient Iterative Time-Domain Beam Propagation Methods for Ultra Short Pulse Propagation: Analysis and Assessment

The time-domain beam propagation method (TD-BPM) has been implemented and analyzed using several iterative numerical techniques to model the propagation of ultra short pulses in optical structures. The methods depend on one-way non-paraxial time domain propagation that use Pade approximant formulation. Several numerical tests showed that the iterative TD-BPM techniques are very stable and converge using few iterations. From accuracy assessment compared to the FDTD, it has been observed that the longitudinal and the temporal steps sizes can be a number of orders of magnitude larger than the FDTD step sizes with little percentage difference. Computer performance analysis showed the TD-BPM is well suited for long dielectric structures interaction of short and ultra short pulse propagation.

Finite-element time-domain beam propagation method with perfectly matched layer for electron waveguide simulations

A finite-element time-domain beam propagation method is described for the solution of electron waveguide discontinuities. Scattering properties in steady state are evaluated with Fourier transform of a pulsed wave in time domain. A perfectly-matched-layer boundary condition is implemented into the electron waveguide simulations. The approach is applied to an electron resonant cavity, and it is confirmed that when treating a slowly varying electron wave function, the converged solution can be obtained with moderate time step size.

Modeling comparison of second-harmonic generation in high-index-contrast devices

In this paper we model second-harmonic generation in a microphotonic structure using two different numerical methods. The proposed two-dimensional waveguide device is challenging as it incorporates a high-contrast grating, which instigates strong local enhancement but also radiation losses. The first simulation method extends the time-domain beam propagation method, whereas the second one builds upon frequency-domain eigenmode expansion. Good agreement between both tools is obtained for both the linear and nonlinear simulations.

A Novel Nonparaxial Time-Domain Beam-Propagation Method for Modeling Ultrashort Pulses in Optical Structures

In this paper, a new nonparaxial time-domain beam-propagation method (TD-BPM) based on Pade approximant for modeling ultrashort optical pulses has been proposed and verified. The high efficiency of the technique in modeling long device interaction comes from solving the TD wave equation along one direction and allowing the time window to follow the evolution of the pulse. The accuracy of the method was tested in three different environments of homogenous and nondispersive medium, metallic, and dielectric waveguides and then was applied to model ultrashort pulse propagation in a directional-coupler device. The characterization of the technique shows excellent performance in terms of accuracy, efficiency, and stability, which the conventional paraxial TD-BPM failed to achieve. The new TD-BPM is particularly well suited for the study of unidirectional propagation of compact ultrashort temporal pulses over long distances in waveguide structures. [All rights reserved Elsevier].

InP photonic wire waveguide using InAlAs oxide cladding layer

We proposed a novel InP based photonic wire waveguide with an InAlAs oxide cladding. The InGaAsP/InAlAs-oxide structure in the vertical direction provides an ultrahigh index contrast waveguide, and it allows a bend radius of a few mum with no vertical leakage loss. The InP photonic wire waveguide with a 500x300-nm rectangular channel core (refractive index n ~ 3.36) and an InAlAs oxide cladding (n ~ 2.4) was numerically analyzed using the three-dimensional time-domain beam propagation method (3D TD-BPM). We predicted that the U-bend waveguide with a 3-mum bend radius can be realized with the propagation loss of < 0.5 dB.

General approach for Nth-order dispersive material

In some recent publications, formulations of a time-domain beam propagation method (TD-BPM) were developed to incorporate dispersive media with complex permittivity described by a single first-order pole or a modified version thereof. However, for many emerging optical applications, procedures are needed for general linear dispersive media with dispersions described by rational functions, such as a combination of multiple second-order poles. The authors present an efficient frequency-dependent full-band TD-BPM formulation for the analysis of general linear dispersive media. In this method, the complex time-domain convolution of the dispersive media is evaluated efficiently via a Z-transform. The formulation is validated by simulating dispersive media with complex permittivity described by single and multiple second-order poles at microwave and optical frequencies. It is shown that the proposed formulation can accurately simulate broadband electromagnetic responses using a much larger time-step size than those required by other conventional numerical techniques. Extension of this formulation to the treatment of any general material, such as dispersive non-linear material, is straightforward.

An efficient split-step time-domain beam-propagation method for modeling of optical waveguide devices

This paper presents a novel split-step time-domain beam-propagation method (TD-BPM) for simulation of time-domain pulse propagating in optical waveguide devices. Different from the traditional methods, where the time-marching step is strictly limited by the relation /spl Delta/t=/spl Delta/z/v/sub g/, the new split-step algorithm allows much more relaxed temporal and spatial steps, and therefore is much more efficient.