Wide-angle Finite-difference Beam Propagation Research Articles

Simulation of spectral stabilization of high-power broad-area edge emitting semiconductor lasers

The simulation of spectral stabilization of broad-area edge-emitting semiconductor diode lasers is presented in this paper. In the reported model light-, temperature- and charge carrier-distributions are solved iteratively in frequency domain for transverse slices along the semiconductor heterostructure using wide-angle finite-difference beam propagation. Depending on the operating current the laser characteristics are evaluated numerically, including near- and far-field patterns of the astigmatic laser beam, optical output power and the emission spectra, with central wavelength and spectral width. The focus of the model lies on the prediction of influences on the spectrum and power characteristics by frequency selective feedback from external optical resonators. Results for the free running and the spectrally stabilized diode are presented.

A large-size SiO 2 waveguide resonator used in integration optical gyroscope

We report on the resonance characteristics of a Si-based ring resonator model with the theory of multiple-beam interference. The resonator consists of a track pattern ring channel waveguides with radius of 2 cm, two input/output directional couplers and one ring resonator coupler. Using the wide angle finite-difference beam propagation method (WA-FDBPM), we presented optimal design of ring resonator and succeed in fabricating the ring resonator by Plasma Enhanced Chemical Vapor Deposition (PECVD) method. Observed from the resonance curve, finesse of 16.7 is measured. And a rate detection limit of 1.7°/h can be evaluated.

Optimization design for polymeric S-shaped ridge waveguide

The dispersion characteristics and transverse field distribution of the fundamental and higher order modes are analyzed for polymeric ridge multimode waveguide by a new technique which is based on the combination of the effective index method and the variational method. An algorithm is implemented to study the effect of the structure parameters and dimensions on the dispersion curves. The optical field distribution of the fundamental and higher order modes for TM modes are computed. The single mode conditions of polymeric ridge waveguide are obtained. The relationship between the curvature radius and the bending loss of S-shaped ridge waveguide are studied with wide-angle finite-difference beam propagation method and effective index method. The conclusion is: when the curvature radius is larger than 5000 μm, the bending loss will not decrease distinctly even if the curvature radius increases, and the light can propagate stably in the S-shaped ridge waveguide.

Wide-Angle Alternating-Direction Implicit Finite-Difference Beam Propagation Method

An alternating direction implicit (ADI), scheme for the wide-angle finite-difference beam propagation method (FD-BPM) based on the wide angled Pade multistep method is presented. The scheme incorporates an iterative technique for correction of the operator splitting error. The resulting equations are efficiently solved by the Thomas algorithm for tri-diagonal band matrices. The dispersion characteristics, accuracy and stability of the scheme is verified analytically and numerically for the cases of a plane wave propagating at fixed angle to the assumed propagation direction of the algorithm and the three dimensional angled propagation of a Gaussian beam. The computational requirements of the method are assessed against a standard wide-angle Pade multistep method that uses direct and iterative sparse matrix solvers.

Narrow-line coherently combined tapered laser diodes in a Talbot external cavity with a volume Bragg grating

We present the phase locking of an array of index-guided tapered laser diodes. An external cavity based on the self-imaging Talbot effect has been built. A volume Bragg grating is used as the output coupler to stabilize and narrow the spectrum at 976nm. A power of 1.7W is achieved in the in-phase single main lobe mode with a high visibility. We have checked that each emitter is locked to the Bragg wavelength with a 100pm spectrum linewidth. The experimental results compare well with numerical simulations performed with two-dimensional wide-angle finite difference beam propagation method.

Design of a multifunctional integrated optical isolator switch based on nonlinear and nonreciprocal effects

The design of a new multifunctional integrated optical device capable of operating simultaneously as an optical switch and optical isolator is presented. The device consists of a multilayer directional coupler employing one nonlinear and one magneto-optic layer, with all other layers being linear and isotropic. Therefore, only phase matching conditions are required for the device operation irrespective of the propagation directions and operation regime (linear/nonlinear). The structure is optimized via a genetic algorithm and tested with a numerical formalism based on the wide-angle finite-difference beam propagation method. The results clearly demonstrate the ability of performing two distinct functions on the same device.

Use of a novel wide-angle FD-BPM for loss performance assessment in randomly perturbed photonic crystal fibers

A novel wide-angle finite-difference beam-propagation method is applied to the analysis of confinement losses in photonic crystal fibers (PCFs). The method is formulated in terms of the locally one-dimensional (LOD) technique and Pade polynomials. It was found that the wide-angle approach allows an acceleration of the convergence rate of up to 50% for the effective-index imaginary part when compared to paraxial formalism. In this framework, an important aspect of PCF structures, namely, the random structural variation of the hole radius and pitch, which occurs during the fabrication process of these devices, is investigated in this paper. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 45: 568–573, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20882

Wide‐angle solution of nonlinear coupled wave equations based on Padé approximants

AbstractA wide‐angle finite‐difference beam propagation method for the solution of coupled nonlinear wave equations is introduced in this paper. The formalism is expanded in terms of Padé approximants for the Crank–Nicolson scheme. An iterative algorithm is utilized to optimize convergence in the nonlinear region. The overall performance of the method is checked for a nonlinear X‐coupler. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 38: 108–113, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10986

Nonlinear properties of tapered laser cavities

The nonlinear phenomena accompanying the process of light generation in high-power tapered semiconductor lasers are studied using a combination of simulation and experiment. Optical pumping, electrical overpumping, filamentation, and spatial hole burning are shown to be the key nonlinear phenomena influencing the operation of tapered lasers at high output powers. In the particular tapered laser studied, the optical pumping effect is found to have the largest impact on the output beam quality. The simulation model used in this study employs the wide-angle finite-difference beam propagation method for the analysis of the optical propagation within the cavity. Quasi-three-dimensional (3-D) thermal and electrical models are used for the calculation of the 3-D distributions of the temperature, electrons, holes, and electrical potential. The simulation results reproduce key features and the experimental trends.

An improved wide-angle FD-BPM for nonlinear and nonreciprocal waveguides

An improved wide-angle finite-difference beam-propagation method for the simulation of multifunction optical waveguides employing simultaneously nonlinear and nonreciprocal materials is introduced in this paper. This formalism can be applied to nonlinear Kerr-type materials exhibiting any kind of nonlinearity mechanisms. The nonreciprocal behavior is based on the difference between forward and backward propagation constants for TM modes. The z derivatives of the inverse permittivity are also taken into account so that longitudinal varying structures can be more accurately simulated.

Modeling of Magnetooptical Waveguides via Transfer Matrix Technique and Wide-Angle Finite Difference Beam Propagation Method

Two extended numerical formulations are simultaneously applied to the investigation of TM mode propagation in magnetooptical waveguides: (1) the transfer matrix technique, applied to the modal propagation constant calculation in multilayer waveguides, and (2) the wide-angle finite difference beam propagation method, applied to the nonparaxial beam propagation simulation in longitudinal varying waveguides. The second utilizes the Crank-Nicholson scheme and Padé approximants for the discretization of the wave equation. The usefulness of these two numerical formulations is tested for the nonreciprocal properties of TM mode propagation in a magnetooptical directional coupler.

Multimode interference photonic switches (MIPS)

The switching characteristics of multimode interference photonic switches (MIPS) are analyzed by wide-angle finite difference beam propagation method (FD-BPM). As a result, it is found that the MIPS with a multimode interference (MMI) length of 599 /spl mu/m can switch the output light polarization insensitively with a crosstalk of less than -20 dB for a wavelength range of 70 nm. These analyses show that the MIPS can also have a 3-dB coupler function. Experimentally, an InGaAsP/InP 1/spl times/2 MIPS with a thicker InP cladding layer was fabricated and exhibited switching operation with crosstalks of -8 dB and -10 dB at 0 and 20 mA current injections, respectively. For a 2/spl times/2 MIPS with a thinner InP cladding layer, better switching characteristics with a crosstalk of -13 dB and an extinction ratio of 17 dB were realized.

Improved wide-angle finite-difference beam propagation method for the analysis of nonlinear optical waveguides

An improved wide-angle finite-difference beam propagation method (WA-FD-BPM) formulated in terms of complex Pade approximants is proposed to investigate nonlinear optical waveguides. The formalism utilizes the Crank-Nicholson scheme. An adaptive update of the reference index and an iterative algorithm in every propagation step are utilized to accelerate convergence. Stability problems relative to high-order approximants are also addressed in this work.

Versatile multimode interference photonic switcheswithpartial index-modulation regions

A new structure is proposed for multimode interference photonic switches which have partial index-modulation regions to obtain control of the power switching between multiple output ports.The switching characteristics for a 3 × 3 configuration are analysed by the wide-angle finite-difference beam propagation method. This analysis confirms that complete switching can be obtained with low crosstalk levels of ~23 dB.

Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods

Efficient nonuniform schemes, based on the generalized Douglas (GD) scheme, are developed for the finite-difference beam propagation method (FD-BPM). For a two-dimensional (2-D) problem, two methods are presented: a computational space method and a physical space method. In the former, the GD scheme is employed, after replacing a nonuniform grid in the physical space with a uniform one in the computational space. In the latter, the GD scheme is directly extended to a nonuniform grid in the physical space. We apply these two methods to paraxial and wide-angle FD-BPM's. The fourth-order accuracy is achieved in the transverse direction, provided that the grid growth factor between two adjacent grids is r=1+O(/spl Delta/x). For the paraxial BPM, the reduction in the truncation error is demonstrated through modal calculations of a graded-index waveguide using an imaginary distance procedure. For the wide-angle BPM, the propagating field in a tilted waveguide is analyzed to show the effectiveness of the present scheme. As an application of the physical space method, an adaptive grid is introduced into the multistep method.

Analysis of a lensed coreless fiber by a hybrid technique combining FD-BPM and FD-TDM

A technique connecting a scalar wide-angle finite-difference beam-propagation method (FD-BPM) with a scalar finite-difference time-domain method (FD-TDM) is systematically described and used to analyze a lensed coreless fiber. The propagating field and its phase distribution are calculated to demonstrate the phase adjustment effect of the lens. The power concentration due to the lens is evaluated by the directive gain used in the antenna engineering. The effect of an antireflection coating on the reflected power is also evaluated.

Hybrid numerical technique combining the finite-difference beam-propagation method and the finite-difference time-domain method

A technique combining a scalar wide-angle finite-difference beam-propagation method with a scalar finite-difference time-domain method is proposed in cylindrical coordinates. The propagating field in a lensed coreless fiber is simulated, and the effect of a lens on the far-field pattern is evaluated.