Pdf assessment of rational approximations for square. Both bpm and the pe were first introduced in the 1970s. Bidirectional beam propagation method applied for lasers. Bidirectional beam propagation method for multilayered. The bidirectional beam propagation method is extended to tm polarisation. Bidirectional beam propagation method applied for lasers with. Simulation results indicate that the bidirectional pumping increases the instabilities threshold by a factor of 30%. This paper reports on the development of a numerically stable and accurate finitedifferencebased bidirectional beam propagation method fdbibpm for analyzing piecewise zinvariant plasmonic structures.
Finite differences beam propagation method in 3d, finite difference beam propagation method discover live editor create scripts with code, output, and formatted text in a single executable document. The range of validity and level of accuracy for the different. Pdf assessment of rational approximations for square root. Fft beam propagation method file exchange matlab central. The dynamic mode profile can be accurately estimated as the wave propagates through the wave guide. Noniterative finitedifference method for wideangle beam. It is essentially the same as the socalled parabolic equation pe method in underwater acoustics.
The design of the filter chip was optimized by simulation based on the beam propagation method. This software running on windows and macos comes with a gui that permits to define with the aid of files or scripts the arbitrary and complex geometry of. Our method is developed based on the scattering operators. Simulation results indicate that the bidirectional pumping increases the. Wide angle and bidirectional beam propagation using the. The basic of the bpm technique in the frequency domain relies on treating the slowly varying envelope of the monochromatic electromagnetic field under paraxial propagation, thus allowing efficient numerical computation in terms of speed and allocated memory. Sep, 2007 read analysis of bragg gratings for longrange surface plasmon polaritons using the bidirectional beam propagation method based on scattering operators, proceedings of spie on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Wave equations for propagation in dielectric media, solutions using the beam propagation method based on spectral fourier, hankel transforms and finite difference methods, with emphasis on thorough understanding of both the underlying physics. Propagation method wpm, the vector wave propagation method vwpm is introduced in the thesis. Comparisons with two previously published results demonstrate its accuracy, as well as its efficiency in computation time and memory. Operator rational approximations developed in the oneway beam propagation method.
In this paper we introduce a bidirectional pulse propagation equation bppe for extreme nonlinear optics and a novel shooting method for solving this equation. In addition the book presents the stateoftheart in computational photonics techniques, covering methods such as fullvectorial finiteelement beam propagation, bidirectional beam propagation, complexenvelope alternative direction implicit finite difference time domain, multiresolution time domain, and finite volume time domain. Propagation characteristics of annular laser beams passing. Pdf the nonparaxial and bidirectional beam propagation method suitable for modelling high na nearfield and holographic optical storage systems is. Osa assessment of rational approximations for square. An assessment and comparison of various commonly used rational approximations is performed for both transverse electric te and transverse magnetic tm waves. High energy laser beam propagation in the atmosphere. The nonparaxial and bidirectional beam propagation method suitable for modelling high na nearfield and holographic optical storage systems is suggested for. Reflectors using a finitedifference beam propagation method youngchul chung and nadir dagli abstractintegrated optical corner reflectors in 111v semiconduc tors are analyzed employing a finitedifference beam propagation method and propagating the beam in parallel with the etched semiconductorair interface. The unidirectional vwpm is extended to bidirectional propagation of vectorial. The bidirectional beam propagation method based on the method of lines is proposed as an innovative and efficient algorithm to investigate the optical properties of photonic band gap pbg structures.
Examples of the applicability of this technique in describing second harmonic generation in photonic crystals are given. Abstract the method of moments is used to define and derive expressions for laser beam deflection and beam radius broadening for highenergy propagation through the earths atmosphere. Beam propagation method theoretical nanooptics s eminar. These show the applicability and the accuracy of the method. We simulate light propagation in perturbed whisperinggallery mode microcavities using a twodimensional. Up to now, beam propagation, bidirectional beam propagation, and the transfermatrix method have been applied to study wave propagation in the vbg. By employing an iterative procedure based on a bidirectional beam propagation method, we develop a numerical algorithm to model light propagation in multilayered structures with secondorder nonlinearities. A few examples illustrate the application of this technique to the modeling of passive, lossy and active onedimensional and index confined pbg structures. An efficient bidirectional propagation method based on dirichletto. Osa assessment of rational approximations for square root. It provides a full vectorial and threedimensional treatment of electromagnetic.
This approach, borrowed from computer graphics, integrates several geometrical methods within the same theoretical framework. Oct 23, 2015 also, special topics in bpm cover the simulation of light propagation in anisotropic media, nonlinear materials, electrooptic materials, and media with gainlosses, and describe how bpm can deal with strong index discontinuities or waveguide gratings, by introducing the bidirectional bpm. Beam propagation method for design of optical waveguide. The basic of the bpm technique in the frequency domain relies on treating the slowly varying envelope of the monochromatic electromagnetic field under paraxial propagation.
Beam propagation method the beam propagation method is a numerical way of determining the fields inside a waveguide. Ion beam simulator library for ion optics, plasma extraction and space charge dominated ion beam transport. Polymeric bidirectional wavelength filter based on. Bessel beam is the important member of the family of nondiffracting beams and has many novel properties which can be used in many areas.
The method can be used for bidirectional propagation as well. Introduction the fibertothehome ftth networks have been. An efficient wideangle beam propagation method using. The focusing characteristics of a laser beam, which may be of interest to anyone using a laser for work or experimentation. The shooting method is based on the existence on a spectral constraint that appears when we reformulate maxwell equations into a system of zpropagation equations for spectral.
It is an iterative method that works on the wave eld components directly. Analysis of bragg gratings for longrange surface plasmon. Extension of an fftbased beam propagation method to. Bpm2dbidi module design and simulation of optical waveguides with 2d bi directional, nonparaxial beam propagation method module overview. Polymeric bidirectional wavelength filter based on multimode. Beam propagation method for design of optical waveguide devices.
Rsm radiation spectrum method is a 2d rigorous tool to solve the maxwell equations for the propagation of light in integrated optics or photonics devices. Combination of beam propagation method and mode expansion propagation method for bidirectional optical beam propagation analysis authors. Wave equations for propagation in dielectric media, solutions using the beam propagation method based on spectral fourier, hankel transforms and finite difference methods, with emphasis on thorough understanding of both the underlying physics and numerical simulation principles. Beam propagation method bpm beam propagation method is a mathematical procedure used to study the evolution of electromagnetic. The formalism of the beam propagation method bpm is extended in a selfconsistent way so as to allow the analysis of reflections in waveguiding structures containing longitudinal discontinuities. Optical waveguide analysis using beam propagation method. Extension of bidirectional beam propagation method to tm. The beam propagation method bpm is an approximation technique for simulating the propagation of light in slowly varying optical waveguides. For access to this article, please select a purchase option. Pdf bidirectional beam propagation method for modelling optical. Index termsbeam propagation method, bidirectional, itera tive methods, multiple dielectric interfaces, pade approximation. Advances in beam propagation method for facet reflectivity. Focusing characteristics of a real laser beam focus spot size due to diffraction.
Bidirectional beam propagation method for modeling optical. Examples on tilted gaussian beam propagation through a homogeneous medium and on gradedindex, tilted stepindex waveguides have been included. A brief overview of wideangle and bi directional bpm is given, but. By shifting the beam opposite to the variation of the waveguide geometry in every step, the propagation in a. Beam propagation method for waveguide device simulation. The beam propagation method college of optical sciences. Beside merely calculating the transition operators by the cdbi scheme, like our previous paper, a new approximation for the bidirectional propagators by using the. Also, special topics in bpm cover the simulation of light propagation in anisotropic media, nonlinear materials, electrooptic materials, and media with gainlosses, and describe how bpm can deal with strong index discontinuities or waveguide gratings, by introducing the bidirectionalbpm. Throughout this work, a transmission matrix based bidirectional beam propagation method tbibpm is proposed and applied on the uncoated facet and the single coating layer reflection problems, including both normal and angled incident situations. One key concept in the equation is the acoustic bidirectional reflectance distribution function 23 abrdf which is the term that models sound reflections. The roundtrip operator technique is presented in the given paper based on the bidirectional beam propagation method bibpm. This module simulates the wave propagation through multiple reflecting interfaces in 2d optical waveguides using a bi directional beam propagation method based on finite difference splitstep, nonparaxial scheme. Beside merely calculating the transition operators by the cdbi scheme, like our previous paper, a new approximation for the bidirectional propagators by using the combination of pade.
Pdf complex pade approximants for bidirectional and. Pdf bidirectional beam propagation method for modeling. An efficient semivectorial bidirectional beam propagation. The nonparaxial and bidirectional beam propagation method suitable for modelling high na nearfield and holographic optical storage systems is suggested for 2d geometry and te polarization of the. Pdf improved bidirectional beampropagation method by a. Sep 25, 20 this lecture steps the student through the formulation and implementation of a basic finitedifference beam propagation method. Dec 22, 2015 bessel beam is the important member of the family of nondiffracting beams and has many novel properties which can be used in many areas. Gerdes, bidirectional eigenmode propagation analysis of opti cal waveguides. It makes use of a modal method to solve the electromagnetic problem. Laser beam propagation well begin our discussion of beam propagation with a practical topic. Nolting, bidirectional eigenmode propagation for large. Combination of beam propagation method and mode expansion. The tbibpm method is developed on the basis of an overview of finite difference beam propagation method fdbpm schemes frequently used in photonic modelling including paraxial fdbpm, imaginary distance id bpm, wide angle wa bpm and existing bidirectional bi bpm methods. An efficient semivectorial bidirectional beam propagation method bibpm based on the complex denmanbeavers iterative cdbi scheme for threedimensional 3d optical waveguide structures is constructed.
A new bidirectional beam propagation method is developed for numerical simulation of waveguiding structures with multiple longitudinal re ecting interfaces. The beam propagation method bpm, rigorous coupled wave analysis. Analytical computation of acoustic bidirectional reflectance. With this method, the mode profile of an unusual waveguides such as ycouplers can be determined with ease.
A bidirectional beam propagation method for multiple. Abstractan efficient wideangle beam propagation method based on denmanbeavers iterative scheme for tilted optical waveguides is proposed, where the beam is shifting along the propagation. May 20, 2006 read bidirectional beam propagation method for modeling optical storage systems, proceedings of spie on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. A novel approach to the bidirectional beam propagation method, which can treat multiple dielectric interfaces, is developed and implemented using iterative methods. The highpower annular laser beams produced by an unstable. Advances in beam propagation method for facet reflectivity analysis. Improved bidirectional beampropagation method by a fourthorder finitedifference scheme. Consequently, the study of the characteristics of laser beams passing through the deformation bragg grating is of great importance. Assessment of rational approximations for square root operator in bidirectional beam propagation method. Similarly to traditional foxli technique our method not requires explicit calculation of matrix of the roundtrip operator and suits perfectly to krylov subspace methods of linear algebra. A new iterative bidirectional beam propagation method. Bpm yields the response of a given device to an external optical sigal, similar to in an experiment. The integral invariants of the nonlinear parabolic equation and the method of moments. Advances in beam propagation method for facet reflectivity analysis by deyun liu, meng thesis submitted to the university of nottingham for the degree of.
A simulation example of tm reflectivity from a gaasalgaas laser facet is presented. This lecture steps the student through the formulation and implementation of a basic finitedifference beam propagation method. In addition, the bpm based on finite differences is an easy way to implement robust and efficient computer codes. Accurate rational approximations to the square root operators are crucial for the bidirectional beam propagation method in simulation of strongly reflective structures. A model for evanescent modes from 1 is utilized and eligible con. Improved bidirectional beam propagation method by a fourthorder finitedifference scheme. However, the source of bessel beam generated by the.
A bidirectional beam propagation method for multiple dielectric interfaces. Bibpm bidirectional beam propagation method bicgstab biconjugate gradient stablized bpm beam propagation method cad computeraided design cg conjugate gradient cji cjiwabpm complex jacobi iterative wideangle beam propagation method using cji dmi direct matrix inversion dtn dirichlettoneumann em electromagnetic eme eigenmode expansion. Bidirectional pulse propagation equation for extreme. Optical properties of whisperinggallery microcavities perturbed by polystyrene nanobeads are investigated through this formulation.