Pdf bidirectional beam propagation method for modeling. A brief overview of wideangle and bi directional bpm is given, but. Combination of beam propagation method and mode expansion. An efficient bidirectional propagation method based on dirichletto. Bidirectional beam propagation method applied for lasers with. The range of validity and level of accuracy for the different. Extension of an fftbased beam propagation method to. 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. Pdf assessment of rational approximations for square root. Pdf complex pade approximants for bidirectional and. The unidirectional vwpm is extended to bidirectional propagation of vectorial. Optical properties of whisperinggallery microcavities perturbed by polystyrene nanobeads are investigated through this formulation.
Nolting, bidirectional eigenmode propagation for large. 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. Improved bidirectional beam propagation method by a fourthorder finitedifference scheme. 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. Noniterative finitedifference method for wideangle beam.
Pdf bidirectional beam propagation method for modelling optical. 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. Consequently, the study of the characteristics of laser beams passing through the deformation bragg grating is of great importance. 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.
The roundtrip operator technique is presented in the given paper based on the bidirectional beam propagation method bibpm. An efficient semivectorial bidirectional beam propagation. The highpower annular laser beams produced by an unstable. For access to this article, please select a purchase option. 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. 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. Beam propagation method for design of optical waveguide. An assessment and comparison of various commonly used rational approximations is performed for both transverse electric te and transverse magnetic tm waves. Advances in beam propagation method for facet reflectivity analysis by deyun liu, meng thesis submitted to the university of nottingham for the degree of. Accurate rational approximations to the square root operators are crucial for the bidirectional beam propagation method in simulation of strongly reflective structures. Analysis of bragg gratings for longrange surface plasmon. Advances in beam propagation method for facet reflectivity. The dynamic mode profile can be accurately estimated as the wave propagates through the wave guide. Focusing characteristics of a real laser beam focus spot size due to diffraction.
One key concept in the equation is the acoustic bidirectional reflectance distribution function 23 abrdf which is the term that models sound reflections. Polymeric bidirectional wavelength filter based on. 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. 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. The focusing characteristics of a laser beam, which may be of interest to anyone using a laser for work or experimentation. Both bpm and the pe were first introduced in the 1970s. An efficient wideangle beam propagation method using. This paper reports on the development of a numerically stable and accurate finitedifferencebased bidirectional beam propagation method fdbibpm for analyzing piecewise zinvariant plasmonic structures. A bidirectional beam propagation method for multiple dielectric interfaces.
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. Analytical computation of acoustic bidirectional reflectance. Gerdes, bidirectional eigenmode propagation analysis of opti cal waveguides. Extension of bidirectional beam propagation method to tm. Bessel beam is the important member of the family of nondiffracting beams and has many novel properties which can be used in many areas.
Examples on tilted gaussian beam propagation through a homogeneous medium and on gradedindex, tilted stepindex waveguides have been included. Beam propagation method theoretical nanooptics s eminar. Pdf improved bidirectional beampropagation method by a. Bidirectional beam propagation method for multilayered. The bidirectional beam propagation method is extended to tm polarisation. Operator rational approximations developed in the oneway beam propagation method. 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. Cylindrical beam propagation modelling of perturbed. A simulation example of tm reflectivity from a gaasalgaas laser facet is presented. Advances in beam propagation method for facet reflectivity analysis. Comparisons with two previously published results demonstrate its accuracy, as well as its efficiency in computation time and memory. Beam propagation method the beam propagation method is a numerical way of determining the fields inside a waveguide. Improved bidirectional beampropagation method by a fourthorder finitedifference 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.
Laser beam propagation well begin our discussion of beam propagation with a practical topic. Propagation characteristics of annular laser beams passing. It is an iterative method that works on the wave eld components directly. High energy laser beam propagation in the atmosphere.
Propagation method wpm, the vector wave propagation method vwpm is introduced in the thesis. 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. The method can be used for bidirectional propagation as well. Fft beam propagation method file exchange matlab central. Bpm2dbidi module design and simulation of optical waveguides with 2d bi directional, nonparaxial beam propagation method module overview. 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. 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. 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.
Osa assessment of rational approximations for square root. Our method is developed based on the scattering operators. This approach, borrowed from computer graphics, integrates several geometrical methods within the same theoretical framework. Simulation results indicate that the bidirectional pumping increases the. Wide angle and bidirectional beam propagation using the. 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. Bidirectional beam propagation method applied for lasers. By shifting the beam opposite to the variation of the waveguide geometry in every step, the propagation in a. The method is applicable for wide angle as well as bi directional propagation. 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. Introduction the fibertothehome ftth networks have been.
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. In addition, the bpm based on finite differences is an easy way to implement robust and efficient computer codes. Hoekstra, on beam propagation methods for modelling in integrated. Beside merely calculating the transition operators by the cdbi scheme, like our previous paper, a new approximation for the bidirectional propagators by using the. Up to now, beam propagation, bidirectional beam propagation, and the transfermatrix method have been applied to study wave propagation in the vbg. Combination of beam propagation method and mode expansion propagation method for bidirectional optical beam propagation analysis authors. Throughout this work, a transmission matrix based bidirectional beam propagation method tbibpm is proposed and applied on the uncoated facet and the single. Osa assessment of rational approximations for square. A model for evanescent modes from 1 is utilized and eligible con. Examples of the applicability of this technique in describing second harmonic generation in photonic crystals are given. Index termsbeam propagation method, bidirectional, itera tive methods, multiple dielectric interfaces, pade approximation. A novel approach to the bidirectional beam propagation method, which can treat multiple dielectric interfaces, is developed and implemented using iterative methods.
It is essentially the same as the socalled parabolic equation pe method in underwater acoustics. Bidirectional beam propagation method for multilayered dieletrics with quadratic nonlinearity article in ieee journal of selected topics in quantum electronics 83. Beam propagation method for waveguide device simulation. Pdf the nonparaxial and bidirectional beam propagation method suitable for modelling high na nearfield and holographic optical storage systems is.
Simulation results indicate that the bidirectional pumping increases the instabilities threshold by a factor of 30%. Bidirectional pulse propagation equation for extreme. Sep 25, 20 this lecture steps the student through the formulation and implementation of a basic finitedifference beam propagation method. It makes use of a modal method to solve the electromagnetic problem. Assessment of rational approximations for square root operator in bidirectional beam propagation method. 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. An efficient semivectorial bidirectional beam propagation method bibpm based on the complex denmanbeavers iterative cdbi scheme for threedimensional 3d optical waveguide structures is constructed. 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. A new bidirectional beam propagation method is developed for numerical simulation of waveguiding structures with multiple longitudinal re ecting interfaces. 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. Ion beam simulator library for ion optics, plasma extraction and space charge dominated ion beam transport. In this paper we introduce a bidirectional pulse propagation equation bppe for extreme nonlinear optics and a novel shooting method for solving this equation.
Beam propagation method bpm beam propagation method is a mathematical procedure used to study the evolution of electromagnetic. However, the source of bessel beam generated by the. 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. The beam propagation method bpm, rigorous coupled wave analysis. The design of the filter chip was optimized by simulation based on the beam propagation method. The integral invariants of the nonlinear parabolic equation and the method of moments. This lecture steps the student through the formulation and implementation of a basic finitedifference beam propagation method. Bidirectional beam propagation method for modeling optical. Methods for description of the total field propagation in the irregular.
The nonparaxial and bidirectional beam propagation method suitable for modelling high na nearfield and holographic optical storage systems is suggested for. Optical waveguide analysis using beam propagation method. These show the applicability and the accuracy of the method. It provides a full vectorial and threedimensional treatment of electromagnetic. With this method, the mode profile of an unusual waveguides such as ycouplers can be determined with ease. Bpm yields the response of a given device to an external optical sigal, similar to in an experiment. 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. 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.
We simulate light propagation in perturbed whisperinggallery mode microcavities using a twodimensional. 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. Beam propagation method for design of optical waveguide devices. 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. 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. 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. 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. The beam propagation method bpm is an approximation technique for simulating the propagation of light in slowly varying optical waveguides. A bidirectional beam propagation method for multiple. A few examples illustrate the application of this technique to the modeling of passive, lossy and active onedimensional and index confined pbg structures. A new iterative bidirectional beam propagation method. Pdf assessment of rational approximations for square.
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