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- Beam_propagation_method abstract "Beam Propagation Method (BPM) refers to a computational technique in Electromagnetics, usedto solve the Helmholtz equation under conditions of a time-harmonic wave. BPM works under slowly varying envelope approximation, for linear and nonlinear equations.The beam propagation method (BPM) is an approximation technique for simulating the propagation of light in slowly varying optical waveguides. It is essentially the same as the so-called Parabolic Equation (PE) method in underwater acoustics. Both BPM and the PE were first introduced in the 1970s. When a wave propagates along a waveguide for a large distance (larger compared with the wavelength), rigorous numerical simulation is difficult. The BPM relies on approximate differential equations which are also called the one-way models. These one-way models involve only a first order derivative in the variable z (for the waveguide axis) and they can be solved as "initial" value problem. The "initial" value problem does not involve time, rather it is for the spatial variable z.The original BPM and PE were derived from the slowly varying envelope approximation and they are the so-called paraxial one-way models. Since then, a number of improved one-way models are introduced. They come from a one-way model involving a square root operator. They are obtained by applying rational approximations to the square root operator. After a one-way model is obtained, one still has to solve it by discretizing the variable z. However, it is possible to merge the two steps (rational approximation to the square root operator and discretization of z) into one step. Namely, one can find rational approximations to the so-called one-way propagator (the exponential of the square root operator) directly. The rational approximations are not trivial. Standard diagonal Padé approximants have trouble with the so-called evanescent modes. These evanescent modes should decay rapidly in z, but the diagonal Padé approximants will incorrectly propagate them as propagating modes along the waveguide. Modified rational approximants that can suppress the evanescent modes are now available. The accuracy of the BPM can be further improved, if you use the energy-conserving one-way model or the single-scatter one-way model.".
- Beam_propagation_method wikiPageExternalLink ee5390cem.htm.
- Beam_propagation_method wikiPageExternalLink Poster_BPM.pdf.
- Beam_propagation_method wikiPageExternalLink optibpm.
- Beam_propagation_method wikiPageExternalLink bpm.php.
- Beam_propagation_method wikiPageID "8179925".
- Beam_propagation_method wikiPageRevisionID "604825523".
- Beam_propagation_method hasPhotoCollection Beam_propagation_method.
- Beam_propagation_method subject Category:Computational_science.
- Beam_propagation_method subject Category:Electrodynamics.
- Beam_propagation_method subject Category:Physical_optics.
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- Beam_propagation_method type PhysicalOptics.
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- Beam_propagation_method comment "Beam Propagation Method (BPM) refers to a computational technique in Electromagnetics, usedto solve the Helmholtz equation under conditions of a time-harmonic wave. BPM works under slowly varying envelope approximation, for linear and nonlinear equations.The beam propagation method (BPM) is an approximation technique for simulating the propagation of light in slowly varying optical waveguides. It is essentially the same as the so-called Parabolic Equation (PE) method in underwater acoustics.".
- Beam_propagation_method label "Beam propagation method".
- Beam_propagation_method sameAs m.026vfx4.
- Beam_propagation_method sameAs Q4876189.
- Beam_propagation_method sameAs Q4876189.
- Beam_propagation_method sameAs Beam_propagation_method.
- Beam_propagation_method wasDerivedFrom Beam_propagation_method?oldid=604825523.
- Beam_propagation_method isPrimaryTopicOf Beam_propagation_method.