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'''Beam Propagation Method''' (BPM) refers to a computational technique in [[Electromagnetics]], used
to 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 [[waveguide]]s. 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 1970's. 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.<ref>{{citation|title=Integrated Photonics|author=Clifford R. Pollock, Michal. Lipson|year= 2003|publisher=Springer|id=ISBN 1402076355 |url=http://books.google.com/books?vid=ISBN1402076355&id=DNJEoypcI6oC&pg=RA1-PA210&lpg=RA1-PA210&ots=o4ORvoHrCJ&dq=%22Beam+propagation+method%22&ie=ISO-8859-1&output=html&sig=kY2xdP7q7iv5MdX_3vzd63LmOpg}}</ref>
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