Beam propagation method: Difference between revisions

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==Numerical methods==

Both ''spatial ___domain'' methods, and ''frequency (spectral) ___domain'' methods are available for the numerical solution of the discretized master equation. Upon discretization into a grid, (using various [[central difference|centralized difference]], [[Crank–NicolsonCrank Nicolson method]], FFT-BPM etc.) and field values rearranged in a causal fashion, the field evolution is computed through iteration, along the propagation direction. The spatial ___domain method computes the field at the next step (in the propagation direction) by solving a linear equation, whereas the spectral ___domain methods use the powerful forward/inverse [[Fast Fourier transform|DFT]] algorithms. Spectral ___domain methods have the advantage of stability even in the presence of nonlinearity (from refractive index or medium properties), while spatial ___domain methods can possibly become numerically unstable.

___domain method computes the field at the next step (in the propagation direction) by solving a linear equation, whereas the spectral ___domain

methods use the powerful forward/inverse [[Fast Fourier Transform|DFT]] algorithms. Spectral ___domain methods have the advantage of stability

even in the presence of nonlinearity (from refractive index or medium properties), while spatial ___domain methods can possibly become numerically unstable.

==Applications==

BPM is a quick and easy method of solving for fields in integrated optical devices. It is typically used only in solving for intensity and modes within shaped (bent, tapered, terminated) waveguide structures, as opposed to scattering problems. These structures typically consist of [[isotropic]] optical materials, but the BPM has also been extended to be applicable to simulate the propagation of light in general [[anisotropic]] materials such as [[liquid crystals]]. This allows one to [http://www.elis.ugent.be/ELISgroups/lcd/research/bpm.php analyze]{{Dead link|date=June 2020 |bot=InternetArchiveBot |fix-attempted=yes }} e.g. the polarization rotation of light in anisotropic materials, the tunability of a directional coupler based on liquid crystals or the light diffraction in LCD pixels.

BPM is a quick and easy method of solving for fields in integrated optical devices. It is typically

used only in solving for intensity and modes within shaped (bent, tapered, terminated) waveguide

structures, as opposed to scattering problems. These structures typically consist of [[isotropic]] optical materials, but the BPM has also been extended to be applicable to simulate the propagation of light in general [[anisotropic]] materials such as [[liquid crystals]]. This allows one to [http://www.elis.ugent.be/ELISgroups/lcd/research/bpm.php analyze]{{Dead link|date=June 2020 |bot=InternetArchiveBot |fix-attempted=yes }} e.g. the polarization rotation of light in anisotropic materials, the tunability of a directional coupler based on liquid crystals or the light diffraction in LCD pixels.

==Limitations of BPM==

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*[[Finite element method]]

*[[Maxwell's equations]]

*[[Method of lines|Method of Lines]]

*[[Light]]

*[[Photon]]