By Ginés Lifante Pedrola
The easy of the BPM procedure within the frequency area depends upon treating the slowly various envelope of the monochromatic electromagnetic box below paraxial propagation, therefore permitting effective numerical computation by way of pace and allotted reminiscence. additionally, the BPM in keeping with finite variations is a straightforward option to enforce powerful and effective laptop codes. This ebook provides a number of ways for treating the sunshine: wide-angle, scalar method, semivectorial remedy, and whole vectorial remedy of the electromagnetic fields. additionally, targeted issues in BPM hide the simulation of sunshine propagation in anisotropic media, non-linear fabrics, electro-optic fabrics, and media with gain/losses, and describe how BPM can care for robust index discontinuities or waveguide gratings, by way of introducing the bidirectional-BPM. BPM within the time area can be defined, and the e-book comprises the robust means of finite distinction time area procedure, which fills the distance while the normal BPM is not any longer applicable. as soon as the outline of those numerical innovations were distinctive, the final bankruptcy contains examples of passive, lively and useful built-in photonic units, akin to waveguide reflectors, demultiplexers, polarization converters, electro-optic modulators, lasers or frequency converters. The e-book might help readers to appreciate a number of BPM methods, to construct their very own codes, or to correctly use the present advertisement software program in accordance with those numerical techniques.
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Extra resources for Beam Propagation Method for Design of Optical Waveguide Devices
The first and second order derivatives that appear in the wave equation are represented by their finite difference approaches, where the field at each grid point is related to the fields at adjacent points, both in the transversal and longitudinal directions. On the other hand, in the FE-BPM the transverse plane is divided into hybrid edge/nodal elements and the transverse and longitudinal field components are expressed as a function of the edge and nodal variables for each element, shape function vectors for edge elements and shape function vector for nodal elements.
Inserting Eq. 62d) into Eq. 63) we have: ∇2 E −∇ ∇ E − μ0 ∂2 εE + P NL = 0 ∂t 2 1 64 and assuming that the permittivity, ε, is time independent: ∇ 2 E − ∇ ∇ E − μ0 ε ∂2 E ∂ 2 P NL − μ =0 0 ∂t 2 ∂t 2 1 65 This equation is known as the non-linear wave equation for light propagating in a non-linear medium. Electromagnetic Theory of Light 15 Here, we will limit the analysis to monochromatic waves in a second-order non-linear medium, and we consider that only three frequencies ω1, ω2 and ω3 are involved.
L. Xu, (1993) Simulation of three-dimensional optical waveguides by a full-vector beam propagation method. Journal of Quantum Electronics 29, 2639–2649. , Chrostowski, J. K. (1994) A full-vectorial beam propagation method for anisotropic waveguides. Journal of Lightwave Technology 12, 1926–1931. 2 The Beam-Propagation Method Introduction Integrated photonic devices are based on light propagation along optical waveguides. The design and optimization of such devices requires numerical wave propagation techniques for the accurate simulation of light along inhomogeneous optical structures.
Beam Propagation Method for Design of Optical Waveguide Devices by Ginés Lifante Pedrola