Beam Propagation Method for Design of Optical Waveguide Devices

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. In addition, the BPM based on finite differences is an easy way to implement robust and efficient computer codes. This book presents several approaches for treating the light: wide-angle, scalar approach, semivectorial treatment, and full vectorial treatment of the electromagnetic fields. Also, special topics in BPM cover the simulation of light propagation in anisotropic media, non-linear materials, electro-optic materials, and media with gain/losses, and describe how BPM can deal with strong index discontinuities or waveguide gratings, by introducing the bidirectional-BPM. BPM in the time domain is also described, and the book includes the powerful technique of finite difference time domain method, which fills the gap when the standard BPM is no longer applicable. Once the description of these numerical techniques have been detailed, the last chapter includes examples of passive, active and functional integrated photonic devices, such as waveguide reflectors, demultiplexers, polarization converters, electro-optic modulators, lasers or frequency converters. The book will help readers to understand several BPM approaches, to build their own codes, or to properly use the existing commercial software based on these numerical techniques.

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. In addition, the BPM based on finite differences is an easy way to implement robust and efficient computer codes. This book presents several approaches for treating the light: wide-angle, scalar approach, semivectorial treatment, and full vectorial treatment of the electromagnetic fields. Also, special topics in BPM cover the simulation of light propagation in anisotropic media, non-linear materials, electro-optic materials, and media with gain/losses, and describe how BPM can deal with strong index discontinuities or waveguide gratings, by introducing the bidirectional-BPM. BPM in the time domain is also described, and the book includes the powerful technique of finite difference time domain method, which fills the gap when the standard BPM is no longer applicable. Once the description of these numerical techniques have been detailed, the last chapter includes examples of passive, active and functional integrated photonic devices, such as waveguide reflectors, demultiplexers, polarization converters, electro-optic modulators, lasers or frequency converters. The book will help readers to understand several BPM approaches, to build their own codes, or to properly use the existing commercial software based on these numerical techniques.

PrefaceList of SymbolsList of Acronyms1 Electromagnetic theory of light2 The beam propagation method3 Vectorial and three dimensional beam propagation techniques4 Special topics on BPM5 BPM analysis of integrated photonic devices.Appendix I Finite difference approximations of derivativesAppendix II Tridiagonal system: the Thomas method algorithmAppendix III Correlation and relative power between optical fieldsAppendix IV Poynting vector associated to an electromagnetic wave using the SVE fieldsAppendix V Finite difference FV-BPM based on the electric field using the scheme parameter controlAppendix VI Linear electro-optic effectAppendix VII Electro-optic effect in GaAs crystalAppendix VIII Electro-optic effect in LiNbO3 crystalAppendix IX Padé polynomials for wide-band TD-BPMAppendix X Obtaining the dispersion relation for a monomode waveguide using FDTDAppendix XI Electric field distribution in coplanar electrodesAppendix XII Three dimensional anisotropic BPM based on the electric field formulationAppendix XIII Rate equations in a four-level atomic systemAppendix XIV Overlap integrals methodIndex