Passive Components for Dense Optical Integration

1 Introduction.- 1.1 Motivation.- 1.2 Outline of the book.- 1.2.1 Theoretical background.- 1.2.2 The FDTD method.- 1.2.3 Resonant channel add/drop filters.- 1.2.4 Low-loss waveguide components.- 1.2.5 Fiber-PIC coupling.- 2 Theoretical Background.- 2.1 Modes in optical waveguides.- 2.1.1 Normal modes.- 2.7.2 General form of guided fields.- 2.1.3 Orthogonality relations.- 2.1.4 Completeness of normal modes.- 2.2 Excitation of modes by localized currents.- 2.3 Scattering matrix.- 2.4 Effective Index Method (EIM).- 2.5 Resonators.- 2.5.1 Coupled resonators.- 2.5.2 Resonator-waveguide coupling.- 2.6 Gaussian Beams.- 2.6.1 Propagation of Gaussian beams.- 2.6.2 ABCD matrices.- 2.6.3 Approximation of effective index and mode profile using Gaussians.- 3 The Finite Difference Time Domain (FDTD) Method.- 3.1 The Yee algorithm.- 3.2 Finite Differencing.- 3.2.1 Three-dimensional algorithm.- 3.2.2 Two-dimensional algorithm.- 3.3 Boundary Conditions.- 3.4 Source Implementation.- 3.5 The use of Discrete Fourier Transform (DFT) in FDTD.- 3.6 Resonator calculations using FDTD.- 4 Resonant Add/Drop Filters.- 4.1 Introduction.- 4.2 Four-port system with single mode resonator.- 4.3 Symmetric standing-wave channel add/drop filters.- 4.3.1 General form of a symmetric channel add/drop filter.- 4.3.2 Symmetric add/drop filter with two identical standing-wave cavities66.- 4.4 FDTD simulations.- 4.4.1 Polygon resonators.- 4.4.2 Single square resonator coupled with two waveguides.- 4.4.3 Channel add/drop filter using a pair of square resonators.- 4.5 High-order symmetric add/drop filters.- 4.6 Phase response and dispersion.- 5 High Density Integrated Optics.- 5.1 Introduction.- 5.2 Sharp 90o bends.- 5.3 3D simulations and measurements on HTC bends.- 5.4 T-splitters.- 5.5 Waveguide crossings.- 6 Fiber-PIC coupling.- 6.1 Introduction.- 6.2 Lateral mode conversion using cascade of square resonators.- 6.3 Mode conversion using dielectric planar lenses.- 6.4 3D mode-conversion scheme.- 7 Conclusions and Future Directions.- 7.1 Summary.- 7.2 Fiber-chip coupling.- 7.3 Polarization dependence.- 7.4 Numerical tools.- References.