Summary of Lecture 18 导波条件 图解法求波导模式 边界条件 波导中模式耦合的微扰理论 Coupling constant 周期波导 Phase difference

§11.5 Coupled-Mode Solutions Coupled-mode equations Reflective wave Incident wave Initial conditions:

§11.5 Coupled-Mode Solutions where

§11.5 Coupled-Mode Solutions Under the matching condition

§11.5 Coupled-Mode Solutions z-dependent parts are exponentials with propagation constants for has an imaginary part “forbidden” region Analogous to the energy gap in semiconductors where the periodic crystal potential causes the electron propagation constants to become complex. For each l, there has a gap with center frequency

§11.5 Coupled-Mode Solutions “forbidden” gap zone and Numerical Example

§11.6 Periodic Fibers How to make a periodic index fiber

§11.6 Periodic Fibers Optical reflectors and filters Filter bandwidth At frequencies near the Bragg frequency, incident mode is strongly reflected; while at frequencies not near Bragg frequency are transmitted with no loss. Filter bandwidth

§11.6 Periodic Fibers Distributed Feedback Lasers

§11.6 Periodic Fibers Consider the condition and infinite Oscillator condition for DFB High-gain constant

§11.6 Periodic Fibers Incident and reflected fileds inside an amplifying periodic waveguide

§11.7 EO Modulation and Mode Coupling Optical modulation and switching (1) Smaller modulation powers (see Eq. 9.5-1) (2) Longer modulation paths (absence of diffraction) TM  TE mode conversion dc field TM mode Excite a TE mode Coupled mode equations Initial conditions:

§11.7 EO Modulation and Mode Coupling Under the matching condition when where

§11.7 EO Modulation and Mode Coupling Power exchange between two coupled modes

§11.7 EO Modulation and Mode Coupling EO modulation in a dielectric waveguide

§11.8 Directional Coupling Exchange of power between guided modes of adjacent waveguides is known as directional coupling. Applications: Power division, modulation, switching, frequency selection, and polarization selection Coupled field

§11.8 Directional Coupling Perturbation polarization Coupled mode equations Initial conditions: solutions Complete power transfer

§11.8 Directional Coupling For Identical waveguides Channel waveguides

§11.8 Directional Coupling EO Switch The directional coupler is designed as: So that Now we apply electric field to control the phase such that: So that

§11.8 Directional Coupling Multiplexing and Demultiplexing

§11.8 Directional Coupling Multiguide directional coupler