This course covers the theories and analyses of integrable optical waveguides and devices such as dielectric waveguides (planar, rectangular, and circular), directional couplers, periodic structures (distributed feedback and distributed Bragg structures), and their applications to integrable solid-state lasers.

- Electromagnetics (undergraduate level)
- Calculus

Lecture Notes will be distributed in class.

Ch1 Fundamentals of Electromagnetic Waves

1.1 Maxwell’s Equations
1.1.1 Time-Domain Representation
1.1.2 Frequency-Domain Representation
1.1.3 Constitutive Relation in Linear Media
1.1.4 Duality Principle
1.1.5 Boundary Conditions
1.1.6 Reciprocity Theorem (Generalized)
1.1.7 Conservation Theorems

1.2 Wave Equations
1.2.1 Vector Wave Equations
1.2.2 Scalar Wave Equations
1.2.3 Plane Waves in Homogeneous Isotropic Media
1.2.4 Reflection and Transmission at a Dielectric Interface
1.2.5 Total Internal Reflection
1.2.6 Brewster Angle

Ch2 Dielectric Waveguides

2.1 Wave Equations in Dielectric Waveguides
2.1.1 Modes in Dielectric Waveguides
2.1.1 Decomposed Maxwell’s Equations
2.1.2 Decomposed Wave Equations
2.1.3 Wave Equations in Dielectric Waveguides
2.1.4 Mode Symmetry
2.1.5 Orthogonality of Modes

2.2 Planar Dielectric Waveguides
2.2.1 Wave Equation in Planar Dielectric Waveguides
2.2.2 TE and TM Modes in Planar Dielectric Waveguides

 
Ch3 Three-Layer Planar Waveguides

3.1 Three-Layer Planar Waveguides
3.1.1 TE and TM Modes in Three-Layer Planar Waveguides
3.1.2 General Solutions
3.1.3 Guided and Radiation Modes: Ray Optics View

3.2 Guided Modes
3.2.1 TE and TM Modes in Three-Layer Planar Waveguides
3.2.2 General Solutions
3.2.3 Normalization of Guided Modes
3.2.4 Special Limits
3.2.5 Confinement Factor
3.2.6 Goos-Hänchen Shift of Wave Packet

3.3 Radiation Modes
3.3.1 Substrate Radiation Modes
3.3.2 Substrate-Cover Radiation Modes
3.3.3 Power of Radiation Modes
3.3.4 Complete Set of Modes and Phase-Matching Diagram

3.4 Leaky Waves
3.4.1 Leaky Waves in Ordinary Planar Waveguides
3.4.2 Leaky Waves in Hollow Planar Waveguides

Ch4 Two-Dimensional Waveguides

4.1 Wave Equations and Polarizations

4.2 Rectangular Waveguides
4.2.1 Marcatili’s Approximation
4.2.2 Boundary Condition in Marcatili’s Method
4.2.3 Guided Modes in Rectangular Waveguides
4.2.4 Intensity Distribution in Rectangular Waveguides

4.3 Cylindrically Layered Waveguides – Optical Fiber
4.3.1 General Solutions and Special Functions in Cylindrical Coordinates
4.3.2 Step-Index Optical Fiber: Guidance Condition
4.3.3 Polarizations in Step-Index Fibers

 
Ch5 Transfer Matrix Theory in Planarly-Layered Media

5.1 Matrix Theory in Planarly-Layered Media
5.1.1 Transfer Matrix
5.1.2 Scattering Matrix
5.1.3 Characteristic Matrix

5.2 Transfer Matrix Theory
5.2.1 Transfer Matrix Formulation
5.2.2 Resonance Conditions of Guides Modes
5.2.3 Decomposition of Planarly Layered Media
5.2.4 Leakage due to Finite Cladding Layers
5.2.5 Distributed Bragg Reflection Mirrors

Ch6 Couple Mode Theory

6.1 Coupled Waveguides
6.1.1 Reciprocity Theorem in Waveguides
6.1.2 Coupled Waveguides
6.1.3 Reciprocity Theorem in Waveguides
6.1.4 Orthogonality of Waveguide Modes
6.1.5 Coupled Mode Equation – I
6.1.6 Coupled Mode Equation – II

6.2 Directional Coupler
6.2.1 Coupled Mode Equations
6.2.1 Power Conservation
6.2.3 Eigen Modes of Directional Coupler
6.2.4 Power Transfer of Directional Coupler
6.2.5 Optical Switch
6.2.6 Tunable Filter
6.2.7 Coupler (Two-Section Directional Coupler)
6.2.8 Single- vs Two-Section Directional Couplers
6.2.9 Semiconductor Laser Arrays

Ch7 Periodic Structures for Device Applications
7.1 Distributed Bragg Reflector (DBR)
7.2 DBR Lasers
7.3 DFB Lasers

Appendices