Photonic crystals I Blochs theorem photonic band structure

Photonic crystals (I) Bloch's theorem, photonic band structure, and energy flow Pi-Gang Luan & Wave Engineering Lab (欒丕綱 & 波動 程實驗室) Institute of Optical Sciences National Central University (中央大學光電科學研究所)

Photonic/Sonic Crystals 1 D Crystal 3 D Crystal 2 D Crystal

3 D Phononic Crystal?

Photonic/Sonic Band Structure

Applications

Photonic crystals as optical components P. Halevi et. al. Appl. Phys. Lett. 75, 2725 (1999) See also Phys. Rev. Lett. 82, 719 (1999)

Periodic function, Fourier Series and Reciprocal Lattice

Lattice Bases vs. Reciprocal Lattice Bases (2 D) Square Lattice Triangular Lattice

Binary System and Structure Factor (2 D)

Example 1: Square Lattice, Circular Rods/Holes

Example 2: Triangular Lattice, Circular Rods/Holes

Example 3: Simple Cubic Lattice, Spheres

Bloch’s Theorem and Brillouin zone Bloch’s Theorem (Electron Systems): First Brillouin Zone

Proving Bloch’s Theorem

Band Structure (Electron System)

Bloch’s Theorem and Photonic Band Structure

Energy Flow in Photonic Crystal See Sakoda

Frequency Contours Square Lattice

Two-Dimensional Inhomogeneous Wave Systems Classical Waves Unified Treatment

Binary System, Harmonic Waves Scattered wave Incident wave

Band Structure Calculation (2 D, Scalar Wave)

Reduced Brillouin Zone and Dimensionless Frequency

Photonic Band Gaps Left: Photonic Band , Right: Transmission (20 layers)