Optical Phenomena in Photonic Crystals - TU Muenchen
Transcript of Optical Phenomena in Photonic Crystals - TU Muenchen
• E. Yablonovich. Inhibited spontaneous emission in solid-state physics and electronics.
Phys. Rev. Lett., Vol. 58, 2059 (1987).
• S. John. Strong localization of photons in certain disordered dielectric superlattices.
Phys. Rev. Lett., Vol. 58, 2486 (1987).
Historical reviewPhotonic crystals for microwave radiation:
1∼d mm
• V. P. Bykov. Spontaneous emission in a periodic structure.
Sov. Phys. JETP, Vol. 35, 269-273 (1972).
• V. P. Bykov. Spontaneous emission from a medium with a band spectrum.
Sov. J. Quant. Electron., Vol. 4, 861-871 (1975).
Historical review
3-D two-component photonic crystalswith FCC lattice
• Opals – SiO2• Polymer opal-like photonic crystals
Objects under study
High dielectric contrast 1
2
εε
2ε1ε
SEM micrographs of polystyrene opal-like photonic crystal
Macromolecule of polystyrene
Objects under study
Opal-like photonic crystals production
crystal assembly
drying
colloidal suspension
gelation or consolidation
pore filling
001 aD
χ⊥
= −
DD
η⊥
=
– coefficient of the isotropic sintering
– coefficient of the axial compression along the (111) direction
Computing photonic band structure
• Plane wave expansion method• Korringa-Kohn-Rostoker (KKR) method• Finite Difference Time Domain (FDTD) method
( )( ) ( ) i k G rk
G
E r A k G e ⋅ − ⋅= −∑
( ) iG rG
G
r eε ε ⋅= ∑
2 2 20 0 0
0
( ) ( ) ( ( )) ( )≠
− − ⋅ = −∑ GG
k k A k k k A k k A k Gε ε
Equation for eigenmodes in photonic crystal
0 ≡kcωSymbols:
( ) ( )=∑ kk
E r E r
1
2
111 1110, 0ε ε→ →
1 – Bragg reflection from plane(111)
2 – Bragg reflection from plane(111)
Dispersion curves of eigenmodes in photonic crystalin empty lattice approximation
57 , 0θ ϕ= ° = °
s-polarizationp-polarization
Dispersion relations
2-Band (only lateral plane) 3-Band (both lateral and oblique planes)
Practical applications
• 2-D: Photonic-crystal fibers
SEM micrographs of US Naval Research Laboratory-produced photonic-crystal fiber.The diameter of the solid core at the center of the fiber is 5 µm, while the diameter of the holes is 4 µm.
Practical applications
• 3-D: Spontaneous emission inhibition
Photonic band structure of inverted opal
photonic band gapmaxωminω
Atoms with can’t emit radiation.min 0 maxω < ω < ω
Literature
• C. Lopez. Material aspects of photonic crystals.Adv. Mater., Vol. 15(20), 1679–1704 (2003).
• K. Sakoda. Optical properties of photonic crystals.Springer series in optical sciences. Vol. 80,Berlin–Heidelberg–New York, Springer (2001).