Optical Phenomenain Photonic Crystals

Vladimir G. FedotovSaint-Petersburg State University

• Historical Review

• Opal-like photonic crystals

• Applications

Introduction

d λ∼

( )a ( )b ( )c

Photonic crystals

1-D (a), 2-D (b) и 3-D (c) photonic crystals

d

400..700nmλ =

• 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 12

εε

2ε1ε

Objects under study

10.000 times magnified modelof photonic crystal with FCC lattice

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

200G

111G

y

x

z

θ

ϕ

vk

Light propagation geometry

Experimental reflection spectra

s-polarization p-polarization

0ϕ = °

Computing photonic band structure

• Plane wave expansion method• Korringa-Kohn-Rostoker (KKR) method• Finite Difference Time Domain (FDTD) method

( )( ) ( ) i k G rkG

E r A k G e ⋅ − ⋅= −∑

( ) iG rGG

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 ≡k cωSymbols:

( ) ( )=∑ kk

E r E r

0ϕ =

TE-modes – s-polarization TM-modes – p-polarization

Dispersion curves

vkrk

pps

sz

TETM

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

57 , 0θ ϕ= ° = °

s-polarizationp-polarization

Dispersion relations

2-Band (only lateral plane) 3-Band (both lateral and oblique planes)

57 , 0θ ϕ= ° = °

s-polarization

Dispersion relations

Stop-band width

stop-band collapse for p-polarized incident light

(s)

(s)

(p)

(p)

Practical applications

• 1-D: Thin-film optics

Mirrors multilayer coating – Bragg mirrors.

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).

Thank You for Your Attention!

Vladimir G. FedotovSaint-Petersburg State University