Photonic Band Gap Structures

Mikhail Rybin

Euler SchoolMarch-April 2004

Saint Petersburg State University,Ioffe Physico-Technical Institute

Photonic Band Gap Structures

Overview1. Photonic crystals and photonic bandgap

2. Artificial opals

3. Photonic bandgap structure of artificial opals:

Transmission experiments

4. 3D diffraction of light in opals: visualization of photonic band gap structure

5. Conclusions

Bragg Diffraction

Wavelength does not correspond to the period

Reflected waves are not in phase.

Wave propagates through.

Wavelength corresponds to the period.

Reflected waves are in phase.

Wave does not propagate inside.

Bragg Reflection

2 ( )B Bnd Sin

~ 2B d

Energy gap

Gap in energy spectra of electrons arises in periodic structure

PBG formation

Energy gap in electromagnetic spectrum

Increasing of the dielectric contrast could lead to the overlapping of energy gaps in any direction in 3D space.

Width of complete band gap

Calculation of bandwidth in dependence of dielectric constantsS. John et al. PRE (1998)

Density of States in fcc structure

There is no states in any direction within complete photonic band gap S. John et al. PRE (1998)

2D PHB Structures

Macro-porous silicon material with incorporated defect line

Sharp band waveguide channel in 2D photonic

crystal

Artificial Phonic StructureE.Yablonovitch et al., PRL (1987, 1991)

Fabrication of artificial fcc material and band gap structure for such

material.

3D Photonic materials

S.Noda, Nature (1999)

E. Yablonovitch, PRL(1989)

K. Robbie, Nature (1996)

Examples of artificial photonic crystals

Bragg diffraction through all electromagnetic region

Natural Opals

Artificial Opal

Artificial opal sample (SEM Image)Several cleaved planes of fcc structure are shown

Artificial Opal

Images of artificial opal.Left: as-growth surface (111) of the sample (SEM image)

Right: surface of the (110)-oriented plane sample (AFM image)

Growing process

Fabrication of artificial opals

Silica spheres settle in close packed hexagonal

layers

There are 3 in-layer positionA – red; B – blue; C –green;Layers could pack infcc lattice: ABCABC or ACBACBhcp lattice: ABABAB

Inverted Opals

Inversed opals obtain greater dielectric contrast than opals.

Diffraction on growth layers

Energy of the gap in transmission and energy of the maximum in reflection spectra are coincided

Transmission for different incident angles:

1. 00

2. 200

3. 300

4. 400

5. 540

Band structure of diamond lattice

Photonic band structure of diamond lattice (refractive index ~3.45) John et. al. PRE (1998)

Scan planes

Angular-resolved transmission spectra

Bandgap position for different incident angle directions

Structure of Photonic Bandgap

Experimental Set

( , ) 1 ( , )T I

k -k

k k - k

Experiment

Geometry of “2-spots” and “4- spots”

Diffraction patterns in two different scattering geometry (Art image)

“2 spots” pattern

Diffraction Pattern (515 nm)

Geometry of “2-spots” and “4- spots”

Diffraction patterns in two different scattering geometry (Art image)

“2 spots” pattern

Visualization of Photonic Band Structure in opals

1 = 515 nm 2 = 578 nm 3 = 633 nm

Features in diffraction patterns

Processing of images

Conclusions1. Photonic band gap structures are new class of material

possessed uncial photonic properties. Opal-based structures are 3D photonic crystals.

2. Photonic band gap structure was obtained for artificial opals in the visible range from angle-resolved transmission measurements.

3. Photonic band gap structure could be visualized by diffraction method. Diffraction patterns provides information about structure of photonic crystal.

Spontaneous Emission Control

Emission is forbidden if energy of photonic bandgap and width of electron’s energy gap are coincided.