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Mikhail Rybin
Euler SchoolMarch-April 2004
Saint Petersburg State University,Ioffe Physico-Technical Institute
Photonic Band Gap Structures
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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
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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.
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Bragg Reflection
2 ( )B Bnd Sin
~ 2B d
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Energy gap
Gap in energy spectra of electrons arises in periodic structure
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PBG formation
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Energy gap in electromagnetic spectrum
Increasing of the dielectric contrast could lead to the overlapping of energy gaps in any direction in 3D space.
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Width of complete band gap
Calculation of bandwidth in dependence of dielectric constantsS. John et al. PRE (1998)
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Density of States in fcc structure
There is no states in any direction within complete photonic band gap S. John et al. PRE (1998)
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2D PHB Structures
Macro-porous silicon material with incorporated defect line
Sharp band waveguide channel in 2D photonic
crystal
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Artificial Phonic StructureE.Yablonovitch et al., PRL (1987, 1991)
Fabrication of artificial fcc material and band gap structure for such
material.
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3D Photonic materials
S.Noda, Nature (1999)
E. Yablonovitch, PRL(1989)
K. Robbie, Nature (1996)
Examples of artificial photonic crystals
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Bragg diffraction through all electromagnetic region
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Natural Opals
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Artificial Opal
Artificial opal sample (SEM Image)Several cleaved planes of fcc structure are shown
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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)
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Growing process
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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
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Inverted Opals
Inversed opals obtain greater dielectric contrast than opals.
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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
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Band structure of diamond lattice
Photonic band structure of diamond lattice (refractive index ~3.45) John et. al. PRE (1998)
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Scan planes
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Angular-resolved transmission spectra
Bandgap position for different incident angle directions
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Structure of Photonic Bandgap
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Experimental Set
( , ) 1 ( , )T I
k -k
k k - k
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Experiment
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Geometry of “2-spots” and “4- spots”
Diffraction patterns in two different scattering geometry (Art image)
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“2 spots” pattern
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Diffraction Pattern (515 nm)
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Geometry of “2-spots” and “4- spots”
Diffraction patterns in two different scattering geometry (Art image)
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“2 spots” pattern
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Visualization of Photonic Band Structure in opals
1 = 515 nm 2 = 578 nm 3 = 633 nm
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Features in diffraction patterns
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Processing of images
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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.
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Spontaneous Emission Control
Emission is forbidden if energy of photonic bandgap and width of electron’s energy gap are coincided.