p7 photonic crystal optics
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7-2E. Photonic crystals
Purdue Univ, Prof. Shalaev, http://cobweb.ecn.purdue.edu/~shalaev/
Univ Central Flor ida, CREOL, Prof Kik, http://sharepoint.optics.ucf.edu/kik/OSE6938I/Handouts/Forms/Al lItems.aspx
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3-D
2-D
1-D
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Consider a two-dimensional hotonic cr stal
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Bloch theorem
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Bloch theorem
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Bloch theorem
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Bloch theorem
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Bloch theorem
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Bloch theorem
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Dispersion curve = Photonic band structure
an gap
Bandgap (no transmission) tan ng wave
vgroup=0
Long wavelength
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Dispersion curve = Photonic band structure
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Remind the Dis ersion Curve of Slab Wave uide
Dispersion curve = Photonic band structure
Because guiding modesredistribute themselves with
Band structure
frequency, for small , the
dispersion curve of guiding
modes approaches the cladding
line;
For lar e it a roaches thecore line.
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Dispersion curve = Photonic band structure
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Photonic band gap
Light in 1-D photonic crystal
H L H L H L
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Photonic band gap
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Photonic band gap
ragg e ec on
2 ( )B B
nd Sin =
2 ~ 2
Bd B
Bd
= =
Ph t i b d
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Photonic band gap
ragg rac on
Wavelength does not correspond to the
period
Wavelength corresponds to the
period.
.
Wave propagates through.
e ec e waves are n p ase.
Wave does not propagate inside.
Ph t i b d
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Photonic band gap
22
2E k
m=
Photonic band gap
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PBG formationPhotonic band gap
1. Dispersion curve forfree space 3. At the band edges, standing wavesform, with the energy being either in
the high or the low index regions
2. In a periodic system, when half the
aka ==2
wavelength corresponds to the periodicity
4. Standing waves transport no energy
propagation.with zero group velocity
Dispersion curve = Photonic band structure
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Dispersion curve = Photonic band structure
n1: g n ex ma er a
n2: low index material4. Standing waves transport no energy
with zero group velocity
n1 n2 n1 n1 n1n2 n2standing wave in n2Air band
Sto band
standing wave in n
0
k
Dispersion curve = Photonic band structure
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Dispersion curve = Photonic band structure
Plot the dispersion curves for both the positive and the negative sides,|>/ |>/ one reciprocal lattice vectors.
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2-D Photonic Crystals
1. In 2-D PBG, different layer spacing, a, can be met along different =
2. PBG Photonic band a = sto bands overla in all directions
2D Photonic band structure
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2D Photonic band structure
an agram
Air band
Stop band
Dielectric band
2D Photonic band structure
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2D Photonic band structure
2D Photonic band structure
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2D Photonic band structure
2D Photonic band structure
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2D Photonic band structure
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1. Stop band
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Four Possible Functionalities of PBG
1. Use of Stop Band
1. Stop Band:
Stop bandomni-directional mirror
PBG wave uides
2. Dielectric band
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.
2. Dielectric Band: Uses the
strong dispersion availablen a p o on c crys a
(dispersion engineeringDielectric band
2. Dielectric band
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2. Dielectric band
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Remind the dispersion relation in bulk media
1. In a homogeneous material in absence of
material dispersion n()=constant =n, thespers on agram s s mp y a s ra g ne:=kc/n.
2. In 2D systems, one can think of this line as a cone.
For a given frequency , this cone becomes a constant frequency circle.
2. Dielectric band
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ky
kx
W ti i k
2. Dielectric band
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Wave propagation in k-space
Real s ace
The wave vector diagram tells us the direction and magnitude of the refracted
and reflected beams. Their direction is normal to the iso-frequency curve and
corresponds to Snells law.
2. Dielectric band
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2. Dielectric band
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2. Dielectric band
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2. Dielectric band
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3. Air band
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3. Use of Air Band
3. Air Band : Couples to radiative
modes for light extraction
- Air bandand fiber coupling.
3. Air band
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4. Defect band
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.
4. Defect Band : Couples to
waveguide/cavity modes forDefect band
spectral control such as PBGpoint defect laser or PBG linedefect filter, etc.
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Line Defect PBG Waveguide4. Defect band
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Line Defect PBG Waveguide
Defect modes
in stop band
Dispersion diagram of W1 line-defect
photonic crystal waveguide:
.
Photons are prohibited in the 2D PBG,
which lead to lossless confinement of
photons in the line defect area.
Defects in PBG4. Defect band
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Defects in PBG
4. Defect band
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4. Defect band
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4. Defect band
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4. Defect band
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3D Photonic band structure
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3D Photonic materialsS.Noda, Nature (1999) K. Robbie, Nature (1996)
E. Yablonovitch, PRL(1989)
Artificial Phonic Structure
3D Photonic band structure
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Artificial Phonic Structure
E.Yablonovitch et al., PRL (1987, 1991)
Fabrication of artificial fcc material
material.
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Natural Opals
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3D Photonic band structure
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Artificial opal sample (SEM Image)
Several cleaved planes of fcc structure are shown
3D Photonic band structure
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There are 3 in-layer position
Silica spheres settle in
close acked hexa onal
A red; B blue; C green;
Layers could pack in
layerscc a ce: or
hcp lattice: ABABAB
3D Photonic band structure
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Inversed opals obtain greater dielectric contrast than opals.
Band structure of diamond lattice3D Photonic band structure
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oton c an structure o amon att ce re ract ve n ex ~ .
John et. al. PRE (1998)
PCF
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PCF
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PCF
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The fiber supports a single mode over the range of at least 458-1550nm!
PCF
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PCF
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PCF
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PCF
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PCF
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