photonic crystals – it’s all about the mirrors
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Photonic Crystals – it’s all about the mirrors. Maksim Skorobogatiy Canada Research Chair in Photonic Band Gap materials and devices. I would like to thank Prof. Yoel Fink fiber research group at MIT, and Prof. Steven Johnson at MIT for their contributions. Periodic electromagnetic media. - PowerPoint PPT PresentationTRANSCRIPT
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Photonic Crystals – it’s all about the mirrors
Maksim Skorobogatiy
Canada Research Chair in Photonic Band Gap materials and devices
I would like to thank Prof. Yoel Fink fiber research group at MIT, and Prof. Steven Johnson at MIT for their contributions.
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Low index of refraction
High index of refraction
3D photonic crystal
Periodic electromagnetic media
3
)(~, trkieHE
n
cnk2
/
n
n
Plane-waves in a uniform dielectric
E
H HEfluxEnergy
~
4 Scattering regimes
a
a
a
a>>incoherent scattering
a<<averaging
a~coherent scattering
Photonic crystals
5 Photonic CrystalsPeriodic electromagnetic media
2-D
periodic intwo directions
3-D
periodic inthree directions
1887
1-D
eriodic inone direction
p
1987
quazi-1D
Bragg fibers quazi-2D
microstructured fibers
1977
6 Photonic Crystals Components
periodic electromagnetic media with defects
3D Photonic Crystal with Defectscan trap light in cavities and waveguides (“wires”)
7 1D Photonic Crystal
1 - D
8 Uniform dielectric
k
n
cnk2
/
)(~, trkieHE
n
c
n
ct
22 k
light cone
light line: = c / n
kt
(transverse wavevector)
n(preferred direction) (propagation constant)
Our first band diagram
no light propagation, kt is IMAGINARY
light propagation
22
c
ntk
9 Two uniform dielectrics (intuitive picture)
1k
22
c
niitk
2k
light cone
light line 1: = c / n1
n1
k1t
n2
<
k2t
no light propagation in dielectrics 1,2
light line 2: = c / n2
light propagation in dielectric 2 only
light propagation in dielectric 1,2
2
ii n
c
sin
10 A quest for a perfect mirror
1
190o0 tan-1(n2/n1)
TM
TE 2
21
221
nn
nn
Reflectance
As index contrast increase
As index contrast increase
Dielectric mirror, low loss, but strong angular and polarization dependence
Reflectance is getting more uniform for all polarizations and wider region of angles as index contrast increases
Metallic mirror, low angular and polarization dependence, but very high loss for optical frequencies
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modesin crystal
TE
TM
propagation perpendicular to the layers
1d b
and
gap
Light in the multilayer
conserved
d1 d2
n1n2
d1n1=d2n2=/4
Quaterwave stack condition
Projected Bands of a 1d Crystal(a.k.a. a Bragg mirror)
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modesin crystal
TE
TM
Omnidirectional Reflection[ J. N. Winn et al, Opt. Lett. 23, 1573 (1998) ]
light
line o
f air =
c
in these ranges, there is no overlap between modes of air & crystal
all incident light(any angle, polarization)
is reflectedfrom flat surface
needs: sufficient index contrast & nhi > nlo > 1
conservedAir
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[ Y. Fink et al, Science 282, 1679 (1998) ]
Omnidirectional Mirrors in Practice
/mid
6 9 1 2 1 50
5 0
1 0 0
0
5 0
1 0 0
0
5 0
1 0 0
0
5 0
1 0 0
0
5 0
1 0 0
normal
450 s
450 p
800 p
800 s
Re
flec
tanc
e (
%)
Wavelength (microns)
Te / polystyrene
Ref
lect
ance
(%
)
contours of omnidirectional gap size
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
Smaller index, n 1
0%
10%
20%
30%
40%
50%