Download 1D Photonic Crystals (Multilayer stacks)

1
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.
2
Periodic electromagnetic media
Low index of
refraction
High index of
refraction
3D photonic crystal
3
Plane-waves in a uniform dielectric
/n

E

H
n
 
Energy flux ~ E  H

 
i ( k r t )
E, H ~ e

2n
k  n / c 

4
Scattering regimes
a>> incoherent scattering
a
a~ coherent scattering
a
a<<
averaging
a
Photonic crystals
Photonic Crystals
5
Periodic electromagnetic media
1887
1987
2-D
3-D
1-D
1977
p eriodic in
one directio n
periodic in
two directions
periodic in
three direction s
quazi-1D
quazi-2D
Bragg fibers
microstructured fibers
6
Photonic Crystals Components
periodic electromagnetic media with defects
can
3D
Ph otrap
to n iclight
C rystain
l wcavities
ith De fe c ts
and waveguides (“wires”)
7
1D Photonic Crystal
1 -D
8
Uniform dielectric
kt
(preferred direction)


2n
k  n / c 

c

n

 
i ( k r t )
E, H ~ e

k
(transverse wavevector)
  kt
2
 n 
2
2
2
kt  



 c 
n
(propagation constant)

c

n
Our first band diagram
light cone
light propagation
light line:
=c/n
no light propagation, kt is IMAGINARY

9
Two uniform dielectrics (intuitive picture)

k2
k 1t
q2
 ni 
2
k  
 
 c 
2
i
t
c
sin q i 
ni
<

k1
n1

n2
k 2t

light cone
light line 1:
 = c  / n1
light line 2:
 = c  / n2
no light propagation in dielectrics 1,2

A quest for a perfect mirror
10
Reflectance
1
As index
contrast
increase
Dielectric mirror, low loss,
but strong angular and
polarization dependence
TE
n1  n2 2
n1  n2 2
TM
As index
contrast
increase
0
tan-1(n
2/n1)
90o
Reflectance is getting more uniform for
all polarizations and wider region of
angles as index contrast increases
q1
Metallic mirror, low angular
and polarization
dependence, but very high
loss for optical frequencies
Projected Bands of a 1d Crystal
(a.k.a. a Bragg mirror)
11

Quaterwave stack condition
d1
d2
 conserved
Light in the multilayer
n1
n2
1d band gap
d1n1=d2n2=/4
TM
TE
modes
in crystal
propagation
perpendicular to the layers

12
Omnidirectional Reflection
[ J. N. Winn et al, Opt. Lett. 23, 1573 (1998) ]

Air
 conserved
in these  ranges, there is no overlap
between modes of air & crystal
all incident light
TM
TE
modes
in crystal
(any angle, polarization)
is reflected
from flat surface

needs: sufficient index contrast & nhi > nlo > 1
13
Omnidirectional Mirrors in Practice
[ Y. Fink et al, Science 282, 1679 (1998) ]
Te / polystyrene
contours of omnidirectional gap size
10 0
3
normal
50
50%
2.8
0
40%
2.4
10 0
Re flec ta nc e (%)
(%)
Reflectance
2.6
30%
2.2
20%
2
10%
1.8
0%
1.6
D/mid
1.4
450 s
50
0
10 0
450 p
50
0
10 0
800 s
50
0
1.2
10 0
1
1
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
Smaller index, n
2
800 p
50
0
6
9
12
1
Wavelength (microns)
15