Polarization effects in optical spectra
of photonic crystals
Anton Samusev
Saint Petersburg State Polytechnical University,
Ioffe Physico-Technical Institute
JASS’05
30 March – 9 April, 2005
Overview
1. Photonic band gap structure of artificial opals
2. Optical polarization-resolved study of photonic crystals:
limited experimental data
3. Polarization effects in transmission spectra of artificial
opals
4. Fresnel theory and Brewster effect (semi-infinite
homogeneous medium)
5. 3D diffraction of light in opals: strong polarization
dependences
6. Conclusions
Bragg Diffraction
B ~ 2d
12
3


 hkl  (Θ )  2 d (111)nef  2 2 2 
h k l 
cos Θ
Energy gap in electromagnetic
spectrum
Increasing of the dielectric contrast could lead to the overlapping
of energy gaps in any direction in 3D space.
Angular-resolved transmission spectra
of artificial opals
Bandgap position for different incident angle directions
Photonic Bandgap Structure of Artificial Opals
Experimental evidence of polarization dependence in
reflectivity spectra of artificial opals
Galisteo-Lopez et al, Appl. Phys. Lett. 82, 4068 (2003)
0° < ext < 39°
450nm <  < 700nm
Bragg diagrams
12
3


 hkl  (Θ )  2 d (111)nef  2 2 2 
h k l 
cos Θ
Light coupling to single and multiple sets of
crystallographic planes
Baryshev et al, our group
LgKL – scanning plane
0° <  < 70°
365nm <  < 825nm
Galisteo-Lopez et al,
Appl. Phys. Lett. 82, 4068 (2003)
LU – scanning plane
0° <  < 39°
450nm <  < 700nm
Fresnel formulas
n1  n2 =>
t  i and aB  45°
a = arctan(n2 / n1 )
B
sin( t   i )
Rs  
As
sin( t   i )
tg( t   i )
Rp 
Ap
tg( t   i )
LgKL scanning plane
_
E
(111)
p
E
(111 )
p
E
(111)
s
E
(111 )
s
_
 E|| ( )
(1a)
 E  ( )
(1b)
E s(200)  E s(020)  E|| (  35) (2a)
0)
E (200)
 E (02
 E  (  35) (2b)
p
p
Polarization dependences of photonic gaps.
Analogy with Fresnel theory. Brewster angle.
Polarization peculiarities in transmission spectra of opals
(theoretical and experimental results
by A.V. Selkin and M.V.Rybin)
Experiment
Calculation
400
00
Fabrication of artificial opals
Silica spheres settle in
close packed hexagonal
layers
There are 3 in-layer position
A – red; B – blue; C –green;
Layers could pack in
fcc lattice: ABCABC or ACBACB
hcp lattice: ABABAB
Diffraction Experimental Scheme
•Laser beam propagates
through:
•Depolarizer
•Polarizer
•Lens in the center of
the screen
•Reflects from the opal
sample
During an experiment
Diffraction pattern from high quality opal
structure fcc I (…ABCABC…)
fcc I
[-110]
Diffraction pattern from high quality opal
structure fcc II (…ACBACB…)
fcc II
[-110]
Diffraction pattern from a twinned opal
structure fcc I + fcc II (…ABCACBA…)
fcc I+fcc II
[-110]
Diffraction pattern on strongly
disordered opal structure
[-110]
Bragg diffraction patterns in
[-110] geometry
Processed images
Image analysis process
1. Modification of the screen
image shape
2. Profile plotting and searching
for a peak in I(a) dependence
[intensity as a function of
coordinate along section]
Q = 0o
Q = 10o
Q = 20o
Q = 30o
Q = 40o
Q = 50o
Q = 60o
Q = 70o
Q = 80o
Q = 90o
Q = 100o
Q = 110o
Q = 120o
Q = 130o
Q = 140o
Q = 150o
Q = 160o
Q = 170o
Q = 180o
Intensity as a function of polarization angle I(Q)
Conclusions
1. It is demonstrated that transmission and diffraction
measurements provide quantitative information on the
complex interaction of polarized light with three-dimensional
photonic crystals.
2. The polarization-resolved transmission spectra can be
discussed in terms of the Fresnel theory and the Brewster
effect taken into account three-dimensional photonic
structure of synthetic opals.
3. Our diffraction data shows experimental evidence of strong
polarization dependence even far from Brewster angle.
4. These experimental results and conclusion bridge optical
spectroscopy of photonic crystals and optical spectroscopy of
conventional bulk homogeneous materials.
The  versus 1 + cos ( dependence linearization
514,5 nm
496,5 nm
488,0 nm
476,5 nm
457,9 nm
Theoretical calculation:
(V.A.Kosobukin):
= neffd(1 + cos)
neff @ 1,365
d @ 268 nm
Artificial Opal
Artificial opal sample (SEM Image)
Several cleaved planes of fcc structure are shown