anton samusev jass’05 30 march – 9 april, 2005 saint petersburg state polytechnical university,...
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Anton Samusev
JASS’0530 March – 9 April, 2005
Saint Petersburg State Polytechnical University,
Ioffe Physico-Technical Institute
Polarization effects in optical spectra of photonic crystals
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Overview1. 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
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Bragg Diffraction
~ 2B d
1 2
(111) ef 2 2 2
3( ) 2 coshkl Θ n Θ
h k ld
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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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Angular-resolved transmission spectra of artificial opals
Bandgap position for different incident angle directions
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Photonic Bandgap Structure of Artificial Opals
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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
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Bragg diagrams
1 2
(111) ef 2 2 2
3( ) 2 coshkl Θ n Θ
h k ld
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Light coupling to single and multiple sets of crystallographic planes
LU – scanning plane0° < < 39°
450nm < < 700nm
Galisteo-Lopez et al,Appl. Phys. Lett. 82, 4068 (2003)
LgKL – scanning plane0° < < 70°
365nm < < 825nm
Baryshev et al, our group
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tg( )
tg( )t i
p pt i
R A
sin( )
sin( )t i
s st i
R A
n1 n2 =>
t i and B 45°
B2 1= arctan( / )n n
Fresnel formulas
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LgKL scanning plane
(2b)
(2a)
(1b)
(1a)
)35(EEE
)35(EEE
)(EEE
)(EEE
)0(02p
(200)p
||)0(02
s(200)s
)1(11s
(111)s
||)1(11
p(111)p
_
_
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Polarization dependences of photonic gaps. Analogy with Fresnel theory. Brewster angle.
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Polarization peculiarities in transmission spectra of opals(theoretical and experimental results
by A.V. Selkin and M.V.Rybin)
400
00
CalculationExperiment
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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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Diffraction Experimental Scheme•Laser beam propagates through:
•Depolarizer•Polarizer•Lens in the center of the screen
•Reflects from the opal sample
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During an experiment
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Diffraction pattern from high quality opal structure fcc I (…ABCABC…)
[-110]
fcc I
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[-110]
fcc II
Diffraction pattern from high quality opal structure fcc II (…ACBACB…)
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[-110]
Diffraction pattern from a twinned opal structure fcc I + fcc II (…
ABCACBA…)fcc I+fcc II
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[-110]
Diffraction pattern on strongly disordered opal structure
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Bragg diffraction patterns in[-110] geometry
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Processed images
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Image analysis process
1. Modification of the screen image shape
2. Profile plotting and searching for a peak in I() dependence [intensity as a function of coordinate along section]
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= 0o
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= 30o
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= 40o
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= 60o
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= 70o
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= 80o
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= 90o
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= 100o
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= 110o
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= 120o
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= 130o
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= 140o
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= 150o
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= 160o
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= 170o
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= 180o
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Intensity as a function of polarization angle I()
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Conclusions1. 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.
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The versus 1 + cos ( dependence linearization
Theoretical calculation:(V.A.Kosobukin):
= neffd(1 + cos)
neff 1,365
d nm
514,5 nm 496,5 nm 488,0 nm 476,5 nm 457,9 nm
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Artificial Opal
Artificial opal sample (SEM Image)Several cleaved planes of fcc structure are shown