Polarization effects in optical spectra of photonic crystals

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Polarization effects in optical spectra of
photonic crystals

Anton Samusev
Saint Petersburg State Polytechnical
University, Ioffe Physico-Technical Institute
JASS05 30 March 9 April, 2005
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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

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Bragg Diffraction
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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
opalsGalisteo-Lopez et al, Appl. Phys. Lett.
82, 4068 (2003)
0 lt ?ext lt 39 450nm lt ? lt 700nm
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Bragg diagrams
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Light coupling to single and multiple sets of
crystallographic planes
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Fresnel formulas
n1 ? n2 gt qt ? qi and aB ? 45
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LgKL scanning plane

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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)
Calculation
Experiment
400
00
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Fabrication of artificial opals
There are 3 in-layer position A red B blue
C green Layers could pack in fcc lattice
ABCABC or ACBACB hcp lattice ABABAB
Silica spheres settle in close packed hexagonal
layers
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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)
fcc I
-110
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Diffraction pattern from high quality opal
structure fcc II (ACBACB)
fcc II

-110
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Diffraction pattern from a twinned opal structure
fcc I fcc II (ABCACBA)
fcc Ifcc II

-110
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Diffraction pattern on strongly disordered opal
structure

-110
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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(a) dependence intensity as a function of
coordinate along section
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Q 0o
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Q 10o
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Q 20o
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Q 30o
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Q 40o
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Q 50o
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Q 60o
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Q 70o
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Q 80o
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Q 90o
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Q 100o
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Q 110o
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Q 120o
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Q 130o
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Q 140o
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Q 150o
40
Q 160o
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Q 170o
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Q 180o
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Intensity as a function of polarization angle
I(Q)
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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.

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The l versus 1 cos (q) dependence
linearization
514,5 nm
496,5 nm
488,0 nm
476,5 nm
457,9 nm

• Theoretical calculation
• (V.A.Kosobukin)
• neffd(1 cosq)
• neff _at_ 1,365
• d _at_ 268 nm

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Artificial Opal
Artificial opal sample (SEM Image) Several
cleaved planes of fcc structure are shown