Polarization effects in optical spectra of photonic crystals

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

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

Bragg Diffraction

~ 2B d

1 2

(111) ef 2 2 2

3( ) 2 coshkl Θ n Θh k l

d

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

1 2

(111) ef 2 2 2

3( ) 2 coshkl Θ n Θh k l

d

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

tg( )tg( )

t ip p

t i

R A

sin( )sin( )

t is s

t i

R A

n1 n2 =>

t i and B 45°

B2 1= arctan( / )n n

Fresnel formulas

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

_

_

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)

400

00

CalculationExperiment

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

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…)

[-110]

fcc I

[-110]

fcc II

Diffraction pattern from high quality opal structure fcc II (…ACBACB…)

[-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

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() dependence [intensity as a function of coordinate along section]

= 0o

= 10o

= 20o

= 30o

= 40o

= 50o

= 60o

= 70o

= 80o

= 90o

= 100o

= 110o

= 120o

= 130o

= 140o

= 150o

= 160o

= 170o

= 180o

Intensity as a function of polarization angle I()

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.

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

Artificial Opal

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