1. Anton Samusev JASS’05 30 March – 9 April, 2005 Saint Petersburg State Polytechnical University, Ioffe Physico-Technical Institute Polarization effects in optical spectra of photonic crystals

2. 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

3. Bragg Diffraction

4. Energy gap in electromagnetic spectrum Increasing of the dielectric contrast could lead to the overlapping of energy gaps in any direction in 3D space.

5. Angular-resolved transmission spectra of artificial opals Bandgap position for different incident angle directions

6. Photonic Bandgap Structure of Artificial Opals

7. 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

8. Bragg diagrams

9. Light coupling to single and multiple sets of crystallographic planes LU – scanning plane 0° <  < 39° 450nm < < 700nm Galisteo-Lopez et al, Appl. Phys. Lett. 82, 4068 (2003) L g KL – scanning plane 0° <  < 70° 365nm < < 825nm Baryshev et al, our group

10. n 1  n 2 =>  t   i and  B  45° Fresnel formulas

11. L g KL scanning plane

12. Polarization dependences of photonic gaps. Analogy with Fresnel theory. Brewster angle.

13. Polarization peculiarities in transmission spectra of opals (theoretical and experimental results by A.V. Selkin and M.V.Rybin) 40 0 0 CalculationExperiment

14. 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

15. Diffraction Experimental Scheme Laser beam propagates through: Depolarizer Polarizer Lens in the center of the screen Reflects from the opal sample

16. During an experiment

17. Diffraction pattern from high quality opal structure fcc I (…ABCABC…) [-110] fcc I

18. [-110] fcc II Diffraction pattern from high quality opal structure fcc II (…ACBACB…)

19. [-110] Diffraction pattern from a twinned opal structure fcc I + fcc II (…ABCACBA…) fcc I+fcc II

20. [-110] Diffraction pattern on strongly disordered opal structure

21. Bragg diffraction patterns in [-110] geometry

22. Processed images

23. 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]

24.  = 0 o

25.  = 10 o

26.  = 20 o

27.  = 30 o

28.  = 40 o

29.  = 50 o

30.  = 60 o

31.  = 70 o

32.  = 80 o

33.  = 90 o

34.  = 100 o

35.  = 110 o

36.  = 120 o

37.  = 130 o

38.  = 140 o

39.  = 150 o

40.  = 160 o

41.  = 170 o

42.  = 180 o

43. Intensity as a function of polarization angle I(  )

44. 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.

45. The versus 1 + cos (  dependence linearization Theoretical calculation: (V.A.Kosobukin): = n eff d(1 + cos  ) n eff  1,365 d  nm 514,5 nm496,5 nm488,0 nm476,5 nm457,9 nm

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