Polarization effects in optical spectra of photonic crystals

1. 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

2. Overview • Photonic band gap structure of artificial opals • Optical polarization-resolved study of photonic crystals: limited experimental data • Polarization effects in transmission spectra of artificial opals • Fresnel theory and Brewster effect (semi-infinite homogeneous medium) • 3D diffraction of light in opals: strong polarization dependences • 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 opalsGalisteo-Lopez et al, Appl. Phys. Lett. 82, 4068 (2003) 0°<ext < 39° 450nm <  < 700nm

8. Bragg diagrams

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

10. Fresnel formulas n1 n2 => qt  qi and aB  45°

11. LgKL 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) Experiment Calculation 400 00

14. 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

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…) fcc I [-110]

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

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

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

21. Bragg diffraction patterns in[-110] geometry

22. Processed images

23. Image analysis process 1. Modification of the screen image shape 2. Profile plottingand searching for a peak in I(a) dependence [intensity as a function of coordinate along section]

24. Q = 0o

25. Q = 10o

26. Q = 20o

27. Q = 30o

28. Q = 40o

29. Q = 50o

30. Q = 60o

31. Q = 70o

32. Q = 80o

33. Q = 90o

34. Q = 100o

35. Q = 110o

36. Q = 120o

37. Q = 130o

38. Q = 140o

39. Q = 150o

40. Q = 160o

41. Q = 170o

42. Q = 180o

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

44. Conclusions • It is demonstrated that transmission and diffraction measurements provide quantitative information on the complex interaction of polarized light with three-dimensional photonic crystals. • 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. • Our diffraction data shows experimental evidence of strong polarization dependence even far from Brewster angle. • These experimental results and conclusion bridge optical spectroscopy of photonic crystals and optical spectroscopy of conventional bulk homogeneous materials.

45. Thel 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@ 1,365 d @ 268 nm

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