Polarization degeneracy at Bragg reflectance in magnetized photonic crystals

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 19, 2009, Pages

  Merzlikin, A M ^a   Levy, Miguel ^b   Jalali, A A ^b   Vinogradov, A P ^a  

^a INSTITUTE FOR THEORETICAL AND APPLIED ELECTRODYNAMICS   (Russian Federation)

^b MICHIGAN TECHNOLOGICAL UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 65649146534     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.195103     Document Type: Article

References (35)

1. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987) 10.1103/PhysRevLett.58. 2059
2. S. John, Phys. Rev. Lett. 58, 2486 (1987). 10.1103/PhysRevLett.58.2486
3. S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 80, 960 (1998) 10.1103/PhysRevLett.80.960
4. S. Fan, Appl. Phys. Lett. 80, 908 (2002). 10.1063/1.1448174 (Pubitemid 34168009)
5. S. Fan, Physica B 394, 221 (2007) 10.1016/j.physb.2006.12.078
6. Z. Yu, G. Veronis, Z. Wang, and S. Fan, Phys. Rev. Lett. 100, 023902 (2008). 10.1103/PhysRevLett.100.023902
7. M. J. Steel, M. Levy, and R. M. Osgood, Jr., J. Lightwave Technol. 18, 1297 (2000). 10.1109/50.871709
8. M. Levy, J. Appl. Phys. 99, 073104 (2006). 10.1063/1.2190072
9. M. Inoue and T. Fujii, J. Appl. Phys. 81, 5659 (1997). 10.1063/1.364687
10. A. Figotin and I. Vitebskiy, Phys. Rev. E 74, 066613 (2006) 10.1103/PhysRevE.74.066613
11. A. Figotin and I. Vitebsky, Phys. Rev. E 63, 066609 (2001). 10.1103/PhysRevE.63.066609
12. A. M. Merzlikin, A. P. Vinogradov, M. Inoue, and A. B. Granovsky, Phys. Rev. E 72, 046603 (2005). 10.1103/PhysRevE.72.046603
13. H. Takeda and S. John, Phys. Rev. A 78, 023804 (2008). 10.1103/PhysRevA.78.023804
14. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
15. I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. Lakhtakia, and Th. Rasing, Appl. Phys. Lett. 85, 5932 (2004). 10.1063/1.1825060
16. Here it is assumed that the Bloch wave propagates from -/ to /. For the Bloch wave propagating in the opposite direction the Bragg condition reads (k Bl + G) 2 - k02 ε0 0 and kBl - k0 ε0, which corresponds to harmonics f 1 and f 0
17. We assume ε (x) to be real. As a consequence εn = (ε-n)
18. I. Åolc, Czech. J. Phys., Sect. A 4, 65 (1954). 10.1007/BF01688109
19. P. Yeh, J. Opt. Soc. Am. 69, 742 (1979). 10.1364/JOSA.69.000742
20. R. Zengerle, J. Mod. Opt. 34, 1589 (1987). 10.1080/09500348714551531
21. E. Cojocaru, Appl. Opt. 39, 4641 (2000). 10.1364/AO.39.004641
22. G. Shabtay, E. Eidinger, Z. Zalevsky, D. Mendlovic, and E. Marom, Opt. Express 10, 1534 (2002).
23. A. M. Merzlikin, A. P. Vinogradov, M. Inoue, A. B. Khanikaev, and A. B. Granovsky, J. Magn. Magn. Mater. 300, 108 (2006). 10.1016/j.jmmm.2005.10.044 (Pubitemid 43326452)
24. A. M. Merzlikin, A. P. Vinogradov, A. V. Dorofeenko, M. Inoue, M. Levy, and A. B. Granovsky, Physica B 394, 277 (2007). 10.1016/j.physb.2006.12.027 (Pubitemid 46635010)
25. A. A. Jalali and M. Levy, J. Opt. Soc. Am. B 25, 119 (2008). 10.1364/JOSAB.25.000119
26. M. Levy, A. A. Jalali, Z. Zhou, and N. Dissanayake, Opt. Express 16, 13421 (2008). 10.1364/OE.16.013421
27. F. Wang and A. Lakhtakia, Appl. Phys. Lett. 92, 011115 (2008). 10.1063/1.2830942
28. M. Levy and A. A. Jalali, J. Opt. Soc. Am. B 24, 1603 (2007). 10.1364/JOSAB.24.001603
29. B (z) is a real quantity and hence B-1 = (B1)
30. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1993).
31. I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, J. Phys. D 36, R277 (2003). 10.1088/0022-3727/36/18/ R01
32. M. Inoue, K. Arai, T. Fujii, and M. Abe, J. Appl. Phys. 83, 6768 (1998). 10.1063/1.367789
33. Particularly, one may consider a more complex structure for the photonic crystal with the unit cell in the form of a supercell consisting of an anisotropic layer adjacent to a quarter-wave-phase-shifted structure (a subcell) with the resonant cavity made up of bismuth-substituted yttrium iron garnet.
34. This bridge AB starts at the upper point (A) of the lower branch of the dispersion curve and comes to an end at the lower point (B) of the upper branch of the dispersion curve.
35. Moreover, it can be shown that we may have polarization degeneracy in Bloch wave vector in some continuous interval of frequencies if and only if we have polarization degeneracy at all frequencies. So, Figs. 4 5 from [P. Yeh, J. Opt. Soc. Am. 69, 742 (1979)] which show only one imaginary root are not complete-inside the band gap there is no polarization degeneracy in the imaginary components of the wave vector. 10.1364/JOSA.69.000742