Photonic Bands Using Vector Spherical Waves. IV. Analogy of Optics of Photonic Crystals to That of Anisotropic Crystals

Journal of the Physical Society of Japan

Volumn 65, Issue 9, 1996, Pages 3068-3077

  Ohtaka, Kazuo ^a   Ueta, Tsuyoshi ^a   Tanabe, Yukito ^b  

^a CHIBA UNIVERSITY   (Japan)

^b Department of Digital Media   (Japan)

Author keywords

Anisotropy; Conical refraction; Crystal optics; Double refraction; Group velocity; Photonic band; Poynting vector

Indexed keywords

EID: 0030518417     PISSN: 00319015     EISSN: None     Source Type: Journal    
DOI: 10.1143/JPSJ.65.3068     Document Type: Article

References (15)

1. K. Ohtaka and T. Tanabe: J. Phys. Soc. Jpn. 65 (1996) 2265, referred to as paper I.
2. K. Ohtaka and T. Tanabe: J. Phys. Soc. Jpn. 65 (1996) 2276, referred to as paper II.
3. K. Ohtaka and T. Tanabe: J. Phys. Soc. Jpn. 65 (1996) 2670, referred to as paper III.
4. M. Born and E. Wolf: Principles of Optics (Pergamon, Oxford, 1975) p. 705.
5. L. M. Brckhovskikh: Waves in Layered Media (Academic, London, 1960) p. 79.
6. J. P. van der Ziel, M. Ilegems and R. M. Mikulyak: Appl. Phys. Lett. 28 (1976) 735.
7. M. Tateda: IEEE/OSA J. Lightwave Technol. LT-2 (1984) 522.
8. M. Kitagawa and M. Tateda: Appl. Opt. 24 (1985) 3359.
9. L. D. Landau, E. M. Lifshitz and L. P. Pitaevskii: Electrody-namics of Continuous Media (Pergamon Press, Oxford, 1984) 2nd ed., p. 331.
10. A. Yariv: Quantum Electronics (John Wiley and Sons, New York, 1989) 3rd ed., p. 87.
11. L. D. Landau, E. M. Lifshitz and L. P. Pitaevskii: Electrody-namics of Continuous Media (Pergamon Press, Oxford, 1984) 2nd ed., p. 268.
12. The normalization with respect to energy is expressed by eq. (2.28). This scheme is consistent with the orthogonality properties between E and D of the eigenvectors of the secular equation (see papers I and III).
13. For group theory, see, e.g., T. Inui, Y. Tanabe and Y. Onodera: Group Theory and Its Applications in Physics (Springer, Berlin, 1990) p. 234.
14. K. Ohtaka: Phys. Rev. B 19 (1979) 5057.
15. 1 for eq. (4.1) with A, B > 0 and C < 0. Therefore, it has nothing to do with what we are discussing. Also, in the 2d band structure of graphite, two sheets of the form eq. (3.3) are known to touch at the point K of the 2d Brillouin zone (see, A. Natori: J. Phys. Soc. Jpn. 55 (1986) 4372). We are discussing here the crossing of the sheets of eq. (3.3) and the touch of the two cones of the constant energy surfaces.