Singular states of photonic crystal local optical field are described based on group theoretic treatments of the fundamental system symmetries expressed through local representations of the singular character of the Bloch modes. The local field response is illustrated, in a purely two-dimensional system for clarity, by an analysis of the local polarization state. The fundamentals of group theory are introduced through the group representation, whose partner functions may be used to express the photonic crystal eigenmodes. We have extended the eigenmode k-group treatment to the derivation of the irreducible matrix representations of the transformation operators of the eigenmode space k-group, which may be applied with respect to any symmetry axis. This permits a comprehensive discussion of the local polarization state, and its symmetry transformation properties, through the set of crystallographic orbits. Transformation relations permit the nature and location of polarization singularities to be identified by the sites' Wyckoff positions. Confirmation with analytic mode determination is presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Allen, L., Beijersbergen, M.W., Spreeuw, R.J.C., Woerdman, J.P.: Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes. Phys. Rev. A 45(11), 8185–8189 (1992)
Berry, M.V., Dennis, M.R.: Singularities polarization singularities in isotropic random vector waves. Proc. R. Soc. Lond. A 457, 141–155 (2001)
Born, M., Wolf, E.: Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, 7th edn. Cambridge University Press, Cambridge (2003)
Evarestov, R.A., Smirnov, V.P.: Site symmetry in crystals theory and applications, Springer series in solid-state sciences 108. Springer, New York (1993)
Hahn, T.: International tables for crystallography, Volume A: space-group symmetry, 4th edn. Kluwer, London (1995)
Hajnal, J.V.: Singularities in the transverse fields of electromagnetic waves, I: Theory. Proc. R. Soc. Lond. A 414, 433–446 (1987)
Jackson, J.D.: Classical electrodynamics, 3rd edn. Wiley, Hoboken, NJ (1999)
John, S.: Strong localization of photons in certain disordered dielectric superlattices. Phys. Rev. Lett. 58(23), 2486–2489 (1987)
Nieminen, T.A., Parkin, S.J.W., Heckenberg, N.R., Rubinsztein-Dunlop, H.: Optical torque and symmetry. Proc. SPIE 5514, 254–263 (2004)
Nye, J.F.: Natural focusing and the fine structure of light: caustics and wave dislocations. IOP, Bristol (1999)
Sakoda, K.: Optical properties of photonic crystals, 2nd edn. Springer, Berlin (2005)
Tinkham, M.: Group theory and quantum mechanics. Dover Mineola, New York (1992)
Wheeldon, J.F.: Group theoretic expressions of optical singularities in photonic crystals. Ph.D thesis, University of Ottawa, Ottawa (2009)
Wheeldon, J.F., Schriemer, H.P.: Wyckoff positions and the expression of polarization singularities in photonic crystals. Opt. Express 17, 2111–2121 (2009)
Wheeldon, J.F., Hall, T.J., Schriemer, H.P.: Symmetry constraints and the existence of Bloch mode vortices in linear photonic crystals. Opt. Express 15, 3531–3542 (2007)
Yablonovitch, E.: Inhibited spontaneous emission in solid-state physics and electronics. Phys. Rev. Lett. 58(20), 2059–2062 (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media B.V.
About this paper
Cite this paper
Wheeldon, J.F., Schriemer, H.P. (2010). Symmetry and the Local Field Response in Photonic Crystals. In: Hall, T.J., Gaponenko, S.V., Paredes, S.A. (eds) Extreme Photonics & Applications. NATO Science for Peace and Security Series B: Physics and Biophysics. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3634-6_10
Download citation
DOI: https://doi.org/10.1007/978-90-481-3634-6_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-3633-9
Online ISBN: 978-90-481-3634-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)