Analysis of two-dimensional photonic band gaps of any rod shape and conductivity using a conical-integral-equation method.

The conical-boundary-integral-equation method has been proposed for calculation of the sensitive optical response of two-dimensional photonic band gaps (PBGs), including dielectric, absorbing, and high-conductive rods of various shapes working in any wavelength range. It is possible to determine the diffracted field by computing the scattering matrices separately for any grating boundary profile. The computation of the matrices is based on the solution of a 2×2 system of singular integral equations at each interface between two different materials. The advantage of our integral formulation is that the discretization of the integral equation system and the factorization of the discrete matrices, which takes the majority of the computing time, are carried out only once for a boundary. It turns out that a small number of collocation points per boundary combined with a high convergence rate can provide an adequate description of the dependence on diffracted energy of very different PBGs illuminated at arbitrary incident and polarization angles. The numerical results presented describe the significant impact of rod shape on diffraction in PBGs supporting polariton-plasmon excitation, particularly in the vicinity of resonances and at high filling ratios. The diffracted energy response calculated vs the array cell geometry parameters was found to vary from a few up to a few hundred percent. The influence of other types of anomalies (i.e., waveguide anomalies, cavity modes, Fabry-Perot and Bragg resonances, Rayleigh orders, etc.), conductivity, and polarization states on the optical response is demonstrated.

[1]  B. Guizal,et al.  Reformulation of the eigenvalue problem in the Fourier modal method with spatial adaptive resolution. , 2009, Optics letters.

[2]  Luis Landesa,et al.  Method-of-moments formulation for the analysis of plasmonic nano-optical antennas. , 2011, Journal of the Optical Society of America. A, Optics, image science, and vision.

[3]  L. Goray,et al.  Application of the boundary integral equation method to very small wavelength-to-period diffraction problems , 2010 .

[4]  Gunther Schmidt,et al.  Integral equation methods from grating theory to photonics: an overview and new approaches for conical diffraction , 2011 .

[5]  Steven G. Johnson,et al.  Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis. , 2001, Optics express.

[6]  Nicolas Bonod,et al.  Differential theory: application to highly conducting gratings. , 2004, Journal of the Optical Society of America. A, Optics, image science, and vision.

[7]  Leonid I. Goray.  Application of the rigorous method to x-ray and neutron beam scattering on rough surfaces , 2010 .

[8]  Ya Yan Lu,et al.  Boundary integral equation Neumann-to-Dirichlet map method for gratings in conical diffraction. , 2011, Journal of the Optical Society of America. A, Optics, image science, and vision.

[9]  Lifeng Li.  Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings , 1996 .

[10]  Harald Giessen,et al.  Optical properties of planar metallic photonic crystal structures: Experiment and theory , 2004 .

[11]  Olivier J. F. Martin,et al.  Controlling the Fano interference in a plasmonic lattice , 2007 .

[12]  Frank Wyrowski,et al.  Integral equation method with parametrization of grating profile theory and experiments , 1996 .

[13]  T. Gaylord,et al.  Rigorous coupled-wave analysis of planar-grating diffraction , 1981 .

[14]  Leonid I. Goray,et al.  Specular and diffuse scattering from random asperities of any profile using the rigorous method for x-rays and neutrons , 2009, Optical Metrology.

[15]  James Bremer,et al.  Characterization of zone plate properties using monochromatic synchrotron radiation in the 2 to 20 nm wavelength range. , 2011, Applied optics.

[16]  John F. Seely,et al.  Spectral Separation of the Efficiencies of the Inside and Outside Orders of Soft X-Ray - Extreme Ultraviolet Gratings at Near Normal Incidence , 2006 .

[17]  Gunther Schmidt,et al.  On the Diffraction by Biperiodic Anisotropic Structures , 2003 .

[18]  Gunther Schmidt,et al.  Solving conical diffraction grating problems with integral equations. , 2010, Journal of the Optical Society of America. A, Optics, image science, and vision.

[19]  E. Popov,et al.  Enhanced transmission due to nonplasmon resonances in one- and two-dimensional gratings. , 2004, Applied optics.

[20]  E. Popov,et al.  Staircase approximation validity for arbitrary-shaped gratings. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[21]  R. W. Christy,et al.  Optical Constants of the Noble Metals , 1972 .

[22]  Leonid I Goray,et al.  Efficiencies of master, replica, and multilayer gratings for the soft-x-ray-extreme-ultraviolet range: modeling based on the modified integral method and comparisons with measurements. , 2002, Applied optics.

[23]  S. A. Schelkunoff,et al.  The impedance concept and its application to problems of reflection, refraction, shielding and power absorption , 1938 .

[24]  D. Nyquist,et al.  Efficient integral-equation-based method for accurate analysis of scattering from periodically arranged nanostructures. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Daniel Maystre,et al.  Electromagnetic study of photonic band gaps , 1994 .