Differential
Method:
General:
E. Popov: “Differential method for periodic media,” in Gratings: Theory and Numeric Applications (Institut Fresnel,
PUP, 2012), Ch.7, 7.1-7.56 www.fresnel.fr/numerical-grating-book
M. Nevière and E. Popov: Light Propagation in Periodic
Media: Diffraction Theory and Design, (Marcel Dekker, New York, 2003)
Spherical coordinates:
link to Spherical Harmonics
Cylindrical coordinates (apertures and
structured fibres):
E. Popov and N. Bonod, “Differential theory of
diffraction in cylindrical coordinates,” phys. stat. sol. (b) 244,
3463-3478 (2007) pdf
Ph. Boyer, G. Renversez, E. Popov, and M. Nevère, “Improved differential method for microstructured optical fibers,”
J. Opt. A: Pure Appl. Opt. 9, 728-740 (2007) pdf
E. Popov, M. Nevière, A. Sentennac,
N. Bonod, A.-L. Ferrenbach, J. Wenger, P.-F. Lenne, H. Rigneault, “Single-scattering theory
of light diffraction by a circular subwavelength
aperture in a finitely conducting screen,” J. Opt. Soc. Am. A 24,
339-358 (2007) pdf
P. Boyer, E. Popov, G. Renversez, and M. Nevière, “A new differential method applied to the study of
arbitrary cross section microstructured optical fibers,” Opt. Quant. Electron. 38, 217-230 (2006) pdf
P. Boyer,
E. Popov, M. Nevière, and G. Renversez:
“Diffraction theory: application of the fast Fourier factorization to
cylindrical devices with arbitrary cross section lighted in conical mounting,”
J. Opt. Soc. Am. A 23, 1146-1158 (2006) pdf
P. Boyer, E. Popov, M. Nevière, G. Tayeb: “Diffraction theory in TM-polarization: Application of the Fast Fourier Factorization method to cylindrical devices with arbitrary cross section,” J. Opt. Soc. Am. A 21, 2146-2153 (2004) pdf
N. Bonod, E. Popov, M. Neviere: “Light transmission through a subwavelength microstructured
aperture: electromagnetic theory and applications,” Opt. Commun. 245, 355-361 (2005) pdf
N. Bonod, E. Popov, M. Neviere:
“Differential theory of diffraction by finite cylindrical objects,” J. Opt. Soc.
Am. A 22, 481-490
(2005) pdf
E. Popov, M. Nevière, and N. Bonod: “Factorization of products of discontinuous
functions applied to Fourier-Bessel basis,” J. Opt. Soc. Am. A, 21, 46-51 (2004) pdf
Gratings with 2D-peridicity:
E. Popov, S. Enoch, G. Tayeb, M. Nevière, B. Gralak, N. Bonod , "Enhanced transmission due to non-plasmon resonances in one and two dimensional gratings," Appl.Opt. 43, 999-1008 (2004) pdf
E. Popov, M. Neviere, S. Enoch, and R. Reinisch: “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B, 62,
16100-16108 (2000) pdf
Gratings with 1D periodicity:
J.-J. Bonnefois, G. Guilda,
M. Nevière, and E. Popov, “Simulation of
two-dimensional Kerr photonic crystals via the fast Fourier factorisation,” J.
Opt. Soc. Am. A 23, 842-847 (2006) pdf
E. Popov, B. Chernov, M. Nevière,
N. Bonod: “Differential theory: application to highly
conducting gratings,” J. Opt. Soc. Am. A, 21, 199-206 (2004) pdf
E.Popov and M.Nevière:
“Maxwell equations in Fourier space: fast converging formulation for
diffraction by arbitrary shaped, periodic, anisotropic media,” J. Opt. Soc. Am.
A 18, 2886-2894 (2001) pdf
E. Popov
and B. Bozhkov: “Differential method applied for
photonic crystals”, Appl. Opt. 39, 4926 (2000) pdf
E. Popov and M. Neviere: “Grating theory: new
equations in Fourier space leading to fast converging results for TM
polarization,” J. Opt. Soc. Am. A 17, 1773-1784 (2000) pdf
E. Popov and M. Neviere: “Differential theory
for diffraction gratings: a new formulation for TM polarization with rapid
convergence,” Opt. Lett. 25, 598 (2000) pdf
M. Nevière and E. Popov: "Analysis of
dielectric gratings of arbitrary profiles and thicknesses: A comment," J.
Opt. Soc. Am. A 9, 2095-2096 (1992) pdf