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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 24 — Nov. 19, 2012
  • pp: 27155–27162

Mason’s rule and Signal Flow Graphs applied to subwavelength resonant structures

Thomas Estruch, Fabrice Pardo, Benjamin Portier, Julien Jaeck, Sophie Derelle, and Riad Haidar  »View Author Affiliations

Optics Express, Vol. 20, Issue 24, pp. 27155-27162 (2012)

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Widely used for the design of resonant electronic devices, Mason’s scalar rule is adapted here to the study of resonant subwavelength optical structures. It turns out to be an efficient formalism, especially when dealing with multiple wave interference mechanisms. Indeed it allows to comprehend the underlying physical mechanisms of the structure in a straightforward way and fast analytical formulae can be retrieved. As an illustration, we apply it to the study of dual metallic gratings, which appear to be promissing optical filters as their spectral shape can be tailored according to needs.

© 2012 OSA

OCIS Codes
(110.4850) Imaging systems : Optical transfer functions
(260.3160) Physical optics : Interference
(250.5403) Optoelectronics : Plasmonics
(050.6624) Diffraction and gratings : Subwavelength structures
(230.7408) Optical devices : Wavelength filtering devices

ToC Category:
Physical Optics

Original Manuscript: July 19, 2012
Revised Manuscript: August 29, 2012
Manuscript Accepted: August 29, 2012
Published: November 16, 2012

Thomas Estruch, Fabrice Pardo, Benjamin Portier, Julien Jaeck, Sophie Derelle, and Riad Haidar, "Mason’s rule and Signal Flow Graphs applied to subwavelength resonant structures," Opt. Express 20, 27155-27162 (2012)

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  1. J. Shen and P. Platzman, “Properties of a One-Dimensional Metallophotonic Crystal”, Phys. Rev. B70, 035101 (2004). [CrossRef]
  2. R. Bakker, V. Drachev, H. Yuan, and V. Shalaev, “Enhanced Transmission in Near-Field Imaging of Layered Plasmonic Structures”, Opt. Express12, 3701–3706 (2004). [CrossRef] [PubMed]
  3. A. Hibbins, J. Sambles, C. Lawrence, and J. Brown, “Squeezing millimeter waves into microns, Phys. Rev. Lett.92, 143904 (2004). [CrossRef] [PubMed]
  4. Y. Ding and R. Magnusson, “Resonant Leaky-Mode spectral-band engineering and device applications”, Opt. Express12, 5661–5674 (2004). [CrossRef] [PubMed]
  5. V. Babicheva and Y. Lozovik, “Extraordinary Transmission and Suppression of Transmission of Dual Metal Gratings with Subwavelength Slits” in “AIP Conference Proceedings”, 291, p. 103 (2010). [CrossRef]
  6. P. Lalanne, J. Hugonin, and P. Chavel, “Optical Properties of Deep Lamellar Gratings: A Coupled Bloch-Mode Insight”, J. Lightwave Technol.24, 2442 (2006). [CrossRef]
  7. H. B. Chan, Z. Marcet, K. Woo, D. B. Tanner, D. W. Carr, J. E. Bower, R. A. Cirelli, E. Ferry, F. Klemens, J. Miner, C. S. Pai, and J. A. Taylor, “Optical Transmission through Double-Layer Metallic Subwavelength Slit Arrays”, Opt. Lett.31, 516–518 (2006). [CrossRef] [PubMed]
  8. T. Estruch, J. Jaeck, F. Pardo, S. Derelle, J. Primot, J. Pelouard, and R. Haidar, “Perfect Extinction in Subwavelength Dual Metallic Transmitting Gratings”, Opt. Lett36, 3160–3162 (2011). [CrossRef] [PubMed]
  9. P. Lalanne and G. Morris, “Highly Improved Convergence of the Coupled-Wave Method for TM Polarization”, J. Opt. Soc. Am. A.13, 779–784 (1996). [CrossRef]
  10. P. Bouchon, F. Pardo, R. Haïdar, and J.-L. Pelouard, “Fast Modal Method for Subwavelength Gratings based on B-Spline Formulation”, J. Opt. Soc. Am. A.27, 696–702 (2010). [CrossRef]
  11. S. Mason, “Feedback Theory-Some Properties of Signal Flow Graphs”, Proceedings of the IRE41, 1144–1156 (1953). [CrossRef]
  12. C. Cheng, J. Chen, D. Shi, Q. Wu, F. Ren, J. Xu, Y. Fan, J. Ding, and H. Wang, “Physical Mechanism of Extraordinary Electromagnetic Transmission in Dual-Metallic Grating Structures”, Phys. Rev. B78, 075406 (2008). [CrossRef]
  13. N. Cotter, T. Preist, and J. Sambles, “Scattering-Matrix Approach to Multilayer Diffraction”, J. Opt. Soc. Am. A.12, 1097–1103 (1995). [CrossRef]
  14. E. Palik and G. Ghosh, Handbook of Optical Constants of Solids, (Academic press, 1985).
  15. R. W. Wood, “Anomalous Diffraction Gratings”, Phys. Rev.48, 928–936 (1935). [CrossRef]

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