OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 10 — Oct. 1, 2007
  • pp: 3100–3114

Modal method for conical diffraction on a rectangular slit metallic grating in a multilayer structure

Yanko Todorov and Christophe Minot  »View Author Affiliations


JOSA A, Vol. 24, Issue 10, pp. 3100-3114 (2007)
http://dx.doi.org/10.1364/JOSAA.24.003100


View Full Text Article

Enhanced HTML    Acrobat PDF (924 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The modal method is applied to the problem of conical diffraction on a rectangular slit metallic grating lying on an arbitrary multilayer medium. In the approximation of the surface impedance boundary condition on the grating walls, a single matrix equation is obtained, whose coefficients are expressed simply by the reflectivities on the different layers. A simple and comprehensive treatment is thus obtained for virtually any multilayer system. The method is illustrated for the case of a cavity formed by a planar metallic mirror and a grating, as well as the system formed by a doped layer with Drude susceptibility in a substrate below the grating. The method could be useful for the design of near- and far-infrared devices.

© 2007 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(230.4170) Optical devices : Multilayers
(240.5420) Optics at surfaces : Polaritons
(260.1960) Physical optics : Diffraction theory
(260.3090) Physical optics : Infrared, far
(260.5740) Physical optics : Resonance

ToC Category:
Diffraction and Gratings

History
Original Manuscript: March 22, 2007
Revised Manuscript: June 21, 2007
Manuscript Accepted: June 25, 2007
Published: September 7, 2007

Citation
Yanko Todorov and Christophe Minot, "Modal method for conical diffraction on a rectangular slit metallic grating in a multilayer structure," J. Opt. Soc. Am. A 24, 3100-3114 (2007)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-10-3100


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667-669 (1998). [CrossRef]
  2. J. A. Porto, F. J. Garcia-Vidal, and J. P. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999). [CrossRef]
  3. P. Lalanne, J. P. Hugonin, S. Astelean, M. Palmaru, and K. D. Möller, "One-mode model and Airy-like formulae for one-dimensional metallic gratings," J. Opt. A, Pure Appl. Opt. 2, 48-51 (2000). [CrossRef]
  4. S. Collin, F. Pardo, R. Teissier, and J. L. Pelouard, "Horizontal and vertical surface resonances in transmission metallic gratings," J. Opt. A, Pure Appl. Opt. 4, S154-S160 (2002). [CrossRef]
  5. F. J. Garcia-Vidal and L. Martin-Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured metals," Phys. Rev. B 66, 155412 (2002). [CrossRef]
  6. A. Barbara, P. Quémerais, E. Bustarret, T. López, and T. Fournier, "Electromagnetic resonances of sub-wavelength rectangular metallic grating," Eur. Phys. J. D 23, 143-154 (2003). [CrossRef]
  7. F. Marquier, J.-J. Greffet, S. Collin, F. Pardo, and J. L. Pelouard, "Resonant transmission through a metallic film due to coupled modes," Opt. Express 13, 70-76 (2005). [CrossRef] [PubMed]
  8. J. L. Coutaz, F. Garet, E. Bonnet, A. V. Tishchenko, O. Parriaux, and M. Nazarov, "Grating diffraction effects in the THz domain," Acta Phys. Pol. A 107, 26-37 (2005).
  9. C. Gmachl, A. Straub, R. Colombelli, F. Capasso, D. L. Sivco, A. M. Sergent, and A. Y. Cho, "Single-mode, tunable distributed feedback and multiple wavelength quantum cascade laser," IEEE J. Quantum Electron. 38, 569-581 (2002). [CrossRef]
  10. A. Wittmann, M. Giovannini, J. Faist, L. Hvozdara, S. Blaser, D. Hofstetter, and E. Gini, "Room temperature, continuous wave operation of distributed feedback quantum cascade lasers with widely spaced operation frequencies," Appl. Phys. Lett. 89, 141116 (2006). [CrossRef]
  11. L. Diehl, B. G. Lee, P. Behroozi, M. Loncar, M. A. Belkin, F. Capasso, T. Aellen, D. Hofstetter, M. Beck, and J. Faist, "Microfluidic tuning of distributed feedback quantum cascade lasers," Opt. Express 14, 11660-11667 (2006). [CrossRef]
  12. O. Demichel, L. Mahler, T. Losco, C. Mauro, R. Green, J. Xu, A. Trediccuci, F. Beltram, H. E. Beere, D. A. Richie, and V. Tamosiunas, "Surface plasmon photonic structures in terahertz quantum cascade lasers," Opt. Express 14, 5335-5345 (2006). [CrossRef]
  13. S. Khanna, M. Lachab, A. G. Davies, E. H. Linfield, J. A. Fan, M. A. Belkin, and F. Capasso, "Surface emitting terahertz quantum cascade laser with a double-metal waveguide," Opt. Express 14, 11672-11680 (2006). [CrossRef]
  14. S. Kumar, B. S. Williams, Q. Qin, A. W. M. Lee, and Q. Hu, "Surface-emitting distributed feedback terahertz quantum cascade lasers in metal-metal waveguides," Opt. Express 15, 113-128 (2007). [CrossRef]
  15. S. S. Jha, J. R. Kirtley, and J. C. Tsang, "Intensity of Raman scattering from molecules adsorbed on a metallic grating," Phys. Rev. B 22, 3973-3982 (1980). [CrossRef]
  16. M. Moskovits, "Surface-enhanced spectroscopy," Rev. Mod. Phys. 57, 783-826 (1985). [CrossRef]
  17. A. Otto, I. Mrozek, H. Grabhorn, and W. Akemann, "Surface-enhanced Raman scattering," J. Phys.: Condens. Matter 4, 1143-1212 (1992). [CrossRef]
  18. N. Felidj, J. Aubard, G. Levi, J. R. Krenn, A. Hohenau, G. Schinder, A. Leitner, and F. R. Aussenegg, "Optimized surface-enhanced Raman scattering on gold nanoparticle arrays," Appl. Phys. Lett. 82, 3095-3097 (2003). [CrossRef]
  19. G. H. Agarwal and C. V. Kunasz, "Dipole radiation in the presence of a rough surface. Conversion of a surface-polariton field into radiation," Phys. Rev. B 26, 5832-5842 (1982). [CrossRef]
  20. P. T. Leung, Y. S. Kim, and T. F. George, "Decay of molecules at corrugated thin metal films," Phys. Rev. B 39, 9888-9893 (1989). [CrossRef]
  21. T. Suzuki and P. K. L. Yu, "Experimental and theoretical study of dipole emission in the two-dimensional photonic band structure of the square lattice with dielectric cylinders," J. Appl. Phys. 79, 582-594 (1996). [CrossRef]
  22. R. Amos and W. Barnes, "Modification of spontaneous emission lifetimes in the presence of corrugated metallic surfaces," Phys. Rev. B 59, 7708-7714 (1999). [CrossRef]
  23. Y. Todorov, I. Abram, and C. Minot, "Dipole emission into rectangular metallic gratings with subwavelength slits," Phys. Rev. B 71, 075116 (2005). [CrossRef]
  24. R. K. Lee, O. J. Painter, B. D'Urso, A. Scherer, and A. Yariv, "Measurement of spontaneous emission from a two-dimensional photonic band gap defined microcavity at near-infrared wavelengths," Appl. Phys. Lett. 74, 1522-1524 (1999). [CrossRef]
  25. H. Rigneault, F. Lemarchand, and A. Sentenac, "Dipole radiation into grating structures," J. Opt. Soc. Am. A 17, 1048-1058 (2000). [CrossRef]
  26. A.-L. Fehrembach, S. Enoch, and A. Sentenac, "Highly directive light sources using two-dimensional photonic crystal slabs," Appl. Phys. Lett. 79, 4280-4282 (2001). [CrossRef]
  27. D. Delbeke, P. Bienstman, R. Bockstaele, and R. Baets, "Rigourous electromagnetic analysis of dipole emission in periodically corrugated layers: the grating-assisted resonant-cavity light-emitting diode," J. Opt. Soc. Am. A 19, 871-880 (2002). [CrossRef]
  28. R. Colombelli, K. Stinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Trennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, "Quantum cascade surface-emitting photonic crystal laser," Science 302, 1374-1377 (2003). [CrossRef] [PubMed]
  29. Y. Todorov, I. Sagnes, U. Gennser, N. Coron, C. Minot, and I. Abram, "Spontaneous emission enhancement in quantum cascade structures in the terahertz domain," Phys. Status Solidi C 4, 524-527 (2007). [CrossRef]
  30. K. W. Gossen and S. A. Lyon, "Grating enhanced quantum well detector," Appl. Phys. Lett. 47, 1257-1259 (1985). [CrossRef]
  31. D. Heitmann and U. Mackens, "Grating-coupler-induced intersubband resonances in electron inversion layer of silicon," Phys. Rev. B 33, 8269-8283 (1986). [CrossRef]
  32. W. J. Li and B. D. McCombe, "Coupling efficiency of metallic gratings for excitation of intersubband transitions in quantum-well structures," J. Appl. Phys. 71, 1038-1040 (1992). [CrossRef]
  33. J. R. Lakowicz, J. Malicka, I. Gryczynski, Z. Gryczynski, and C. D. Geddes, "Radiative decay engineering: the role of photonic mode density in biotechnology," J. Phys. D 36, R240-R249 (2003). [CrossRef]
  34. I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "Highly conducting lamellar diffraction grating," Opt. Acta 28, 1103-1106 (1981). [CrossRef]
  35. P. Sheng, R. S. Stepleman, and P. N. Sanda, "Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations," Phys. Rev. B 26, 2907-2917 (1982). [CrossRef]
  36. L. Li, "A modal analysis of lamellar diffraction gratings in conical mountings," J. Mod. Opt. 40, 553-573 (1993). [CrossRef]
  37. H. Lochbihler, "Diffraction from highly conducting lamellar gratings in conical mountings," J. Mod. Opt. 43, 1867-1890 (1996). [CrossRef]
  38. R.Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, 1980). [CrossRef]
  39. L. Landau and L. Lifchitz, Electrodynamics of Continuous Media (Mir, 1969).
  40. M.Bass, ed. Handbook of Optics II (McGraw-Hill, 1995).
  41. A. Hessel and A. A. Oliner, "A new theory of Wood's anomalies on optical gratings," Appl. Opt. 4, 1275-1297 (1965). [CrossRef]
  42. R. W. Wood, "Anomalous diffraction gratings," Phys. Rev. 48, 928-937 (1935). [CrossRef]
  43. M. Balkanski and R. F. Wallis, Semiconductor Physics and Applications (Oxford U. Press, 2000).
  44. D. G. Esaev, S. G. Matsik, M. B. M. Rinzan, A. G. U. Perera, H. C. Liu, and M. Buchanan, "Resonant cavity enhancement in heterojunction GaAs/AlGaAs terahertz detectors," J. Appl. Phys. 93, 1879-1873 (2003). [CrossRef]
  45. R. Zengerle, "Light propagation in singly and doubly periodic planar waveguides," J. Mod. Opt. 34, 1589-1617 (1987). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited