Skip to main content
SpringerLink
Log in

Theory of Crossed Gratings

  • Chapter
Electromagnetic Theory of Gratings

Part of the book series: Topics in Current Physics ((TCPHY,volume 22))

Abstract

In this chapter we will consider the theoretical analysis and the properties of doubly periodic diffraction gratings (“bigratings”). Our interest in these structures has been stimulated by two factors. Firstly, their theoretical study represents a natural extension of previous work on mono-periodic structures. Secondly, HORWITZ [7.1] suggested the use of metallic grids as selective filters (heat mirrors) in solar energy absorption. Of course such devices have application in far infrared spectroscopy as beam splitters [7.2], filters [7.3–5] and the reflecting elements in Fabry-Perot interferometers [7.5–10]. Similar applications exist in the field of microwave engineering [7.11.13].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. CM. Horwitz: Opt. Commun. 11, 210 (1974)

    Article  ADS  Google Scholar 

  2. E.E. Russell, E.E. Bell: Infrared Phys. 6, 75 (1966)

    Article  ADS  Google Scholar 

  3. R. Ulrich: Infrared Phys. 7, 37 (1967)

    Article  ADS  Google Scholar 

  4. R. Ulrich: Infrared Phys., 7, 65 (1967)

    Article  ADS  Google Scholar 

  5. R. Ulrich: Appl. Opt. 7, 1987 (1968)

    Article  ADS  Google Scholar 

  6. J.P. Casey, E.A. Lewis: J. Opt. Soc. Am. 42, 971 (1952)

    Article  ADS  Google Scholar 

  7. G.D. Holah, J.P. Auton: Infrared Phys. 14, 217 (1974)

    Article  ADS  Google Scholar 

  8. R.D. Rawcliffe, CM. Randall: Appl. Opt. 6, 1353 (1967)

    Article  ADS  Google Scholar 

  9. J.C Lecullier: Nouv. Rev. Opt. 5, 313 (1974)

    Article  Google Scholar 

  10. M.M. Pradhan: Infrared Phys. 11, 241 (1971)

    Article  ADS  Google Scholar 

  11. C-C Chen: IEEE Trans. MTT-18, 627 (1970)

    Google Scholar 

  12. C-C Chen: IEEE Trans. MTT-19, 475 (1971)

    Google Scholar 

  13. C-C Chen: IEEE Trans. MTT-21, 1 (1973)

    Google Scholar 

  14. R.C McPhedran, D. Maystre: Appl. Phys. 14, 1 (1977)

    Article  ADS  Google Scholar 

  15. L.C Botten: “Theories of Singly and Doubly Periodic Diffraction Gratings”; Ph.D. Thesis, University of Tasmania (1978)

    Google Scholar 

  16. N. Amitay, V. Galindo: IEEE Trans. AP-17, 747 (1969)

    ADS  Google Scholar 

  17. G.H. Derrick, R.C. McPhedran, D. Maystre, M. Nevière: Appl. Phys. 18, 39 (1979)

    Article  ADS  Google Scholar 

  18. R.C McPhedran, L.C. Botten: “Inductive Grids with Circular Apertures”; Report SP 77/5, University of Sydney (1977)

    Google Scholar 

  19. R.C. McPhedran, L.C. Botten, P. Bliek, R. Deleuil, D. Maystre: 8th European Microwave Conf., Paris (1978)

    Google Scholar 

  20. N. Amitay, V. Galindo: IEEE Trans. MTT-16, 265 (1968)

    Google Scholar 

  21. M. Born, E. Wolf: Principles of Optics, 3rd ed. (Pergamon, Oxford 1965) pp.559–560

    Google Scholar 

  22. D.S. Jones: The Theory of Electromagnetism, 1st ed. (Pergamon, Oxford 1964) pp.569–572

    MATH  Google Scholar 

  23. W.H. Eggimann, R.E. Collin: IRE Trans. MTT-10, 528 (1962)

    Article  Google Scholar 

  24. R.H. Ott, R.G. Kouyoumjian, L. Peters: Radio Sci. 2, 1347 (1967)

    ADS  Google Scholar 

  25. K. Sakai, T. Yoshida: Infrared Phys. 18, 137 (1978)

    Article  ADS  Google Scholar 

  26. J.A. Arnaud, F.A. Pelow: Bell Syst. Tech. J. 54, 263 (1975)

    Google Scholar 

  27. J.L. Adams, L.C Botten, R.C McPhedran: J. Opt. (Paris) 9, 91 (1978)

    ADS  Google Scholar 

  28. J.L. Adams, L.C. Botten: “The Crossed Lamellar Transmission Grating”; Report DGRG 77/3, University of Tasmania (1977)

    Google Scholar 

  29. H. Blok, G. Mur: Appl. Sci. Res. 26, 389 (1972)

    Article  Google Scholar 

  30. J.L. Adams, L.C. Botten: “Double Gratings and Their Application as Fabry-Perot Interferometers”, J. Opt. (Paris) 10, 109 (1979)

    ADS  Google Scholar 

  31. L.C. Botten, J.L. Adams, R.C. McPhedran, G.H. Derrick: “Symmetry Properties of Lossless Diffraction Gratings”, J. Opt. (Paris) 11, 43 (1980)

    ADS  Google Scholar 

  32. P. Grivet: “Time Reversibility in an Optical Proof of the Reciprocity Theorem of Electromagnetism”, in Proc. Symposium on Modern Optics, ed. by J. Fox, Microwave Research Institute Symposia Series, Vol.17 (Polytechnic Press, New York 1967) pp.467–479

    Google Scholar 

  33. D.S. Jones: The Theory of Electromagnetism, 1st ed. (Pergamon, Oxford 1964) pp. 56–57, 562-566

    MATH  Google Scholar 

  34. M.M. Pradhan, R.K. Garg: Infrared Phys. 16, 449 (1976)

    Article  ADS  Google Scholar 

  35. M.M. Pradhan, R.K. Garg: Infrared Phys. 17, 253 (1977)

    Article  ADS  Google Scholar 

  36. L.C. Botten: “A Generalized Treatment of Multielement Interference Filters for the Far Infrared”. Infrared Phys. 19, 659 (1979)

    Article  ADS  Google Scholar 

  37. L.C. Botten: “On the Use of Fibonacci Recurrence Relations in the Design of Long Wavelength Filters and Interferometers”, The Fibonacci Quarterly, to be published

    Google Scholar 

  38. D. Maystre, M. Nevière: J. Opt. 9, 301 (1978)

    Article  ADS  Google Scholar 

  39. P. Vincent: Opt. Commun. 26, 293 (1978)

    Article  ADS  Google Scholar 

  40. M. Nevière, M. Cadilhac, R. Petit: IEEE Trans. AP-21, 37 (1973)

    ADS  Google Scholar 

  41. J.M. Elson: Appl. Opt. 16, 2872 (1977)

    Article  ADS  Google Scholar 

  42. J. Chandezon, D. Maystre, G. Raoult: J. Opt., to be published

    Google Scholar 

  43. G.A. Korn, T.M. Korn: Mathematical Handbook for Scientists and Engineers, 2nd ed. (McGraw-Hill, New York 1968) pp.535–560

    Google Scholar 

  44. G.H. Derrick, R.C. McPhedran, D. Maystre, M. Nevière: “A Theory for Crossed Gratings of Finite Conductivity”; Report TP 78/1, University of Sydney (1979)

    Google Scholar 

  45. M. Nevière, D. Maystre, R. McPhedran, G. Derrick, M. Hutley: 11th Congress of the Intern. Commission for Optics, Madrid (1978)

    Google Scholar 

  46. C.G. Bernhard: Endeavour 26, 79 (1967)

    Google Scholar 

  47. P.B. Clapham, M.C. Hutley: Nature 244, 281 (1973)

    Article  ADS  Google Scholar 

  48. B.S. Thornton: J. Opt. Soc. Am. 65, 267 (1975)

    Article  ADS  Google Scholar 

  49. L.C. Botten, I.T. Ritchie: Opt. Commun. 23, 421 (1977)

    Article  ADS  Google Scholar 

  50. G.H. Derrick, R.C. McPhedran: Submitted to J. Opt.

    Google Scholar 

  51. A. Wirgin: Simplified theory of the diffraction of an electromagnetic wave by a perfectly conducting biaxial periodic surface. Opt. Commun. 28, 2.15 (1979)

    Article  Google Scholar 

  52. R. Petit: Sur l’étude électromagnétique de l’absorption par les surfaces rugueuses. J. Phys. 42, Colloque Cl (1981, in preparation)

    Google Scholar 

  53. A. Wirgin: Sur la réponse spectrale de certaines surfaces texturées. S. J. Phys. 42, Colloque Cl (1981, in preparation)

    Google Scholar 

Download references

Authors
  1. R. C. McPhedran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. H. Derrick
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. C. Botten
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratoire d’Optique Electromagnétique, Faculté des Sciences et Techniques de Saint-Jérome, Université d’Aix-Marseille III, Rue Henri-Poincaré, F-13397, Marseille Cédex 13, France

    Roger Petit

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

McPhedran, R.C., Derrick, G.H., Botten, L.C. (1980). Theory of Crossed Gratings. In: Petit, R. (eds) Electromagnetic Theory of Gratings. Topics in Current Physics, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81500-3_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-81500-3_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-81502-7

  • Online ISBN: 978-3-642-81500-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation