Skip to main content

Diffraction Grating Theory

  • Chapter
  • First Online:
Maxwell’s Equations in Periodic Structures

Part of the book series: Applied Mathematical Sciences ((AMS,volume 208))

  • 1379 Accesses

Abstract

Scattering theory in periodic diffractive structures, known as  diffraction gratings, has many important applications in micro-optics, which include the design and fabrication of diffractive optical elements such as corrective lenses, anti-reflective interfaces, beam splitters, and sensors.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover 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

References

  1. P. Rayleigh, On the dynamical theory of gratings. R. Soc. Lond. Ser. A 79, 399–416 (1907)

    MATH  Google Scholar 

  2. J.A. Cox, D. Dobson, Mathematical modeling for diffractive optics, in Diffractive and Miniaturized Optics (Critical Reviews), ed. by S. Lee. SPIE, vol. 49, pp. 32–53 (1994)

    Google Scholar 

  3. N. Bonod, J. Neauport, Diffraction gratings: from principles to applications in high-intensity lasers. Adv. Opt. Photonics 8, 156–199 (2016)

    Article  Google Scholar 

  4. C.H. Wilcox, Scattering Theory for Diffraction Gratings. Applied Mathematical Sciences, vol. 46 (Springer, New York, 1984)

    Google Scholar 

  5. A. Friedman, Mathematics in Industrial Problems, IMA, vol. 16 (Springer, New York, 1988)

    Book  Google Scholar 

  6. A. Friedman, Mathematics in Industrial Problems, Part 3, IMA, vol. 38 (Springer, New York, 1991)

    Book  Google Scholar 

  7. A. Friedman, Mathematics in Industrial Problems, Part 7 (Springer, New York, 1994)

    Book  Google Scholar 

  8. G. Bao, L. Cowsar, W. Masters, Mathematical Modeling in Optical Sciences Frontiers in Applied Mathematics. (SIAM, Philadelphia, 2001)

    Book  Google Scholar 

  9. R. Petit (ed.), Electromagnetic Theory of Gratings, Topics in Current Physics, vol. 22 (Springer, Heidelberg, 1980)

    Google Scholar 

  10. E. Popov (ed.), Gratings: Theory and Numeric Applications, , 2nd edn. CNRS, Institut Fresnel UMR (2014)

    Google Scholar 

  11. R.W. Wood, On a remarkable case of uneven distribution of light in a diffraction grating spectrum. Proc. Phys. Soc. Lond. 18, 269–275 (1902)

    Article  Google Scholar 

  12. J. Lin, S. Shipman, H. Zhang, A mathematical theory for Fano resonance in a periodic array of narrow slits. SIAM J. Appl. Math. 80, 2045–2070 (2020)

    Article  MathSciNet  Google Scholar 

  13. J. Lin, H. Zhang, Scattering by a periodic array of subwavelength slits I: field enhancement in the diffraction regime. Multiscale Model. Simul. 16, 922–953 (2018)

    Article  MathSciNet  Google Scholar 

  14. J. Lin, H. Zhang, Scattering by a periodic array of subwavelength slits II: surface bound state, total transmission, and field enhancement in homogenization regimes. Multiscale Model. Simul. 16, 954–990 (2018)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gang Bao .

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Science Press

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Bao, G., Li, P. (2022). Diffraction Grating Theory. In: Maxwell’s Equations in Periodic Structures. Applied Mathematical Sciences, vol 208. Springer, Singapore. https://doi.org/10.1007/978-981-16-0061-6_2

Download citation

Publish with us

Policies and ethics