Abstract

A high-accuracy solution of the diffraction problem has become necessary for the treatment of certain special questions of statistical physics. This article reports the creation of a computer program that serves as an instrumental method of calculating the parameters of diffraction phenomena when complex optical systems are being theoretically investigated. The program solves the diffraction problem by a rigorous method based on Maxwell’s equations under specified boundary conditions. An arbitrary—for instance, diffuse—configuration of the initial light field is allowed. Reflective gratings with a linear or crossed sinusoidal profile of the surface microrelief are considered as the diffraction optical elements. The characteristics of the self-consistent total light field can be calculated when several diffraction elements are present in the system.

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  1. I. M. Sobol’, Monte Carlo Numerical Methods (Nauka, Moscow, 1973).
  2. V. V. Savukov, “Breakdown of the isotropy of diffuse radiation as a consequence of its diffraction at multidimensional regular structures,” Opt. Zh. 77, No. 1, 95 (2010). [J. Opt. Technol. 77, 74 (2010)].
  3. V. V. Savukov, “Refining the axiomatic principles of statistical physics,” Deposited at the All-Russia Institute of Scientific and Technical Information, No. 1249B2004 on 7/16/2004. URL: http://www.savukov.ru/viniti_1249_b2004_full_rus.pdf.
  4. V. V. Savukov, “Breakdown of Lambert’s law when a diffuse photon gas is diffracted at multidimensional regular structures,” Deposited at the All-Russia Institute of Scientific and Technical Information, No. 507-B2009 on 8/3/2009. URL: http://www.savukov.ru/viniti_0507_b2009_full_rus.pdf.
  5. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
  6. J. Chandezon, G. Cornet, and G. Raoult, “Propagation des ondes dans les guides cylindriques à génératrices sinusoïdales,” C. R. Acad. Sci. (Paris) No. 276B, 507 (1973).
  7. J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235 (1980).
  8. J. Chandezon, M. T. Dupuis, G. Cornet, and D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. 72, 839 (1982).
  9. E. J. Post, Formal Structure of Electromagnetics: General Covariance and Electromagnetics (North Holland Pub. Co, Amsterdam, 1962).
  10. G. Granet, “Diffraction par des surfaces biperiodiques: resolution en coordonnées non orthogonales,” Pure Appl. Opt. 4, 777 (1995).
  11. G. Granet, “Analysis of diffraction by surface-relief crossed gratings with use of the Chandezon method: application to multilayer crossed gratings,” J. Opt. Soc. Am. A 15, 1121 (1998).
  12. I. M. Sobol’, Multidimensional Quadrature Formulas and the Haar Function (Nauka, Moscow, 1969).
  13. I. M. Sobol’ and R. B. Statnikov, Choosing the Optimum Parameters in Problems with Many Criteria (Nauka, Moscow, 1981).
  14. D. Maystre and R. Petit, “Brewster incidence for metallic gratings,” Opt. Commun. 17, 196 (1976).
  15. R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396 (1902).
  16. Lord Rayleigh, “On the dynamical theory of gratings,” Proc. Royal Soc. London Ser. A 79, 399 (1907).

2010

V. V. Savukov, “Breakdown of the isotropy of diffuse radiation as a consequence of its diffraction at multidimensional regular structures,” Opt. Zh. 77, No. 1, 95 (2010). [J. Opt. Technol. 77, 74 (2010)].

1998

1995

G. Granet, “Diffraction par des surfaces biperiodiques: resolution en coordonnées non orthogonales,” Pure Appl. Opt. 4, 777 (1995).

1982

1980

J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235 (1980).

1976

D. Maystre and R. Petit, “Brewster incidence for metallic gratings,” Opt. Commun. 17, 196 (1976).

1973

J. Chandezon, G. Cornet, and G. Raoult, “Propagation des ondes dans les guides cylindriques à génératrices sinusoïdales,” C. R. Acad. Sci. (Paris) No. 276B, 507 (1973).

1907

Lord Rayleigh, “On the dynamical theory of gratings,” Proc. Royal Soc. London Ser. A 79, 399 (1907).

1902

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396 (1902).

Chandezon, J.

J. Chandezon, M. T. Dupuis, G. Cornet, and D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. 72, 839 (1982).

J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235 (1980).

J. Chandezon, G. Cornet, and G. Raoult, “Propagation des ondes dans les guides cylindriques à génératrices sinusoïdales,” C. R. Acad. Sci. (Paris) No. 276B, 507 (1973).

Cornet, G.

J. Chandezon, M. T. Dupuis, G. Cornet, and D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. 72, 839 (1982).

J. Chandezon, G. Cornet, and G. Raoult, “Propagation des ondes dans les guides cylindriques à génératrices sinusoïdales,” C. R. Acad. Sci. (Paris) No. 276B, 507 (1973).

Dupuis, M. T.

Granet, G.

G. Granet, “Analysis of diffraction by surface-relief crossed gratings with use of the Chandezon method: application to multilayer crossed gratings,” J. Opt. Soc. Am. A 15, 1121 (1998).

G. Granet, “Diffraction par des surfaces biperiodiques: resolution en coordonnées non orthogonales,” Pure Appl. Opt. 4, 777 (1995).

Maystre, D.

J. Chandezon, M. T. Dupuis, G. Cornet, and D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. 72, 839 (1982).

J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235 (1980).

D. Maystre and R. Petit, “Brewster incidence for metallic gratings,” Opt. Commun. 17, 196 (1976).

Petit, R.

D. Maystre and R. Petit, “Brewster incidence for metallic gratings,” Opt. Commun. 17, 196 (1976).

Post, E. J.

E. J. Post, Formal Structure of Electromagnetics: General Covariance and Electromagnetics (North Holland Pub. Co, Amsterdam, 1962).

Raoult, G.

J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235 (1980).

J. Chandezon, G. Cornet, and G. Raoult, “Propagation des ondes dans les guides cylindriques à génératrices sinusoïdales,” C. R. Acad. Sci. (Paris) No. 276B, 507 (1973).

Rayleigh, Lord

Lord Rayleigh, “On the dynamical theory of gratings,” Proc. Royal Soc. London Ser. A 79, 399 (1907).

Savukov, V. V.

V. V. Savukov, “Breakdown of the isotropy of diffuse radiation as a consequence of its diffraction at multidimensional regular structures,” Opt. Zh. 77, No. 1, 95 (2010). [J. Opt. Technol. 77, 74 (2010)].

V. V. Savukov, “Refining the axiomatic principles of statistical physics,” Deposited at the All-Russia Institute of Scientific and Technical Information, No. 1249B2004 on 7/16/2004. URL: http://www.savukov.ru/viniti_1249_b2004_full_rus.pdf.

V. V. Savukov, “Breakdown of Lambert’s law when a diffuse photon gas is diffracted at multidimensional regular structures,” Deposited at the All-Russia Institute of Scientific and Technical Information, No. 507-B2009 on 8/3/2009. URL: http://www.savukov.ru/viniti_0507_b2009_full_rus.pdf.

Sobol’, I. M.

I. M. Sobol’, Monte Carlo Numerical Methods (Nauka, Moscow, 1973).

I. M. Sobol’, Multidimensional Quadrature Formulas and the Haar Function (Nauka, Moscow, 1969).

I. M. Sobol’ and R. B. Statnikov, Choosing the Optimum Parameters in Problems with Many Criteria (Nauka, Moscow, 1981).

Statnikov, R. B.

I. M. Sobol’ and R. B. Statnikov, Choosing the Optimum Parameters in Problems with Many Criteria (Nauka, Moscow, 1981).

Wood, R. W.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396 (1902).

C. R. Acad. Sci. (Paris)

J. Chandezon, G. Cornet, and G. Raoult, “Propagation des ondes dans les guides cylindriques à génératrices sinusoïdales,” C. R. Acad. Sci. (Paris) No. 276B, 507 (1973).

J. Opt. (Paris)

J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235 (1980).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

D. Maystre and R. Petit, “Brewster incidence for metallic gratings,” Opt. Commun. 17, 196 (1976).

Opt. Zh.

V. V. Savukov, “Breakdown of the isotropy of diffuse radiation as a consequence of its diffraction at multidimensional regular structures,” Opt. Zh. 77, No. 1, 95 (2010). [J. Opt. Technol. 77, 74 (2010)].

Philos. Mag.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396 (1902).

Proc. Royal Soc. London Ser. A

Lord Rayleigh, “On the dynamical theory of gratings,” Proc. Royal Soc. London Ser. A 79, 399 (1907).

Pure Appl. Opt.

G. Granet, “Diffraction par des surfaces biperiodiques: resolution en coordonnées non orthogonales,” Pure Appl. Opt. 4, 777 (1995).

Other

I. M. Sobol’, Monte Carlo Numerical Methods (Nauka, Moscow, 1973).

I. M. Sobol’, Multidimensional Quadrature Formulas and the Haar Function (Nauka, Moscow, 1969).

I. M. Sobol’ and R. B. Statnikov, Choosing the Optimum Parameters in Problems with Many Criteria (Nauka, Moscow, 1981).

V. V. Savukov, “Refining the axiomatic principles of statistical physics,” Deposited at the All-Russia Institute of Scientific and Technical Information, No. 1249B2004 on 7/16/2004. URL: http://www.savukov.ru/viniti_1249_b2004_full_rus.pdf.

V. V. Savukov, “Breakdown of Lambert’s law when a diffuse photon gas is diffracted at multidimensional regular structures,” Deposited at the All-Russia Institute of Scientific and Technical Information, No. 507-B2009 on 8/3/2009. URL: http://www.savukov.ru/viniti_0507_b2009_full_rus.pdf.

R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).

E. J. Post, Formal Structure of Electromagnetics: General Covariance and Electromagnetics (North Holland Pub. Co, Amsterdam, 1962).

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