Abstract

Generalization of the Jones vector for partially polarized radiation carried out by Kakichashvili is given. Partially polarized light is presented as two noncoherent components of mutually orthogonal polarization. The formal operation of amplitude summation of mutually noncoherent components and the symbol of this operation are introduced. The rules of operating with this symbol are determined. The regularity of the Weigert effect is modified for partial polarization of the inducing light. On this basis the modification of the Jones matrix for partially polarized light is made. The rules for the formation of the resulting matrix from the Jones matrices corresponding to the noncoherent components of partially polarized light are determined.

© 2010 Optical Society of America

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  1. R. C. Jones, “A new calculus for the treatment of optical systems: I. Description and discussion of the calculus,” J. Opt. Soc. Am. 31, 488–493 (1941).
    [CrossRef]
  2. H. Hurwitz, Jr. and R. C. Jones, “New calculus for the treatment of optical systems. II. Proof of three general equivalence theorems,” J. Opt. Soc. Am. 31, 493–500 (1941).
    [CrossRef]
  3. R. C. Jones, “New calculus for the treatment of optical systems. III. The Sohncke theory of optical activity,” J. Opt. Soc. Am. 31, 500–503 (1941).
    [CrossRef]
  4. R. C. Jones, “New calculus for the treatment of optical systems. IV,” J. Opt. Soc. Am. 32, 486–493 (1942).
    [CrossRef]
  5. R. C. Jones, “A new calculus for the treatment of optical systems. V. More general formulation and description of another calculus,” J. Opt. Soc. Am. 37, 107–110 (1947).
    [CrossRef]
  6. R. C. Jones, “New calculus for the treatment of optical systems. VI. Experimental determination of the matrix,” J. Opt. Soc. Am. 37, 110–112 (1947).
    [CrossRef]
  7. R. C. Jones, “New calculus for the treatment of optical systems. VII. Properties of the N matrices,” J. Opt. Soc. Am. 38, 671–685 (1948).
    [CrossRef]
  8. R. C. Jones, “New calculus for the treatment of optical systems: VIII. Electromagnetic theory,” J. Opt. Soc. Am. 46, 126–131 (1956).
    [CrossRef]
  9. W. A. Shurcliff, Polarized Light (Harvard Univ. Press, 1966).
  10. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).
  11. A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Wiley-Interscience, 1975).
  12. Sh. Kakichashvili, “On polarization recording of holograms,” Opt. Spectrosc. 33, 324–327 (1972).
  13. Sh. Kakichashvili, “Polarization holography,” Usp. Fiz. Nauk 126, 681–683 (1978).
    [CrossRef]
  14. Sh. Kakichashvili, Polarization Holography (Nauka, 1989).
  15. B. Kilosanidze and G. Kakauridze, “Polarization-holographic gratings for analysis of light: 1. Analysis of completely polarized light,” Appl. Opt. 46, 1040–1049 (2007).
    [CrossRef] [PubMed]
  16. B. Kilosanidze, G. Kakauridze, L. Margolin, and I. Kobulashvili, “Real-time objects recognition by photoanisotropic copies,” Appl. Opt. 46, 7537–7543 (2007).
    [CrossRef] [PubMed]
  17. N. Volkenshtein, Molecular Optics (The State Publishing of Technical-Theoretical Literature, Moscow–Leningrad, 1951).
  18. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).
  19. P. Feofilov, Polarization Luminescence of Atoms, Molecules and Crystals (The State Publishing of Physical and Mathematical Literature, Moscow, 1959).
  20. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).
  21. E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, 1963).
  22. M. Laue, “Die Entropie von partiell kohärenten Strahlenbündeln,” Ann. Phys. 328, 1–43 (1907).
    [CrossRef]
  23. M. Laue, “Die Entropie von partiell kohärenten Strahlenbündeln: Nachtrag,” Ann. Phys. 328, 795–797 (1907).
    [CrossRef]
  24. F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica (Utrecht) 5, 785–795 (1938).
    [CrossRef]
  25. D. Gabor, “Light and information,” in Proceedings of the Symposium on Astronomical Optics and Related Subjects (Interscience, 1956), p. 17.
  26. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).
  27. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007).
  28. Ph. Réfrégier and F. Goudail, “Kullback relative entropy and characterization of partially polarized optical waves,” J. Opt. Soc. Am. A 23, 671–678 (2006).
    [CrossRef]
  29. B. DeBoo, J. Sasian, and R. Chipman, “Degree of polarization surfaces and maps for analysis of depolarization,” Opt. Express 12, 4941–4958 (2004).
    [CrossRef] [PubMed]
  30. R. Chipman, “Depolarization index and the average degree of polarization,” Appl. Opt. 44, 2490–2495 (2005).
    [CrossRef] [PubMed]
  31. F. Chatelain, J.-Y. Tourneret, M. Roche, and M. Alouini, “Estimating the polarization degree of polarimetric images in coherent illumination using maximum likelihood methods,” J. Opt. Soc. Am. A 26, 1348–1359 (2009).
    [CrossRef]
  32. P. Yeh, “Extended Jones matrix method,” J. Opt. Soc. Am. 72, 507–513 (1982).
    [CrossRef]
  33. R. J. Vernon and B. D. Huggins, “Extension of the Jones matrix formalism to reflection problems and magnetic materials,” J. Opt. Soc. Am. 70, 1364–1370 (1980).
    [CrossRef]
  34. Sh. Kakichashvili, “On modification of the Jones method on a partial polarization of light,” J. Tech. Physics (Russia) 65, 200–204 (1995).
  35. F. Weigert, “Über einen neunen effekt der strahlung in lichtempfindlichen schichten,” Verhandl. Deutsc. Physik. Ges. 21, 479–483 (1919).
  36. H. Zocher and K. Coper, “Über die erzougung Optisher aktivität durch zirkulares Licht,” Z. Phys. Chem. 132, 313–319 (1928).
  37. Sh. Kakichashvili, “On the regularity in polarization phenomenon,” Opt. Spectrosc. 52, 317–322 (1982).
  38. Sh. Kakichashvili, “On the regularity in the phenomena of photoanisotropy and photogyrotropy,” Opt. Spectrosc. 63, 911–917 (1987).
  39. G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers. Definitions, Theorems and Formulas for Reference and Review (McGraw-Hill, 1961).
    [PubMed]
  40. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  41. Sh. Kakichashvili, “Polarization holographic recording at partial light polarization,” J. Tech. Phys. (USSR) 59, 26–34 (1989).
  42. Sh. Kakichashvili and B. Kilosanidze, “The modification of polarization holographic method for partial polarization of field of electromagnetic waves,” J. Tech. Phys. (Russia) 67, 36–139 (1997).
  43. Sh. Kakichashvili, “An a posteriori experiment in polarization holography,” Opt. Spectrosc. 83, 348–351 (1997).
  44. Sh. Kakichashvili, B. Kilosanidze, and V. Shaverdova, “Anisotropy and gyrotropy of dye mordant pure-yellow induced by linear polarized light,” Opt. Spectrosc. 68, 1309–1312 (1990).

2009 (1)

2007 (3)

2006 (1)

2005 (1)

2004 (1)

1997 (2)

Sh. Kakichashvili and B. Kilosanidze, “The modification of polarization holographic method for partial polarization of field of electromagnetic waves,” J. Tech. Phys. (Russia) 67, 36–139 (1997).

Sh. Kakichashvili, “An a posteriori experiment in polarization holography,” Opt. Spectrosc. 83, 348–351 (1997).

1995 (2)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

Sh. Kakichashvili, “On modification of the Jones method on a partial polarization of light,” J. Tech. Physics (Russia) 65, 200–204 (1995).

1990 (1)

Sh. Kakichashvili, B. Kilosanidze, and V. Shaverdova, “Anisotropy and gyrotropy of dye mordant pure-yellow induced by linear polarized light,” Opt. Spectrosc. 68, 1309–1312 (1990).

1989 (2)

Sh. Kakichashvili, “Polarization holographic recording at partial light polarization,” J. Tech. Phys. (USSR) 59, 26–34 (1989).

Sh. Kakichashvili, Polarization Holography (Nauka, 1989).

1987 (1)

Sh. Kakichashvili, “On the regularity in the phenomena of photoanisotropy and photogyrotropy,” Opt. Spectrosc. 63, 911–917 (1987).

1982 (2)

Sh. Kakichashvili, “On the regularity in polarization phenomenon,” Opt. Spectrosc. 52, 317–322 (1982).

P. Yeh, “Extended Jones matrix method,” J. Opt. Soc. Am. 72, 507–513 (1982).
[CrossRef]

1980 (1)

1978 (1)

Sh. Kakichashvili, “Polarization holography,” Usp. Fiz. Nauk 126, 681–683 (1978).
[CrossRef]

1977 (1)

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

1975 (2)

A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Wiley-Interscience, 1975).

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

1972 (1)

Sh. Kakichashvili, “On polarization recording of holograms,” Opt. Spectrosc. 33, 324–327 (1972).

1968 (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

1966 (1)

W. A. Shurcliff, Polarized Light (Harvard Univ. Press, 1966).

1963 (1)

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, 1963).

1961 (1)

G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers. Definitions, Theorems and Formulas for Reference and Review (McGraw-Hill, 1961).
[PubMed]

1959 (1)

P. Feofilov, Polarization Luminescence of Atoms, Molecules and Crystals (The State Publishing of Physical and Mathematical Literature, Moscow, 1959).

1957 (1)

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

1956 (2)

D. Gabor, “Light and information,” in Proceedings of the Symposium on Astronomical Optics and Related Subjects (Interscience, 1956), p. 17.

R. C. Jones, “New calculus for the treatment of optical systems: VIII. Electromagnetic theory,” J. Opt. Soc. Am. 46, 126–131 (1956).
[CrossRef]

1951 (1)

N. Volkenshtein, Molecular Optics (The State Publishing of Technical-Theoretical Literature, Moscow–Leningrad, 1951).

1948 (1)

1947 (2)

1942 (1)

1941 (3)

1938 (1)

F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica (Utrecht) 5, 785–795 (1938).
[CrossRef]

1928 (1)

H. Zocher and K. Coper, “Über die erzougung Optisher aktivität durch zirkulares Licht,” Z. Phys. Chem. 132, 313–319 (1928).

1919 (1)

F. Weigert, “Über einen neunen effekt der strahlung in lichtempfindlichen schichten,” Verhandl. Deutsc. Physik. Ges. 21, 479–483 (1919).

1907 (2)

M. Laue, “Die Entropie von partiell kohärenten Strahlenbündeln,” Ann. Phys. 328, 1–43 (1907).
[CrossRef]

M. Laue, “Die Entropie von partiell kohärenten Strahlenbündeln: Nachtrag,” Ann. Phys. 328, 795–797 (1907).
[CrossRef]

Alouini, M.

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Born, M.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

Burch, J. M.

A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Wiley-Interscience, 1975).

Chatelain, F.

Chipman, R.

Coper, K.

H. Zocher and K. Coper, “Über die erzougung Optisher aktivität durch zirkulares Licht,” Z. Phys. Chem. 132, 313–319 (1928).

DeBoo, B.

Feofilov, P.

P. Feofilov, Polarization Luminescence of Atoms, Molecules and Crystals (The State Publishing of Physical and Mathematical Literature, Moscow, 1959).

Gabor, D.

D. Gabor, “Light and information,” in Proceedings of the Symposium on Astronomical Optics and Related Subjects (Interscience, 1956), p. 17.

Gerrard, A.

A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Wiley-Interscience, 1975).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Goudail, F.

Huggins, B. D.

Hurwitz, H.

Jones, R. C.

Kakauridze, G.

Kakichashvili, Sh.

Sh. Kakichashvili, “An a posteriori experiment in polarization holography,” Opt. Spectrosc. 83, 348–351 (1997).

Sh. Kakichashvili and B. Kilosanidze, “The modification of polarization holographic method for partial polarization of field of electromagnetic waves,” J. Tech. Phys. (Russia) 67, 36–139 (1997).

Sh. Kakichashvili, “On modification of the Jones method on a partial polarization of light,” J. Tech. Physics (Russia) 65, 200–204 (1995).

Sh. Kakichashvili, B. Kilosanidze, and V. Shaverdova, “Anisotropy and gyrotropy of dye mordant pure-yellow induced by linear polarized light,” Opt. Spectrosc. 68, 1309–1312 (1990).

Sh. Kakichashvili, Polarization Holography (Nauka, 1989).

Sh. Kakichashvili, “Polarization holographic recording at partial light polarization,” J. Tech. Phys. (USSR) 59, 26–34 (1989).

Sh. Kakichashvili, “On the regularity in the phenomena of photoanisotropy and photogyrotropy,” Opt. Spectrosc. 63, 911–917 (1987).

Sh. Kakichashvili, “On the regularity in polarization phenomenon,” Opt. Spectrosc. 52, 317–322 (1982).

Sh. Kakichashvili, “Polarization holography,” Usp. Fiz. Nauk 126, 681–683 (1978).
[CrossRef]

Sh. Kakichashvili, “On polarization recording of holograms,” Opt. Spectrosc. 33, 324–327 (1972).

Kilosanidze, B.

B. Kilosanidze and G. Kakauridze, “Polarization-holographic gratings for analysis of light: 1. Analysis of completely polarized light,” Appl. Opt. 46, 1040–1049 (2007).
[CrossRef] [PubMed]

B. Kilosanidze, G. Kakauridze, L. Margolin, and I. Kobulashvili, “Real-time objects recognition by photoanisotropic copies,” Appl. Opt. 46, 7537–7543 (2007).
[CrossRef] [PubMed]

Sh. Kakichashvili and B. Kilosanidze, “The modification of polarization holographic method for partial polarization of field of electromagnetic waves,” J. Tech. Phys. (Russia) 67, 36–139 (1997).

Sh. Kakichashvili, B. Kilosanidze, and V. Shaverdova, “Anisotropy and gyrotropy of dye mordant pure-yellow induced by linear polarized light,” Opt. Spectrosc. 68, 1309–1312 (1990).

Kobulashvili, I.

Korn, G.

G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers. Definitions, Theorems and Formulas for Reference and Review (McGraw-Hill, 1961).
[PubMed]

Korn, T.

G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers. Definitions, Theorems and Formulas for Reference and Review (McGraw-Hill, 1961).
[PubMed]

Laue, M.

M. Laue, “Die Entropie von partiell kohärenten Strahlenbündeln,” Ann. Phys. 328, 1–43 (1907).
[CrossRef]

M. Laue, “Die Entropie von partiell kohärenten Strahlenbündeln: Nachtrag,” Ann. Phys. 328, 795–797 (1907).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

Margolin, L.

O’Neill, E. L.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, 1963).

Réfrégier, Ph.

Roche, M.

Sasian, J.

Shaverdova, V.

Sh. Kakichashvili, B. Kilosanidze, and V. Shaverdova, “Anisotropy and gyrotropy of dye mordant pure-yellow induced by linear polarized light,” Opt. Spectrosc. 68, 1309–1312 (1990).

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard Univ. Press, 1966).

Tourneret, J.-Y.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

Vernon, R. J.

Volkenshtein, N.

N. Volkenshtein, Molecular Optics (The State Publishing of Technical-Theoretical Literature, Moscow–Leningrad, 1951).

Weigert, F.

F. Weigert, “Über einen neunen effekt der strahlung in lichtempfindlichen schichten,” Verhandl. Deutsc. Physik. Ges. 21, 479–483 (1919).

Wolf, E.

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

Yeh, P.

Zernike, F.

F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica (Utrecht) 5, 785–795 (1938).
[CrossRef]

Zocher, H.

H. Zocher and K. Coper, “Über die erzougung Optisher aktivität durch zirkulares Licht,” Z. Phys. Chem. 132, 313–319 (1928).

Ann. Phys. (2)

M. Laue, “Die Entropie von partiell kohärenten Strahlenbündeln,” Ann. Phys. 328, 1–43 (1907).
[CrossRef]

M. Laue, “Die Entropie von partiell kohärenten Strahlenbündeln: Nachtrag,” Ann. Phys. 328, 795–797 (1907).
[CrossRef]

Appl. Opt. (3)

J. Opt. Soc. Am. (10)

R. C. Jones, “A new calculus for the treatment of optical systems: I. Description and discussion of the calculus,” J. Opt. Soc. Am. 31, 488–493 (1941).
[CrossRef]

H. Hurwitz, Jr. and R. C. Jones, “New calculus for the treatment of optical systems. II. Proof of three general equivalence theorems,” J. Opt. Soc. Am. 31, 493–500 (1941).
[CrossRef]

R. C. Jones, “New calculus for the treatment of optical systems. III. The Sohncke theory of optical activity,” J. Opt. Soc. Am. 31, 500–503 (1941).
[CrossRef]

R. C. Jones, “New calculus for the treatment of optical systems. IV,” J. Opt. Soc. Am. 32, 486–493 (1942).
[CrossRef]

R. C. Jones, “New calculus for the treatment of optical systems. VII. Properties of the N matrices,” J. Opt. Soc. Am. 38, 671–685 (1948).
[CrossRef]

R. C. Jones, “New calculus for the treatment of optical systems: VIII. Electromagnetic theory,” J. Opt. Soc. Am. 46, 126–131 (1956).
[CrossRef]

R. J. Vernon and B. D. Huggins, “Extension of the Jones matrix formalism to reflection problems and magnetic materials,” J. Opt. Soc. Am. 70, 1364–1370 (1980).
[CrossRef]

P. Yeh, “Extended Jones matrix method,” J. Opt. Soc. Am. 72, 507–513 (1982).
[CrossRef]

R. C. Jones, “A new calculus for the treatment of optical systems. V. More general formulation and description of another calculus,” J. Opt. Soc. Am. 37, 107–110 (1947).
[CrossRef]

R. C. Jones, “New calculus for the treatment of optical systems. VI. Experimental determination of the matrix,” J. Opt. Soc. Am. 37, 110–112 (1947).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Tech. Phys. (Russia) (1)

Sh. Kakichashvili and B. Kilosanidze, “The modification of polarization holographic method for partial polarization of field of electromagnetic waves,” J. Tech. Phys. (Russia) 67, 36–139 (1997).

J. Tech. Phys. (USSR) (1)

Sh. Kakichashvili, “Polarization holographic recording at partial light polarization,” J. Tech. Phys. (USSR) 59, 26–34 (1989).

J. Tech. Physics (Russia) (1)

Sh. Kakichashvili, “On modification of the Jones method on a partial polarization of light,” J. Tech. Physics (Russia) 65, 200–204 (1995).

Opt. Express (1)

Opt. Spectrosc. (5)

Sh. Kakichashvili, “An a posteriori experiment in polarization holography,” Opt. Spectrosc. 83, 348–351 (1997).

Sh. Kakichashvili, B. Kilosanidze, and V. Shaverdova, “Anisotropy and gyrotropy of dye mordant pure-yellow induced by linear polarized light,” Opt. Spectrosc. 68, 1309–1312 (1990).

Sh. Kakichashvili, “On the regularity in polarization phenomenon,” Opt. Spectrosc. 52, 317–322 (1982).

Sh. Kakichashvili, “On the regularity in the phenomena of photoanisotropy and photogyrotropy,” Opt. Spectrosc. 63, 911–917 (1987).

Sh. Kakichashvili, “On polarization recording of holograms,” Opt. Spectrosc. 33, 324–327 (1972).

Physica (Utrecht) (1)

F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica (Utrecht) 5, 785–795 (1938).
[CrossRef]

Usp. Fiz. Nauk (1)

Sh. Kakichashvili, “Polarization holography,” Usp. Fiz. Nauk 126, 681–683 (1978).
[CrossRef]

Verhandl. Deutsc. Physik. Ges. (1)

F. Weigert, “Über einen neunen effekt der strahlung in lichtempfindlichen schichten,” Verhandl. Deutsc. Physik. Ges. 21, 479–483 (1919).

Z. Phys. Chem. (1)

H. Zocher and K. Coper, “Über die erzougung Optisher aktivität durch zirkulares Licht,” Z. Phys. Chem. 132, 313–319 (1928).

Other (14)

W. A. Shurcliff, Polarized Light (Harvard Univ. Press, 1966).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Wiley-Interscience, 1975).

D. Gabor, “Light and information,” in Proceedings of the Symposium on Astronomical Optics and Related Subjects (Interscience, 1956), p. 17.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007).

Sh. Kakichashvili, Polarization Holography (Nauka, 1989).

N. Volkenshtein, Molecular Optics (The State Publishing of Technical-Theoretical Literature, Moscow–Leningrad, 1951).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

P. Feofilov, Polarization Luminescence of Atoms, Molecules and Crystals (The State Publishing of Physical and Mathematical Literature, Moscow, 1959).

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, 1963).

G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers. Definitions, Theorems and Formulas for Reference and Review (McGraw-Hill, 1961).
[PubMed]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

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Equations (66)

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V = I max I min I max + I min , V = I a I a + I b ,
E = M E = E ̂ ( m 11 m 12 m 21 m 22 ) ( 1 ± i ϵ ) = E A + E B ,
E ̂ = E x exp [ i ( ϖ 0 c z α ) ] exp { i [ ϖ 0 t ϖ 0 2 c ( n x + n y ) ] } , ϵ = E y E x ,
m 11 = m 22 * = cos ( ϖ 0 2 c Δ n ) i sin ( ϖ 0 2 c Δ n ) cos 2 ρ ,
m 12 = m 21 = i sin ( ϖ 0 2 c Δ n ) sin 2 ρ ,
E A = E ̂ ( m 11 ± i ϵ m 22 ) , E B = E ̂ ( ± i ϵ m 12 m 21 ) .
D [ Re m 11 ( t ) , Re m 12 ( t ) ] = D [ Re m 22 ( t ) , Re m 21 ( t ) ] = 0 ,
D [ Im m 11 ( t ) , Im m 12 ( t ) ] = ω 0 8 c Δ n ( t ) t sin [ ω 0 c Δ n ( t ) ] sin 4 ρ ( t ) + 2 ρ ( t ) t sin 2 [ ω 0 2 c Δ n ( t ) ] cos 4 ρ ( t ) ,
D [ Im m 22 ( t ) , Im m 21 ( t ) ] = ω 0 8 c Δ n ( t ) t sin [ ω 0 c Δ n ( t ) ] sin 4 ρ ( t ) 2 ρ ( t ) t sin 2 [ ω 0 2 c Δ n ( t ) ] cos 4 ρ ( t ) .
E A = 1 2 π E ̂ ( + + m 11 ( τ ) exp [ i ϖ ( t τ ) ] d τ d ϖ ± i ϵ + + m 11 * ( τ ) exp [ i ϖ ( t τ ) ] d τ d ϖ ) ,
E B = 1 2 π E ̂ ( ± i ϵ + + m 12 ( τ ) exp [ i ϖ ( t τ ) ] d τ d ϖ + + m 12 * ( τ ) exp [ i ϖ ( t τ ) ] d τ d ϖ ) ,
I A = lim T 1 2 T T T [ Re E A ] 2 d t = E A + E A ,
I B = lim T 1 2 T T T [ Re E B ] 2 d t = E B + E B ,
lim T 1 2 T T + T ( Re E i ) 2 d t , i = A , B
{ Re E T ( t ) = Re E i ( t ) , i = A , B , | t T | ; Re E T ( t ) = 0 , | t T | . }
I A = E x 2 ( 1 + ϵ 2 ) 1 2 π + + m 11 * ( τ ) exp [ i ω ( t τ ) ] d τ d ω 1 2 π + + m 11 ( τ ) exp [ i ω ( t τ ) ] d τ d ω = E x 2 ( 1 + ϵ 2 ) + m 11 ( τ ) m 11 * ( τ ) d τ .
I B = E x 2 ( 1 + ϵ 2 ) + m 12 ( τ ) m 12 * ( τ ) d τ .
V = I A I B I A + I B = + cos 2 [ ϖ 0 2 c Δ n ( t ) ] d t + + sin 2 [ ϖ 0 2 c Δ n ( t ) ] cos 4 ρ ( t ) d t + cos 2 [ ϖ 0 2 c Δ n ( t ) ] d t + + sin 2 [ ϖ 0 2 c Δ n ( t ) ] d t .
E = E A , x exp [ i ( ω t + φ ) ] ( 1 ± i ϵ ) E B , y exp [ i ( ω t + ψ π 2 ) ] ( ± i ϵ 1 ) ,
ϵ = E A , y E A , x = E B , x E B , y , 0 ϵ 1 ,
1. E = E A E B = E B E A ,
2. E = i = 1 n E i ; E i = E A , i E B , i ;
E A = i = 1 n E A , i ; E B = i = 1 n E B , i ,
3. E θ = S ( θ ) E = S ( θ ) E A S ( θ ) E B ,
4. E = S ( θ ) M S ( θ ) E = S ( θ ) M S ( θ ) E A S ( θ ) M S ( θ ) E B ,
5. Re ( E ( x , y , z , t ) ) = p cos ω t + q sin ω t ,
p = Re E A Re E B = p A p B ,
q = Im E A Im E B = q A q B ,
f ( p ) = f ( p A ) + f ( p B ) ,
f ( q ) = f ( q A ) + f ( q B ) ,
6. I = E + E = ( E A E B ) + ( E A E B ) = E A + E A + E B + E B .
E = E A , x exp [ i ( ω t + φ ) ] ( 1 ± i ϵ ) E A , x exp [ i ( ω t + ψ π 2 ) ] ( ± i ϵ 1 ) ,
I = 2 ( E A , x 2 + E A , y 2 ) ; V = 0 .
E = E A , x exp [ i ( ω t + φ ) ] ( 1 ± i ϵ ) ,
I = E A , x 2 + E A , y 2 ; V = 1 .
E = E A E B ,
E A = E x exp [ i ( ω 0 t κ 0 z ) ] exp [ i κ 0 d 2 ( n ̂ x + n ̂ y ) ] ( m ̂ 11 ( t ) ± i ϵ m 22 ( t ) )
E B = E x exp [ i ( ω 0 t κ 0 z ) ] exp [ i κ 0 d 2 ( n ̂ x + n ̂ y ) ] m ̂ 12 ( t ) ( ± i ϵ 1 )
ϵ ̂ x + ϵ ̂ y 2 = ϵ ̂ 0 + s ̂ ( E 1 2 + E 2 2 ) .
ϵ ̂ x ϵ ̂ y 2 = v ̂ L ( E 1 2 E 2 2 ) .
ϵ ̂ x ϵ ̂ 0 = s ̂ ( E 1 2 + E 2 2 ) + v ̂ L ( E 1 2 E 2 2 ) ,
ϵ ̂ y ϵ ̂ 0 = s ̂ ( E 1 2 + E 2 2 ) v ̂ L ( E 1 2 E 2 2 ) .
n ̂ 1 2 n ̂ 0 2 = s ̂ ( E 1 2 + E 2 2 ) + [ v ̂ L ( E 1 2 E 2 2 ) ] 2 + [ v ̂ G ( 2 E 1 E 2 sin δ ) ] 2
n ̂ 2 2 n ̂ 0 2 = s ̂ ( E 1 2 + E 2 2 ) [ v ̂ L ( E 1 2 E 2 2 ) ] 2 + [ v ̂ G ( 2 E 1 E 2 sin δ ) ] 2 .
X = 0
( n ̂ 1 2 ) X = 0 = n ̂ 0 2 + s ̂ ( I 1 + I 2 ) A + s ̂ ( I 1 + I 2 ) B v ̂ L ( I 1 I 2 ) A v ̂ L ( I 1 I 2 ) B ,
( n ̂ 2 2 ) X = 0 = n ̂ 0 2 + s ̂ ( I 1 + I 2 ) A + s ̂ ( I 1 + I 2 ) B v ̂ L ( I 1 + I 2 ) A v ̂ L ( I 1 + I 2 ) B ,
( sin 2 θ A ) X = 0 = 0 , ( sin 2 θ B ) X = 0 = [ sin 2 ( θ A + π 2 ) ] X = 0 ,
( cos 2 θ A ) X = 0 = 1 , ( cos 2 θ B ) X = 0 = [ cos 2 ( θ A + π 2 ) ] X = 0 ;
Y = 0
( n ̂ 1 2 ) Y = 0 = n ̂ 0 2 + s ̂ ( I 1 + I 2 ) A + s ̂ ( I 1 + I 2 ) B + v ̂ L ( I 1 I 2 ) A + v ̂ L ( I 1 I 2 ) B ,
( n ̂ 2 2 ) Y = 0 = n ̂ 0 2 + s ̂ ( I 1 + I 2 ) A + s ̂ ( I 1 + I 2 ) B v ̂ L ( I 1 + I 2 ) A v ̂ L ( I 1 + I 2 ) B ,
( sin 2 θ A ) Y = 0 = 0 , ( sin 2 θ B ) Y = 0 = [ sin 2 ( θ A + π 2 ) ] Y = 0 ,
( cos 2 θ A ) Y = 0 = 1 ( cos 2 θ B ) Y = 0 = [ cos 2 ( θ A + π 2 ) ] Y = 0 ,
Z = 0
( n ̂ 1 2 ) Z = 0 = n ̂ 0 2 + s ̂ ( I 1 + I 2 ) A + s ̂ ( I 1 + I 2 ) B + [ v ̂ L ( I 1 I 2 ) A ] 2 + [ v ̂ G ( I + I ) A ] 2 + [ v ̂ L ( I 1 I 2 ) B ] 2 + [ v ̂ G ( I + I ) B ] 2 ,
( n ̂ 1 2 ) Z = 0 = n ̂ 0 2 + s ̂ ( I 1 + I 2 ) A + s ̂ ( I 1 + I 2 ) B [ v ̂ L ( I 1 I 2 ) A ] 2 + [ v ̂ G ( I + I ) A ] 2 [ v ̂ L ( I 1 I 2 ) B ] 2 + [ v ̂ G ( I + I ) B ] 2 ,
( sin 2 θ A ) Z = 0 = ( I + I ) A ( I 1 I 2 ) A 2 + ( I + I ) A 2 ( sin 2 θ B ) Z = 0 = [ sin 2 ( θ A + π 2 ) ] Z = 0 ,
( cos 2 θ A ) Z = 0 = ( I 1 I 2 ) A ( I 1 I 2 ) A 2 + ( I + I ) A 2 ( cos 2 θ B ) Z = 0 = [ cos 2 ( θ A + π 2 ) ] Z = 0 .
1. M = M A M B ;
2. M = i = 1 n j = 1 n M A i M B j ;
M A = i = 1 n M A i ; M B = j = 1 n M B j ;
3. M ( θ ) = S ( θ ) M S ( θ ) .
M exp ( 2 i κ d n ̂ 0 ) ( 1 i κ d 2 ( n ̂ x n ̂ y ) 0 0 1 + i κ d 2 ( n ̂ x n ̂ y ) ) ,
M = M A M B exp ( 2 i κ d n ̂ 0 ) ( m 11 0 0 m 22 ) ,
m 11 , 22 = 1 i κ d 2 n ̂ 0 [ s ̂ ( I 1 + I 2 ) A + s ̂ ( I 1 + I 2 ) B ± v ̂ L ( I I 2 ) A ± v ̂ L ( I I 2 ) B ] .

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