Abstract

Optical polarimetric techniques to identify and characterize biological and chemical materials have received much attention recently for their broad applications in biophotonics, biochemistry, biomedicine, and pharmacology. We present here several options for the measurement of optical rotation, diattenuation, and the index of depolarization. These include polar decomposition, identification of specific pairs of Mueller matrix elements that are proportional to optical activity, and the cross-polarized components of lateral waves and surface waves at the interface between free space and the optically active material.

© 2011 Optical Society of America

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  1. W. S. Bickel, J. F. Davidson, D. R. Huffman, and R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
    [CrossRef] [PubMed]
  2. E. Bahar, “Detection and identification of optical activity using polarimetry—applications in biophotonics biomedicine and biochemistry,” J. Biophotonics 1, 230–237 (2008).
    [CrossRef]
  3. W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
    [CrossRef]
  4. S. L. Jacques and R. J. Ramella-Roman, “Propagation of polarized light beams through biological tissues,” Proc. SPIE 3914, 345–352 (2000).
    [CrossRef]
  5. V. Sankaran, J. T. Walsh, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7, 300–306 (2002).
    [CrossRef] [PubMed]
  6. L. Wang and S. Jacques, “Non-invasive detection of skin cancers by measuring optical properties of tissue,” Proc. SPIE 2395, 548–558 (1995).
    [CrossRef]
  7. R. C. N. Studinski and I. A. Vitkin, “Methodology for examining polarized light interactions with tissues and tissue-like media in the exact backscattering direction,” J. Biomed. Opt. 5, 330–337(2000).
    [CrossRef] [PubMed]
  8. S. L. Jacques, J. R. Roman, and K. Lee, “Imaging superficial tissue with polarized light,” Lasers Surg. Med. 26, 119–129 (2000).
    [CrossRef] [PubMed]
  9. M. H. Smith, A. Lompado, and P. Burke, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3911, 210–216 (2000).
    [CrossRef]
  10. M. H. Smith, “Interpreting Mueller matrix images of tissues,” Proc. SPIE 4257, 82–89 (2001).
    [CrossRef]
  11. G. L. Liu, Y. Li, and B. D. Cameron, “Polarization-based optical imaging and processing techniques with application to cancer diagnostics,” Proc. SPIE 4617, 208–220 (2002).
    [CrossRef]
  12. L. V. Wang, G. L. Coté, and S. L. Jacques, eds, “Special section on tissue polarimetry,” J. Biomed. Opt. 7, 278–397 (2002).
    [CrossRef]
  13. S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340(2002).
    [CrossRef] [PubMed]
  14. N. G. Khlebtsov, I. L. Maksimova, V. V. Tuchin, and L. Wang, “Introduction to light scattering by biological objects,” in Handbook of Optical Biomedical Diagnostics, Vol. PM107 of SPIE Press Monographs (SPIE, 2002), pp. 31–167.
  15. V. V. Tuchin, L. Wang, and D. A. Zimnyakov, Optical Polarization in Biomedical Applications (Springer-Verlag, 2006).
  16. J. Chung, W. Jung, M. J. Hammer-Wilson, P. Wilder-Smith, and Z. Chen, “Use of polar decomposition for the diagnosis of oral pre-cancer,” Appl. Opt. 46, 3038–3045 (2007).
    [CrossRef] [PubMed]
  17. N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
    [CrossRef] [PubMed]
  18. R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadigan, I. Itzkan, R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
    [CrossRef] [PubMed]
  19. C. A. Browne and F. W. Zerban, Physical and Chemical Methods of Sugar Analysis (Wiley, 1941).
  20. E. Bahar, “Mueller matrices for waves reflected and transmitted through chiral materials, waveguide modal solutions and applications,” J. Opt. Soc. Am. B 24, 1610–1619 (2007).
    [CrossRef]
  21. M. Silverman, “Reflection and refraction at the surfaces of achiral medium: comparison of gyrotropic constitutive relations invariant or non-invariant under duality transformations,” J. Opt. Soc. Am. A 3, 830–837 (1986).
    [CrossRef]
  22. E. Bahar, “Reflection and transmission matrices at a free-space-chiral interface based on the invariant constitutive relations and for gyrotropic media and the Drude–Born–Feredov constitutive relations,” J. Opt. Soc. Am. A 26, 1834–1838(2009).
    [CrossRef]
  23. J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
    [CrossRef]
  24. S. Lu and R. A. Chipman, “Mueller matrices and the degree of polarization,” Opt. Commun. 146, 11–14 (1998).
    [CrossRef]
  25. N. J. Higham, “Computing the polar decomposition-with applications,” SIAM J. Sci. Statist. Comput. 7, 1100–1174(1986).
  26. N. J. Higham, C. Mehl, and F. Tisseur, “The canonical generalized polar decomposition,” SIAM J. Matrix Anal. Appl. 31, 2163–2180 (2010).
    [CrossRef]
  27. A. Vitkin, N. Ghosh, and M. F. G. Wood, “Diagnostic photomedicine: probing biological tissues with polarized light,” SPIE Newsroom, DOI: 10.1117/2.1200808.1238 (2008), http://spie.org/x27101.xml?ArticleID=x27101.
    [CrossRef]
  28. S. Manhas, M. K. Swami, P. Buddhiwant, N. Gosh, P. K. Gupta and K. Sing, “Mueller matrix approach for determination of optical rotation in chiral turbid media in backscatter geometry,” Opt. Express 14, 190–202 (2006).
    [CrossRef] [PubMed]
  29. J. Morio and A. Goudail, “Influence of the order of diattenuator, retarder and polarizer in polar decomposition of Mueller matrices,” Opt. Lett. 29, 2234–2236 (2004).
    [CrossRef] [PubMed]
  30. S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–36 (1986).
  31. A. H. Carrieri, “Neural network pattern recognition by means of differential absorption Mueller matrices spectroscopy,” Appl. Opt. 38, 3759–3766 (1999).
    [CrossRef]
  32. A. H. Carrieri, J. R. Bottinger, D. J. Owens, and E. S. Roese, “Differential absorption Mueller matrix spectroscopy and the infrared detection of crystalline organics,” Appl. Opt. 37, 6550–6557 (1998).
    [CrossRef]
  33. E. Bahar, “The relationship between optical rotation and circular dichroism and elements of the Mueller matrix for natural and artificial materials,” J. Opt. Soc. Am. B 25, 218–222(2008).
    [CrossRef]
  34. E. Bahar, “Characterization of natural and artificial optical activity by the Mueller matrix for oblique incidence, total internal reflection and Brewster angle,” J. Opt. Soc. Am. B 25, 1294–1302(2008).
    [CrossRef]
  35. E. Bahar, “Roadmaps for the use of Mueller matrix measurements to detect and identify biological and chemical materials through their optical activity: potential applications in biomedicine, biochemistry, security, and industry,” J. Opt. Soc. Am. B 26, 364–370 (2009).
    [CrossRef]
  36. E. Bahar, “Total transmission of incident plane waves that satisfy the Brewster conditions at a free-space-chiral interface,” J. Opt. Soc. Am. A 27, 2055–2060 (2010).
    [CrossRef]
  37. M. Silverman, Waves and Grains (Princeton University Press, 1998).
  38. E. Bahar, “Optimum electromagnetic wave excitations of complex media characterized by positive or negative refractive indices and by chiral properties,” J. Opt. Soc. Am. B 24, 2807–2813 (2007).
    [CrossRef]
  39. M. Silverman and T. Black, “Experimental method to detect chiral asymmetry in specular light scattering from a naturally optically active medium,” Phys. Lett. A 126, 171–176 (1987).
    [CrossRef]
  40. M. Silverman, N. Ritchie, G. Cushman, and B. Fisher, “Experimental configurations using optical phase modulation to measure chiral asymmetries in light specularly reflected from a naturally gyrotropic medium,” J. Opt. Soc. Am. A 5, 1852–1862(1988).
    [CrossRef]
  41. E. Bahar, “Guided surface waves over a free-space-chiral interface: applications to identification of optically active materials,” J. Opt. Soc. Am. B 28, 868–872 (2011).
    [CrossRef]
  42. E. Bahar, “Cross polarization of lateral waves propagating along a free-space-chiral planar interface: application to identification of optically active materials,” J. Opt. Soc. Am. B 28, 1194–1199(2011).
    [CrossRef]
  43. E. Bahar and R. Kubik, “Description of a versatile optical polarimetric scatterometer that measures all 16 elements of Mueller matrix for reflection and transmission: application to measurements of scatter cross sections, ellipsometric parameters, optical activity, and the complex chiral parameters,” Opt. Eng. 47, 093603 (2008).
    [CrossRef]
  44. E. Bahar, “Like and cross-polarized scatter cross sections for two-dimensional, multiscale rough surfaces based on a unified full wave variational technique,” Radio Sci. 46, RS4002, doi:10.1029/2010RS004441 (2011).
    [CrossRef]
  45. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1987).
  46. E. J. Ariens, W. Soudijin, and P. B. M. W. M. Timmermans, Stereochemistry and Biological Activity of Drugs (Blackwell, 1983).
  47. J. W. Wamer, Drug Stereochemistry (Dekker, 1993).
  48. G. J. Thomas, Jr., “Raman spectroscopy of protein and nucleic acid assemblies,” Annu. Rev. Biophys. Biomol. Struct. 28, 1–27(1999).
    [CrossRef] [PubMed]
  49. E. W. Blanch, L. Hecht, L. A. Day, D. M. Pederson, and L. D. Barron, “Tryptophan absolute stereochemistry in viral coat proteins from Raman optical activity,” J. Am. Chem. Soc. 123, 4863–4864 (2001).
    [CrossRef] [PubMed]
  50. E. W. Blanch, D. J. Robinson, L. Hecht, and L. D. Barron, “Solution structures of potato virus X and narcissus mosaic virus from Raman optical activity,” J. Gen. Virol. 83, 241–246(2002).
  51. E. W. Blanch, L. Hecht, C. D. Syme, V. Volpetti, G. P. Lomonossoff, K. Nielsen, and L. D. Barron, “Molecular structures of viruses from Raman optical activity,” J. Gen. Virol. 83, 2593–2600 (2002).
    [PubMed]
  52. M. Buenemann and P. Lenz, “Elastic properties and mechanical stability of chiral and filled viral capsids,” Phys. Rev. E 78, 051924 (2008).
    [CrossRef]
  53. J. Arsuaga, M. Vazquez, P. McGuirk, S. Trigueros, D. Sumners, and J. Roca, “DNA knots reveal a chiral organization of DNA in phage capsids,” Proc. Natl. Acad. Sci. USA 102, 9165–9169(2005).
    [CrossRef] [PubMed]
  54. M. Quaglia, A. Mai, G. Sbardella, M. Artico, R. Ragno, S. Massa, D. del Piano, G. Setzu, S. Doratiotto, and V. Cotichini, “Chiral resolution and molecular modeling investigation of rac-2-cyclopentylthio-6-[1-(2,6-difluorophenyl)ethyl]-3,4-dihydro-5-methylpyrimidin-4(3H)-one (MC-1047), a potent anti-HIV-1 reverse transcriptase agent of the DABO class,” Chirality 13, 75–80 (2001).
    [CrossRef] [PubMed]
  55. M. A. Siddiqui, S. H. Hughes, P. L. Boyer, H. Mitsuya, Q. N. Van, C. George, S. G. Sarafinanos, and V. E. Marquez, “A 4′-C-ethynyl-2′,3′-dideoxynucleoside analogue highlights the role of the 3′-OH in anti-HIV active 4′-C-ethynyl-2′-deoxy nucleosides,” J. Med. Chem. 47, 5041–5048 (2004).
    [CrossRef] [PubMed]
  56. T. K. Venkatachalam, C. Mao, and F. M. Uckun, “Stereochemistry as a major determinant of the anti-HIV activity of chiral naphthyl thiourea compounds,” Antivir. Chem. Chemother. 12, 213–221 (2001).
  57. T. K. Venkatachalam, C. Mao, and F. M. Uckun, “Effect of stereochemistry on the anti-HIV activity of chiral thiourea compounds,” Bioorg. Med. Chem. 12, 4275–4284 (2004).
    [CrossRef] [PubMed]

2011 (3)

E. Bahar, “Like and cross-polarized scatter cross sections for two-dimensional, multiscale rough surfaces based on a unified full wave variational technique,” Radio Sci. 46, RS4002, doi:10.1029/2010RS004441 (2011).
[CrossRef]

E. Bahar, “Guided surface waves over a free-space-chiral interface: applications to identification of optically active materials,” J. Opt. Soc. Am. B 28, 868–872 (2011).
[CrossRef]

E. Bahar, “Cross polarization of lateral waves propagating along a free-space-chiral planar interface: application to identification of optically active materials,” J. Opt. Soc. Am. B 28, 1194–1199(2011).
[CrossRef]

2010 (2)

E. Bahar, “Total transmission of incident plane waves that satisfy the Brewster conditions at a free-space-chiral interface,” J. Opt. Soc. Am. A 27, 2055–2060 (2010).
[CrossRef]

N. J. Higham, C. Mehl, and F. Tisseur, “The canonical generalized polar decomposition,” SIAM J. Matrix Anal. Appl. 31, 2163–2180 (2010).
[CrossRef]

2009 (3)

2008 (5)

E. Bahar, “The relationship between optical rotation and circular dichroism and elements of the Mueller matrix for natural and artificial materials,” J. Opt. Soc. Am. B 25, 218–222(2008).
[CrossRef]

E. Bahar, “Characterization of natural and artificial optical activity by the Mueller matrix for oblique incidence, total internal reflection and Brewster angle,” J. Opt. Soc. Am. B 25, 1294–1302(2008).
[CrossRef]

E. Bahar, “Detection and identification of optical activity using polarimetry—applications in biophotonics biomedicine and biochemistry,” J. Biophotonics 1, 230–237 (2008).
[CrossRef]

M. Buenemann and P. Lenz, “Elastic properties and mechanical stability of chiral and filled viral capsids,” Phys. Rev. E 78, 051924 (2008).
[CrossRef]

E. Bahar and R. Kubik, “Description of a versatile optical polarimetric scatterometer that measures all 16 elements of Mueller matrix for reflection and transmission: application to measurements of scatter cross sections, ellipsometric parameters, optical activity, and the complex chiral parameters,” Opt. Eng. 47, 093603 (2008).
[CrossRef]

2007 (3)

2006 (1)

2005 (1)

J. Arsuaga, M. Vazquez, P. McGuirk, S. Trigueros, D. Sumners, and J. Roca, “DNA knots reveal a chiral organization of DNA in phage capsids,” Proc. Natl. Acad. Sci. USA 102, 9165–9169(2005).
[CrossRef] [PubMed]

2004 (3)

M. A. Siddiqui, S. H. Hughes, P. L. Boyer, H. Mitsuya, Q. N. Van, C. George, S. G. Sarafinanos, and V. E. Marquez, “A 4′-C-ethynyl-2′,3′-dideoxynucleoside analogue highlights the role of the 3′-OH in anti-HIV active 4′-C-ethynyl-2′-deoxy nucleosides,” J. Med. Chem. 47, 5041–5048 (2004).
[CrossRef] [PubMed]

T. K. Venkatachalam, C. Mao, and F. M. Uckun, “Effect of stereochemistry on the anti-HIV activity of chiral thiourea compounds,” Bioorg. Med. Chem. 12, 4275–4284 (2004).
[CrossRef] [PubMed]

J. Morio and A. Goudail, “Influence of the order of diattenuator, retarder and polarizer in polar decomposition of Mueller matrices,” Opt. Lett. 29, 2234–2236 (2004).
[CrossRef] [PubMed]

2002 (6)

E. W. Blanch, D. J. Robinson, L. Hecht, and L. D. Barron, “Solution structures of potato virus X and narcissus mosaic virus from Raman optical activity,” J. Gen. Virol. 83, 241–246(2002).

E. W. Blanch, L. Hecht, C. D. Syme, V. Volpetti, G. P. Lomonossoff, K. Nielsen, and L. D. Barron, “Molecular structures of viruses from Raman optical activity,” J. Gen. Virol. 83, 2593–2600 (2002).
[PubMed]

V. Sankaran, J. T. Walsh, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7, 300–306 (2002).
[CrossRef] [PubMed]

G. L. Liu, Y. Li, and B. D. Cameron, “Polarization-based optical imaging and processing techniques with application to cancer diagnostics,” Proc. SPIE 4617, 208–220 (2002).
[CrossRef]

L. V. Wang, G. L. Coté, and S. L. Jacques, eds, “Special section on tissue polarimetry,” J. Biomed. Opt. 7, 278–397 (2002).
[CrossRef]

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340(2002).
[CrossRef] [PubMed]

2001 (5)

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadigan, I. Itzkan, R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef] [PubMed]

E. W. Blanch, L. Hecht, L. A. Day, D. M. Pederson, and L. D. Barron, “Tryptophan absolute stereochemistry in viral coat proteins from Raman optical activity,” J. Am. Chem. Soc. 123, 4863–4864 (2001).
[CrossRef] [PubMed]

M. H. Smith, “Interpreting Mueller matrix images of tissues,” Proc. SPIE 4257, 82–89 (2001).
[CrossRef]

T. K. Venkatachalam, C. Mao, and F. M. Uckun, “Stereochemistry as a major determinant of the anti-HIV activity of chiral naphthyl thiourea compounds,” Antivir. Chem. Chemother. 12, 213–221 (2001).

M. Quaglia, A. Mai, G. Sbardella, M. Artico, R. Ragno, S. Massa, D. del Piano, G. Setzu, S. Doratiotto, and V. Cotichini, “Chiral resolution and molecular modeling investigation of rac-2-cyclopentylthio-6-[1-(2,6-difluorophenyl)ethyl]-3,4-dihydro-5-methylpyrimidin-4(3H)-one (MC-1047), a potent anti-HIV-1 reverse transcriptase agent of the DABO class,” Chirality 13, 75–80 (2001).
[CrossRef] [PubMed]

2000 (4)

R. C. N. Studinski and I. A. Vitkin, “Methodology for examining polarized light interactions with tissues and tissue-like media in the exact backscattering direction,” J. Biomed. Opt. 5, 330–337(2000).
[CrossRef] [PubMed]

S. L. Jacques, J. R. Roman, and K. Lee, “Imaging superficial tissue with polarized light,” Lasers Surg. Med. 26, 119–129 (2000).
[CrossRef] [PubMed]

M. H. Smith, A. Lompado, and P. Burke, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3911, 210–216 (2000).
[CrossRef]

S. L. Jacques and R. J. Ramella-Roman, “Propagation of polarized light beams through biological tissues,” Proc. SPIE 3914, 345–352 (2000).
[CrossRef]

1999 (2)

G. J. Thomas, Jr., “Raman spectroscopy of protein and nucleic acid assemblies,” Annu. Rev. Biophys. Biomol. Struct. 28, 1–27(1999).
[CrossRef] [PubMed]

A. H. Carrieri, “Neural network pattern recognition by means of differential absorption Mueller matrices spectroscopy,” Appl. Opt. 38, 3759–3766 (1999).
[CrossRef]

1998 (2)

1995 (2)

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

L. Wang and S. Jacques, “Non-invasive detection of skin cancers by measuring optical properties of tissue,” Proc. SPIE 2395, 548–558 (1995).
[CrossRef]

1990 (1)

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

1988 (1)

1987 (1)

M. Silverman and T. Black, “Experimental method to detect chiral asymmetry in specular light scattering from a naturally optically active medium,” Phys. Lett. A 126, 171–176 (1987).
[CrossRef]

1986 (3)

M. Silverman, “Reflection and refraction at the surfaces of achiral medium: comparison of gyrotropic constitutive relations invariant or non-invariant under duality transformations,” J. Opt. Soc. Am. A 3, 830–837 (1986).
[CrossRef]

N. J. Higham, “Computing the polar decomposition-with applications,” SIAM J. Sci. Statist. Comput. 7, 1100–1174(1986).

S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–36 (1986).

1976 (1)

W. S. Bickel, J. F. Davidson, D. R. Huffman, and R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[CrossRef] [PubMed]

Ariens, E. J.

E. J. Ariens, W. Soudijin, and P. B. M. W. M. Timmermans, Stereochemistry and Biological Activity of Drugs (Blackwell, 1983).

Arsuaga, J.

J. Arsuaga, M. Vazquez, P. McGuirk, S. Trigueros, D. Sumners, and J. Roca, “DNA knots reveal a chiral organization of DNA in phage capsids,” Proc. Natl. Acad. Sci. USA 102, 9165–9169(2005).
[CrossRef] [PubMed]

Artico, M.

M. Quaglia, A. Mai, G. Sbardella, M. Artico, R. Ragno, S. Massa, D. del Piano, G. Setzu, S. Doratiotto, and V. Cotichini, “Chiral resolution and molecular modeling investigation of rac-2-cyclopentylthio-6-[1-(2,6-difluorophenyl)ethyl]-3,4-dihydro-5-methylpyrimidin-4(3H)-one (MC-1047), a potent anti-HIV-1 reverse transcriptase agent of the DABO class,” Chirality 13, 75–80 (2001).
[CrossRef] [PubMed]

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1987).

Backman, V.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadigan, I. Itzkan, R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef] [PubMed]

Badizadigan, K.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadigan, I. Itzkan, R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef] [PubMed]

Bahar, E.

E. Bahar, “Guided surface waves over a free-space-chiral interface: applications to identification of optically active materials,” J. Opt. Soc. Am. B 28, 868–872 (2011).
[CrossRef]

E. Bahar, “Like and cross-polarized scatter cross sections for two-dimensional, multiscale rough surfaces based on a unified full wave variational technique,” Radio Sci. 46, RS4002, doi:10.1029/2010RS004441 (2011).
[CrossRef]

E. Bahar, “Cross polarization of lateral waves propagating along a free-space-chiral planar interface: application to identification of optically active materials,” J. Opt. Soc. Am. B 28, 1194–1199(2011).
[CrossRef]

E. Bahar, “Total transmission of incident plane waves that satisfy the Brewster conditions at a free-space-chiral interface,” J. Opt. Soc. Am. A 27, 2055–2060 (2010).
[CrossRef]

E. Bahar, “Reflection and transmission matrices at a free-space-chiral interface based on the invariant constitutive relations and for gyrotropic media and the Drude–Born–Feredov constitutive relations,” J. Opt. Soc. Am. A 26, 1834–1838(2009).
[CrossRef]

E. Bahar, “Roadmaps for the use of Mueller matrix measurements to detect and identify biological and chemical materials through their optical activity: potential applications in biomedicine, biochemistry, security, and industry,” J. Opt. Soc. Am. B 26, 364–370 (2009).
[CrossRef]

E. Bahar and R. Kubik, “Description of a versatile optical polarimetric scatterometer that measures all 16 elements of Mueller matrix for reflection and transmission: application to measurements of scatter cross sections, ellipsometric parameters, optical activity, and the complex chiral parameters,” Opt. Eng. 47, 093603 (2008).
[CrossRef]

E. Bahar, “Characterization of natural and artificial optical activity by the Mueller matrix for oblique incidence, total internal reflection and Brewster angle,” J. Opt. Soc. Am. B 25, 1294–1302(2008).
[CrossRef]

E. Bahar, “Detection and identification of optical activity using polarimetry—applications in biophotonics biomedicine and biochemistry,” J. Biophotonics 1, 230–237 (2008).
[CrossRef]

E. Bahar, “The relationship between optical rotation and circular dichroism and elements of the Mueller matrix for natural and artificial materials,” J. Opt. Soc. Am. B 25, 218–222(2008).
[CrossRef]

E. Bahar, “Mueller matrices for waves reflected and transmitted through chiral materials, waveguide modal solutions and applications,” J. Opt. Soc. Am. B 24, 1610–1619 (2007).
[CrossRef]

E. Bahar, “Optimum electromagnetic wave excitations of complex media characterized by positive or negative refractive indices and by chiral properties,” J. Opt. Soc. Am. B 24, 2807–2813 (2007).
[CrossRef]

Barron, L. D.

E. W. Blanch, L. Hecht, C. D. Syme, V. Volpetti, G. P. Lomonossoff, K. Nielsen, and L. D. Barron, “Molecular structures of viruses from Raman optical activity,” J. Gen. Virol. 83, 2593–2600 (2002).
[PubMed]

E. W. Blanch, D. J. Robinson, L. Hecht, and L. D. Barron, “Solution structures of potato virus X and narcissus mosaic virus from Raman optical activity,” J. Gen. Virol. 83, 241–246(2002).

E. W. Blanch, L. Hecht, L. A. Day, D. M. Pederson, and L. D. Barron, “Tryptophan absolute stereochemistry in viral coat proteins from Raman optical activity,” J. Am. Chem. Soc. 123, 4863–4864 (2001).
[CrossRef] [PubMed]

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1987).

Bickel, W. S.

W. S. Bickel, J. F. Davidson, D. R. Huffman, and R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[CrossRef] [PubMed]

Black, T.

M. Silverman and T. Black, “Experimental method to detect chiral asymmetry in specular light scattering from a naturally optically active medium,” Phys. Lett. A 126, 171–176 (1987).
[CrossRef]

Blanch, E. W.

E. W. Blanch, D. J. Robinson, L. Hecht, and L. D. Barron, “Solution structures of potato virus X and narcissus mosaic virus from Raman optical activity,” J. Gen. Virol. 83, 241–246(2002).

E. W. Blanch, L. Hecht, C. D. Syme, V. Volpetti, G. P. Lomonossoff, K. Nielsen, and L. D. Barron, “Molecular structures of viruses from Raman optical activity,” J. Gen. Virol. 83, 2593–2600 (2002).
[PubMed]

E. W. Blanch, L. Hecht, L. A. Day, D. M. Pederson, and L. D. Barron, “Tryptophan absolute stereochemistry in viral coat proteins from Raman optical activity,” J. Am. Chem. Soc. 123, 4863–4864 (2001).
[CrossRef] [PubMed]

Bottinger, J. R.

Boyer, P. L.

M. A. Siddiqui, S. H. Hughes, P. L. Boyer, H. Mitsuya, Q. N. Van, C. George, S. G. Sarafinanos, and V. E. Marquez, “A 4′-C-ethynyl-2′,3′-dideoxynucleoside analogue highlights the role of the 3′-OH in anti-HIV active 4′-C-ethynyl-2′-deoxy nucleosides,” J. Med. Chem. 47, 5041–5048 (2004).
[CrossRef] [PubMed]

Browne, C. A.

C. A. Browne and F. W. Zerban, Physical and Chemical Methods of Sugar Analysis (Wiley, 1941).

Buddhiwant, P.

Buenemann, M.

M. Buenemann and P. Lenz, “Elastic properties and mechanical stability of chiral and filled viral capsids,” Phys. Rev. E 78, 051924 (2008).
[CrossRef]

Burke, P.

M. H. Smith, A. Lompado, and P. Burke, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3911, 210–216 (2000).
[CrossRef]

Cameron, B. D.

G. L. Liu, Y. Li, and B. D. Cameron, “Polarization-based optical imaging and processing techniques with application to cancer diagnostics,” Proc. SPIE 4617, 208–220 (2002).
[CrossRef]

Carrieri, A. H.

Chen, Z.

Cheong, W. F.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Chipman, R. A.

S. Lu and R. A. Chipman, “Mueller matrices and the degree of polarization,” Opt. Commun. 146, 11–14 (1998).
[CrossRef]

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

Chung, J.

Cloude, S. R.

S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–36 (1986).

Coté, G. L.

L. V. Wang, G. L. Coté, and S. L. Jacques, eds, “Special section on tissue polarimetry,” J. Biomed. Opt. 7, 278–397 (2002).
[CrossRef]

Cotichini, V.

M. Quaglia, A. Mai, G. Sbardella, M. Artico, R. Ragno, S. Massa, D. del Piano, G. Setzu, S. Doratiotto, and V. Cotichini, “Chiral resolution and molecular modeling investigation of rac-2-cyclopentylthio-6-[1-(2,6-difluorophenyl)ethyl]-3,4-dihydro-5-methylpyrimidin-4(3H)-one (MC-1047), a potent anti-HIV-1 reverse transcriptase agent of the DABO class,” Chirality 13, 75–80 (2001).
[CrossRef] [PubMed]

Cushman, G.

Dasari, R.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadigan, I. Itzkan, R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef] [PubMed]

Davidson, J. F.

W. S. Bickel, J. F. Davidson, D. R. Huffman, and R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[CrossRef] [PubMed]

Day, L. A.

E. W. Blanch, L. Hecht, L. A. Day, D. M. Pederson, and L. D. Barron, “Tryptophan absolute stereochemistry in viral coat proteins from Raman optical activity,” J. Am. Chem. Soc. 123, 4863–4864 (2001).
[CrossRef] [PubMed]

del Piano, D.

M. Quaglia, A. Mai, G. Sbardella, M. Artico, R. Ragno, S. Massa, D. del Piano, G. Setzu, S. Doratiotto, and V. Cotichini, “Chiral resolution and molecular modeling investigation of rac-2-cyclopentylthio-6-[1-(2,6-difluorophenyl)ethyl]-3,4-dihydro-5-methylpyrimidin-4(3H)-one (MC-1047), a potent anti-HIV-1 reverse transcriptase agent of the DABO class,” Chirality 13, 75–80 (2001).
[CrossRef] [PubMed]

Doratiotto, S.

M. Quaglia, A. Mai, G. Sbardella, M. Artico, R. Ragno, S. Massa, D. del Piano, G. Setzu, S. Doratiotto, and V. Cotichini, “Chiral resolution and molecular modeling investigation of rac-2-cyclopentylthio-6-[1-(2,6-difluorophenyl)ethyl]-3,4-dihydro-5-methylpyrimidin-4(3H)-one (MC-1047), a potent anti-HIV-1 reverse transcriptase agent of the DABO class,” Chirality 13, 75–80 (2001).
[CrossRef] [PubMed]

Feld, M. S.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadigan, I. Itzkan, R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef] [PubMed]

Fisher, B.

Georgakoudi, I.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadigan, I. Itzkan, R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef] [PubMed]

George, C.

M. A. Siddiqui, S. H. Hughes, P. L. Boyer, H. Mitsuya, Q. N. Van, C. George, S. G. Sarafinanos, and V. E. Marquez, “A 4′-C-ethynyl-2′,3′-dideoxynucleoside analogue highlights the role of the 3′-OH in anti-HIV active 4′-C-ethynyl-2′-deoxy nucleosides,” J. Med. Chem. 47, 5041–5048 (2004).
[CrossRef] [PubMed]

Ghosh, N.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
[CrossRef] [PubMed]

A. Vitkin, N. Ghosh, and M. F. G. Wood, “Diagnostic photomedicine: probing biological tissues with polarized light,” SPIE Newsroom, DOI: 10.1117/2.1200808.1238 (2008), http://spie.org/x27101.xml?ArticleID=x27101.
[CrossRef]

Gosh, N.

Goudail, A.

Gupta, P. K.

Gurjar, R. S.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadigan, I. Itzkan, R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef] [PubMed]

Hammer-Wilson, M. J.

Hecht, L.

E. W. Blanch, L. Hecht, C. D. Syme, V. Volpetti, G. P. Lomonossoff, K. Nielsen, and L. D. Barron, “Molecular structures of viruses from Raman optical activity,” J. Gen. Virol. 83, 2593–2600 (2002).
[PubMed]

E. W. Blanch, D. J. Robinson, L. Hecht, and L. D. Barron, “Solution structures of potato virus X and narcissus mosaic virus from Raman optical activity,” J. Gen. Virol. 83, 241–246(2002).

E. W. Blanch, L. Hecht, L. A. Day, D. M. Pederson, and L. D. Barron, “Tryptophan absolute stereochemistry in viral coat proteins from Raman optical activity,” J. Am. Chem. Soc. 123, 4863–4864 (2001).
[CrossRef] [PubMed]

Higham, N. J.

N. J. Higham, C. Mehl, and F. Tisseur, “The canonical generalized polar decomposition,” SIAM J. Matrix Anal. Appl. 31, 2163–2180 (2010).
[CrossRef]

N. J. Higham, “Computing the polar decomposition-with applications,” SIAM J. Sci. Statist. Comput. 7, 1100–1174(1986).

Huffman, D. R.

W. S. Bickel, J. F. Davidson, D. R. Huffman, and R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[CrossRef] [PubMed]

Hughes, S. H.

M. A. Siddiqui, S. H. Hughes, P. L. Boyer, H. Mitsuya, Q. N. Van, C. George, S. G. Sarafinanos, and V. E. Marquez, “A 4′-C-ethynyl-2′,3′-dideoxynucleoside analogue highlights the role of the 3′-OH in anti-HIV active 4′-C-ethynyl-2′-deoxy nucleosides,” J. Med. Chem. 47, 5041–5048 (2004).
[CrossRef] [PubMed]

Itzkan, I.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadigan, I. Itzkan, R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef] [PubMed]

Jacques, S.

L. Wang and S. Jacques, “Non-invasive detection of skin cancers by measuring optical properties of tissue,” Proc. SPIE 2395, 548–558 (1995).
[CrossRef]

Jacques, S. L.

L. V. Wang, G. L. Coté, and S. L. Jacques, eds, “Special section on tissue polarimetry,” J. Biomed. Opt. 7, 278–397 (2002).
[CrossRef]

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340(2002).
[CrossRef] [PubMed]

S. L. Jacques, J. R. Roman, and K. Lee, “Imaging superficial tissue with polarized light,” Lasers Surg. Med. 26, 119–129 (2000).
[CrossRef] [PubMed]

S. L. Jacques and R. J. Ramella-Roman, “Propagation of polarized light beams through biological tissues,” Proc. SPIE 3914, 345–352 (2000).
[CrossRef]

Jung, W.

Khlebtsov, N. G.

N. G. Khlebtsov, I. L. Maksimova, V. V. Tuchin, and L. Wang, “Introduction to light scattering by biological objects,” in Handbook of Optical Biomedical Diagnostics, Vol. PM107 of SPIE Press Monographs (SPIE, 2002), pp. 31–167.

Kilkson, R.

W. S. Bickel, J. F. Davidson, D. R. Huffman, and R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[CrossRef] [PubMed]

Kubik, R.

E. Bahar and R. Kubik, “Description of a versatile optical polarimetric scatterometer that measures all 16 elements of Mueller matrix for reflection and transmission: application to measurements of scatter cross sections, ellipsometric parameters, optical activity, and the complex chiral parameters,” Opt. Eng. 47, 093603 (2008).
[CrossRef]

Lee, K.

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340(2002).
[CrossRef] [PubMed]

S. L. Jacques, J. R. Roman, and K. Lee, “Imaging superficial tissue with polarized light,” Lasers Surg. Med. 26, 119–129 (2000).
[CrossRef] [PubMed]

Lenz, P.

M. Buenemann and P. Lenz, “Elastic properties and mechanical stability of chiral and filled viral capsids,” Phys. Rev. E 78, 051924 (2008).
[CrossRef]

Li, R.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
[CrossRef] [PubMed]

Li, S.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
[CrossRef] [PubMed]

Li, Y.

G. L. Liu, Y. Li, and B. D. Cameron, “Polarization-based optical imaging and processing techniques with application to cancer diagnostics,” Proc. SPIE 4617, 208–220 (2002).
[CrossRef]

Liu, G. L.

G. L. Liu, Y. Li, and B. D. Cameron, “Polarization-based optical imaging and processing techniques with application to cancer diagnostics,” Proc. SPIE 4617, 208–220 (2002).
[CrossRef]

Lomonossoff, G. P.

E. W. Blanch, L. Hecht, C. D. Syme, V. Volpetti, G. P. Lomonossoff, K. Nielsen, and L. D. Barron, “Molecular structures of viruses from Raman optical activity,” J. Gen. Virol. 83, 2593–2600 (2002).
[PubMed]

Lompado, A.

M. H. Smith, A. Lompado, and P. Burke, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3911, 210–216 (2000).
[CrossRef]

Lu, S.

S. Lu and R. A. Chipman, “Mueller matrices and the degree of polarization,” Opt. Commun. 146, 11–14 (1998).
[CrossRef]

Mai, A.

M. Quaglia, A. Mai, G. Sbardella, M. Artico, R. Ragno, S. Massa, D. del Piano, G. Setzu, S. Doratiotto, and V. Cotichini, “Chiral resolution and molecular modeling investigation of rac-2-cyclopentylthio-6-[1-(2,6-difluorophenyl)ethyl]-3,4-dihydro-5-methylpyrimidin-4(3H)-one (MC-1047), a potent anti-HIV-1 reverse transcriptase agent of the DABO class,” Chirality 13, 75–80 (2001).
[CrossRef] [PubMed]

Maitland, D. J.

V. Sankaran, J. T. Walsh, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7, 300–306 (2002).
[CrossRef] [PubMed]

Maksimova, I. L.

N. G. Khlebtsov, I. L. Maksimova, V. V. Tuchin, and L. Wang, “Introduction to light scattering by biological objects,” in Handbook of Optical Biomedical Diagnostics, Vol. PM107 of SPIE Press Monographs (SPIE, 2002), pp. 31–167.

Manhas, S.

Mao, C.

T. K. Venkatachalam, C. Mao, and F. M. Uckun, “Effect of stereochemistry on the anti-HIV activity of chiral thiourea compounds,” Bioorg. Med. Chem. 12, 4275–4284 (2004).
[CrossRef] [PubMed]

T. K. Venkatachalam, C. Mao, and F. M. Uckun, “Stereochemistry as a major determinant of the anti-HIV activity of chiral naphthyl thiourea compounds,” Antivir. Chem. Chemother. 12, 213–221 (2001).

Marquez, V. E.

M. A. Siddiqui, S. H. Hughes, P. L. Boyer, H. Mitsuya, Q. N. Van, C. George, S. G. Sarafinanos, and V. E. Marquez, “A 4′-C-ethynyl-2′,3′-dideoxynucleoside analogue highlights the role of the 3′-OH in anti-HIV active 4′-C-ethynyl-2′-deoxy nucleosides,” J. Med. Chem. 47, 5041–5048 (2004).
[CrossRef] [PubMed]

Massa, S.

M. Quaglia, A. Mai, G. Sbardella, M. Artico, R. Ragno, S. Massa, D. del Piano, G. Setzu, S. Doratiotto, and V. Cotichini, “Chiral resolution and molecular modeling investigation of rac-2-cyclopentylthio-6-[1-(2,6-difluorophenyl)ethyl]-3,4-dihydro-5-methylpyrimidin-4(3H)-one (MC-1047), a potent anti-HIV-1 reverse transcriptase agent of the DABO class,” Chirality 13, 75–80 (2001).
[CrossRef] [PubMed]

McGuirk, P.

J. Arsuaga, M. Vazquez, P. McGuirk, S. Trigueros, D. Sumners, and J. Roca, “DNA knots reveal a chiral organization of DNA in phage capsids,” Proc. Natl. Acad. Sci. USA 102, 9165–9169(2005).
[CrossRef] [PubMed]

Mehl, C.

N. J. Higham, C. Mehl, and F. Tisseur, “The canonical generalized polar decomposition,” SIAM J. Matrix Anal. Appl. 31, 2163–2180 (2010).
[CrossRef]

Mitsuya, H.

M. A. Siddiqui, S. H. Hughes, P. L. Boyer, H. Mitsuya, Q. N. Van, C. George, S. G. Sarafinanos, and V. E. Marquez, “A 4′-C-ethynyl-2′,3′-dideoxynucleoside analogue highlights the role of the 3′-OH in anti-HIV active 4′-C-ethynyl-2′-deoxy nucleosides,” J. Med. Chem. 47, 5041–5048 (2004).
[CrossRef] [PubMed]

Morio, J.

Nielsen, K.

E. W. Blanch, L. Hecht, C. D. Syme, V. Volpetti, G. P. Lomonossoff, K. Nielsen, and L. D. Barron, “Molecular structures of viruses from Raman optical activity,” J. Gen. Virol. 83, 2593–2600 (2002).
[PubMed]

Owens, D. J.

Pederson, D. M.

E. W. Blanch, L. Hecht, L. A. Day, D. M. Pederson, and L. D. Barron, “Tryptophan absolute stereochemistry in viral coat proteins from Raman optical activity,” J. Am. Chem. Soc. 123, 4863–4864 (2001).
[CrossRef] [PubMed]

Perelman, L. T.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadigan, I. Itzkan, R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef] [PubMed]

Pezzaniti, J. L.

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

Prahl, S. A.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Quaglia, M.

M. Quaglia, A. Mai, G. Sbardella, M. Artico, R. Ragno, S. Massa, D. del Piano, G. Setzu, S. Doratiotto, and V. Cotichini, “Chiral resolution and molecular modeling investigation of rac-2-cyclopentylthio-6-[1-(2,6-difluorophenyl)ethyl]-3,4-dihydro-5-methylpyrimidin-4(3H)-one (MC-1047), a potent anti-HIV-1 reverse transcriptase agent of the DABO class,” Chirality 13, 75–80 (2001).
[CrossRef] [PubMed]

Ragno, R.

M. Quaglia, A. Mai, G. Sbardella, M. Artico, R. Ragno, S. Massa, D. del Piano, G. Setzu, S. Doratiotto, and V. Cotichini, “Chiral resolution and molecular modeling investigation of rac-2-cyclopentylthio-6-[1-(2,6-difluorophenyl)ethyl]-3,4-dihydro-5-methylpyrimidin-4(3H)-one (MC-1047), a potent anti-HIV-1 reverse transcriptase agent of the DABO class,” Chirality 13, 75–80 (2001).
[CrossRef] [PubMed]

Ramella-Roman, J. C.

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340(2002).
[CrossRef] [PubMed]

Ramella-Roman, R. J.

S. L. Jacques and R. J. Ramella-Roman, “Propagation of polarized light beams through biological tissues,” Proc. SPIE 3914, 345–352 (2000).
[CrossRef]

Ritchie, N.

Robinson, D. J.

E. W. Blanch, D. J. Robinson, L. Hecht, and L. D. Barron, “Solution structures of potato virus X and narcissus mosaic virus from Raman optical activity,” J. Gen. Virol. 83, 241–246(2002).

Roca, J.

J. Arsuaga, M. Vazquez, P. McGuirk, S. Trigueros, D. Sumners, and J. Roca, “DNA knots reveal a chiral organization of DNA in phage capsids,” Proc. Natl. Acad. Sci. USA 102, 9165–9169(2005).
[CrossRef] [PubMed]

Roese, E. S.

Roman, J. R.

S. L. Jacques, J. R. Roman, and K. Lee, “Imaging superficial tissue with polarized light,” Lasers Surg. Med. 26, 119–129 (2000).
[CrossRef] [PubMed]

Sankaran, V.

V. Sankaran, J. T. Walsh, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7, 300–306 (2002).
[CrossRef] [PubMed]

Sarafinanos, S. G.

M. A. Siddiqui, S. H. Hughes, P. L. Boyer, H. Mitsuya, Q. N. Van, C. George, S. G. Sarafinanos, and V. E. Marquez, “A 4′-C-ethynyl-2′,3′-dideoxynucleoside analogue highlights the role of the 3′-OH in anti-HIV active 4′-C-ethynyl-2′-deoxy nucleosides,” J. Med. Chem. 47, 5041–5048 (2004).
[CrossRef] [PubMed]

Sbardella, G.

M. Quaglia, A. Mai, G. Sbardella, M. Artico, R. Ragno, S. Massa, D. del Piano, G. Setzu, S. Doratiotto, and V. Cotichini, “Chiral resolution and molecular modeling investigation of rac-2-cyclopentylthio-6-[1-(2,6-difluorophenyl)ethyl]-3,4-dihydro-5-methylpyrimidin-4(3H)-one (MC-1047), a potent anti-HIV-1 reverse transcriptase agent of the DABO class,” Chirality 13, 75–80 (2001).
[CrossRef] [PubMed]

Setzu, G.

M. Quaglia, A. Mai, G. Sbardella, M. Artico, R. Ragno, S. Massa, D. del Piano, G. Setzu, S. Doratiotto, and V. Cotichini, “Chiral resolution and molecular modeling investigation of rac-2-cyclopentylthio-6-[1-(2,6-difluorophenyl)ethyl]-3,4-dihydro-5-methylpyrimidin-4(3H)-one (MC-1047), a potent anti-HIV-1 reverse transcriptase agent of the DABO class,” Chirality 13, 75–80 (2001).
[CrossRef] [PubMed]

Siddiqui, M. A.

M. A. Siddiqui, S. H. Hughes, P. L. Boyer, H. Mitsuya, Q. N. Van, C. George, S. G. Sarafinanos, and V. E. Marquez, “A 4′-C-ethynyl-2′,3′-dideoxynucleoside analogue highlights the role of the 3′-OH in anti-HIV active 4′-C-ethynyl-2′-deoxy nucleosides,” J. Med. Chem. 47, 5041–5048 (2004).
[CrossRef] [PubMed]

Silverman, M.

Sing, K.

Smith, M. H.

M. H. Smith, “Interpreting Mueller matrix images of tissues,” Proc. SPIE 4257, 82–89 (2001).
[CrossRef]

M. H. Smith, A. Lompado, and P. Burke, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3911, 210–216 (2000).
[CrossRef]

Soudijin, W.

E. J. Ariens, W. Soudijin, and P. B. M. W. M. Timmermans, Stereochemistry and Biological Activity of Drugs (Blackwell, 1983).

Studinski, R. C. N.

R. C. N. Studinski and I. A. Vitkin, “Methodology for examining polarized light interactions with tissues and tissue-like media in the exact backscattering direction,” J. Biomed. Opt. 5, 330–337(2000).
[CrossRef] [PubMed]

Sumners, D.

J. Arsuaga, M. Vazquez, P. McGuirk, S. Trigueros, D. Sumners, and J. Roca, “DNA knots reveal a chiral organization of DNA in phage capsids,” Proc. Natl. Acad. Sci. USA 102, 9165–9169(2005).
[CrossRef] [PubMed]

Swami, M. K.

Syme, C. D.

E. W. Blanch, L. Hecht, C. D. Syme, V. Volpetti, G. P. Lomonossoff, K. Nielsen, and L. D. Barron, “Molecular structures of viruses from Raman optical activity,” J. Gen. Virol. 83, 2593–2600 (2002).
[PubMed]

Thomas, G. J.

G. J. Thomas, Jr., “Raman spectroscopy of protein and nucleic acid assemblies,” Annu. Rev. Biophys. Biomol. Struct. 28, 1–27(1999).
[CrossRef] [PubMed]

Timmermans, P. B. M. W. M.

E. J. Ariens, W. Soudijin, and P. B. M. W. M. Timmermans, Stereochemistry and Biological Activity of Drugs (Blackwell, 1983).

Tisseur, F.

N. J. Higham, C. Mehl, and F. Tisseur, “The canonical generalized polar decomposition,” SIAM J. Matrix Anal. Appl. 31, 2163–2180 (2010).
[CrossRef]

Trigueros, S.

J. Arsuaga, M. Vazquez, P. McGuirk, S. Trigueros, D. Sumners, and J. Roca, “DNA knots reveal a chiral organization of DNA in phage capsids,” Proc. Natl. Acad. Sci. USA 102, 9165–9169(2005).
[CrossRef] [PubMed]

Tuchin, V. V.

V. V. Tuchin, L. Wang, and D. A. Zimnyakov, Optical Polarization in Biomedical Applications (Springer-Verlag, 2006).

N. G. Khlebtsov, I. L. Maksimova, V. V. Tuchin, and L. Wang, “Introduction to light scattering by biological objects,” in Handbook of Optical Biomedical Diagnostics, Vol. PM107 of SPIE Press Monographs (SPIE, 2002), pp. 31–167.

Uckun, F. M.

T. K. Venkatachalam, C. Mao, and F. M. Uckun, “Effect of stereochemistry on the anti-HIV activity of chiral thiourea compounds,” Bioorg. Med. Chem. 12, 4275–4284 (2004).
[CrossRef] [PubMed]

T. K. Venkatachalam, C. Mao, and F. M. Uckun, “Stereochemistry as a major determinant of the anti-HIV activity of chiral naphthyl thiourea compounds,” Antivir. Chem. Chemother. 12, 213–221 (2001).

Van, Q. N.

M. A. Siddiqui, S. H. Hughes, P. L. Boyer, H. Mitsuya, Q. N. Van, C. George, S. G. Sarafinanos, and V. E. Marquez, “A 4′-C-ethynyl-2′,3′-dideoxynucleoside analogue highlights the role of the 3′-OH in anti-HIV active 4′-C-ethynyl-2′-deoxy nucleosides,” J. Med. Chem. 47, 5041–5048 (2004).
[CrossRef] [PubMed]

Vazquez, M.

J. Arsuaga, M. Vazquez, P. McGuirk, S. Trigueros, D. Sumners, and J. Roca, “DNA knots reveal a chiral organization of DNA in phage capsids,” Proc. Natl. Acad. Sci. USA 102, 9165–9169(2005).
[CrossRef] [PubMed]

Venkatachalam, T. K.

T. K. Venkatachalam, C. Mao, and F. M. Uckun, “Effect of stereochemistry on the anti-HIV activity of chiral thiourea compounds,” Bioorg. Med. Chem. 12, 4275–4284 (2004).
[CrossRef] [PubMed]

T. K. Venkatachalam, C. Mao, and F. M. Uckun, “Stereochemistry as a major determinant of the anti-HIV activity of chiral naphthyl thiourea compounds,” Antivir. Chem. Chemother. 12, 213–221 (2001).

Vitkin, A.

A. Vitkin, N. Ghosh, and M. F. G. Wood, “Diagnostic photomedicine: probing biological tissues with polarized light,” SPIE Newsroom, DOI: 10.1117/2.1200808.1238 (2008), http://spie.org/x27101.xml?ArticleID=x27101.
[CrossRef]

Vitkin, I. A.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
[CrossRef] [PubMed]

R. C. N. Studinski and I. A. Vitkin, “Methodology for examining polarized light interactions with tissues and tissue-like media in the exact backscattering direction,” J. Biomed. Opt. 5, 330–337(2000).
[CrossRef] [PubMed]

Volpetti, V.

E. W. Blanch, L. Hecht, C. D. Syme, V. Volpetti, G. P. Lomonossoff, K. Nielsen, and L. D. Barron, “Molecular structures of viruses from Raman optical activity,” J. Gen. Virol. 83, 2593–2600 (2002).
[PubMed]

Walsh, J. T.

V. Sankaran, J. T. Walsh, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7, 300–306 (2002).
[CrossRef] [PubMed]

Wamer, J. W.

J. W. Wamer, Drug Stereochemistry (Dekker, 1993).

Wang, L.

L. Wang and S. Jacques, “Non-invasive detection of skin cancers by measuring optical properties of tissue,” Proc. SPIE 2395, 548–558 (1995).
[CrossRef]

N. G. Khlebtsov, I. L. Maksimova, V. V. Tuchin, and L. Wang, “Introduction to light scattering by biological objects,” in Handbook of Optical Biomedical Diagnostics, Vol. PM107 of SPIE Press Monographs (SPIE, 2002), pp. 31–167.

V. V. Tuchin, L. Wang, and D. A. Zimnyakov, Optical Polarization in Biomedical Applications (Springer-Verlag, 2006).

Wang, L. V.

L. V. Wang, G. L. Coté, and S. L. Jacques, eds, “Special section on tissue polarimetry,” J. Biomed. Opt. 7, 278–397 (2002).
[CrossRef]

Weisel, R. D.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
[CrossRef] [PubMed]

Welch, A. J.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Wilder-Smith, P.

Wilson, B. C.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
[CrossRef] [PubMed]

Wood, M. F. G.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
[CrossRef] [PubMed]

A. Vitkin, N. Ghosh, and M. F. G. Wood, “Diagnostic photomedicine: probing biological tissues with polarized light,” SPIE Newsroom, DOI: 10.1117/2.1200808.1238 (2008), http://spie.org/x27101.xml?ArticleID=x27101.
[CrossRef]

Zerban, F. W.

C. A. Browne and F. W. Zerban, Physical and Chemical Methods of Sugar Analysis (Wiley, 1941).

Zimnyakov, D. A.

V. V. Tuchin, L. Wang, and D. A. Zimnyakov, Optical Polarization in Biomedical Applications (Springer-Verlag, 2006).

Annu. Rev. Biophys. Biomol. Struct. (1)

G. J. Thomas, Jr., “Raman spectroscopy of protein and nucleic acid assemblies,” Annu. Rev. Biophys. Biomol. Struct. 28, 1–27(1999).
[CrossRef] [PubMed]

Antivir. Chem. Chemother. (1)

T. K. Venkatachalam, C. Mao, and F. M. Uckun, “Stereochemistry as a major determinant of the anti-HIV activity of chiral naphthyl thiourea compounds,” Antivir. Chem. Chemother. 12, 213–221 (2001).

Appl. Opt. (3)

Bioorg. Med. Chem. (1)

T. K. Venkatachalam, C. Mao, and F. M. Uckun, “Effect of stereochemistry on the anti-HIV activity of chiral thiourea compounds,” Bioorg. Med. Chem. 12, 4275–4284 (2004).
[CrossRef] [PubMed]

Chirality (1)

M. Quaglia, A. Mai, G. Sbardella, M. Artico, R. Ragno, S. Massa, D. del Piano, G. Setzu, S. Doratiotto, and V. Cotichini, “Chiral resolution and molecular modeling investigation of rac-2-cyclopentylthio-6-[1-(2,6-difluorophenyl)ethyl]-3,4-dihydro-5-methylpyrimidin-4(3H)-one (MC-1047), a potent anti-HIV-1 reverse transcriptase agent of the DABO class,” Chirality 13, 75–80 (2001).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

J. Am. Chem. Soc. (1)

E. W. Blanch, L. Hecht, L. A. Day, D. M. Pederson, and L. D. Barron, “Tryptophan absolute stereochemistry in viral coat proteins from Raman optical activity,” J. Am. Chem. Soc. 123, 4863–4864 (2001).
[CrossRef] [PubMed]

J. Biomed. Opt. (4)

R. C. N. Studinski and I. A. Vitkin, “Methodology for examining polarized light interactions with tissues and tissue-like media in the exact backscattering direction,” J. Biomed. Opt. 5, 330–337(2000).
[CrossRef] [PubMed]

L. V. Wang, G. L. Coté, and S. L. Jacques, eds, “Special section on tissue polarimetry,” J. Biomed. Opt. 7, 278–397 (2002).
[CrossRef]

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340(2002).
[CrossRef] [PubMed]

V. Sankaran, J. T. Walsh, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7, 300–306 (2002).
[CrossRef] [PubMed]

J. Biophotonics (2)

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
[CrossRef] [PubMed]

E. Bahar, “Detection and identification of optical activity using polarimetry—applications in biophotonics biomedicine and biochemistry,” J. Biophotonics 1, 230–237 (2008).
[CrossRef]

J. Gen. Virol. (2)

E. W. Blanch, D. J. Robinson, L. Hecht, and L. D. Barron, “Solution structures of potato virus X and narcissus mosaic virus from Raman optical activity,” J. Gen. Virol. 83, 241–246(2002).

E. W. Blanch, L. Hecht, C. D. Syme, V. Volpetti, G. P. Lomonossoff, K. Nielsen, and L. D. Barron, “Molecular structures of viruses from Raman optical activity,” J. Gen. Virol. 83, 2593–2600 (2002).
[PubMed]

J. Med. Chem. (1)

M. A. Siddiqui, S. H. Hughes, P. L. Boyer, H. Mitsuya, Q. N. Van, C. George, S. G. Sarafinanos, and V. E. Marquez, “A 4′-C-ethynyl-2′,3′-dideoxynucleoside analogue highlights the role of the 3′-OH in anti-HIV active 4′-C-ethynyl-2′-deoxy nucleosides,” J. Med. Chem. 47, 5041–5048 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (4)

J. Opt. Soc. Am. B (7)

E. Bahar, “Cross polarization of lateral waves propagating along a free-space-chiral planar interface: application to identification of optically active materials,” J. Opt. Soc. Am. B 28, 1194–1199(2011).
[CrossRef]

E. Bahar, “Mueller matrices for waves reflected and transmitted through chiral materials, waveguide modal solutions and applications,” J. Opt. Soc. Am. B 24, 1610–1619 (2007).
[CrossRef]

E. Bahar, “Optimum electromagnetic wave excitations of complex media characterized by positive or negative refractive indices and by chiral properties,” J. Opt. Soc. Am. B 24, 2807–2813 (2007).
[CrossRef]

E. Bahar, “The relationship between optical rotation and circular dichroism and elements of the Mueller matrix for natural and artificial materials,” J. Opt. Soc. Am. B 25, 218–222(2008).
[CrossRef]

E. Bahar, “Characterization of natural and artificial optical activity by the Mueller matrix for oblique incidence, total internal reflection and Brewster angle,” J. Opt. Soc. Am. B 25, 1294–1302(2008).
[CrossRef]

E. Bahar, “Roadmaps for the use of Mueller matrix measurements to detect and identify biological and chemical materials through their optical activity: potential applications in biomedicine, biochemistry, security, and industry,” J. Opt. Soc. Am. B 26, 364–370 (2009).
[CrossRef]

E. Bahar, “Guided surface waves over a free-space-chiral interface: applications to identification of optically active materials,” J. Opt. Soc. Am. B 28, 868–872 (2011).
[CrossRef]

Lasers Surg. Med. (1)

S. L. Jacques, J. R. Roman, and K. Lee, “Imaging superficial tissue with polarized light,” Lasers Surg. Med. 26, 119–129 (2000).
[CrossRef] [PubMed]

Nat. Med. (1)

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadigan, I. Itzkan, R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef] [PubMed]

Opt. Commun. (1)

S. Lu and R. A. Chipman, “Mueller matrices and the degree of polarization,” Opt. Commun. 146, 11–14 (1998).
[CrossRef]

Opt. Eng. (2)

E. Bahar and R. Kubik, “Description of a versatile optical polarimetric scatterometer that measures all 16 elements of Mueller matrix for reflection and transmission: application to measurements of scatter cross sections, ellipsometric parameters, optical activity, and the complex chiral parameters,” Opt. Eng. 47, 093603 (2008).
[CrossRef]

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Optik (1)

S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–36 (1986).

Phys. Lett. A (1)

M. Silverman and T. Black, “Experimental method to detect chiral asymmetry in specular light scattering from a naturally optically active medium,” Phys. Lett. A 126, 171–176 (1987).
[CrossRef]

Phys. Rev. E (1)

M. Buenemann and P. Lenz, “Elastic properties and mechanical stability of chiral and filled viral capsids,” Phys. Rev. E 78, 051924 (2008).
[CrossRef]

Proc. Natl. Acad. Sci. USA (2)

J. Arsuaga, M. Vazquez, P. McGuirk, S. Trigueros, D. Sumners, and J. Roca, “DNA knots reveal a chiral organization of DNA in phage capsids,” Proc. Natl. Acad. Sci. USA 102, 9165–9169(2005).
[CrossRef] [PubMed]

W. S. Bickel, J. F. Davidson, D. R. Huffman, and R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[CrossRef] [PubMed]

Proc. SPIE (5)

S. L. Jacques and R. J. Ramella-Roman, “Propagation of polarized light beams through biological tissues,” Proc. SPIE 3914, 345–352 (2000).
[CrossRef]

M. H. Smith, A. Lompado, and P. Burke, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3911, 210–216 (2000).
[CrossRef]

M. H. Smith, “Interpreting Mueller matrix images of tissues,” Proc. SPIE 4257, 82–89 (2001).
[CrossRef]

G. L. Liu, Y. Li, and B. D. Cameron, “Polarization-based optical imaging and processing techniques with application to cancer diagnostics,” Proc. SPIE 4617, 208–220 (2002).
[CrossRef]

L. Wang and S. Jacques, “Non-invasive detection of skin cancers by measuring optical properties of tissue,” Proc. SPIE 2395, 548–558 (1995).
[CrossRef]

Radio Sci. (1)

E. Bahar, “Like and cross-polarized scatter cross sections for two-dimensional, multiscale rough surfaces based on a unified full wave variational technique,” Radio Sci. 46, RS4002, doi:10.1029/2010RS004441 (2011).
[CrossRef]

SIAM J. Matrix Anal. Appl. (1)

N. J. Higham, C. Mehl, and F. Tisseur, “The canonical generalized polar decomposition,” SIAM J. Matrix Anal. Appl. 31, 2163–2180 (2010).
[CrossRef]

SIAM J. Sci. Statist. Comput. (1)

N. J. Higham, “Computing the polar decomposition-with applications,” SIAM J. Sci. Statist. Comput. 7, 1100–1174(1986).

Other (8)

A. Vitkin, N. Ghosh, and M. F. G. Wood, “Diagnostic photomedicine: probing biological tissues with polarized light,” SPIE Newsroom, DOI: 10.1117/2.1200808.1238 (2008), http://spie.org/x27101.xml?ArticleID=x27101.
[CrossRef]

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1987).

E. J. Ariens, W. Soudijin, and P. B. M. W. M. Timmermans, Stereochemistry and Biological Activity of Drugs (Blackwell, 1983).

J. W. Wamer, Drug Stereochemistry (Dekker, 1993).

M. Silverman, Waves and Grains (Princeton University Press, 1998).

C. A. Browne and F. W. Zerban, Physical and Chemical Methods of Sugar Analysis (Wiley, 1941).

N. G. Khlebtsov, I. L. Maksimova, V. V. Tuchin, and L. Wang, “Introduction to light scattering by biological objects,” in Handbook of Optical Biomedical Diagnostics, Vol. PM107 of SPIE Press Monographs (SPIE, 2002), pp. 31–167.

V. V. Tuchin, L. Wang, and D. A. Zimnyakov, Optical Polarization in Biomedical Applications (Springer-Verlag, 2006).

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Figures (4)

Fig. 1
Fig. 1

Reflection and transmission of plane waves incident on an optically active slab of thickness d.

Fig. 2
Fig. 2

Function F = T 01 H H T 10 V V tan 2 ( θ 1 ) as function of the angle of incidence θ 0 . The constant parameter is the refractive index.

Fig. 3
Fig. 3

Excitation of lateral waves over an optically active medium.

Fig. 4
Fig. 4

Excitation of guided surface waves over an optically active medium.

Equations (85)

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R = R 10 + T 01 [ 1 P L R 01 P L R 01 ] 1 P L R 01 P L T 10 ,
T = T 01 [ 1 P L R 01 P L R 01 ] 1 P L T 10 .
R 10 = ( R 10 V V 0 0 R 10 H H ) , T = ( T 10 V V 0 0 R 0 H H ) .
P L = ( e j u 1 d 0 0 e j u 1 d ) = e j u 1 d I .
u 1 = ( k 1 2 q 2 ) 1 2 = k 1 cos ( θ 1 ) , q = k 0 sin ( θ 0 ) = k 1 sin ( θ 1 ) , ( Im ( u 1 ) < 0 ) .
k 0 = ω ( μ 0 ε 0 ) 1 2 and k 1 = ω ( μ 1 ε 1 ) 1 2 .
R c = R 10 c + T 01 c [ 1 P c R 01 c P c R 01 c ] 1 P c R 01 c P c T 10 c ,
T c = T 01 c [ 1 P c R 01 c P c R 01 c ] 1 P c T 10 c .
R L = A 1 R c A , T L = A 1 T c A .
A = [ 1 j 1 j ] , A 1 = 1 2 [ 1 1 j j ] .
P c = ( e j u 1 R d 0 0 e j u 1 L d ) .
u 1 R = [ ( γ 1 R ) 2 q 2 ] 1 2 , u 1 L = [ ( γ 1 L ) 2 q 2 ] 1 2 .
γ 1 R = k 1 1 k 1 β 1 , γ 1 L = k 1 1 + k 1 β 1 .
R L = R 10 L + T 01 L [ I P T R 01 L P T R 01 L ] 1 P T R 01 L P T T 10 L ,
T L = T 01 L [ 1 P T R 01 L P T R 01 L ] 1 P T T 01 L .
R 10 L = ( R 10 V V R 10 V H R 10 H V R 10 H H ) and T 10 L = ( T 10 V V T 10 V H T 10 H V T 10 H H ) .
R 10 V H = j k 1 β 1 R L L = j 2 k 1 β 1 T 01 H H T 10 V V tan 2 θ 1 = j 2 k 1 β 1 F = R 10 H V .
T 01 H H T 10 V V = T 01 V V T 10 H H = 4 cos ( θ 0 ) cos ( θ 1 ) { Y 0 cos ( θ 0 ) + Y 1 cos ( θ 1 ) } { Z 0 cos ( θ 0 ) + Z 1 cos ( θ 1 ) } .
Z 0 = ( μ 0 0 ) 1 2 = 1 Y 0 and Z 1 = ( μ 1 1 ) 1 2 = 1 Y 1 .
T V H = T H V ( Z 1 Z 0 ) = R V H = R H V .
P T = A 1 P c A = e j u d ( C S S C ) .
u = u 1 R + u 1 L 2 ,
u 1 R = [ ( γ 1 R ) 2 q 2 ] 1 2 , u 1 L = [ ( γ 2 L ) 2 q 2 ] 1 2 , Im ( u 1 P ) < 0 , P = R , L ,
C = cos { ( u 1 L u 1 R ) d 2 } = cos ( θ ) , S = sin { ( u 1 L u 1 R ) d 2 } = sin ( θ ) .
θ = ( a + j b ) .
a = Re ( u 1 L u 1 R ) d 2 and b = Im ( u 1 L u 1 R ) d 2 ,
tan ( θ ) = tan ( a ) + j tanh ( b ) 1 j tan ( a ) tanh ( b ) .
tan ( θ ) tan ( a ) + j tanh ( b ) .
R = P T R 01 L P T R 01 L = e j 2 u d ( C R 01 V V + S R 01 H V C R 01 V H + S R 01 H H S R 01 V V + C R 01 H V S R 01 V H + C R 01 H H ) 2 .
R = e j 2 γ 1 d R 01 2 ( C S S C ) ( C S S C ) = e j 2 γ 1 d R 01 2 I .
P T R 01 L P L R 01 L = e j 2 u d ( C R 01 V V + S R 01 H V C R 01 V H + S R 01 H H S R 01 V V + C R 01 H V S R 01 V H + C R 01 H H ) ( C T 10 V V + S T 10 H V C T 10 V H + S T 10 H H S T 10 V V + C T 10 H V S T 10 V H + C T 10 H H ) .
R L = [ 1 T 01 T 10 e j 2 γ 1 d ] [ 1 e j 2 γ 1 d R 01 2 ] 1 [ R 10 0 0 R 10 ] ,
T L = [ T 01 T 10 e j γ 1 d ] [ 1 e j 2 γ 1 d R 01 2 ] 1 [ C S S C ] .
[ 1 R ] 1 = I + R + + R n + = [ 1 + e j 2 γ 1 d R 01 2 + + e j 2 n γ 1 d R 01 2 n + ] I ,
R 01 = ( Z 1 Z 0 ) ( Z 0 + Z 1 ) , T 01 T 10 = 4 Z 0 Z 1 ( Z 0 + Z 1 ) 2 .
R L = ( 1 T 01 T 10 e j 2 γ 1 d ) [ R 10 0 0 R 10 ] ,
T L = T 01 T 10 e j γ 1 d [ c s s c ] .
E r = ( E r V E r H ) = R L ( 1 0 ) = [ 1 T 01 T 10 R 01 2 e j 2 γ 1 d ] ( R 10 0 ) ,
E t = ( E t V E t H ) = T 01 T 10 e j γ 1 d [ c s ] .
1 d [ tan Ψ = tanh b ] Ψ d b d .
M = [ M T L M T R M B L M B R ] .
M T L = 1 2 [ | R H H | 2 + | R V V | 2 | R H H | 2 | R V V | 2 | R H H | 2 | R V V | 2 | R H H | 2 + | R V V | 2 ] = [ m 11 m 12 m 21 m 22 ] ,
M B R = [ Re [ R V V R H H * ] Im [ R V V R H H * ] Im [ R V V R H H * ] Re [ R V V R H H * ] ] = [ m 33 m 34 m 43 m 44 ] ,
M B L = [ Re [ ( R H H R V V ) R H V * ] Re [ ( R H H + R V V ) R H V * ] Im [ ( R H H + R V V ) R H V * ] Im [ ( R H H R V V ) R H V * ] ] = [ m 31 m 32 m 41 m 42 ] ,
M T R = [ Re [ ( R H H R V V ) R H V * ] Im [ ( R H H + R V V ) R H V * ] Re [ ( R H H + R V V ) R H V * ] Im [ ( R H H R V V ) R H V * ] ] = [ m 13 m 14 m 23 m 24 ] .
M = M Δ M R M D .
ψ = tan 1 ( m R 32 m R 23 m R 22 + m R 33 ) .
D = 1 m D 11 [ m D 12 2 + m D 13 2 + m D 14 2 ] 1 / 2 .
Δ = 1 | tr ( M Δ ) 1 | 3 .
( γ 1 R γ 1 L ) 2 k 1 2 β 1 = k 0 [ ( n r R n r L ) j ( n i R n i L ) ] 2 = O R + j C D .
O R + j C D = 2 k 1 ( m 14 + j m 23 ) ( R 10 H H + R 10 V V ) F ,
O R + j C D = 2 k 1 ( m 24 + j m 13 ) ( R 10 H H R 10 V V ) F .
F = T 01 H H T 10 V V ( tan θ 1 ) 2 .
R = R V V R H H = | R V V R H H | e [ j ( Φ V V Φ H H ) ] = tan ( Ψ ) e j δ .
Ψ = 1 2 cos 1 ( m 12 + m 21 m 11 + m 22 ) ,
δ = tan 1 ( m 43 m 34 m 33 + m 44 ) .
Δ = | R 10 V H | = | m 14 + j m 23 | | R 10 H H + R 10 V V | = ( m 14 2 + m 23 2 ) 1 2 | R 10 H H + R 10 V V | = DCR 2 .
Δ = ( m 14 2 + m 23 2 ) 1 2 2 = DCR 2 .
u 1 R = [ ( γ 1 R ) 2 q 2 ] 1 2 and u 1 L = [ ( γ 1 L ) 2 q 2 ] 1 2 .
E r c = [ E r R E r L ] = P 1 c T 1 c P L c T 0 c P 0 c [ E i R E i L ] .
P k c = ( e j k 0 L k 0 0 e j k 0 L k ) = e j k 0 L k I , k = 0 , 1.
P L c = ( e j γ 1 R L 0 0 e j γ 1 L L ) .
T k c = ( T k R R T k R L T k L R T k L L ) , k = 0 , 1.
E r L = [ E r V E r V ] = P 1 c T 1 c P L c T 0 c P 0 c [ E i V E i H ] .
P k L = P k c = A 1 P k c A = P k c , k = 0 , 1.
P L L = P L c = A 1 P L c A ,
T k L = T K c = A 1 T k c A = ( T k V V T k V H T k H V T k H H ) , k = 0 , 1.
q R = k 0 sin ( θ 0 R ) = γ 1 R sin ( θ 1 R ) = γ 1 R ,
q L = k 0 sin ( θ 0 L ) = γ 1 L sin ( θ 1 L ) = γ 1 L .
O R + j C D = k 1 2 β 1 = γ 1 R γ 1 L 2 .
E r L = [ E r V E r H ] = P 1 L R L P 0 L [ E i V E i H ] .
P m L = ( e j k 0 L m 0 0 e j k 0 L m ) , m = 0 , 1 ,
E r s L = [ E r s V E r s H ] = P 1 P P s P R s L P 0 P [ E i s V E s i H ] .
P k P = ( e j k 0 L k 0 0 e j k 0 L k ) , k = 0 , 1.
P s P = ( e j q V L L 0 0 e j q H L L ) .
q V = k 1 [ Y r 2 1 ] [ 1 ε r 2 ] 1 2 1 2 , q H = k 1 [ Z r 2 1 ] 1 2 [ 1 μ r 2 ] 1 2 .
R S L = 2 π i ( Res ( R 0 V V / q ) Res ( R 0 V H / q ) Res ( R 0 H V / q ) Res ( R 0 H H / q ) ) .
Res ( R 0 V V / q ) = 2 u 0 2 ( q V ) 2 [ 1 ( 0 1 ) 2 ] ,
Res ( R 0 H H / q ) = 2 u 0 2 ( q H ) 2 [ 1 ( μ 0 μ 1 ) 2 ] .
Res ( R 0 V H / q ) = Res ( R 0 H V q ) = j 2 k 1 β 1 Res F / q = j k 1 β 1 ( 1 η r 2 ) [ 1 r 2 1 + 1 1 μ r 2 ] .
u 0 P = { k 0 2 ( q P ) 2 } 1 2 = j [ ( q P ) 2 k 0 2 ] 1 2 , p = V , H .
P s P = ( e [ j q V | x x | 0 0 e [ j q H | x x | ) ,
P 0 P = ( e [ { ( q V ) 2 k 0 2 } 1 2 ] y 0 0 e [ { ( q H ) 2 k 0 2 } 1 2 ] y ) ,
P 0 P = ( e [ { ( q V ) 2 k 0 2 } 1 2 ] y 0 0 e [ { ( q H ) 2 k 0 2 } 1 2 ] y ) .
O R + j C D = k 1 2 β 1 = Res ( R 0 V H / q ) ( 1 η r 2 ) 2 j k 1 / [ 1 r 2 1 + 1 ( 1 μ r 2 ) ] .

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