Abstract

We describe a novel polarization interferometer which permits the determination of the refractive indices for circularly-polarized light. It is based on a Jamin-Lebedeff interferometer, modified with waveplates, and permits us to experimentally determine the refractive indices nL and nR of the respectively left- and right-circularly polarized modes in a cholesteric liquid crystal. Whereas optical rotation measurements only determine the circular birefringence, i.e. the difference (nL – nR), the interferometer also permits the determination of their absolute values. We report refractive indices of a cholesteric liquid crystal in the region of selective (Bragg) reflection as a function of temperature.

© 2014 Optical Society of America

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References

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    [Crossref]
  4. R. Fleischmann, “Interferenzverfahren zur Messung der absoluten Phasen bei der Untersuchung absorbierender Medien,” Z. Phys. 29, 275–284 (1950).
  5. S. B. Mehta and C. J. R. Sheppard, “Partially coherent image formation in differential interference contrast (DIC) microscope,” Opt. Express 16(24), 19462–19479 (2008).
    [Crossref] [PubMed]
  6. F. J. Schaefer and W. Kleemann, “High-precision refractive index measurements revealing order parameter fluctuations in KMnF3 and NiO,” J. Appl. Phys. 57(7), 2606 (1985).
    [Crossref]
  7. A. F. Brown and G. A. Dunn, “Microinterferometry of the movement of dry matter in fibroblasts,” J. Cell Sci. 92(Pt 3), 379–389 (1989).
    [PubMed]
  8. Z. Kam, “Microscopic imaging of cells,” Q. Rev. Biophys. 20(3-4), 201–259 (1987).
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  9. V. P. Drachev, W. Cai, U. Chettiar, H. K. Yuan, A. K. Sarychev, A. V. Kildishev, G. Klimeck, and V. M. Shalaev, “Experimental verification of an optical negative refractive-index material,” Laser Phys. Lett. 3(1), 49–55 (2006).
    [Crossref]
  10. Z.-C. Jian, J.-Y. Lin, P.-J. Hsieh, and D.-C. Su, “Measurements of material refractive index with a circular heterodyne interferometer,” Proc. SPIE 5856, 882–892 (2005).
    [Crossref]
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  23. H. Stegemeyer and K.-J. Mainusch, “Optical rotatory power of liquid crystal mixtures,” Chem. Phys. Lett. 6(1), 5–6 (1970).
    [Crossref]
  24. L. Melamed and D. Rubin, “Selected Optical Properties of Mixtures of Cholesteric Liquid Crystals,” Appl. Opt. 10(5), 1103–1107 (1971).
    [Crossref] [PubMed]
  25. R. D. Ennulat, “The selective light reflection by plane textures,” Mol Crys. Liq. Cryst. 13(4), 337–355 (1971).
    [Crossref]
  26. C. Kim, K. L. Marshall, J. U. Wallace, and S. H. Chen, “Photochromic glassy liquid crystals comprising mesogenic pendants to dithienylethene cores,” J. Mater. Chem. 18(46), 5592 (2008).
    [Crossref]
  27. N. Bitri, A. Gharbi, and J. P. Marcerou, “Scanning conoscopy measurement of the optical properties of chiral smectic liquid crystals,” Phys. B 403(21–22), 3921–3927 (2008).
    [Crossref]
  28. A. S. Sonin, A. V. Tolmachev, V. G. Tishchenko, and V. G. Rak, “Optical activity of the planar texture of a number of cholesterol esters,” Sov. Phys. JETP 41(5), 977 (1976).
  29. F. Beaubois, J. P. Marceroua, H. T. Nguyen, and J. C. Rouillon, “Optical rotatory power in tilted smectic phases,” Eur. Phys. J. E 3(3), 273–281 (2000).
    [Crossref]
  30. P. E. Sokol and J. T. Ho, “Optical rotatory power near a cholesteric–smectic A transition,” Appl. Phys. Lett. 31(8), 487 (1977).
    [Crossref]
  31. M. Evans, R. Moutran, and A. H. Price, “Dielectric properties, refractive index and far infrared spectrum of cholesteryl oleyl carbonate,” J. Chem. Soc., Faraday Trans. II 71, 1854–1862 (1975).
    [Crossref]
  32. H. S. Tai and J. Y. Lee, “Phase transition behaviors and selective optical properties of a binary cholesteric liquid crystals system: Mixtures of cholesteryl carbonate and cholesteryl nananoate,” J. Appl. Phys. 67(2), 1001–1006 (1990).
    [Crossref]
  33. R. Somashekar and D. Krishnamurti, “Optical anisotropy of cholesteryl oleyl carbonate,” Mol. Crys. Liq. Cryst. 84(1), 31–37 (1982).
    [Crossref]
  34. M. Goh, S. Matsushita, and K. Akagi, “From helical polyacetylene to helical graphite: synthesis in the chiral nematic liquid crystal field and morphology-retaining carbonisation,” Chem. Soc. Rev. 39(7), 2466–2476 (2010).
    [Crossref] [PubMed]
  35. D. K. Yang, X. Y. Huang, and Y. M. Zhu, “Bistable cholesteric reflective displays: Materials and drive schemes,” Annu. Rev. Mater. Sci. 27(1), 117–146 (1997).
    [Crossref]
  36. C. Bohley and T. Scharf, “Depolarization effects of light reflected by domain-structured cholesteric liquid crystal,” Opt. Commun. 214(1-6), 193–198 (2002).
    [Crossref]

2013 (1)

D. G. Stavenga, H. L. Leertouwer, and B. D. Wilts, “Quantifying the refractive index dispersion of a pigmented biological tissue using Jamin–Lebedeff interference microscopy,” Light: Sci. Appl. 2(9), e100 (2013).
[Crossref]

2011 (2)

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, J. A. Rayas-Álvarez, and G. Rodríguez-Zurita, “Simultaneous phase shifting interferometry based in a Mach-Zehnder interferometer for measurement of transparent samples,” Proc. SPIE 8011, 80110M (2011).
[Crossref]

M. Pfeifer and P. Fischer, “Weak value amplified optical activity measurements,” Opt. Express 19(17), 16508–16517 (2011).
[Crossref] [PubMed]

2010 (1)

M. Goh, S. Matsushita, and K. Akagi, “From helical polyacetylene to helical graphite: synthesis in the chiral nematic liquid crystal field and morphology-retaining carbonisation,” Chem. Soc. Rev. 39(7), 2466–2476 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (3)

S. B. Mehta and C. J. R. Sheppard, “Partially coherent image formation in differential interference contrast (DIC) microscope,” Opt. Express 16(24), 19462–19479 (2008).
[Crossref] [PubMed]

C. Kim, K. L. Marshall, J. U. Wallace, and S. H. Chen, “Photochromic glassy liquid crystals comprising mesogenic pendants to dithienylethene cores,” J. Mater. Chem. 18(46), 5592 (2008).
[Crossref]

N. Bitri, A. Gharbi, and J. P. Marcerou, “Scanning conoscopy measurement of the optical properties of chiral smectic liquid crystals,” Phys. B 403(21–22), 3921–3927 (2008).
[Crossref]

2006 (2)

V. P. Drachev, W. Cai, U. Chettiar, H. K. Yuan, A. K. Sarychev, A. V. Kildishev, G. Klimeck, and V. M. Shalaev, “Experimental verification of an optical negative refractive-index material,” Laser Phys. Lett. 3(1), 49–55 (2006).
[Crossref]

A. Ghosh and P. Fischer, “Chiral Molecules Split Light: Reflection and Refraction in a Chiral Liquid,” Phys. Rev. Lett. 97(17), 173002 (2006).
[Crossref] [PubMed]

2005 (1)

Z.-C. Jian, J.-Y. Lin, P.-J. Hsieh, and D.-C. Su, “Measurements of material refractive index with a circular heterodyne interferometer,” Proc. SPIE 5856, 882–892 (2005).
[Crossref]

2003 (1)

2002 (1)

C. Bohley and T. Scharf, “Depolarization effects of light reflected by domain-structured cholesteric liquid crystal,” Opt. Commun. 214(1-6), 193–198 (2002).
[Crossref]

2000 (1)

F. Beaubois, J. P. Marceroua, H. T. Nguyen, and J. C. Rouillon, “Optical rotatory power in tilted smectic phases,” Eur. Phys. J. E 3(3), 273–281 (2000).
[Crossref]

1997 (1)

D. K. Yang, X. Y. Huang, and Y. M. Zhu, “Bistable cholesteric reflective displays: Materials and drive schemes,” Annu. Rev. Mater. Sci. 27(1), 117–146 (1997).
[Crossref]

1990 (1)

H. S. Tai and J. Y. Lee, “Phase transition behaviors and selective optical properties of a binary cholesteric liquid crystals system: Mixtures of cholesteryl carbonate and cholesteryl nananoate,” J. Appl. Phys. 67(2), 1001–1006 (1990).
[Crossref]

1989 (1)

A. F. Brown and G. A. Dunn, “Microinterferometry of the movement of dry matter in fibroblasts,” J. Cell Sci. 92(Pt 3), 379–389 (1989).
[PubMed]

1987 (1)

Z. Kam, “Microscopic imaging of cells,” Q. Rev. Biophys. 20(3-4), 201–259 (1987).
[Crossref] [PubMed]

1985 (1)

F. J. Schaefer and W. Kleemann, “High-precision refractive index measurements revealing order parameter fluctuations in KMnF3 and NiO,” J. Appl. Phys. 57(7), 2606 (1985).
[Crossref]

1982 (1)

R. Somashekar and D. Krishnamurti, “Optical anisotropy of cholesteryl oleyl carbonate,” Mol. Crys. Liq. Cryst. 84(1), 31–37 (1982).
[Crossref]

1979 (1)

V. A. Belyakov, V. E. Dmitrienko, and V. P. Orlov, “Optics of cholesteric liquid crystals,” Sov. Phys. Usp. 22(2), 64–88 (1979).
[Crossref]

1977 (1)

P. E. Sokol and J. T. Ho, “Optical rotatory power near a cholesteric–smectic A transition,” Appl. Phys. Lett. 31(8), 487 (1977).
[Crossref]

1976 (1)

A. S. Sonin, A. V. Tolmachev, V. G. Tishchenko, and V. G. Rak, “Optical activity of the planar texture of a number of cholesterol esters,” Sov. Phys. JETP 41(5), 977 (1976).

1975 (1)

M. Evans, R. Moutran, and A. H. Price, “Dielectric properties, refractive index and far infrared spectrum of cholesteryl oleyl carbonate,” J. Chem. Soc., Faraday Trans. II 71, 1854–1862 (1975).
[Crossref]

1971 (2)

L. Melamed and D. Rubin, “Selected Optical Properties of Mixtures of Cholesteric Liquid Crystals,” Appl. Opt. 10(5), 1103–1107 (1971).
[Crossref] [PubMed]

R. D. Ennulat, “The selective light reflection by plane textures,” Mol Crys. Liq. Cryst. 13(4), 337–355 (1971).
[Crossref]

1970 (1)

H. Stegemeyer and K.-J. Mainusch, “Optical rotatory power of liquid crystal mixtures,” Chem. Phys. Lett. 6(1), 5–6 (1970).
[Crossref]

1968 (1)

S. Chandrasekhar and K. N. Rao, “Optical Rotatory Power of Liquid Crystals,” Acta Crystallogr. A 24(4), 445–451 (1968).
[Crossref]

1951 (1)

H. L. de Vries, “Rotatory Power and Other Optical Properties of Certain Liquid Crystals,” Acta Crystallogr. 4(3), 219–226 (1951).
[Crossref]

1950 (1)

R. Fleischmann, “Interferenzverfahren zur Messung der absoluten Phasen bei der Untersuchung absorbierender Medien,” Z. Phys. 29, 275–284 (1950).

1856 (1)

Jamin, “Neuer interferential-refractor,” Ann. Phys. Chem. 174(6), 345–349 (1856).
[Crossref]

Akagi, K.

M. Goh, S. Matsushita, and K. Akagi, “From helical polyacetylene to helical graphite: synthesis in the chiral nematic liquid crystal field and morphology-retaining carbonisation,” Chem. Soc. Rev. 39(7), 2466–2476 (2010).
[Crossref] [PubMed]

Beaubois, F.

F. Beaubois, J. P. Marceroua, H. T. Nguyen, and J. C. Rouillon, “Optical rotatory power in tilted smectic phases,” Eur. Phys. J. E 3(3), 273–281 (2000).
[Crossref]

Belyakov, V. A.

V. A. Belyakov, V. E. Dmitrienko, and V. P. Orlov, “Optics of cholesteric liquid crystals,” Sov. Phys. Usp. 22(2), 64–88 (1979).
[Crossref]

Bitri, N.

N. Bitri, A. Gharbi, and J. P. Marcerou, “Scanning conoscopy measurement of the optical properties of chiral smectic liquid crystals,” Phys. B 403(21–22), 3921–3927 (2008).
[Crossref]

Bohley, C.

C. Bohley and T. Scharf, “Depolarization effects of light reflected by domain-structured cholesteric liquid crystal,” Opt. Commun. 214(1-6), 193–198 (2002).
[Crossref]

Brown, A. F.

A. F. Brown and G. A. Dunn, “Microinterferometry of the movement of dry matter in fibroblasts,” J. Cell Sci. 92(Pt 3), 379–389 (1989).
[PubMed]

Cai, W.

V. P. Drachev, W. Cai, U. Chettiar, H. K. Yuan, A. K. Sarychev, A. V. Kildishev, G. Klimeck, and V. M. Shalaev, “Experimental verification of an optical negative refractive-index material,” Laser Phys. Lett. 3(1), 49–55 (2006).
[Crossref]

Chandrasekhar, S.

S. Chandrasekhar and K. N. Rao, “Optical Rotatory Power of Liquid Crystals,” Acta Crystallogr. A 24(4), 445–451 (1968).
[Crossref]

Chen, S. H.

C. Kim, K. L. Marshall, J. U. Wallace, and S. H. Chen, “Photochromic glassy liquid crystals comprising mesogenic pendants to dithienylethene cores,” J. Mater. Chem. 18(46), 5592 (2008).
[Crossref]

Chettiar, U.

V. P. Drachev, W. Cai, U. Chettiar, H. K. Yuan, A. K. Sarychev, A. V. Kildishev, G. Klimeck, and V. M. Shalaev, “Experimental verification of an optical negative refractive-index material,” Laser Phys. Lett. 3(1), 49–55 (2006).
[Crossref]

Chou, C.

Davis, J. A.

de Vries, H. L.

H. L. de Vries, “Rotatory Power and Other Optical Properties of Certain Liquid Crystals,” Acta Crystallogr. 4(3), 219–226 (1951).
[Crossref]

Dmitrienko, V. E.

V. A. Belyakov, V. E. Dmitrienko, and V. P. Orlov, “Optics of cholesteric liquid crystals,” Sov. Phys. Usp. 22(2), 64–88 (1979).
[Crossref]

Drachev, V. P.

V. P. Drachev, W. Cai, U. Chettiar, H. K. Yuan, A. K. Sarychev, A. V. Kildishev, G. Klimeck, and V. M. Shalaev, “Experimental verification of an optical negative refractive-index material,” Laser Phys. Lett. 3(1), 49–55 (2006).
[Crossref]

Dunn, G. A.

A. F. Brown and G. A. Dunn, “Microinterferometry of the movement of dry matter in fibroblasts,” J. Cell Sci. 92(Pt 3), 379–389 (1989).
[PubMed]

Ennulat, R. D.

R. D. Ennulat, “The selective light reflection by plane textures,” Mol Crys. Liq. Cryst. 13(4), 337–355 (1971).
[Crossref]

Evans, M.

M. Evans, R. Moutran, and A. H. Price, “Dielectric properties, refractive index and far infrared spectrum of cholesteryl oleyl carbonate,” J. Chem. Soc., Faraday Trans. II 71, 1854–1862 (1975).
[Crossref]

Fischer, P.

M. Pfeifer and P. Fischer, “Weak value amplified optical activity measurements,” Opt. Express 19(17), 16508–16517 (2011).
[Crossref] [PubMed]

A. Ghosh and P. Fischer, “Chiral Molecules Split Light: Reflection and Refraction in a Chiral Liquid,” Phys. Rev. Lett. 97(17), 173002 (2006).
[Crossref] [PubMed]

Fleischmann, R.

R. Fleischmann, “Interferenzverfahren zur Messung der absoluten Phasen bei der Untersuchung absorbierender Medien,” Z. Phys. 29, 275–284 (1950).

Gharbi, A.

N. Bitri, A. Gharbi, and J. P. Marcerou, “Scanning conoscopy measurement of the optical properties of chiral smectic liquid crystals,” Phys. B 403(21–22), 3921–3927 (2008).
[Crossref]

Ghosh, A.

A. Ghosh and P. Fischer, “Chiral Molecules Split Light: Reflection and Refraction in a Chiral Liquid,” Phys. Rev. Lett. 97(17), 173002 (2006).
[Crossref] [PubMed]

Goh, M.

M. Goh, S. Matsushita, and K. Akagi, “From helical polyacetylene to helical graphite: synthesis in the chiral nematic liquid crystal field and morphology-retaining carbonisation,” Chem. Soc. Rev. 39(7), 2466–2476 (2010).
[Crossref] [PubMed]

Han, C. Y.

Ho, J. T.

P. E. Sokol and J. T. Ho, “Optical rotatory power near a cholesteric–smectic A transition,” Appl. Phys. Lett. 31(8), 487 (1977).
[Crossref]

Hsieh, P.-J.

Z.-C. Jian, J.-Y. Lin, P.-J. Hsieh, and D.-C. Su, “Measurements of material refractive index with a circular heterodyne interferometer,” Proc. SPIE 5856, 882–892 (2005).
[Crossref]

Huang, X. Y.

D. K. Yang, X. Y. Huang, and Y. M. Zhu, “Bistable cholesteric reflective displays: Materials and drive schemes,” Annu. Rev. Mater. Sci. 27(1), 117–146 (1997).
[Crossref]

Jamin,

Jamin, “Neuer interferential-refractor,” Ann. Phys. Chem. 174(6), 345–349 (1856).
[Crossref]

Jian, Z.-C.

Z.-C. Jian, J.-Y. Lin, P.-J. Hsieh, and D.-C. Su, “Measurements of material refractive index with a circular heterodyne interferometer,” Proc. SPIE 5856, 882–892 (2005).
[Crossref]

Kam, Z.

Z. Kam, “Microscopic imaging of cells,” Q. Rev. Biophys. 20(3-4), 201–259 (1987).
[Crossref] [PubMed]

Kildishev, A. V.

V. P. Drachev, W. Cai, U. Chettiar, H. K. Yuan, A. K. Sarychev, A. V. Kildishev, G. Klimeck, and V. M. Shalaev, “Experimental verification of an optical negative refractive-index material,” Laser Phys. Lett. 3(1), 49–55 (2006).
[Crossref]

Kim, C.

C. Kim, K. L. Marshall, J. U. Wallace, and S. H. Chen, “Photochromic glassy liquid crystals comprising mesogenic pendants to dithienylethene cores,” J. Mater. Chem. 18(46), 5592 (2008).
[Crossref]

Kleemann, W.

F. J. Schaefer and W. Kleemann, “High-precision refractive index measurements revealing order parameter fluctuations in KMnF3 and NiO,” J. Appl. Phys. 57(7), 2606 (1985).
[Crossref]

Klimeck, G.

V. P. Drachev, W. Cai, U. Chettiar, H. K. Yuan, A. K. Sarychev, A. V. Kildishev, G. Klimeck, and V. M. Shalaev, “Experimental verification of an optical negative refractive-index material,” Laser Phys. Lett. 3(1), 49–55 (2006).
[Crossref]

Krishnamurti, D.

R. Somashekar and D. Krishnamurti, “Optical anisotropy of cholesteryl oleyl carbonate,” Mol. Crys. Liq. Cryst. 84(1), 31–37 (1982).
[Crossref]

Kuo, W.-C.

Lee, J. Y.

H. S. Tai and J. Y. Lee, “Phase transition behaviors and selective optical properties of a binary cholesteric liquid crystals system: Mixtures of cholesteryl carbonate and cholesteryl nananoate,” J. Appl. Phys. 67(2), 1001–1006 (1990).
[Crossref]

Leertouwer, H. L.

D. G. Stavenga, H. L. Leertouwer, and B. D. Wilts, “Quantifying the refractive index dispersion of a pigmented biological tissue using Jamin–Lebedeff interference microscopy,” Light: Sci. Appl. 2(9), e100 (2013).
[Crossref]

Lin, J.-Y.

Z.-C. Jian, J.-Y. Lin, P.-J. Hsieh, and D.-C. Su, “Measurements of material refractive index with a circular heterodyne interferometer,” Proc. SPIE 5856, 882–892 (2005).
[Crossref]

Mainusch, K.-J.

H. Stegemeyer and K.-J. Mainusch, “Optical rotatory power of liquid crystal mixtures,” Chem. Phys. Lett. 6(1), 5–6 (1970).
[Crossref]

Marcerou, J. P.

N. Bitri, A. Gharbi, and J. P. Marcerou, “Scanning conoscopy measurement of the optical properties of chiral smectic liquid crystals,” Phys. B 403(21–22), 3921–3927 (2008).
[Crossref]

Marceroua, J. P.

F. Beaubois, J. P. Marceroua, H. T. Nguyen, and J. C. Rouillon, “Optical rotatory power in tilted smectic phases,” Eur. Phys. J. E 3(3), 273–281 (2000).
[Crossref]

Marshall, K. L.

C. Kim, K. L. Marshall, J. U. Wallace, and S. H. Chen, “Photochromic glassy liquid crystals comprising mesogenic pendants to dithienylethene cores,” J. Mater. Chem. 18(46), 5592 (2008).
[Crossref]

Martínez-García, A.

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, J. A. Rayas-Álvarez, and G. Rodríguez-Zurita, “Simultaneous phase shifting interferometry based in a Mach-Zehnder interferometer for measurement of transparent samples,” Proc. SPIE 8011, 80110M (2011).
[Crossref]

Matsushita, S.

M. Goh, S. Matsushita, and K. Akagi, “From helical polyacetylene to helical graphite: synthesis in the chiral nematic liquid crystal field and morphology-retaining carbonisation,” Chem. Soc. Rev. 39(7), 2466–2476 (2010).
[Crossref] [PubMed]

Mehta, S. B.

Melamed, L.

Moreno, I.

Moutran, R.

M. Evans, R. Moutran, and A. H. Price, “Dielectric properties, refractive index and far infrared spectrum of cholesteryl oleyl carbonate,” J. Chem. Soc., Faraday Trans. II 71, 1854–1862 (1975).
[Crossref]

Nava-Vega, A.

Nguyen, H. T.

F. Beaubois, J. P. Marceroua, H. T. Nguyen, and J. C. Rouillon, “Optical rotatory power in tilted smectic phases,” Eur. Phys. J. E 3(3), 273–281 (2000).
[Crossref]

Orlov, V. P.

V. A. Belyakov, V. E. Dmitrienko, and V. P. Orlov, “Optics of cholesteric liquid crystals,” Sov. Phys. Usp. 22(2), 64–88 (1979).
[Crossref]

Pascoguin, B. M. L.

Pfeifer, M.

Price, A. H.

M. Evans, R. Moutran, and A. H. Price, “Dielectric properties, refractive index and far infrared spectrum of cholesteryl oleyl carbonate,” J. Chem. Soc., Faraday Trans. II 71, 1854–1862 (1975).
[Crossref]

Rak, V. G.

A. S. Sonin, A. V. Tolmachev, V. G. Tishchenko, and V. G. Rak, “Optical activity of the planar texture of a number of cholesterol esters,” Sov. Phys. JETP 41(5), 977 (1976).

Rao, K. N.

S. Chandrasekhar and K. N. Rao, “Optical Rotatory Power of Liquid Crystals,” Acta Crystallogr. A 24(4), 445–451 (1968).
[Crossref]

Rayas-Álvarez, J. A.

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, J. A. Rayas-Álvarez, and G. Rodríguez-Zurita, “Simultaneous phase shifting interferometry based in a Mach-Zehnder interferometer for measurement of transparent samples,” Proc. SPIE 8011, 80110M (2011).
[Crossref]

Rodríguez-Zurita, G.

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, J. A. Rayas-Álvarez, and G. Rodríguez-Zurita, “Simultaneous phase shifting interferometry based in a Mach-Zehnder interferometer for measurement of transparent samples,” Proc. SPIE 8011, 80110M (2011).
[Crossref]

Rouillon, J. C.

F. Beaubois, J. P. Marceroua, H. T. Nguyen, and J. C. Rouillon, “Optical rotatory power in tilted smectic phases,” Eur. Phys. J. E 3(3), 273–281 (2000).
[Crossref]

Rubin, D.

Sarychev, A. K.

V. P. Drachev, W. Cai, U. Chettiar, H. K. Yuan, A. K. Sarychev, A. V. Kildishev, G. Klimeck, and V. M. Shalaev, “Experimental verification of an optical negative refractive-index material,” Laser Phys. Lett. 3(1), 49–55 (2006).
[Crossref]

Schaefer, F. J.

F. J. Schaefer and W. Kleemann, “High-precision refractive index measurements revealing order parameter fluctuations in KMnF3 and NiO,” J. Appl. Phys. 57(7), 2606 (1985).
[Crossref]

Scharf, T.

C. Bohley and T. Scharf, “Depolarization effects of light reflected by domain-structured cholesteric liquid crystal,” Opt. Commun. 214(1-6), 193–198 (2002).
[Crossref]

Serrano-García, D.-I.

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, J. A. Rayas-Álvarez, and G. Rodríguez-Zurita, “Simultaneous phase shifting interferometry based in a Mach-Zehnder interferometer for measurement of transparent samples,” Proc. SPIE 8011, 80110M (2011).
[Crossref]

Shalaev, V. M.

V. P. Drachev, W. Cai, U. Chettiar, H. K. Yuan, A. K. Sarychev, A. V. Kildishev, G. Klimeck, and V. M. Shalaev, “Experimental verification of an optical negative refractive-index material,” Laser Phys. Lett. 3(1), 49–55 (2006).
[Crossref]

Sheppard, C. J. R.

Sokol, P. E.

P. E. Sokol and J. T. Ho, “Optical rotatory power near a cholesteric–smectic A transition,” Appl. Phys. Lett. 31(8), 487 (1977).
[Crossref]

Somashekar, R.

R. Somashekar and D. Krishnamurti, “Optical anisotropy of cholesteryl oleyl carbonate,” Mol. Crys. Liq. Cryst. 84(1), 31–37 (1982).
[Crossref]

Sonin, A. S.

A. S. Sonin, A. V. Tolmachev, V. G. Tishchenko, and V. G. Rak, “Optical activity of the planar texture of a number of cholesterol esters,” Sov. Phys. JETP 41(5), 977 (1976).

Stavenga, D. G.

D. G. Stavenga, H. L. Leertouwer, and B. D. Wilts, “Quantifying the refractive index dispersion of a pigmented biological tissue using Jamin–Lebedeff interference microscopy,” Light: Sci. Appl. 2(9), e100 (2013).
[Crossref]

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H. Stegemeyer and K.-J. Mainusch, “Optical rotatory power of liquid crystal mixtures,” Chem. Phys. Lett. 6(1), 5–6 (1970).
[Crossref]

Su, D.-C.

Z.-C. Jian, J.-Y. Lin, P.-J. Hsieh, and D.-C. Su, “Measurements of material refractive index with a circular heterodyne interferometer,” Proc. SPIE 5856, 882–892 (2005).
[Crossref]

Tai, H. S.

H. S. Tai and J. Y. Lee, “Phase transition behaviors and selective optical properties of a binary cholesteric liquid crystals system: Mixtures of cholesteryl carbonate and cholesteryl nananoate,” J. Appl. Phys. 67(2), 1001–1006 (1990).
[Crossref]

Tishchenko, V. G.

A. S. Sonin, A. V. Tolmachev, V. G. Tishchenko, and V. G. Rak, “Optical activity of the planar texture of a number of cholesterol esters,” Sov. Phys. JETP 41(5), 977 (1976).

Tolmachev, A. V.

A. S. Sonin, A. V. Tolmachev, V. G. Tishchenko, and V. G. Rak, “Optical activity of the planar texture of a number of cholesterol esters,” Sov. Phys. JETP 41(5), 977 (1976).

Toto-Arellano, N.-I.

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, J. A. Rayas-Álvarez, and G. Rodríguez-Zurita, “Simultaneous phase shifting interferometry based in a Mach-Zehnder interferometer for measurement of transparent samples,” Proc. SPIE 8011, 80110M (2011).
[Crossref]

Wallace, J. U.

C. Kim, K. L. Marshall, J. U. Wallace, and S. H. Chen, “Photochromic glassy liquid crystals comprising mesogenic pendants to dithienylethene cores,” J. Mater. Chem. 18(46), 5592 (2008).
[Crossref]

Wilts, B. D.

D. G. Stavenga, H. L. Leertouwer, and B. D. Wilts, “Quantifying the refractive index dispersion of a pigmented biological tissue using Jamin–Lebedeff interference microscopy,” Light: Sci. Appl. 2(9), e100 (2013).
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Yuan, H. K.

V. P. Drachev, W. Cai, U. Chettiar, H. K. Yuan, A. K. Sarychev, A. V. Kildishev, G. Klimeck, and V. M. Shalaev, “Experimental verification of an optical negative refractive-index material,” Laser Phys. Lett. 3(1), 49–55 (2006).
[Crossref]

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D. K. Yang, X. Y. Huang, and Y. M. Zhu, “Bistable cholesteric reflective displays: Materials and drive schemes,” Annu. Rev. Mater. Sci. 27(1), 117–146 (1997).
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H. L. de Vries, “Rotatory Power and Other Optical Properties of Certain Liquid Crystals,” Acta Crystallogr. 4(3), 219–226 (1951).
[Crossref]

Acta Crystallogr. A (1)

S. Chandrasekhar and K. N. Rao, “Optical Rotatory Power of Liquid Crystals,” Acta Crystallogr. A 24(4), 445–451 (1968).
[Crossref]

Ann. Phys. Chem. (1)

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[Crossref]

Annu. Rev. Mater. Sci. (1)

D. K. Yang, X. Y. Huang, and Y. M. Zhu, “Bistable cholesteric reflective displays: Materials and drive schemes,” Annu. Rev. Mater. Sci. 27(1), 117–146 (1997).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

P. E. Sokol and J. T. Ho, “Optical rotatory power near a cholesteric–smectic A transition,” Appl. Phys. Lett. 31(8), 487 (1977).
[Crossref]

Chem. Phys. Lett. (1)

H. Stegemeyer and K.-J. Mainusch, “Optical rotatory power of liquid crystal mixtures,” Chem. Phys. Lett. 6(1), 5–6 (1970).
[Crossref]

Chem. Soc. Rev. (1)

M. Goh, S. Matsushita, and K. Akagi, “From helical polyacetylene to helical graphite: synthesis in the chiral nematic liquid crystal field and morphology-retaining carbonisation,” Chem. Soc. Rev. 39(7), 2466–2476 (2010).
[Crossref] [PubMed]

Eur. Phys. J. E (1)

F. Beaubois, J. P. Marceroua, H. T. Nguyen, and J. C. Rouillon, “Optical rotatory power in tilted smectic phases,” Eur. Phys. J. E 3(3), 273–281 (2000).
[Crossref]

J. Appl. Phys. (2)

H. S. Tai and J. Y. Lee, “Phase transition behaviors and selective optical properties of a binary cholesteric liquid crystals system: Mixtures of cholesteryl carbonate and cholesteryl nananoate,” J. Appl. Phys. 67(2), 1001–1006 (1990).
[Crossref]

F. J. Schaefer and W. Kleemann, “High-precision refractive index measurements revealing order parameter fluctuations in KMnF3 and NiO,” J. Appl. Phys. 57(7), 2606 (1985).
[Crossref]

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J. Mater. Chem. (1)

C. Kim, K. L. Marshall, J. U. Wallace, and S. H. Chen, “Photochromic glassy liquid crystals comprising mesogenic pendants to dithienylethene cores,” J. Mater. Chem. 18(46), 5592 (2008).
[Crossref]

Laser Phys. Lett. (1)

V. P. Drachev, W. Cai, U. Chettiar, H. K. Yuan, A. K. Sarychev, A. V. Kildishev, G. Klimeck, and V. M. Shalaev, “Experimental verification of an optical negative refractive-index material,” Laser Phys. Lett. 3(1), 49–55 (2006).
[Crossref]

Light: Sci. Appl. (1)

D. G. Stavenga, H. L. Leertouwer, and B. D. Wilts, “Quantifying the refractive index dispersion of a pigmented biological tissue using Jamin–Lebedeff interference microscopy,” Light: Sci. Appl. 2(9), e100 (2013).
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R. D. Ennulat, “The selective light reflection by plane textures,” Mol Crys. Liq. Cryst. 13(4), 337–355 (1971).
[Crossref]

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R. Somashekar and D. Krishnamurti, “Optical anisotropy of cholesteryl oleyl carbonate,” Mol. Crys. Liq. Cryst. 84(1), 31–37 (1982).
[Crossref]

Opt. Commun. (1)

C. Bohley and T. Scharf, “Depolarization effects of light reflected by domain-structured cholesteric liquid crystal,” Opt. Commun. 214(1-6), 193–198 (2002).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. B (1)

N. Bitri, A. Gharbi, and J. P. Marcerou, “Scanning conoscopy measurement of the optical properties of chiral smectic liquid crystals,” Phys. B 403(21–22), 3921–3927 (2008).
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Phys. Rev. Lett. (1)

A. Ghosh and P. Fischer, “Chiral Molecules Split Light: Reflection and Refraction in a Chiral Liquid,” Phys. Rev. Lett. 97(17), 173002 (2006).
[Crossref] [PubMed]

Proc. SPIE (2)

Z.-C. Jian, J.-Y. Lin, P.-J. Hsieh, and D.-C. Su, “Measurements of material refractive index with a circular heterodyne interferometer,” Proc. SPIE 5856, 882–892 (2005).
[Crossref]

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, J. A. Rayas-Álvarez, and G. Rodríguez-Zurita, “Simultaneous phase shifting interferometry based in a Mach-Zehnder interferometer for measurement of transparent samples,” Proc. SPIE 8011, 80110M (2011).
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Z. Kam, “Microscopic imaging of cells,” Q. Rev. Biophys. 20(3-4), 201–259 (1987).
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A. S. Sonin, A. V. Tolmachev, V. G. Tishchenko, and V. G. Rak, “Optical activity of the planar texture of a number of cholesterol esters,” Sov. Phys. JETP 41(5), 977 (1976).

Sov. Phys. Usp. (1)

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Other (5)

M. Francon, Optical Interferometry (Academic New York and London, 1966).

P. Oswald and P. Pieranski, Nematic and Cholesteric Liquid Crystals: Concepts and Physical Properties Illustrated by Experiments (CRC Taylor & Francis Group, 2005) Chap. B VII.

P. Yeh and C. Gu, Optics of Liquid CrystalsDisplays, 2nd ed. (John Wiley & Soncs Inc, 2010) Chap 7.

S. Chandrasekhar, Liquid crystals 2nd ed. (Cambridge University, 1977) Chap 4.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals - 6th ed. (Clarendon Oxford, 1993) Chap 6.

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Figures (5)

Fig. 1
Fig. 1 (a) In the nematic phase, rod-like molecules are oriented preferentially along the director n (black arrow). (b) The cholesteric phase reassembles a spatially twisted nematic phase with helical distribution of the director along the helical axis (dashed arrow) and period P. (c) The periodic twisted array of the cholesteric phase can develop over several microns. Hence, a considerable number of full turns of the helix is achieved with typical LC cells.
Fig. 2
Fig. 2 (a) Schematic representation of a cholesteric liquid crystal cell with imposed planar alignment. For a left-handed CLC, RHCP light propagating along the helix is transmitted without any change. In contrast, LHCP light is strongly reflected. ki, kr and kt, respectively represent the wavevectors of the incident, reflected and transmitted waves. The dashed arrows indicate the direction of propagation as well as the intensity of the wave. (b) Around the Bragg regime, a peak of reflection (solid line) is observed corresponding to the excitation of the k1 mode. Here, the difference in velocities of the diffracted and non-diffracted wave leads to a strong optical rotatory power (ORP) (dashed line). The ordinary axis corresponds to the wavelengths interacting with the CLC. (c) Dispersion of ω vs. k for a CLC. Four polarized normal modes appear, k1 and k2 (solid lines) propagating to the right and the other two equivalent modes (dashed lines) propagating to the left. k1 and k2 are left- and right-handed elliptically polarized modes, respectively. For k1, a stop band appears where the Bragg diffraction occurs. This is the region of interest of this work.
Fig. 3
Fig. 3 Experimental setup. A Glan-Thompson polarizer P linearly polarizes the incident beam, the first λ/2 waveplate is used to balance the intensity of the o and e polarized waves (in the interferometer arms). A λ/4 waveplate transforms the linearly polarized e and o waves into circular polarization states of opposite handedness. One of the circular polarization states is sent through the sample, the other through a reference. Rotating the λ/4 waveplate switches the circular polarization states. The second λ/4 waveplate converts the circular components to linear polarization states before the two waves are recombined in the second calcite crystal. With the compensator C (variable linear birefringent element) an additional phase shift can be introduced between the vertical and the horizontal polarization states so that the intensity measured after the analyzer (A) can be determined as a function of this known retardation. A measurement protocol may thus consist of the following steps: First the phase difference between the circular polarized states is nulled. Then the substrate (sample or cuvette) is measured relative to air.
Fig. 4
Fig. 4 Temperature-dependent transmission (a) and phase Δϕ (b) measurements of COC at 633 nm. Change in color of the sample observed at TI-Ch –T ≈i) 10 °C; ii) 14.2 °C; iii) 14.35 °C; iv) 14.45 °C. As expected, the LHCP laser spot is strongly reflected in iv). (b) Along the region of selective reflection, an almost constant Δϕ value appears for RHCP and LP light. In contrast, the LHCP component experiences a discontinuity in the vicinity of the reflection maximum, i.e. at the Bragg frequency ωB. (c) Shows a map of the polarization state of the beam. The profile exhibits the C4 symmetry that appears at TI-Ch –T ≈14.35 °C. Changing the temperature from TI-Ch –T ≈14.45 °C to ≈14.55 °C rotates the direction of the profile (rotation of the arrows) by ≈45° near the Bragg frequency ωB.
Fig. 5
Fig. 5 (a) Temperature-dependent refractive indices nL (triangles) and nR (dots) of the LHCP and RHCP modes of the cholesteric liquid crystal COC in the region of selective reflection. While variations of nR with temperature are small, nL changes abruptly around the Bragg frequency. The dashed and dotted lines are a guide to the eye. (b) Theoretical curves predicted for nL ∝Re{KL} (dashed line) and nR∝Re{KR} (dotted line) at different wavelengths (adapted and reproduced from [18] Chandrasekhar). (c) ORP ρ of COC measured at different temperatures in the region of selective reflection. The open circles show the ORP obtained with optical polarization rotation measurements. Using the values of nL and nR in Fig. 5(a) and Eq. (2), the ORP is determined from the interferometrically-determined circular birefringence of the COC (shown by the crosses in the graph). The continuous and dashed lines are a guide to the eye.

Equations (6)

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ρ= 1 2 ( k 1 k 2 ),
ρ= π λ ( n L n R ),
Δϕ= 2π λ (n n Ref )d,
I( θ )= I y sin 2 θ+ I x cos 2 θ+2 I y I x sinθcosθcosΔϕ,
I( ±π/4 )= I 0 ( 1±cosΔϕ ).
n L,R ( T )= λ 2πd Δ ϕ L,R ( T )+ n Ref ,

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