Abstract

The transition from the continuously rotating dielectric ellipsoid approach to the discrete periodic collection of wave plates is investigated by comparing an exact analytic solution found using a Bloch–Lyaponov transformation on the 4×4 matrix form of Maxwell’s equations and the numerical solution. The validity of the analytic solution depends only on the number of sublayers within the unit cell and not on the number of periods in the sample. The circularly polarized Bragg-type selective reflection peak is shown to exist with helices containing as few as Nl=3 sublayers in a single period, but due to the appearance of higher Fourier harmonics in the dielectric tensor, additional selective reflection peaks appear. The case of Nl=4 corresponds to the folded Solc-type filter case with a twist angle of π/4, but it acts as a reflection filter for unpolarized light. Hence using this fact with liquid crystalline structures, polarization insensitive tunable filters can be built.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]

2006

L. Zhang, E. Ruh, D. Grutzmacher, D. J. Bell, B. J. Nelson, and C. Schonenberger, “Anomalous coiling of SiGe/Si and SiGe/Si/Cr helical nanobelts,” Nano Lett. 6, 1311-1317 (2006).
[CrossRef] [PubMed]

I. Abdulhalim, “Unique optical properties of anisotropic helical structures in Fabry-Perot cavity,” Opt. Lett. 31, 3019-3021(2006).
[CrossRef] [PubMed]

2005

I. Hodgkinson, Q. H. Wu, L. De Silva, M. Arnold, A. Lakhtakia, and M. McCall, “Structurally perturbed chiral Bragg reflectors for elliptically polarized light,” Opt. Lett. 30, 2629-2631(2005).
[CrossRef] [PubMed]

A. Figotin and I. Vitebskiy, “Gigantic transmission band-edge resonance in periodic stacks of anisotropic layers,” Phys. Rev. E 72, 036619-036632 (2005).
[CrossRef]

2003

N. W. Roberts, H. F. Gleeson, N. Bowring, A. Seed, L. N. Nassif, M. R. Herbert, J. W. Goodby, and M. Hird, “An experimental and theoretical investigation into the reflection spectra of SmC* and SmC*A phases,” J. Mater. Chem. 13, 353-359(2003).
[CrossRef]

2000

I. Abdulhalim, “Omnidirectional reflection from anisotropic periodic dielectric stack,” Opt. Commun. 174, 43-50 (2000).
[CrossRef]

G. T. Pickett, M. Gross, and H. Okuyama, “Spontaneous chirality in simple systems,” Phys. Rev. Lett. 85, 3652-3655 (2000).
[CrossRef] [PubMed]

Z. Zhuang, Y. J. Kim, and J. S. Patel, “Behavior of the cholesteric liquid crystal Fabry-Perot cavity in the Brag reflection band,” Phys. Rev. Lett. 84, 1168-1170 (2000).
[CrossRef] [PubMed]

1999

I. Abdulhalim, “Point of ultra-sensitivity to perturbations for axial propagation in helicoidal bianisotropic structures,” Europhys. Lett. 48, 177-181 (1999).
[CrossRef]

I. Abdulhalim, “Analytic propagation matrix method for linear optics of arbitrary biaxial layered media,” J. Opt. A 1, 646-653(1999).
[CrossRef]

Z. Zhuang and J. S. Patel, “Behavior of cholesteric liquid crystal in a Fabry-Perot cavity,” Opt. Lett. 24, 1759-1761 (1999).
[CrossRef]

1998

V. I. Kopp, B. Fan, and H. K. M. Vithana, “Low threshold lasing at the edge of a photonic stop band in cholesteric liquid crystals,” Opt. Lett. 23, 1707-1709 (1998).
[CrossRef]

T. W. Odom, J.-L. Huang, P. Kim, and C. M. Lieber, “Atomic structure and electronic properties of single-walled carbon nanotubes,” Nature 391, 62-64 (1998).
[CrossRef]

1996

D. Bimberg, N. N. Ledentsov, M. Grundmann, N. Kirstaedter, O. G. Schmidt, M. H. Mao, M. V. Ustinov, A. Yu. Egorov, A. E Zhukov, P. S. Kopev, Z. I. Alferov, S. S. Ruvimov, U. Gosele, and J. Heydenreich, “InAs-GaAs quantum dots: from growth to lasers,” Phys. Status Solidi B 194, 159-173 (1996).
[CrossRef]

K. Robbie, M. J. Brett, and A. Lakhtakia, “Chiral sculptured thin films,” Nature 384, 616-618 (1996).
[CrossRef]

1995

A. Lakhtakia and W. S. Weiglhofer, “On light propagation in helicoidal bianisotropic media,” Proc. R. Soc. London Ser. A 448, 419-437 (1995).
[CrossRef]

1994

1993

M. Land, “Old twist in a new tale,” Nature 363, 581-582(1993).
[CrossRef]

R. Wehner and G. D. Bernard, “Photoreceptor twist: a solution to the false-color problem,” Proc. Natl. Acad. Sci. USA 90, 4132-4135 (1993).
[CrossRef] [PubMed]

1992

T. W. Ebbesen and P. M. Ajayan, “Large scale synthesis of carbon nanotubes,” Nature 358, 220-222 (1992).
[CrossRef]

1991

S. Iijima, “Helical microtubules of graphitic carbon,” Nature 354, 56-58 (1991).
[CrossRef]

I. J. Lalov and A. I. Miteva, “Optically active Fabry-Perot etalon,” J. Mod. Opt. 38, 395-411 (1991).
[CrossRef]

1990

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S.-D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718-1720 (1990).
[CrossRef]

I. Abdulhalim and L. Benguigui, “Optics of chiral smectic liquid crystals near Lifshitz point,” Phys. Rev. A 42, 2114-2125 (1990).
[CrossRef] [PubMed]

1987

I. Abdulhalim, “Light propagation along the helix of chiral smectics and twisted nematics,” Opt. Commun. 64, 443-448(1987).
[CrossRef]

1985

I. Abdulhalim, L. Benguigui, and R. Weil, “Light transmission measurements in the liquid crystal SMC* phase of DOBAMBC at normal incidence,” J. Phys. (Paris) 46, 1429-1433 (1985).
[CrossRef]

I. Abdulhalim, L. Benguigui, and R. Weil, “Selective reflection by helicoidal liquid crystals: results of an exact calculation using the 4×4 characteristic matrix method,” J. Phys. (Paris) 46, 815-825 (1985).
[CrossRef]

1975

O. Parodi, “Light propagation along the helical axis in chiral. smectics C,” J. Phys. Colloq. 36, 325-326 (1975).
[CrossRef]

1972

D. W. Berreman, “Optics in stratified and anisotropic media: 4×4-matrix formulation,” J. Opt. Soc. Am. 61, 502-510 (1972).
[CrossRef]

1951

H. L. De Vries, “Rotatory power and other optical properties of certain liquid crystals,” Acta Cryst. 4, 219-226 (1951).
[CrossRef]

Abdulhalim, I.

I. Abdulhalim, “Unique optical properties of anisotropic helical structures in Fabry-Perot cavity,” Opt. Lett. 31, 3019-3021(2006).
[CrossRef] [PubMed]

I. Abdulhalim, “Omnidirectional reflection from anisotropic periodic dielectric stack,” Opt. Commun. 174, 43-50 (2000).
[CrossRef]

I. Abdulhalim, “Analytic propagation matrix method for linear optics of arbitrary biaxial layered media,” J. Opt. A 1, 646-653(1999).
[CrossRef]

I. Abdulhalim, “Point of ultra-sensitivity to perturbations for axial propagation in helicoidal bianisotropic structures,” Europhys. Lett. 48, 177-181 (1999).
[CrossRef]

I. Abdulhalim and L. Benguigui, “Optics of chiral smectic liquid crystals near Lifshitz point,” Phys. Rev. A 42, 2114-2125 (1990).
[CrossRef] [PubMed]

I. Abdulhalim, “Light propagation along the helix of chiral smectics and twisted nematics,” Opt. Commun. 64, 443-448(1987).
[CrossRef]

I. Abdulhalim, L. Benguigui, and R. Weil, “Light transmission measurements in the liquid crystal SMC* phase of DOBAMBC at normal incidence,” J. Phys. (Paris) 46, 1429-1433 (1985).
[CrossRef]

I. Abdulhalim, L. Benguigui, and R. Weil, “Selective reflection by helicoidal liquid crystals: results of an exact calculation using the 4×4 characteristic matrix method,” J. Phys. (Paris) 46, 815-825 (1985).
[CrossRef]

Ajayan, P. M.

T. W. Ebbesen and P. M. Ajayan, “Large scale synthesis of carbon nanotubes,” Nature 358, 220-222 (1992).
[CrossRef]

Alferov, Z. I.

D. Bimberg, N. N. Ledentsov, M. Grundmann, N. Kirstaedter, O. G. Schmidt, M. H. Mao, M. V. Ustinov, A. Yu. Egorov, A. E Zhukov, P. S. Kopev, Z. I. Alferov, S. S. Ruvimov, U. Gosele, and J. Heydenreich, “InAs-GaAs quantum dots: from growth to lasers,” Phys. Status Solidi B 194, 159-173 (1996).
[CrossRef]

Andreadakis, N.

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S.-D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718-1720 (1990).
[CrossRef]

Arnold, M.

Badoz, J.

Baltimore, D.

H. Lodish, A. Berk, L. S. Zipursky, P. Matsudaira, D. Baltimore, and J. Darnell, Molecular Cell Biology, 4th ed. (Freeman, 2000).

Bell, D. J.

L. Zhang, E. Ruh, D. Grutzmacher, D. J. Bell, B. J. Nelson, and C. Schonenberger, “Anomalous coiling of SiGe/Si and SiGe/Si/Cr helical nanobelts,” Nano Lett. 6, 1311-1317 (2006).
[CrossRef] [PubMed]

Benguigui, L.

I. Abdulhalim and L. Benguigui, “Optics of chiral smectic liquid crystals near Lifshitz point,” Phys. Rev. A 42, 2114-2125 (1990).
[CrossRef] [PubMed]

I. Abdulhalim, L. Benguigui, and R. Weil, “Light transmission measurements in the liquid crystal SMC* phase of DOBAMBC at normal incidence,” J. Phys. (Paris) 46, 1429-1433 (1985).
[CrossRef]

I. Abdulhalim, L. Benguigui, and R. Weil, “Selective reflection by helicoidal liquid crystals: results of an exact calculation using the 4×4 characteristic matrix method,” J. Phys. (Paris) 46, 815-825 (1985).
[CrossRef]

Berk, A.

H. Lodish, A. Berk, L. S. Zipursky, P. Matsudaira, D. Baltimore, and J. Darnell, Molecular Cell Biology, 4th ed. (Freeman, 2000).

Bernard, G. D.

R. Wehner and G. D. Bernard, “Photoreceptor twist: a solution to the false-color problem,” Proc. Natl. Acad. Sci. USA 90, 4132-4135 (1993).
[CrossRef] [PubMed]

Berreman, D. W.

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S.-D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718-1720 (1990).
[CrossRef]

D. W. Berreman, “Optics in stratified and anisotropic media: 4×4-matrix formulation,” J. Opt. Soc. Am. 61, 502-510 (1972).
[CrossRef]

Bimberg, D.

D. Bimberg, N. N. Ledentsov, M. Grundmann, N. Kirstaedter, O. G. Schmidt, M. H. Mao, M. V. Ustinov, A. Yu. Egorov, A. E Zhukov, P. S. Kopev, Z. I. Alferov, S. S. Ruvimov, U. Gosele, and J. Heydenreich, “InAs-GaAs quantum dots: from growth to lasers,” Phys. Status Solidi B 194, 159-173 (1996).
[CrossRef]

Blinc, R.

I. Muševic, R. Blinc, and B. Zekš, The Physics of Ferroelectric and Antiferroelectric Liquid Crystals (World Scientific, 2000), p. 200.

Bowring, N.

N. W. Roberts, H. F. Gleeson, N. Bowring, A. Seed, L. N. Nassif, M. R. Herbert, J. W. Goodby, and M. Hird, “An experimental and theoretical investigation into the reflection spectra of SmC* and SmC*A phases,” J. Mater. Chem. 13, 353-359(2003).
[CrossRef]

Brett, M. J.

K. Robbie, M. J. Brett, and A. Lakhtakia, “Chiral sculptured thin films,” Nature 384, 616-618 (1996).
[CrossRef]

Darnell, J.

H. Lodish, A. Berk, L. S. Zipursky, P. Matsudaira, D. Baltimore, and J. Darnell, Molecular Cell Biology, 4th ed. (Freeman, 2000).

De Gennes, P. G.

P. G. De Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Clarendon, 1993).

De Silva, L.

De Vries, H. L.

H. L. De Vries, “Rotatory power and other optical properties of certain liquid crystals,” Acta Cryst. 4, 219-226 (1951).
[CrossRef]

Ebbesen, T. W.

T. W. Ebbesen and P. M. Ajayan, “Large scale synthesis of carbon nanotubes,” Nature 358, 220-222 (1992).
[CrossRef]

Egorov, A. Yu.

D. Bimberg, N. N. Ledentsov, M. Grundmann, N. Kirstaedter, O. G. Schmidt, M. H. Mao, M. V. Ustinov, A. Yu. Egorov, A. E Zhukov, P. S. Kopev, Z. I. Alferov, S. S. Ruvimov, U. Gosele, and J. Heydenreich, “InAs-GaAs quantum dots: from growth to lasers,” Phys. Status Solidi B 194, 159-173 (1996).
[CrossRef]

Elston, S.

S. Elston and R. Sambles, The Optics Of Thermotropic Liquid Crystals (Taylor and Francis, 1998).

Fan, B.

Figotin, A.

A. Figotin and I. Vitebskiy, “Gigantic transmission band-edge resonance in periodic stacks of anisotropic layers,” Phys. Rev. E 72, 036619-036632 (2005).
[CrossRef]

Gleeson, H. F.

N. W. Roberts, H. F. Gleeson, N. Bowring, A. Seed, L. N. Nassif, M. R. Herbert, J. W. Goodby, and M. Hird, “An experimental and theoretical investigation into the reflection spectra of SmC* and SmC*A phases,” J. Mater. Chem. 13, 353-359(2003).
[CrossRef]

Goodby, J. W.

N. W. Roberts, H. F. Gleeson, N. Bowring, A. Seed, L. N. Nassif, M. R. Herbert, J. W. Goodby, and M. Hird, “An experimental and theoretical investigation into the reflection spectra of SmC* and SmC*A phases,” J. Mater. Chem. 13, 353-359(2003).
[CrossRef]

Gosele, U.

D. Bimberg, N. N. Ledentsov, M. Grundmann, N. Kirstaedter, O. G. Schmidt, M. H. Mao, M. V. Ustinov, A. Yu. Egorov, A. E Zhukov, P. S. Kopev, Z. I. Alferov, S. S. Ruvimov, U. Gosele, and J. Heydenreich, “InAs-GaAs quantum dots: from growth to lasers,” Phys. Status Solidi B 194, 159-173 (1996).
[CrossRef]

Gross, M.

G. T. Pickett, M. Gross, and H. Okuyama, “Spontaneous chirality in simple systems,” Phys. Rev. Lett. 85, 3652-3655 (2000).
[CrossRef] [PubMed]

Grundmann, M.

D. Bimberg, N. N. Ledentsov, M. Grundmann, N. Kirstaedter, O. G. Schmidt, M. H. Mao, M. V. Ustinov, A. Yu. Egorov, A. E Zhukov, P. S. Kopev, Z. I. Alferov, S. S. Ruvimov, U. Gosele, and J. Heydenreich, “InAs-GaAs quantum dots: from growth to lasers,” Phys. Status Solidi B 194, 159-173 (1996).
[CrossRef]

Grutzmacher, D.

L. Zhang, E. Ruh, D. Grutzmacher, D. J. Bell, B. J. Nelson, and C. Schonenberger, “Anomalous coiling of SiGe/Si and SiGe/Si/Cr helical nanobelts,” Nano Lett. 6, 1311-1317 (2006).
[CrossRef] [PubMed]

Herbert, M. R.

N. W. Roberts, H. F. Gleeson, N. Bowring, A. Seed, L. N. Nassif, M. R. Herbert, J. W. Goodby, and M. Hird, “An experimental and theoretical investigation into the reflection spectra of SmC* and SmC*A phases,” J. Mater. Chem. 13, 353-359(2003).
[CrossRef]

Heydenreich, J.

D. Bimberg, N. N. Ledentsov, M. Grundmann, N. Kirstaedter, O. G. Schmidt, M. H. Mao, M. V. Ustinov, A. Yu. Egorov, A. E Zhukov, P. S. Kopev, Z. I. Alferov, S. S. Ruvimov, U. Gosele, and J. Heydenreich, “InAs-GaAs quantum dots: from growth to lasers,” Phys. Status Solidi B 194, 159-173 (1996).
[CrossRef]

Hird, M.

N. W. Roberts, H. F. Gleeson, N. Bowring, A. Seed, L. N. Nassif, M. R. Herbert, J. W. Goodby, and M. Hird, “An experimental and theoretical investigation into the reflection spectra of SmC* and SmC*A phases,” J. Mater. Chem. 13, 353-359(2003).
[CrossRef]

Hodgkinson, I.

Huang, J.-L.

T. W. Odom, J.-L. Huang, P. Kim, and C. M. Lieber, “Atomic structure and electronic properties of single-walled carbon nanotubes,” Nature 391, 62-64 (1998).
[CrossRef]

Iijima, S.

S. Iijima, “Helical microtubules of graphitic carbon,” Nature 354, 56-58 (1991).
[CrossRef]

Kim, P.

T. W. Odom, J.-L. Huang, P. Kim, and C. M. Lieber, “Atomic structure and electronic properties of single-walled carbon nanotubes,” Nature 391, 62-64 (1998).
[CrossRef]

Kim, Y. J.

Z. Zhuang, Y. J. Kim, and J. S. Patel, “Behavior of the cholesteric liquid crystal Fabry-Perot cavity in the Brag reflection band,” Phys. Rev. Lett. 84, 1168-1170 (2000).
[CrossRef] [PubMed]

Kirstaedter, N.

D. Bimberg, N. N. Ledentsov, M. Grundmann, N. Kirstaedter, O. G. Schmidt, M. H. Mao, M. V. Ustinov, A. Yu. Egorov, A. E Zhukov, P. S. Kopev, Z. I. Alferov, S. S. Ruvimov, U. Gosele, and J. Heydenreich, “InAs-GaAs quantum dots: from growth to lasers,” Phys. Status Solidi B 194, 159-173 (1996).
[CrossRef]

Kopev, P. S.

D. Bimberg, N. N. Ledentsov, M. Grundmann, N. Kirstaedter, O. G. Schmidt, M. H. Mao, M. V. Ustinov, A. Yu. Egorov, A. E Zhukov, P. S. Kopev, Z. I. Alferov, S. S. Ruvimov, U. Gosele, and J. Heydenreich, “InAs-GaAs quantum dots: from growth to lasers,” Phys. Status Solidi B 194, 159-173 (1996).
[CrossRef]

Kopp, V. I.

Lakhtakia, A.

I. Hodgkinson, Q. H. Wu, L. De Silva, M. Arnold, A. Lakhtakia, and M. McCall, “Structurally perturbed chiral Bragg reflectors for elliptically polarized light,” Opt. Lett. 30, 2629-2631(2005).
[CrossRef] [PubMed]

K. Robbie, M. J. Brett, and A. Lakhtakia, “Chiral sculptured thin films,” Nature 384, 616-618 (1996).
[CrossRef]

A. Lakhtakia and W. S. Weiglhofer, “On light propagation in helicoidal bianisotropic media,” Proc. R. Soc. London Ser. A 448, 419-437 (1995).
[CrossRef]

Lalov, I. J.

I. J. Lalov and A. I. Miteva, “Optically active Fabry-Perot etalon,” J. Mod. Opt. 38, 395-411 (1991).
[CrossRef]

Land, M.

M. Land, “Old twist in a new tale,” Nature 363, 581-582(1993).
[CrossRef]

Ledentsov, N. N.

D. Bimberg, N. N. Ledentsov, M. Grundmann, N. Kirstaedter, O. G. Schmidt, M. H. Mao, M. V. Ustinov, A. Yu. Egorov, A. E Zhukov, P. S. Kopev, Z. I. Alferov, S. S. Ruvimov, U. Gosele, and J. Heydenreich, “InAs-GaAs quantum dots: from growth to lasers,” Phys. Status Solidi B 194, 159-173 (1996).
[CrossRef]

Lee, S.-D.

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S.-D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718-1720 (1990).
[CrossRef]

Lieber, C. M.

T. W. Odom, J.-L. Huang, P. Kim, and C. M. Lieber, “Atomic structure and electronic properties of single-walled carbon nanotubes,” Nature 391, 62-64 (1998).
[CrossRef]

Lin, C.

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S.-D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718-1720 (1990).
[CrossRef]

Lodish, H.

H. Lodish, A. Berk, L. S. Zipursky, P. Matsudaira, D. Baltimore, and J. Darnell, Molecular Cell Biology, 4th ed. (Freeman, 2000).

Mao, M. H.

D. Bimberg, N. N. Ledentsov, M. Grundmann, N. Kirstaedter, O. G. Schmidt, M. H. Mao, M. V. Ustinov, A. Yu. Egorov, A. E Zhukov, P. S. Kopev, Z. I. Alferov, S. S. Ruvimov, U. Gosele, and J. Heydenreich, “InAs-GaAs quantum dots: from growth to lasers,” Phys. Status Solidi B 194, 159-173 (1996).
[CrossRef]

Matsudaira, P.

H. Lodish, A. Berk, L. S. Zipursky, P. Matsudaira, D. Baltimore, and J. Darnell, Molecular Cell Biology, 4th ed. (Freeman, 2000).

McCall, M.

Miteva, A. I.

I. J. Lalov and A. I. Miteva, “Optically active Fabry-Perot etalon,” J. Mod. Opt. 38, 395-411 (1991).
[CrossRef]

Muševic, I.

I. Muševic, R. Blinc, and B. Zekš, The Physics of Ferroelectric and Antiferroelectric Liquid Crystals (World Scientific, 2000), p. 200.

Nassif, L. N.

N. W. Roberts, H. F. Gleeson, N. Bowring, A. Seed, L. N. Nassif, M. R. Herbert, J. W. Goodby, and M. Hird, “An experimental and theoretical investigation into the reflection spectra of SmC* and SmC*A phases,” J. Mater. Chem. 13, 353-359(2003).
[CrossRef]

Nelson, B. J.

L. Zhang, E. Ruh, D. Grutzmacher, D. J. Bell, B. J. Nelson, and C. Schonenberger, “Anomalous coiling of SiGe/Si and SiGe/Si/Cr helical nanobelts,” Nano Lett. 6, 1311-1317 (2006).
[CrossRef] [PubMed]

Odom, T. W.

T. W. Odom, J.-L. Huang, P. Kim, and C. M. Lieber, “Atomic structure and electronic properties of single-walled carbon nanotubes,” Nature 391, 62-64 (1998).
[CrossRef]

Okuyama, H.

G. T. Pickett, M. Gross, and H. Okuyama, “Spontaneous chirality in simple systems,” Phys. Rev. Lett. 85, 3652-3655 (2000).
[CrossRef] [PubMed]

Parodi, O.

O. Parodi, “Light propagation along the helical axis in chiral. smectics C,” J. Phys. Colloq. 36, 325-326 (1975).
[CrossRef]

Patel, J. S.

Z. Zhuang, Y. J. Kim, and J. S. Patel, “Behavior of the cholesteric liquid crystal Fabry-Perot cavity in the Brag reflection band,” Phys. Rev. Lett. 84, 1168-1170 (2000).
[CrossRef] [PubMed]

Z. Zhuang and J. S. Patel, “Behavior of cholesteric liquid crystal in a Fabry-Perot cavity,” Opt. Lett. 24, 1759-1761 (1999).
[CrossRef]

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S.-D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718-1720 (1990).
[CrossRef]

Pickett, G. T.

G. T. Pickett, M. Gross, and H. Okuyama, “Spontaneous chirality in simple systems,” Phys. Rev. Lett. 85, 3652-3655 (2000).
[CrossRef] [PubMed]

Prost, J.

P. G. De Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Clarendon, 1993).

Robbie, K.

K. Robbie, M. J. Brett, and A. Lakhtakia, “Chiral sculptured thin films,” Nature 384, 616-618 (1996).
[CrossRef]

Roberts, N. W.

N. W. Roberts, H. F. Gleeson, N. Bowring, A. Seed, L. N. Nassif, M. R. Herbert, J. W. Goodby, and M. Hird, “An experimental and theoretical investigation into the reflection spectra of SmC* and SmC*A phases,” J. Mater. Chem. 13, 353-359(2003).
[CrossRef]

Ruh, E.

L. Zhang, E. Ruh, D. Grutzmacher, D. J. Bell, B. J. Nelson, and C. Schonenberger, “Anomalous coiling of SiGe/Si and SiGe/Si/Cr helical nanobelts,” Nano Lett. 6, 1311-1317 (2006).
[CrossRef] [PubMed]

Ruvimov, S. S.

D. Bimberg, N. N. Ledentsov, M. Grundmann, N. Kirstaedter, O. G. Schmidt, M. H. Mao, M. V. Ustinov, A. Yu. Egorov, A. E Zhukov, P. S. Kopev, Z. I. Alferov, S. S. Ruvimov, U. Gosele, and J. Heydenreich, “InAs-GaAs quantum dots: from growth to lasers,” Phys. Status Solidi B 194, 159-173 (1996).
[CrossRef]

Saifi, M. A.

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S.-D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718-1720 (1990).
[CrossRef]

Sambles, R.

S. Elston and R. Sambles, The Optics Of Thermotropic Liquid Crystals (Taylor and Francis, 1998).

Schmidt, O. G.

D. Bimberg, N. N. Ledentsov, M. Grundmann, N. Kirstaedter, O. G. Schmidt, M. H. Mao, M. V. Ustinov, A. Yu. Egorov, A. E Zhukov, P. S. Kopev, Z. I. Alferov, S. S. Ruvimov, U. Gosele, and J. Heydenreich, “InAs-GaAs quantum dots: from growth to lasers,” Phys. Status Solidi B 194, 159-173 (1996).
[CrossRef]

Schonenberger, C.

L. Zhang, E. Ruh, D. Grutzmacher, D. J. Bell, B. J. Nelson, and C. Schonenberger, “Anomalous coiling of SiGe/Si and SiGe/Si/Cr helical nanobelts,” Nano Lett. 6, 1311-1317 (2006).
[CrossRef] [PubMed]

Seed, A.

N. W. Roberts, H. F. Gleeson, N. Bowring, A. Seed, L. N. Nassif, M. R. Herbert, J. W. Goodby, and M. Hird, “An experimental and theoretical investigation into the reflection spectra of SmC* and SmC*A phases,” J. Mater. Chem. 13, 353-359(2003).
[CrossRef]

Silverman, M. P.

Ustinov, M. V.

D. Bimberg, N. N. Ledentsov, M. Grundmann, N. Kirstaedter, O. G. Schmidt, M. H. Mao, M. V. Ustinov, A. Yu. Egorov, A. E Zhukov, P. S. Kopev, Z. I. Alferov, S. S. Ruvimov, U. Gosele, and J. Heydenreich, “InAs-GaAs quantum dots: from growth to lasers,” Phys. Status Solidi B 194, 159-173 (1996).
[CrossRef]

Vitebskiy, I.

A. Figotin and I. Vitebskiy, “Gigantic transmission band-edge resonance in periodic stacks of anisotropic layers,” Phys. Rev. E 72, 036619-036632 (2005).
[CrossRef]

Vithana, H. K. M.

Wehner, R.

R. Wehner and G. D. Bernard, “Photoreceptor twist: a solution to the false-color problem,” Proc. Natl. Acad. Sci. USA 90, 4132-4135 (1993).
[CrossRef] [PubMed]

Weiglhofer, W. S.

A. Lakhtakia and W. S. Weiglhofer, “On light propagation in helicoidal bianisotropic media,” Proc. R. Soc. London Ser. A 448, 419-437 (1995).
[CrossRef]

Weil, R.

I. Abdulhalim, L. Benguigui, and R. Weil, “Light transmission measurements in the liquid crystal SMC* phase of DOBAMBC at normal incidence,” J. Phys. (Paris) 46, 1429-1433 (1985).
[CrossRef]

I. Abdulhalim, L. Benguigui, and R. Weil, “Selective reflection by helicoidal liquid crystals: results of an exact calculation using the 4×4 characteristic matrix method,” J. Phys. (Paris) 46, 815-825 (1985).
[CrossRef]

Wu, Q. H.

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

Zekš, B.

I. Muševic, R. Blinc, and B. Zekš, The Physics of Ferroelectric and Antiferroelectric Liquid Crystals (World Scientific, 2000), p. 200.

Zhang, L.

L. Zhang, E. Ruh, D. Grutzmacher, D. J. Bell, B. J. Nelson, and C. Schonenberger, “Anomalous coiling of SiGe/Si and SiGe/Si/Cr helical nanobelts,” Nano Lett. 6, 1311-1317 (2006).
[CrossRef] [PubMed]

Zhuang, Z.

Z. Zhuang, Y. J. Kim, and J. S. Patel, “Behavior of the cholesteric liquid crystal Fabry-Perot cavity in the Brag reflection band,” Phys. Rev. Lett. 84, 1168-1170 (2000).
[CrossRef] [PubMed]

Z. Zhuang and J. S. Patel, “Behavior of cholesteric liquid crystal in a Fabry-Perot cavity,” Opt. Lett. 24, 1759-1761 (1999).
[CrossRef]

Zhukov, A. E

D. Bimberg, N. N. Ledentsov, M. Grundmann, N. Kirstaedter, O. G. Schmidt, M. H. Mao, M. V. Ustinov, A. Yu. Egorov, A. E Zhukov, P. S. Kopev, Z. I. Alferov, S. S. Ruvimov, U. Gosele, and J. Heydenreich, “InAs-GaAs quantum dots: from growth to lasers,” Phys. Status Solidi B 194, 159-173 (1996).
[CrossRef]

Zipursky, L. S.

H. Lodish, A. Berk, L. S. Zipursky, P. Matsudaira, D. Baltimore, and J. Darnell, Molecular Cell Biology, 4th ed. (Freeman, 2000).

Acta Cryst.

H. L. De Vries, “Rotatory power and other optical properties of certain liquid crystals,” Acta Cryst. 4, 219-226 (1951).
[CrossRef]

Appl. Phys. Lett.

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S.-D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718-1720 (1990).
[CrossRef]

Europhys. Lett.

I. Abdulhalim, “Point of ultra-sensitivity to perturbations for axial propagation in helicoidal bianisotropic structures,” Europhys. Lett. 48, 177-181 (1999).
[CrossRef]

J. Mater. Chem.

N. W. Roberts, H. F. Gleeson, N. Bowring, A. Seed, L. N. Nassif, M. R. Herbert, J. W. Goodby, and M. Hird, “An experimental and theoretical investigation into the reflection spectra of SmC* and SmC*A phases,” J. Mater. Chem. 13, 353-359(2003).
[CrossRef]

J. Mod. Opt.

I. J. Lalov and A. I. Miteva, “Optically active Fabry-Perot etalon,” J. Mod. Opt. 38, 395-411 (1991).
[CrossRef]

J. Opt. A

I. Abdulhalim, “Analytic propagation matrix method for linear optics of arbitrary biaxial layered media,” J. Opt. A 1, 646-653(1999).
[CrossRef]

J. Opt. Soc. Am.

D. W. Berreman, “Optics in stratified and anisotropic media: 4×4-matrix formulation,” J. Opt. Soc. Am. 61, 502-510 (1972).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. (Paris)

I. Abdulhalim, L. Benguigui, and R. Weil, “Light transmission measurements in the liquid crystal SMC* phase of DOBAMBC at normal incidence,” J. Phys. (Paris) 46, 1429-1433 (1985).
[CrossRef]

I. Abdulhalim, L. Benguigui, and R. Weil, “Selective reflection by helicoidal liquid crystals: results of an exact calculation using the 4×4 characteristic matrix method,” J. Phys. (Paris) 46, 815-825 (1985).
[CrossRef]

J. Phys. Colloq.

O. Parodi, “Light propagation along the helical axis in chiral. smectics C,” J. Phys. Colloq. 36, 325-326 (1975).
[CrossRef]

Nano Lett.

L. Zhang, E. Ruh, D. Grutzmacher, D. J. Bell, B. J. Nelson, and C. Schonenberger, “Anomalous coiling of SiGe/Si and SiGe/Si/Cr helical nanobelts,” Nano Lett. 6, 1311-1317 (2006).
[CrossRef] [PubMed]

Nature

K. Robbie, M. J. Brett, and A. Lakhtakia, “Chiral sculptured thin films,” Nature 384, 616-618 (1996).
[CrossRef]

S. Iijima, “Helical microtubules of graphitic carbon,” Nature 354, 56-58 (1991).
[CrossRef]

T. W. Ebbesen and P. M. Ajayan, “Large scale synthesis of carbon nanotubes,” Nature 358, 220-222 (1992).
[CrossRef]

T. W. Odom, J.-L. Huang, P. Kim, and C. M. Lieber, “Atomic structure and electronic properties of single-walled carbon nanotubes,” Nature 391, 62-64 (1998).
[CrossRef]

M. Land, “Old twist in a new tale,” Nature 363, 581-582(1993).
[CrossRef]

Opt. Commun.

I. Abdulhalim, “Light propagation along the helix of chiral smectics and twisted nematics,” Opt. Commun. 64, 443-448(1987).
[CrossRef]

I. Abdulhalim, “Omnidirectional reflection from anisotropic periodic dielectric stack,” Opt. Commun. 174, 43-50 (2000).
[CrossRef]

Opt. Lett.

Phys. Rev. A

I. Abdulhalim and L. Benguigui, “Optics of chiral smectic liquid crystals near Lifshitz point,” Phys. Rev. A 42, 2114-2125 (1990).
[CrossRef] [PubMed]

Phys. Rev. E

A. Figotin and I. Vitebskiy, “Gigantic transmission band-edge resonance in periodic stacks of anisotropic layers,” Phys. Rev. E 72, 036619-036632 (2005).
[CrossRef]

Phys. Rev. Lett.

Z. Zhuang, Y. J. Kim, and J. S. Patel, “Behavior of the cholesteric liquid crystal Fabry-Perot cavity in the Brag reflection band,” Phys. Rev. Lett. 84, 1168-1170 (2000).
[CrossRef] [PubMed]

G. T. Pickett, M. Gross, and H. Okuyama, “Spontaneous chirality in simple systems,” Phys. Rev. Lett. 85, 3652-3655 (2000).
[CrossRef] [PubMed]

Phys. Status Solidi B

D. Bimberg, N. N. Ledentsov, M. Grundmann, N. Kirstaedter, O. G. Schmidt, M. H. Mao, M. V. Ustinov, A. Yu. Egorov, A. E Zhukov, P. S. Kopev, Z. I. Alferov, S. S. Ruvimov, U. Gosele, and J. Heydenreich, “InAs-GaAs quantum dots: from growth to lasers,” Phys. Status Solidi B 194, 159-173 (1996).
[CrossRef]

Proc. Natl. Acad. Sci. USA

R. Wehner and G. D. Bernard, “Photoreceptor twist: a solution to the false-color problem,” Proc. Natl. Acad. Sci. USA 90, 4132-4135 (1993).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. A

A. Lakhtakia and W. S. Weiglhofer, “On light propagation in helicoidal bianisotropic media,” Proc. R. Soc. London Ser. A 448, 419-437 (1995).
[CrossRef]

Other

I. Muševic, R. Blinc, and B. Zekš, The Physics of Ferroelectric and Antiferroelectric Liquid Crystals (World Scientific, 2000), p. 200.

S. Elston and R. Sambles, The Optics Of Thermotropic Liquid Crystals (Taylor and Francis, 1998).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

H. Lodish, A. Berk, L. S. Zipursky, P. Matsudaira, D. Baltimore, and J. Darnell, Molecular Cell Biology, 4th ed. (Freeman, 2000).

P. G. De Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Clarendon, 1993).

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Figures (7)

Fig. 1
Fig. 1

Schematic of (a) continuum of twisted anisotropic structure and (b) discrete stack of periodically oriented pile of anisotropic wave plates.

Fig. 2
Fig. 2

Schematic of the dielectric tensor ellipsoid for the general biaxial layer.

Fig. 3
Fig. 3

(a) Reflection of right circularly polarized light from a CLC with a right handed helix versus the normalized wavelength. (b) Real and imaginary parts of k s h p for the case N l = 50 . The principal refractive indices used are n 1 = 1.52 , n 2 = 1.65 in between two glass plates with index n 0 = 1.45 and number of periods N p = 15 .

Fig. 4
Fig. 4

Comparison between the analytic and numerical approaches for different numbers of periods in the sample showing coincidence between the two for samples as thin as one single period. The number of sublayers is 50.

Fig. 5
Fig. 5

Reflection spectrum R r r calculated for sublayer numbers N l = 3 , 5 , 20 and N p = 15 showing the large decrease of the peak and its narrowing when N l = 3 . It can be seen that the peak maintains its polarization properties although, for N l = 3 , a larger number of periods is required to obtain 100% reflectivity.

Fig. 6
Fig. 6

Variation of the R r r peak with the number of periods when N l = 3 , showing that the same reflection peak remains even for the case of a small number of sublayers, but a larger number of periods is required to obtain 100% reflectivity.

Fig. 7
Fig. 7

Reflection spectra for the case of N l = 4 and N p = 15 : (a)  R p p , (b)  R p s = R s p , (c)  R s s , (d)  R r r , (e)  R r l = R l r , and (f)  R l l . Note that the main reflection peak occurs both in R r r and R l l , and hence it is polarization independent.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Ψ z = i k 0 [ 0 1 0 0 ε a + δ cos 2 q z 0 δ sin 2 q z 0 0 0 0 1 δ sin 2 q z 0 ε a δ cos 2 q z 0 ] Ψ ,
d Ψ d z = ( i k 0 T Δ T 1 T d T 1 d z ) Ψ .
T = [ exp ( i q z ) 0 i exp ( i q z ) 0 exp ( i q z ) 0 i exp ( i q z ) 0 0 i exp ( i q z ) 0 exp ( i q z ) 0 i exp ( i q z ) 0 exp ( i q z ) ] ,
T 1 = 1 2 [ exp ( i q z ) exp ( i q z ) 0 0 0 0 i exp ( i q z ) i exp ( i q z ) i exp ( i q z ) i exp ( i q z ) 0 0 0 0 exp ( i q z ) exp ( i q z ) ] .
d Ψ d z = [ i q 0 k 0 0 0 i q 0 k 0 ε a k 0 k 0 δ i q 0 k 0 δ k 0 ε a 0 i q ] Ψ .
k o h , s h = k 0 n a 1 + λ r 2 ± 4 λ r 2 + δ r 2 .

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