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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 3 — Feb. 5, 2007
  • pp: 1024–1029
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Simultaneous RGB reflections from single-pitched cholesteric liquid crystal films with Fibonaccian defects

Na Young Ha, Yoichi Takanishi, Ken Ishikawa, and Hideo Takezoe  »View Author Affiliations


Optics Express, Vol. 15, Issue 3, pp. 1024-1029 (2007)
http://dx.doi.org/10.1364/OE.15.001024


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Abstract

We introduce quasi-periodic Fibonaccian phase defects into single-pitched cholesteric liquid crystalline systems. Numerical simulations of reflection spectra from the proposed systems demonstrate simultaneous red, green, and blue reflections or multiple photonic band gaps. Fundamental optical properties are discussed as functions of phase jump (orientational defect angles), unit lengths and the orders of Fibonacci systems.

© 2007 Optical Society of America

1. Introduction

Quasicrystals are a class of systems presenting long-range order but no periodicity. They have fascinating physical properties like the formation of multiple photonic band gaps (PBGs), the presence of fractal transmission resonance, and the occurrence of critically localized states[1

1. A. G. Barriuso, J. J. Monzon, L. L. Sanshez-Soto, and A. Felipe, “Comparing omnidirectional reflection from periodic and quasiperiodic one-dimensional photonic crystals,” Opt. Express 13,3913–3920 (2005). [CrossRef] [PubMed]

, 2

2. W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72,633–636 (1994). [CrossRef] [PubMed]

, 3

3. R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80,3063–3065 (2002). [CrossRef]

, 4

4. L. D. Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90,0555011–0555014 (2003).

, 5

5. M. Ghulinyan, C. J. Oton, L. D. Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. S. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71,0942041–0942048 (2005). [CrossRef]

, 6

6. L. D. Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, “Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals,” Appl. Phys. Lett. 84,5186–5188 (2004). [CrossRef]

, 7

7. M. S. Vasconcelos and E. L. Albuquerque, “Transmission fingerprints in quasiperiodic dielectric multilayers,” Phys. Rev. B 59,11128–11131 (1999). [CrossRef]

]. Among the various one-dimensional (1D) quasicrystals described by the sequences named Fibonacci[1

1. A. G. Barriuso, J. J. Monzon, L. L. Sanshez-Soto, and A. Felipe, “Comparing omnidirectional reflection from periodic and quasiperiodic one-dimensional photonic crystals,” Opt. Express 13,3913–3920 (2005). [CrossRef] [PubMed]

, 2

2. W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72,633–636 (1994). [CrossRef] [PubMed]

, 3

3. R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80,3063–3065 (2002). [CrossRef]

, 4

4. L. D. Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90,0555011–0555014 (2003).

, 5

5. M. Ghulinyan, C. J. Oton, L. D. Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. S. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71,0942041–0942048 (2005). [CrossRef]

], Thue-Morse[6

6. L. D. Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, “Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals,” Appl. Phys. Lett. 84,5186–5188 (2004). [CrossRef]

], or Rudin-Shapiro[7

7. M. S. Vasconcelos and E. L. Albuquerque, “Transmission fingerprints in quasiperiodic dielectric multilayers,” Phys. Rev. B 59,11128–11131 (1999). [CrossRef]

], a Fibonacci system has been studied in various material systems theoretically and experimentally. Most experimental reports were limited to inorganic multilayered systems such as TiO2/SiO2[2

2. W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72,633–636 (1994). [CrossRef] [PubMed]

, 3

3. R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80,3063–3065 (2002). [CrossRef]

] and porous silicon structures[4

4. L. D. Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90,0555011–0555014 (2003).

, 5

5. M. Ghulinyan, C. J. Oton, L. D. Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. S. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71,0942041–0942048 (2005). [CrossRef]

]. Recently, as a different Fibonacci system from the dielectric multilayers, Fibonacci number patterns in Ag core/SiOX shell microstructures were reported[8

8. C. Li, X. Zhang, and Z. Cao, “Triangular and Fibonacci number patterns driven by stress on core/shell microstructures,” Science 309,909–911 (2005). [CrossRef] [PubMed]

]. So far, however, no organic Fibonacci systems have been even proposed.

A cholesteric liquid crystal (CLC) used in this study is an 1D self-assembled photonic crystal showing a PBG for circularly polarized light with the same handedness as a cholesteric helix[9

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

]. These characteristics such as selective reflection in a specific wavelength region and circular polarization of the reflected light are attractive for reflective color-displays without the need for back-lightening, polarizers, or color filters[10

10. J. Lub, P. Witte, C. Doornkamp, J. P. A. Vogels, and R. T. Wegh, “Stable photopatterned cholesteric layers made by photoisomerization and subsequent photopolymerization for use as color filters in liquid-crystal displays,” Adv. Mater. 15,1420–1425 (2003). [CrossRef]

, 11

11. G. D. Filpo, F. P. Nicoletta, and G. Chidichimo, “Cholesteric emulsions for colored displays,” Adv. Mater. 17,1150–1152 (2005). [CrossRef]

, 12

12. T. Yoshioka, T. Ogata, T. Nonaka, M. Moritsugu, S. -N. Kim, and S. Kurihara, “Reversible-photon-mode full-color display by means of photochemical modulation of a helically cholesteric structure,” Adv. Mater. 17,1226–1229 (2005). [CrossRef]

].

In this paper, we introduce Fibonaccian defects into organic CLC systems and simulate reflection spectra from the proposed system numerically. A quasi-periodic system is considered as a sample to exemplify its intrinsic property such as multiple PBGs. Among several sequences mentioned above, we employ the simplest system, the Fibonacci sequence, for the purpose of future experimental demonstrations: that is, the number of building units of a Rudin-Shapiro sequence is larger than that of the other sequences[7

7. M. S. Vasconcelos and E. L. Albuquerque, “Transmission fingerprints in quasiperiodic dielectric multilayers,” Phys. Rev. B 59,11128–11131 (1999). [CrossRef]

] and, at the same order, total number of layers of the Thue-Morse sequence is larger than that of the Fibonacci sequence[6

6. L. D. Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, “Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals,” Appl. Phys. Lett. 84,5186–5188 (2004). [CrossRef]

]. The helical CLC has a single PBG or one reflection color, in which the PBG width of CLC is proportional to the anisotropy of refractive indices and is in the range of 50—100nm. By using the Fibonaccian defects, however, we can achieve simultaneous red, green, and blue reflections or multiple PBGs using single-pitched CLC systems. Without introducing any other materials, a series of conventional CLC films with Fibonaccian phase defects can give rise to such optical characteristics. This Fibonaccian CLC system can in practice be achieved by a polymeric cholesteric liquid crystal (PCLC)[13

13. M. H. Song, N. Y. Ha, K. Amemiya, B. Park, Y. Takanishi, K. Ishikawa, J. W. Wu, S. Nishimura, T. Toyooka, and H. Takezoe, “Defect-mode lasing with lowered threshold in a three-layered hetero-cholesteric liquid-crystal structure,” Adv. Mater. 18,193–197 (2006). [CrossRef]

].

2. Fibonaccian defects in CLCs

A Fibonacci sequence is based on the recursive relation F 0={A}, F 1={B}, and Fj=F j-2 F j-1 for j≥2. The lower order sequences are F 2={AB}, F 3={BAB}, F 4={ABBAB}, etc. In general, a 1D quasi-periodic system has been formed by stacking two different dielectric materials, A and B, according to the Fibonacci generation scheme[1

1. A. G. Barriuso, J. J. Monzon, L. L. Sanshez-Soto, and A. Felipe, “Comparing omnidirectional reflection from periodic and quasiperiodic one-dimensional photonic crystals,” Opt. Express 13,3913–3920 (2005). [CrossRef] [PubMed]

, 2

2. W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72,633–636 (1994). [CrossRef] [PubMed]

, 3

3. R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80,3063–3065 (2002). [CrossRef]

]. In CLCs, however, the periodicity comes from the structure formed by rodlike molecules including chiral molecules arranging themselves in a helical fashion[9

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

]. Hence, the controllable factors for forming Fibonacci structures are different from those in dielectric multilayered systems. Since the origin of the periodicity in cholesteric structures is a spontaneous orientational order of molecules, it is difficult to control a fundamental unit of the periodicity and make a quasi-periodic Fibonacci system with CLCs. Therefore we propose the Fibonacci structure by introducing defects into the CLCs theoretically.

Defects of PCs have been generated by inserting isotropic materials with different refractive index or thickness in periodic structures. In addition to such a defect, a different type of defect is possible in CLCs; introduction of a phase jump (orientational defect) into a cholesteric helix[14

14. I. J. Hodgkinson, Q. H. Wu, K. E. Thorn, A. Lakhtakia, and M. W. McCall, “Spaceless circular-polarization spectral-hole filters using chiral sculptured thin films: theory and experiment,” Opt. Commun. 184,57–66 (2000). [CrossRef]

, 15

15. V. I. Kopp and A. Z. Genack, “Twist defect in chiral photonic structures,” Phys. Rev. Lett. 89,0339011–0339014 (2002). [CrossRef]

, 16

16. H. Hoshi, K. Ishikawa, and H. Takezoe, “Optical second-harmonic generation enhanced by a twist defect in ferroelectric liquid crystals,” Phys. Rev. E 68,0207011–0207013 (2003). [CrossRef]

, 17

17. J. Schmidtke, W. Stille, and H. Finkelmann, “Defect mode emission of a dye doped cholesteric polymer network,” Phys. Rev. Lett. 90,0839021–083902 (2003). [CrossRef]

]. To make a quasi-periodic structure with a CLC, we employed the second approach to photonic defects and introduced Fibonaccian defects into CLCs as shown in Fig. 1.

Fig. 1. (Color online) Schematic view of Fibonaccian defects in periodic cholesteric structures: F 2={AB} and F 3={BAB} with ϕ=0 and ϕ=π/2. A (blue) and B (red) are two units of the quasi-periodic Fibonacci system, i.e., F 0={A} and F 1={B}. ϕ is an orientational defect angle between the molecular director in A layer and that in B layer at the interface (yellow).

Figure 1 shows a schematic illustration of Fibonaccian defects, F 2 and F 3 with ϕ=0 and ϕ=π/2, in periodic cholesteric structure, where A (blue) and B (red) are two units of the Fibonacci system, F 0 and F 1, and ϕ is an orientational defect angle between the molecular director in A layer and that in B layer at the interface (yellow). The case of ϕ=0 in Fig. 1 corresponds to the unmodified structure without a defect or a conventional cholesteric structure.

3. Multiple PBGs from the single-pitched CLCs

In order to investigate the optical properties of these quasi-periodic systems, we performed a theoretical calculation of the light propagation in the single pitch CLCs with the Fibonaccian defects using a 4×4 Berreman matrix[18

18. D. W. Berreman, “Optics in stratified and anisotropic media: 4×4-matrix formation,” J. Opt. Soc. Am. 62,502–510 (1972). [CrossRef]

].

The refractive indices of the birefringent planes are taken to be no=1.56 and ne=1.78, which are typical values for a PCLC [13

13. M. H. Song, N. Y. Ha, K. Amemiya, B. Park, Y. Takanishi, K. Ishikawa, J. W. Wu, S. Nishimura, T. Toyooka, and H. Takezoe, “Defect-mode lasing with lowered threshold in a three-layered hetero-cholesteric liquid-crystal structure,” Adv. Mater. 18,193–197 (2006). [CrossRef]

]. We considered the right-handed helical CLC (R-CLC) with a cholesteric pitch P and an optical pitch λP=P=532nm, where is an average refractive index and is given by =[(n 2 o+n 2 e)/2]1/2. Here, λP was so chosen that the center of multiple PBGs was located at a wavelength of green between primary colors such as red, green, and blue. The incident light was fixed in a right circularly polarized (RCP) light, since RCP light cannot propagate through the R-CLCs in a spectral range corresponding to the PBG. Under these fixed conditions, we calculated reflection spectra of samples changing the orientational defect angle, the order of the Fibonacci sequence, and a unit length UL of A or B in the Fibonacci system.

Figure 2 shows the dependence of reflection spectra on a defect angle when the order of the Fibonacci system is F 4={ABBAB} with 5 layers and a unit length of the sequence is UL=1P. As a reference, the reflection spectrum of a conventional CLC without a defect, i.e., ϕ=0 was calculated as shown in Fig. 2(a). It shows a single green-colored reflection, placing the center of the PBG at the spectral position of λP.

Fig. 2. (Color online) Reflection spectra for the Fibonacci system F 4={ABBAB} with orientational defect angles (a) ϕ=0, (b) ϕ=π/3, (c) ϕ=π/2, and (d) ϕ=π/6. For all simulations, we have considered a RCP incident light and the R-CLC with refractive indices ne=1.78 and no=1.56, an optical pitch λP=532nm, and an unit length of A or B layer UL=1P.

As shown in Fig. 2(b), multiple PBGs with three red-, green-, and blue-colored reflections are generated by introducing the Fibonaccian defect with ϕ=π/3 into a single green-colored CLC. The PBG width of a conventional CLC, depending on the difference between refractive indices ne and no, is about 50nm or 100nm and is limited to a single-colored region. In this sense, it is important to note that, without introducing any other materials or with the only single-pitched CLC, multiple reflections covering full colors could be obtained only by the structural change of the system.

The colors of such multiple PBGs could be controlled by changing an orientational defect angle. For example, Fig. 2(c) exhibits the reflection spectrum of the Fibonacci system with ϕ=π/2, where, as compared with Fig. 2(b), the reflectance due to the green-colored PBG at the center diminishes and that due to the red- and blue-colored PBGs increases. On the contrary, in the case of Fig. 2(d) with ϕ=π/6, a green-colored reflection becomes dominant. This optical behavior of multiple PBGs depending on an orientational defect angle has not been found in other Fibonacci systems[1

1. A. G. Barriuso, J. J. Monzon, L. L. Sanshez-Soto, and A. Felipe, “Comparing omnidirectional reflection from periodic and quasiperiodic one-dimensional photonic crystals,” Opt. Express 13,3913–3920 (2005). [CrossRef] [PubMed]

, 2

2. W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72,633–636 (1994). [CrossRef] [PubMed]

, 3

3. R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80,3063–3065 (2002). [CrossRef]

, 4

4. L. D. Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90,0555011–0555014 (2003).

, 5

5. M. Ghulinyan, C. J. Oton, L. D. Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. S. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71,0942041–0942048 (2005). [CrossRef]

]. The effect of tunable colors is similar to that discussed in the periodic CLC structure with orientational defects[14

14. I. J. Hodgkinson, Q. H. Wu, K. E. Thorn, A. Lakhtakia, and M. W. McCall, “Spaceless circular-polarization spectral-hole filters using chiral sculptured thin films: theory and experiment,” Opt. Commun. 184,57–66 (2000). [CrossRef]

, 15

15. V. I. Kopp and A. Z. Genack, “Twist defect in chiral photonic structures,” Phys. Rev. Lett. 89,0339011–0339014 (2002). [CrossRef]

], where the introduction of the phase jump in the CLC helix gives the phase difference between the reflections from the two parts separated by the phase jump. Hence, varying the orientational defect angle from ϕ=0 to ϕ=π adjusts the spectral position of defects from the low to the high wavelength band edge.

Next, Fig. 3 shows reflection spectra of the Fibonacci systems F 5={BABABBAB} with 8 layers, F 6={ABBABBABABBAB} with 13 layers, and F 7={BABABBABABBABBABABBAB} with 21 layers when orientational defect angles are (a) ϕ=π/3 and (b) ϕ=π/2. Colors in Fig. 3 represent the reflectance calculated from the quasi-periodic Fibonacci system. In Fig. 3, the whole reflectance and the number of multiple PBGs are proportional to the order of the Fibonacci system, and the increase in the Fibonacci order from F 5 to F 7 results in narrower widths of the central PBGs located in the green-colored region. These behaviors are similar to those of a general PBG material, i.e., the increasing of reflectance and the narrowing of the PBG width with increasing sample thickness. Particularly, the reflectance of the central PBG located in the green-colored region of Fig. 3(b) with ϕ=π/2 displays a pronounced dramatic dependence on the Fibonaccian order.

Fig. 3. (Color online) Reflection spectra for the Fibonacci systems F 5={BABABBAB}, F 6={ABBABBABABBAB}, and F 7={BABABBABABBABBABABBAB} with orientational defect angles (a) ϕ=π/3 and (b) π/2. Simulation conditions for CLCs and incident lights are the same as those of Fig. 2. Colors represent the reflectance calculated from the Fibonacci systems.
Fig. 4. (Color online) Reflection spectra as a function of the unit length UL for the Fibonacci systems (a)F 4, (b)F 5, (c)F 6, and (d)F 7 with an orientational defect angle ϕ=π/3. UL is normalized with a cholesteric pitch P. Simulation conditions are fixed as those employed for calculations in Fig. 2 and colors refer to reflectance of the systems.

In the Fibonacci system of CLCs, we also investigated the dependence of reflection spectra on the unit length of the quasi-periodicity. Figure 4 shows reflection spectra as a function of UL for the Fibonacci systems (a) F 4, (b) F 5, (c) F 6, and (d) F 7 with ϕ=π/3, where UL is normalized with P. Increasing UL from 2P to 5P, the width of the principal PBGs near λP becomes narrow. For example, in Fig. 4(a) the principal PBGs between 430 nm and 650 nm for UL=2P become narrower by 90 nm, resulting in those between 460 nm and 590 nm for UL=5P. It is also noticed that all principal PBGs in Fig. 2 and Fig. 3 always exist between 380 nm and 700 nm due to a constant UL=1P, although other simulation conditions such as the order of the Fibonacci sequence and an orientational defect angle are different from each other. Hence, we can conclude that broader multiple PBGs covering full colors are obtained by use of the Fibonaccian CLCs with shorter UL. With the increase of UL, transmission regions between principal PBGs (shown by dips in reflection spectra) become narrow and the reflectance of whole PBGs increases, as shown in Fig. 4. Considering finer PBG structures around the principal PBGs, the number and reflectance of the fine structures are proportional to UL of the quasi-periodic Fibonacci system (See Fig. 4). Finally, we should note that only negligible reflectance arises for left circularly polarized (LCP) light at least for small orders of Fibonacci system with R-CLCs such as F 2, F 3, and F 4.

4. Conclusions

In summary, by introducing Fibonaccian defects into organic CLC systems, we demonstrated simultaneous red-, green-, and blue-colored reflections or multiple PBGs from single-pitched CLCs theoretically. The color of reflections calculated from the quasi-periodic Fibonacci system could be controlled by an orientational defect angle. Moreover we investigated the dependence of reflection spectra on the order and the unit length of the Fibonacci system and found that the PBG width decreases and reflectance increases with increasing the order and the unit length of the Fibonacci system. This Fibonaccian CLC system could be fabricated using PCLCs and provide a range of possibilities for reflective color-displays. The experiments are undertaken in our lab and will be reported in the future.

References and links

1.

A. G. Barriuso, J. J. Monzon, L. L. Sanshez-Soto, and A. Felipe, “Comparing omnidirectional reflection from periodic and quasiperiodic one-dimensional photonic crystals,” Opt. Express 13,3913–3920 (2005). [CrossRef] [PubMed]

2.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72,633–636 (1994). [CrossRef] [PubMed]

3.

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80,3063–3065 (2002). [CrossRef]

4.

L. D. Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90,0555011–0555014 (2003).

5.

M. Ghulinyan, C. J. Oton, L. D. Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. S. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71,0942041–0942048 (2005). [CrossRef]

6.

L. D. Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, “Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals,” Appl. Phys. Lett. 84,5186–5188 (2004). [CrossRef]

7.

M. S. Vasconcelos and E. L. Albuquerque, “Transmission fingerprints in quasiperiodic dielectric multilayers,” Phys. Rev. B 59,11128–11131 (1999). [CrossRef]

8.

C. Li, X. Zhang, and Z. Cao, “Triangular and Fibonacci number patterns driven by stress on core/shell microstructures,” Science 309,909–911 (2005). [CrossRef] [PubMed]

9.

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

10.

J. Lub, P. Witte, C. Doornkamp, J. P. A. Vogels, and R. T. Wegh, “Stable photopatterned cholesteric layers made by photoisomerization and subsequent photopolymerization for use as color filters in liquid-crystal displays,” Adv. Mater. 15,1420–1425 (2003). [CrossRef]

11.

G. D. Filpo, F. P. Nicoletta, and G. Chidichimo, “Cholesteric emulsions for colored displays,” Adv. Mater. 17,1150–1152 (2005). [CrossRef]

12.

T. Yoshioka, T. Ogata, T. Nonaka, M. Moritsugu, S. -N. Kim, and S. Kurihara, “Reversible-photon-mode full-color display by means of photochemical modulation of a helically cholesteric structure,” Adv. Mater. 17,1226–1229 (2005). [CrossRef]

13.

M. H. Song, N. Y. Ha, K. Amemiya, B. Park, Y. Takanishi, K. Ishikawa, J. W. Wu, S. Nishimura, T. Toyooka, and H. Takezoe, “Defect-mode lasing with lowered threshold in a three-layered hetero-cholesteric liquid-crystal structure,” Adv. Mater. 18,193–197 (2006). [CrossRef]

14.

I. J. Hodgkinson, Q. H. Wu, K. E. Thorn, A. Lakhtakia, and M. W. McCall, “Spaceless circular-polarization spectral-hole filters using chiral sculptured thin films: theory and experiment,” Opt. Commun. 184,57–66 (2000). [CrossRef]

15.

V. I. Kopp and A. Z. Genack, “Twist defect in chiral photonic structures,” Phys. Rev. Lett. 89,0339011–0339014 (2002). [CrossRef]

16.

H. Hoshi, K. Ishikawa, and H. Takezoe, “Optical second-harmonic generation enhanced by a twist defect in ferroelectric liquid crystals,” Phys. Rev. E 68,0207011–0207013 (2003). [CrossRef]

17.

J. Schmidtke, W. Stille, and H. Finkelmann, “Defect mode emission of a dye doped cholesteric polymer network,” Phys. Rev. Lett. 90,0839021–083902 (2003). [CrossRef]

18.

D. W. Berreman, “Optics in stratified and anisotropic media: 4×4-matrix formation,” J. Opt. Soc. Am. 62,502–510 (1972). [CrossRef]

OCIS Codes
(160.3710) Materials : Liquid crystals
(160.4760) Materials : Optical properties
(230.4170) Optical devices : Multilayers
(330.1690) Vision, color, and visual optics : Color

ToC Category:
Materials

History
Original Manuscript: November 29, 2006
Revised Manuscript: January 13, 2007
Manuscript Accepted: January 22, 2007
Published: February 5, 2007

Virtual Issues
Vol. 2, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Na Young Ha, Yoichi Takanishi, Ken Ishikawa, and Hideo Takezoe, "Simultaneous RGB reflections from single-pitched cholesteric liquid crystal films with Fibonaccian defects," Opt. Express 15, 1024-1029 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-3-1024


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