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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 5 — Feb. 28, 2011
  • pp: 4611–4617

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Electrooptic jumps in natural helicoidal photonic bandgap structures

Karen Allahverdyan and Tigran Galstian  »View Author Affiliations


Optics Express, Vol. 19, Issue 5, pp. 4611-4617 (2011)
http://dx.doi.org/10.1364/OE.19.004611


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Abstract

Strong electro mechanical effect was used to generate and study self adaptation and pitch jumps in a helicoidal photonic bandgap structure naturally formed by a cholesteric liquid crystal. The negative dielectric anisotropy of the material allowed its stabilization by the electric field and important thickness changes, achieved thanks to the use of a very thin substrate, allowed the observation of multiple dynamic jumps at fixed deformation conditions. Spectral and morphological studies of the material during those jumps were performed too.

© 2011 OSA

Helicodial periodic structures, such as cholesteric liquid crystals (CLCs) [1

P. G. de Gennes, and J. Prost, The Physics of Liquid Crystals , (Oxford University Press, 1995), 2nd Edition.

], are one-dimensional photonic band gaps (PBG), which are present in the nature in different forms [2

A. C. Neville and S. Caveney, “Scarabaeid beetle exocuticle as an optical analogue of cholesteric liquid crystals,” Biol. Rev. Camb. Philos. Soc. 44(4), 531–562 (1969). [CrossRef] [PubMed]

]. Those are very promising systems for tunable distributed feedback lasing [3

H. Finkelmann, S. T. Kim, A. Muñoz, P. Palffy-Muhoray, and B. Taheri, “Tunable Mirrorless Lasing in Cholesteric Liquid Crystalline Elastomers,” Adv. Mater. 13(14), 1069–1072 (2001). [CrossRef]

–5

Y. Huang, Y. Zhou, C. Doyle, and S.-T. Wu, “Tuning the photonic band gap in cholesteric liquid crystals by temperature-dependent dopant solubility,” Opt. Express 14(3), 1236–1242 (2006). [CrossRef] [PubMed]

], large band reflection [6

D. J. Broer, J. Lub, and G. N. Mol, “Wide-band reflective polarizers from cholesteric polymer networks with a pitch gradient,” Nature 378(6556), 467–469 (1995). [CrossRef]

], tunable filtering [7

M. Mitov, E. Nouvet, and N. Dessaud, “Polymer-stabilized cholesteric liquid crystals as switchable photonic broad bandgaps,” Eur Phys J E Soft Matter 15(4), 413–419 (2004). [CrossRef] [PubMed]

–9

W. C. Yip and H. S. Kwok, “Helix unwinding of doped cholesteric liquid crystals,” Appl. Phys. Lett. 78(4), 425–427 (2001). [CrossRef]

], etc. In addition to their spatial periodic character, CLCs have unique vectorial properties, which are related to their helicoidal nature and which affect significantly the character of modes of the PBG [1

P. G. de Gennes, and J. Prost, The Physics of Liquid Crystals , (Oxford University Press, 1995), 2nd Edition.

]. Thus, for example, the eighenmodes of such a PBG are circularly polarized waves and the momentum conservation requirement prohibits the existence of higher order Bragg reflections at normal incidence [1

P. G. de Gennes, and J. Prost, The Physics of Liquid Crystals , (Oxford University Press, 1995), 2nd Edition.

,10

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

]. This well known phenomenon is demonstrated in Fig. 1 , where we can see the transmission spectra of a mono domain cell filled by a CLC mixture, composed of 46 wt % of CB15 (from Merck) and 54 wt % of a homemade nematic liquid crystal 1756-6: the absence of the second order Bragg reflection is shown by the vertical arrow. Another unique property of those structures is their “spatial adaptivity”. That is, the chemical composition and the molecular chirality ofthe CLC define the natural period PN of complete (2π) helical molecular rotation for “free” boundary conditions only. In reality, there are always given boundary conditions, which define the “adjusted” period PA of the helix depending upon the distance L of substrates of the cell that contains the CLC and upon the molecular anchoring conditions on those substrates. Thus, if the alignment angle of the director n (average alignment of molecular axes [1

P. G. de Gennes, and J. Prost, The Physics of Liquid Crystals , (Oxford University Press, 1995), 2nd Edition.

], ) on two opposite substrates (at z=0 and z=L) of the cell is fixed by strong boundary conditions, say providing a total rotation of θ(L), then the PA of the CLC will be naturally “self-adjusted” to provide a constant rate of spatial rotation Q≡ ∂θ/ ∂z= 2π/ PA of its director in a way to satisfy the above mentioned boundary conditions with θ(L)= 2πL/ PA. The associated (to this adjustment) energy of director’s deformation will be counter-balanced by the anchoring energy of substrates. This total rotation angle may be split into NC complete rotations (on 2π) and some additional rotation θ(L)=2π NC+δθ. Thus, we will have NC= L/ PA for δθ=0, which is the case of the present experiment (see later). It must be noticed also that, given the local equivalence of n and - n, the optical periodicity and corresponding resonance wavelength λR of the CLC are defined by the half period PR= PA/2 of the helix (corresponding to director’s rotation on angle π) as λR=2 n av PR,where n av= ( n∥+ n⊥)/2 is the average refractive index of the CLC, n∥ and n⊥ being the local extraordinary and ordinary refractive indexes of the CLC, respectively. That is why; the number of those half-helixes (or pitches) N=2 NC is often used for the analyses of the CLC’s behaviour.

Fig. 1 Transmission spectra of a CLC mixture, measured with an unpolarized probe beam, demonstrating the key characteristics of a CLC: the absence of the second order Bragg reflection (shown by the vertical arrow) and the large bandwidth of the resonance defined by the local anisotropy of the CLC.

Finally, the value of PR depends also upon various external stimuli, such as temperature, electric and magnetic fields [1

P. G. de Gennes, and J. Prost, The Physics of Liquid Crystals , (Oxford University Press, 1995), 2nd Edition.

–12

S. P. Palto, “On Mechanisms of the Helix Pitch Variation in a Thin Cholesteric Layer Confined between Two Surfaces,” J. Exp. Theor. Phys. 94(2), 260–269 (2002). [CrossRef]

]. This dependence attracted significant interest in view of possible applications in dynamic electro optic modulation devices, see also Ref [13

L. M. Blinov, and V. G. Chigrinov, Electrooptics Effects in Liquid Crystal Materials (Springer-Verlag, New York, 1994).

]. In particular, the behaviour of CLC under the action of electric field has been intensively studied for CLCs having positive and negative dielectric anisotropies ∆ε (see Ref [14

C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010). [CrossRef]

] and references therein). Various mechanisms of PR modulation have been considered so far, but finally the electromechanical deformation, induced by DC voltage was clearly identified as a dominating mechanism in CLCs with negative ∆ε [14

C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010). [CrossRef]

]. This work reported very interesting data and analyses, including the detailed description of smooth variations of λR upon the electric field induced deformation of cell substrates. The possibility of dynamic breaking of the boundary condition, to change the number of pitches by jumps, was briefly mentioned in the stationary excitation regime and also was demonstrated when periodically tightening and loosening the clamp, which held the sample [14

C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010). [CrossRef]

].

In the present work, we further investigate this phenomenon but in much stronger excitation regime. This is achieved by means of the use of a very thin cell substrate subjected to AC voltage. We show that those CLCs may demonstrate multiple abrupt transient pitch changes even at stationary regime of excitation, at predetermined values of fixed electric field (without tightening and loosening the clamp) and that this “jumping” process is happening via the formation of a transient disclination (line of abrupt change of director orientation), while maintaining its bulk helical characteristics.

The material composition used in the present work was the mixture CB15, purchased from Merck and used without modifications. It is a CLC with negative ∆ε, thus, the application of an electric field is stabilizing the helix. The cell was built by using an ITO coated glass substrate of thickness 0.7 mm, which was additionally coated by a uniformly rubbed planar alignment Polyimide (PI 150, from Nissan). An adhesive wall was dispensed on the periphery of this substrate providing a square shaped working area (optical window) of ≈6.5 x 6.5 mm2 size. The adhesive contained spacers to provide the desired thickness of the cell L=5 μm (±0.5 μm). Then a second substrate, similar to the first one, but with thickness of 0.1 mm, was pressed on the first one and the peripheral adhesive was photo polymerized by using a UV lamp exposure. The CLC mixture was then injected into the obtained sandwich-like cell by capillary action at room temperature. All our experiments have been done at room temperature (the isotropic phase transition of CB15 happening approximately at 37.5°C±0.5°C).

We have started our experiments by spectral studies using a Scienctech spectrophotometer with THI Halogen lamp and LDA 2000 monochromator. It is interesting to note that the transmission spectra (Fig. 2 ) of obtained cells were not perfectly symmetric, which could be related to the imperfections of the helix (tilted domains generating effective “blue shift” of reflection) as well as to the non ideal collimation of the probe beam (which creates an artificial “apodization” effect of the grating structure). However, it is also important to mention that even in perfect experimental conditions the resonance of the CLC has certain width ∆λ, which is defined as Δλ=Δn PAwhere the Δn≡ n∥− n⊥is the local optical anisotropy of the CLC [1

P. G. de Gennes, and J. Prost, The Physics of Liquid Crystals , (Oxford University Press, 1995), 2nd Edition.

,11

V. A. Belyakov, “Untwisting of the Helical Structure in a Plane Layer of Chiral Liquid Crystal,” JETP Lett. 76(2), 88–92 (2002). [CrossRef]

].

Fig. 2 The transmission spectra of the CLC cell for unpolarized input light at different RMS voltages applied to the cell up to the first jump of the pitch (voltages are growing from 0 to 18 RMS Volts; low excitation regime).

We have analyzed the spectral characteristics of the cell for different voltages applied to ITOs (waiting 5-10 minutes after each voltage change, before taking the data) by means of an Avtech power supply (AV-151 B-C) generating sin shaped AC signal of 1 kHz frequency.

As one can see in the Fig. 2 and Fig. 3 , the moderate increase of the voltage brings to smooth changes of λR, as already reported in Ref [14

C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010). [CrossRef]

]. One of the noticeable differences (apart of the material and AC excitation) here is the slope of this variation, which is very high in our case; approximately 18 nm for 17 V (applied to the 5 μm thick cell), providing thus a shift coefficient ≈5.3 nm/V/μm, which is more than twice the maximum value reported so far [15

L. V. Natarajan, J. M. Wofford, V. P. Tondiglia, R. L. Sutherland, H. Koerner, R. A. Vaia, and T. J. Bunning, “Electro-thermal tuning in a negative dielectric cholesteric liquid crystal material,” J. Appl. Phys. 103(9), 093107 (2008). [CrossRef]

], thanks to the thin cell substrate used here.

Fig. 3 The dependence of the resonance wavelength of the CLC upon the RMS voltage applied to the cell (growing voltage: open squares and decreasing voltage: filled circles).

As we can see also in the Fig. 2, the value of λR of the CLC is approximately equal to 0.542 μm in the ground state (U=0 volt; the resonance shifting towards shorter wavelengths with the temperature increase). Surprisingly, in spite of the rather large utilisation of the CB15 mixture, to the best of our knowledge, there is no information about its optical properties. We have done measurements of its average refractive index, which gave us the following value: n av≈1.567±0.002. We can thus estimate the room temperature ( T≈21°C) value of PA= 0.542μm/ 1.567≈0.35μm. Thus, for an initial thickness of L=5μm, the number of helixes would then be NC= 5/ 0.35≈14 (so, 28 half helixes). In the same time, we used also the corresponding width of the resonance Δλ=40nm (from Fig. 2) to evaluate the local anisotropy of that compound Δn= Δλ/ PA≈ 40 nm/0.35μm=0.114, supposing an ideal helix which is a rather high value for CLC materials.

The further increase of the voltage shows an abrupt “return jump” of λR, at U≈17 V RMS, see Fig. 2 (curve for 18 V) and Fig. 3 (open squares). This jump happens within approximately 3 min at fixed voltage (observed with a probe beam of diameter ≈1 mm). In fact, with the continued increase of the voltage, we observe multiple zones of such smooth modulations followed by abrupt changes of the value of λR. We estimate that the cell thickness is reduced (from initial 5μm) to approximately 4.4μm for the voltage value of 30 V. The decrease of the voltage then brings to the inverse transformation (Fig. 3, filled circles) with however some variations of the positions of those jumps and also of the depth of modulation of the values of λR. This hysteresis-like behaviour may be related to the mechanical movement of the substrate, which in addition, is coupled with the mechanical movement of the CLC and with the deformation of its director. Thus, the starting point during our experiments was λR=0.528μm or λR=0.542μm in a non regular manner. We would need more studies to better understand the origins of such bistability, while similar phenomena have been also described in [16

(a)V. A. Belyakov and W. Kuczynski, “Motion of Nonsingular Walls in Plane Layer of Twistwd Nematics,” MCLC 480, 243 (2008).

(b)V. A. Belyakov, “ Cano-Grangjean Wedge at Weak Surface Anchoring,” MCLC 480, 262 (2008).

c) V.A. Belyakov, D.V. Shmeliova, Nonsingular Walls in Cano-Grangjean Wedge, MCLC v.527, p.53/[2009] (2010).

]).

It is clear that the use of a thin (0.1 mm) substrate allowed us to obtain significantly stronger (more deformation is obtained at much lower voltages) electro-mechanical effect compared to Ref [14

C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010). [CrossRef]

]. As we can see in the Fig. 4 , the bending of the thin substrate is easily observed (at room temperature) in the reflected, from the cell, light after filling it by the CLC (the cell is illuminated by the broad band light of the ambient illumination, and its reflection is observed at the optimal angle to visualize the periodic transverse modulation of reflection).

Fig. 4 Ring structure observed in the reflected, from the CLC-filled cell, for various voltages applied 20 V (left picture) and 10 V (right picture). Vertically aligned half ellipsoidal white zones (on right and left sides of each picture) are the conductive adhesive zones with vertical wires in the bottom zones of the figure.

In fact, the electro-mechanical modulation of the cell thickness L is so strong that the energy of director deformation (needed to adapt the value of PR ) is overcoming the energy necessary to create a transient disclination of the director. This disclination is the transition mechanism, which allows the re-adjustment of the PR for the given value of L, while preserving the overall helical structure of the CLC, as demonstrated in the Fig. 5 . In fact, the spectral monitoring of the cell during this transition was done when the applied voltage was set just above the critical voltage UC (that is necessary to cause the jump of λR). The consecutive moments of the same jump are represented by the curves 1 (squares), 2 (circles) and 3 (triangles), taken with approximately 1 min of delay. This monitoring confirms that the spectral and vectorial characteristics of the resonance do not change significantly (obviously, averaged on the area covered by the probe beam, approximately 1 mm2) during those jumps, the second order Bragg reflection being always non observable (not shown here).

Fig. 5 Spectral modifications of the cell during the evolution of the disclination (at a fixed voltage, slightly above the jumping threshold voltage) allowing the re-adjustment of the pitch of the helix. Consecutive spectra (labelled 1, 2 and 3) are taken with approximately 1 min of delay.

Observations of the same transition, using Zeiss polarizing microscope, allow the confirmation of the above mentioned scenario. As it can be seen in the Fig. 6 (bottom left), in this particular case, the disclination is generated almost simultaneously in the top right corner and the left side of the picture, when the voltage exceeds the threshold value 20V (which, by the way, differs from cell to cell, but also can be slightly different for the same cell from experiment to experiment, on approximately ±10%). Then, for a fixed voltage (20 V), the left-side disclination wall propagates faster and merges with the top right corner zone providing a stabilized CLC with a new PR . It must be emphasized however that this picture shows only the central part of the cell where the disclination walls usually appear. From cell to cell, various surface or volume defects were at the origin of those disclinations.

Fig. 6 Microscope observation of the transient propagation of the disclination wall allowing the establishement of a self-adjusted (to the new value of L) period of director rotation. Consecutive pictures (at 20 V) are taken with approximately 0.5 min of delay.

Discussion

One can notice (from the Fig. 3) that the slope of the dependence λR(U) in the first zone (for voltages below 17 V) is relatively small and the corresponding voltage range of smooth changes (before the first jump) is rather broad. In contrast, the slope increases and the smooth zone’s width decreases for further zones. This is consistent with the hypothesis of periodic generation of transient disclination lines allowing the jumps of PA . In fact, for a given value of cell thickness L, its reduction ΔL must be redistributed equally on the number of pitches and the director’s rotation rate Q (between jumps) must then be increased consequently Q+ΔQ= 2π/ ( P A0− ΔL/ NC) to reduce the initial period PA0 of the helix on the amount ΔL/ NC. In the same time, the appearance and propagation of the disclination wall is a rather complex phenomenon [1

P. G. de Gennes, and J. Prost, The Physics of Liquid Crystals , (Oxford University Press, 1995), 2nd Edition.

,16

(a)V. A. Belyakov and W. Kuczynski, “Motion of Nonsingular Walls in Plane Layer of Twistwd Nematics,” MCLC 480, 243 (2008).

(b)V. A. Belyakov, “ Cano-Grangjean Wedge at Weak Surface Anchoring,” MCLC 480, 262 (2008).

c) V.A. Belyakov, D.V. Shmeliova, Nonsingular Walls in Cano-Grangjean Wedge, MCLC v.527, p.53/[2009] (2010).

]. The situation here is further complicated due to the presence of the mechanical movement and stabilizing electrical field (since Δε<0). Qualitatively, we can imagine the process of observed pitch jumps as the transient analogy of structures observed in the stationary Cano wedge cell [17

B. Cano, Soc. Fr. Mineral. Cristallogr. 90, 333 (1967).

,18

E.P. Raynes, “Twisted wedges for the measurement of long pitch lengths in chiral nematic liquid crystals,” Liquid Crystals, 34(6), 697–699 (2007).

]. This analogy however is limited to the role of disclination wall spliting two neighboring zones with clearly distinguishable pitches. Closer analyses of the disclination wall, dynamically propagating from the left corner, shows that its width is at the order of l ~3 μm with some “fine structure” (not shown here) of light transmission modulation (across the wall) with characteristic sizes of ≤ 0.5 μm. In the same time, the character (and structure) of the disclination line, which started from the top right corner, is different, which perhaps could explain its lower spatial mobility. Further studies must be conducted to understand this difference, but the possibility of generating singularity lines of different forces has been already discussed in the literature [1

P. G. de Gennes, and J. Prost, The Physics of Liquid Crystals , (Oxford University Press, 1995), 2nd Edition.

]. For the moment, in a very rough approximation, we could imagine that the additional density of free energy (due to the additional rotation rate ΔQ allowing the pitch adaptation) could be estimated to be at the order of FA∼0.5 K2Δ Q2, where K2 is the twist elasticity constant, typically at the order of 10−6 erg/cm [1

P. G. de Gennes, and J. Prost, The Physics of Liquid Crystals , (Oxford University Press, 1995), 2nd Edition.

]. Given the complexity of the disclination wall (including various types of deformation), we could consider the so called one-constant elasticity approximation ( K1= K2= K3≡K) to evaluate very roughly the corresponding energy. Thus, with the scale of this deformation l, the corresponding energy Fd might be estimated by the following expression Fd≈ K/ l2 [1

P. G. de Gennes, and J. Prost, The Physics of Liquid Crystals , (Oxford University Press, 1995), 2nd Edition.

]. Thus, the generation of the disclination wall will be energetically justified for voltage values (and corresponding deformations) satisfying the condition FA≥ Fd+Δ FS, where ΔFS is the difference in anchoring energy before and after the generation of the disclination. In the framework of present approximation, we shall consider the ΔFS to be independent upon the thickness of the cell (it could be interesting to use the described here experimental technique to estimate the surface anchoring potential [19

We thank the referee for pointing out this possibility.

]). Thus, for approximately the same value of Fd , the pitch jumps should happen when the thickness reduction ΔL would generate the critical change of rotation rate Δ Q2≈2 (K l2+Δ FS)/ K2. Given the definition of ΔQ= 2πΔL/ [ P A0( NC P A0−ΔL)], we obtain, for small deformations (ΔL<<L), that those critical values of ΔQ (and thus the corresponding pitch jumps) would be achieved for larger values of ΔL if the number of pitches NC was initially high. In the same way, the slopes of both dependences ΔQ(ΔL) and λR(ΔL), will be higher for lower values of NC. Both above mentioned hypotheses are in agreement with our experimental observations (Fig. 3).

In conclusion, we believe that the present work allowed us to observe significantly higher electro-optic effect by using a thin cell substrate. The combination of two conditions (more flexibility and helix stabilizing field) allowed us to generate multiple pitch jumps. The spectral and polarizing microscope observations confirmed that the key features of the helix are preserved and the self-adaptation proceeds via a transient disclination propagation. This work however shows also that the modulation range of λR in those self-adaptive CLCs is limited (in our case, to approximately ± 5%) due to the self-adaptivity of the CLC, which generates transient disclination and re-adjusts its period when the deformation of the pitch becomes energetically “unfavorable”.

Acknowledgments

We acknowledge the financial support of Canadian Institute for Photonic Innovations (CIPI), Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT) and Natural Sciences and Engineering Research Council of Canada (NSERC). We also thank TLCL Research Optics inc for the material support.

References and links

1.

P. G. de Gennes, and J. Prost, The Physics of Liquid Crystals , (Oxford University Press, 1995), 2nd Edition.

2.

A. C. Neville and S. Caveney, “Scarabaeid beetle exocuticle as an optical analogue of cholesteric liquid crystals,” Biol. Rev. Camb. Philos. Soc. 44(4), 531–562 (1969). [CrossRef] [PubMed]

3.

H. Finkelmann, S. T. Kim, A. Muñoz, P. Palffy-Muhoray, and B. Taheri, “Tunable Mirrorless Lasing in Cholesteric Liquid Crystalline Elastomers,” Adv. Mater. 13(14), 1069–1072 (2001). [CrossRef]

4.

G. Chilaya, A. Chanishvili, G. Petriashvili, R. Barberi, R. Bartolino, G. Cipparrone, A. Mazzulla, and P. V. Shibaev, “Reversible Tuning of Lasing in Cholesteric Liquid Crystals Controlled by Light-Emitting Diodes,” Adv. Mater. 19(4), 565–568 (2007). [CrossRef]

5.

Y. Huang, Y. Zhou, C. Doyle, and S.-T. Wu, “Tuning the photonic band gap in cholesteric liquid crystals by temperature-dependent dopant solubility,” Opt. Express 14(3), 1236–1242 (2006). [CrossRef] [PubMed]

6.

D. J. Broer, J. Lub, and G. N. Mol, “Wide-band reflective polarizers from cholesteric polymer networks with a pitch gradient,” Nature 378(6556), 467–469 (1995). [CrossRef]

7.

M. Mitov, E. Nouvet, and N. Dessaud, “Polymer-stabilized cholesteric liquid crystals as switchable photonic broad bandgaps,” Eur Phys J E Soft Matter 15(4), 413–419 (2004). [CrossRef] [PubMed]

8.

S.-Y. Lu and L.-C. Chien, “A polymer-stabilized single-layer color cholesteric liquid crystal display with anisotropic reflection,” Appl. Phys. Lett. 91(13), 131119 (2007). [CrossRef]

9.

W. C. Yip and H. S. Kwok, “Helix unwinding of doped cholesteric liquid crystals,” Appl. Phys. Lett. 78(4), 425–427 (2001). [CrossRef]

10.

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

11.

V. A. Belyakov, “Untwisting of the Helical Structure in a Plane Layer of Chiral Liquid Crystal,” JETP Lett. 76(2), 88–92 (2002). [CrossRef]

12.

S. P. Palto, “On Mechanisms of the Helix Pitch Variation in a Thin Cholesteric Layer Confined between Two Surfaces,” J. Exp. Theor. Phys. 94(2), 260–269 (2002). [CrossRef]

13.

L. M. Blinov, and V. G. Chigrinov, Electrooptics Effects in Liquid Crystal Materials (Springer-Verlag, New York, 1994).

14.

C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010). [CrossRef]

15.

L. V. Natarajan, J. M. Wofford, V. P. Tondiglia, R. L. Sutherland, H. Koerner, R. A. Vaia, and T. J. Bunning, “Electro-thermal tuning in a negative dielectric cholesteric liquid crystal material,” J. Appl. Phys. 103(9), 093107 (2008). [CrossRef]

16.

(a)V. A. Belyakov and W. Kuczynski, “Motion of Nonsingular Walls in Plane Layer of Twistwd Nematics,” MCLC 480, 243 (2008).

(b)V. A. Belyakov, “ Cano-Grangjean Wedge at Weak Surface Anchoring,” MCLC 480, 262 (2008).

c) V.A. Belyakov, D.V. Shmeliova, Nonsingular Walls in Cano-Grangjean Wedge, MCLC v.527, p.53/[2009] (2010).

17.

B. Cano, Soc. Fr. Mineral. Cristallogr. 90, 333 (1967).

18.

E.P. Raynes, “Twisted wedges for the measurement of long pitch lengths in chiral nematic liquid crystals,” Liquid Crystals, 34(6), 697–699 (2007).

19.

We thank the referee for pointing out this possibility.

OCIS Codes
(160.3710) Materials : Liquid crystals
(160.5293) Materials : Photonic bandgap materials

ToC Category:
Photonic Crystals

History
Original Manuscript: November 24, 2010
Revised Manuscript: December 28, 2010
Manuscript Accepted: December 31, 2010
Published: February 24, 2011

Citation
Karen Allahverdyan and Tigran Galstian, "Electrooptic jumps in natural helicoidal photonic bandgap structures," Opt. Express 19, 4611-4617 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-5-4611


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References

  1. P. G. de Gennes, and J. Prost, The Physics of Liquid Crystals, (Oxford University Press, 1995), 2nd Edition.
  2. A. C. Neville and S. Caveney, “Scarabaeid beetle exocuticle as an optical analogue of cholesteric liquid crystals,” Biol. Rev. Camb. Philos. Soc. 44(4), 531–562 (1969). [CrossRef] [PubMed]
  3. H. Finkelmann, S. T. Kim, A. Muñoz, P. Palffy-Muhoray, and B. Taheri, “Tunable Mirrorless Lasing in Cholesteric Liquid Crystalline Elastomers,” Adv. Mater. 13(14), 1069–1072 (2001). [CrossRef]
  4. G. Chilaya, A. Chanishvili, G. Petriashvili, R. Barberi, R. Bartolino, G. Cipparrone, A. Mazzulla, and P. V. Shibaev, “Reversible Tuning of Lasing in Cholesteric Liquid Crystals Controlled by Light-Emitting Diodes,” Adv. Mater. 19(4), 565–568 (2007). [CrossRef]
  5. Y. Huang, Y. Zhou, C. Doyle, and S.-T. Wu, “Tuning the photonic band gap in cholesteric liquid crystals by temperature-dependent dopant solubility,” Opt. Express 14(3), 1236–1242 (2006). [CrossRef] [PubMed]
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  19. We thank the referee for pointing out this possibility.

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