1. Electrically-Switchable Liquid Crystal Gratings

Optical diffraction gratings play a central role in current technologies in areas such as multiplexing

and processing optical signals (optical interconnection, beam steering, and sensor array interrogation)

and protecting vital sensors from hostile radiation.1-5 Liquid crystals, whose refractive indices can be

modulated by external species with a profile, enable the design of very high efficiency phase gratings.

Further, perhaps the most compelling advantage of liquid crystals relates to the demand in many

important applications for thin film gratings whose optical properties such as birefringence are

dynamically adjustable.

Several approaches for liquid crystal gratings have been suggested. These strategies involve either

the use of patterned alignment layer (or electrode) on substrate sandwiching a low molecular weight

liquid crystal, an approach which produces domains of alternating orientation of LC optic axis, or the use

of polymer-liquid crystal composites, where a controlled polymer-liquid crystal phase separation induces

the grating structure. In all those systems, a refractive index gradient is imposed by lithographically (or

holographically) patterning the alignment layer/electrode or distribution of liquid crystal droplets with

random average director orientation within a polymer binder.

Switchable diffraction gratings based on polymer-stabilized dual-frequency nematic LCs

A switchable liquid crystal diffraction grating, responsive to both the frequency and magnitude of an applied voltage, is demonstrated in Fig. 1.6 The grating is based on polymer stabilization of modulated states of the liquid crystal optic axis induced at frequencies near a sign inversion of the dielectric anisotropy. In a particular case of frequency-based switching, 70% of the transmitted intensity of a 633 nm laser beam can be shifted into or out of a ±12° forward arc by changing the frequency of an applied voltage between 10 and 16 kHz at a fixed amplitude of 27 V.

FIG. 1. Forward diffraction patterns recorded for the stabilized 10 mm grating using a 633 nm laser at normal incidence and polarized along the grating axis. The applied voltage is Vp=50 V in (a), Vp =27 V at f=10 kHz in (b), and Vp=27 V at f=16 kHz in (c). (d) shows the diffraction efficiency (ratio of diffracted intensity to total transmitted intensity) as a function of input polarization for conditions of the applied voltage corresponding to (a) (filled circles) and (b) (open circles).

Polymer-Stabilized Cholesteric Gratings Polymer-stabilized cholesteric gratings have become a subject of attention because of the potential

as active diffractive optical elements.7,8 These gratings, formed by stabilizing the "fingerprint" texture of

a cholesteric LC induced in a standard electro-optical cell (Fig. 2), can function in either the Bragg or

Raman-Nath (phase grating) limits, and are particularly suited for optical beam steering, optical routing,

sensors or sensor protection applications requiring operation in transmission, high efficiency, and

millisecond response to a low voltage.

Fig. 2. The thickness to the pitch (d/p) ratio dependence of 1D stripe formation in a cholesteric liquid

crystal in response to applied voltage. When the d/p ratio ~1 the director of helix and grating vector are

parallel to the rubbing direction, by contrast, when the d/p>1 both the director of helix and grating

vector are perpendicular to the rubbing direction.

The free energy of the polymerizable diffraction grating system can be expressed as F = Felas + Fdiel + Fsur +

Fmix . The proposed model of periodic distortion of the LC host induces a spatial variation of Felas.

Reactive monomer molecules located at the less deformed regions. Reactive monomer phase separated

prior to the polymerization to minimize the elastic free energy of the system. Polymerization fixes a

director field driven monomer/polymer profile. Figure 3 is the pictorial illustration of elastic distortion

of a spatial variation of monomer rich and liquid crystal rich regions.

(a)

Von

Von

d/p = 1

d/p = 1.5

(b)

Fig. 3. (a) Pictorial illustration of field-induced periodical distortion of liquid crystal director and the polymerization

stabilized phase separation, (b) the electrically switchable light diffraction pattern and dynamics between the

grating off and granting on states, and (c) the morphology of 1-D periodical polymer wall with 10 micron space

between walls (scale bare is 10 m).

Two-Dimensional Switchable LC Gratings

Two dimensional (2D) electrically switchable cholesteric gratings may be achieved by applying

electric field to a cholesteric at the optimum field conditions (frequency and voltage) and cholesteric

pitch to cell thickness ratio.8,9 However, this type of gratings require a warm-up field to achieve the 2D

optical pattern forming state of a cholesteric and thus, it is inappropriate for practical applications. The

square-lattice texture shown in Fig.4 can function as a two-dimensional phase grating. Various

diffraction patterns obtained from the 2D-II texture prior to polymer stabilization are presented in

Figure 5.

(c) (d) (e) (f)

Fig.4. The square-lattice pattern of a cholesteric liquid crystal, induced by applying an alternating

electric field (1 kHz, 0.25 V/m) to the initial planar state. Polarizing optical micrographs show the square-lattice patterns (a) near the surface and (b) in the middle of the cell, respectively. The graphic illustration of (c) initial planar state of the sample at 0 V, (d) polymer stabilization via UV-initiated

polymerization under applied electric field V1 (1 kHz, 0.25 V/m); the arrows represent the helix tilting direction, (e) the “grating-off” state, and (f) the “grating-on” state under applied electric field V2 (The arrows represent the incident and exit light beam).

Fig.5. Optical diffraction patterns obtained by applying various amplitudes of applied electric fields to the cholesteric square-lattice pattern prior to polymer stabilization. In this case, the grating shows a poor reproducibility of the spatial orientation of diffraction patterns when the applied field is cycled.

PI rubbing

Fig. 6. The cholesteric grating is switchable among non-diffracting, one-dimensional, and two-

dimensional diffracting states. In this case, the grating is not stable in zero-field, but the “memory”

effect of the internal polymer network allows for precise reproducibility of the diffraction patterns when

the field is cycled.

The four panels of Fig. 7 show switching for a two-dimensional grating based on the stabilized square-lattice texture of Fig. 5. Three distinct diffracting states with two, four, and eight

dominant spots are accessible at relatively low fields of 0.18, 0.21, and 0.23 V/m, respectively. The corresponding diffraction efficiencies are 47%, 68%, and 84%. A dependence of the two dimensional diffraction patterns before and after the polymer stabilization as a function of magnitude of applied voltage is due to the dissolved reactive mesogen (with negative dielectric anisotropy).

Fig. 7. The cholesteric grating is switchable among non-diffracting, one-dimensional, and two-

dimensional diffracting states. In this case, the grating is not stable in zero-field, but the “memory”

effect of the internal polymer network allows for precise reproducibility of the diffraction patterns when

the field is cycled.

Polymer-Stabilized Liquid Crystal Blazed Gratings

A polymer-stabilized liquid crystal blazed grating having a prismatic polymer microstructure has been developed.10 The polymer structure is fabricated by photo-induced localization and polymerization of a small concentration of monomer onto one substrate of an electro-optical cell by using ultraviolet light

irradiation at 45o direction from normal incident. Using this method a periodical one-dimensional pattern with a prismatic shape of polymer can be formed on a one-dimensional pattern-forming state of a cholesteric host. The optical diffraction properties of the grating are evaluated by the application of electric field and light incident angles.

(a) (b)

(c) (d)

Fig.4. (a) Schematic illustration of the UV polymerization apparatus with slantwise irradiation. (b) Curved arrow represents rotation of the UV light source for the various slantwise irradiation, (c) the polymer-stabilized blazed grating is switched to display from asymmetric light intensities at zero volt to

symmetric light diffraction pattern at 0.9 V/m and to non-diffraction state at 2.0 V/m, (d) the surface localized polymer morphology exhibits a prism-like feature.

1. McManamon,P. F., Watson,E. A., Dorschner,T. A., Barnes, L. J. Applications look at the use of liquid crystal writable gratings for steering passive radiation, Opt. Eng. 32, 2657-2664 (1993).

2. Minewicz, A., Gniewwek, A., Parka, J. Liquid crystals for photonic applications, Optical Materials, 21, 605 (2003).

3. Klaus, W., Ide, M., Morokaw, S., Tsuchiya, M., Kamiya, T. Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes, Optics Communication, 138, 151 (1997).

4. Gibbsons, W.M., Sun, S. T. Optically generated liquid crystal gratings, Appl. Phys. Lett., 65, 2542 (1994).

5. Nose, T. Masuda, S. Sato, S. Li, J. Chien, L.-C. and Bos, P., “Effects of Low Polymer Content in a Liquid-Crystal Microlens,” Optics Letters, 22, 351 (1997).

6. Kang, S.W., Sprunt, S. Sprunt, Chien, L.C., Appl. Phys. Lett., 78, 3783 (2001) 7. Lee, S. N., Sprunt, S., Chien, L. C. Morphology-dependent Switching of Polymer-Stabilized Cholesteric

Gratings, Liq. Cryst., 28, 637 (2001). 8. Helfrich, W. Appl. Phys. Lett. 17, 531 (1970). 9. Kang, S.-W., Chien, L.-C., “Field-induced and polymer-stabilized two-dimensional cholesteric liquid

crystal gratings.” Appl. Phys. Lett. 90, 221110/1-221110/3 (2007). Kang, S. W. Ph.D. Dissertation of Kent State University (2002).

10. Kim, S. H. and Chien, L. C. Liquid crystal blazed gratings formed in a single-step through photo-induced localization of polymer into a prismatic structure, Opt. Express, 12, 1238-1242 (2004).

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