**4. Photorefractive effect of FLCs**

*II l* = G <sup>0</sup> exp , ( ) (1)

(2)

 

 

**Figure 8.** Schematic illustrations of (a) photochromic and (b) photorefractive gratings.

of the transmitted signal beam is given by:

regime, *Q* > 10 is often required.

according to the following equation [5]:


regime. The diffraction conditions are distinguished by a parameter *Q* [3]:

where *λ* is the wavelength of the laser, *L* is the interaction path length, *n* is the refractive index, and Λ is the grating spacing. If the *Q* value is larger than 1, the condition is classified to the Bragg regime of optical diffraction in which only one order of diffraction is allowed. If *Q* value is smaller than 1, the condition is classified to the Raman-Nath regime of optical diffraction in which many orders of diffraction are allowed. In order to guarantee the entire Bragg diffraction

The two-beam coupling gain coefficient Γ (cm-1) for the Bragg diffraction condition is calculated

*Q Ln* <sup>2</sup> = L 2/, pl

where *I0* is the signal beam intensity, *l* is the interaction length in the sample, and Γ is the gain coefficient. In order to obtain the two-beam coupling gain coefficient, the diffraction condition must be clarified whether it is in the Bragg diffraction regime or in the Raman-Nath diffraction

 

132 Ferroelectric Materials – Synthesis and Characterization

 

A schematic illustration of the setup used for the two-beam coupling experiment is shown in Figure 9(a). Laser beams (p-polarized) are interfered in the sample. An electric field (external electric field) is applied to the sample to increase the efficiency of charge generation in the film. The transmitted intensities of the laser beams through the sample are monitored. If a material exhibits photorefractive effect, an asymmetric energy exchange is observed. The magnitude of photorefractive effect is evaluated by the magnitude of gain coefficient, which is obtained from the two-beam coupling experiment [3]. According to the standard theory of the photo‐ refractive effect with the limit of the ratio of beam intensities (pump/signal) >>1, the intensity

### **4.1. Two-beam coupling experiments on FLCs**

 Investigations into the photorefractive effect of FLCs started in the year 2000 [12, 13]; the photorefractive FLC is a mixture of FLC and photoconductive compounds. Further details of the photorefractivity in FLC materials have since been investigated by Sasaki et al. and Talarico et al. [14-19]. The structures of the photoconductive compounds used are shown in Figure 10. A commercially available FLC, SCE8 (Clariant, SmC\* 60 °C SmA 80 °C N\* 104 °C I, spontaneous polarization = 4.5 nC/cm2 ), was used in preliminary investigations. SCE8 is a mixture of LC compounds and chiral compounds. Carbazole diphenylhydrazone (CDH) as a photoconduc‐ tive compound and trinitrofluorenone (TNF) as a sensitizer were used at concentrations of 2 wt.% and 0.1 wt.%, respectively. The samples were injected into a 10 μm gap glass cell equipped with 1 cm2 indium tin oxide electrodes and a polyimide alignment layer (Figure 11). A typical example of asymmetric energy exchange observed in the FLC (SCE8)/CDH/TNF sample under an applied DC electric field of 0.1 V/μm [17] is shown in Figure 12. The grating formation was within the Bragg diffraction regime. Interference of the laser beams in the FLC medium resulted in increased transmittance of one beam and decreased transmittance of the other. The transmitted intensities of the two beams changed symmetrically, indicating that the phase of the refractive index grating is shifted from that of the interference fringe as shown in Figure 12.

The temperature dependence of the gain coefficient of the FLC (SCE8) doped with 2 wt.% CDH and 0.1 wt.% TNF is shown in Figure 13(a). In this sample, asymmetric energy exchange was observed only at temperatures below 46 °C. Figure 13(b) shows the temperature dependence of the spontaneous polarization of the identical sample. When the temperature was raised above 46 °C, the magnitude of the spontaneous polarization dropped to zero. Thus, the photorefractive effect of the FLC was observed only at temperatures where the sample exhibits ferroelectric phase. The reorientation associated with spontaneous polarization is induced by the internal electric field in the ferroelectric phase. The change in the direction of spontaneous polarization causes a change at the orientation of FLC molecules in the corresponding area. A maximum resolution of 0.8 μm was obtained for this sample [16].

 

 

**Figure 10.** Structures of the photoconductive compound CDH and the sensitizer TNF.

**Figure 11.** Laser beam incidence condition and the structure of the LC cell.

transmitted intensities of the two beams changed symmetrically, indicating that the phase of the refractive index grating is shifted from that of the interference fringe as shown in Figure 12.

The temperature dependence of the gain coefficient of the FLC (SCE8) doped with 2 wt.% CDH and 0.1 wt.% TNF is shown in Figure 13(a). In this sample, asymmetric energy exchange was observed only at temperatures below 46 °C. Figure 13(b) shows the temperature dependence of the spontaneous polarization of the identical sample. When the temperature was raised above 46 °C, the magnitude of the spontaneous polarization dropped to zero. Thus, the photorefractive effect of the FLC was observed only at temperatures where the sample exhibits ferroelectric phase. The reorientation associated with spontaneous polarization is induced by the internal electric field in the ferroelectric phase. The change in the direction of spontaneous polarization causes a change at the orientation of FLC molecules in the corresponding area. A

 

 

maximum resolution of 0.8 μm was obtained for this sample [16].

**Figure 10.** Structures of the photoconductive compound CDH and the sensitizer TNF.

134 Ferroelectric Materials – Synthesis and Characterization

**Figure 12.** Typical example of asymmetric energy exchange observed in an FLC (SCE8) mixed with 2 wt.% CDH and 0.1 wt.% TNF with an electric field of +0.3 V/μm applied to the sample.

### **4.2. Effect of the applied electric field magnitude**

 The strength of the externally applied electric field is a very important factor for polymeric photorefractive materials. An external electric field is necessary to sufficiently increase the charge separation efficiency to induce a photorefractive effect; the photorefractivity of the polymer is obtained only with an electric field larger than a few volts per micrometer. The typical thickness of the polymer film for investigation of photorefractive effect is 100 μm. The strength of the voltage necessary to activate the photorefractive effect in polymer materials reaches to a few kilovolts. In contrast, the photorefractive effect in FLCs can be activated by a very weak external electric field application. The maximum gain coefficient for the FLC (SCE8)

**Figure 13.** Temperature dependence of the (a) gain coefficient and (b) spontaneous polarization for an FLC (SCE8) mixed with 2 wt.% CDH and 0.1 wt.% TNF. For two-beam coupling experiments, an electric field of 0.1 V/μm was applied to the sample.

sample was obtained by only 0.2–0.4 V/μm electric field. The typical thickness of the photo‐ refractive FLC sample is 10 μm; therefore, the voltage necessary to activate the photorefractive effect is only a few volts. Figure 14 shows the electric field dependence of the gain coefficient for a mixture of FLC (SCE8)/CDH/TNF. As the strength of the external electric field increased, the gain coefficient of SCE8 doped with 0.5 wt.% to 1 wt.% CDH increased. On the other hand, the gain coefficient of SCE8 doped with 2 wt.% CDH decreased when the external electric field larger than 0.4 V/μm was applied. The same tendency was also observed for another com‐ mercially available FLC; M4851/050 (Clariant, SmC\* 65 °C SmA 70 °C N\* 74 °C I, spontaneous polarization=14 nC/cm2 ). The formation of an orientational grating is enhanced when the external electric field is increased from 0 to 0.2 V/μm due to the induced charge separation. However, when the external electric field exceeded 0.2 V/μm, a number of zigzag defects appeared in the SS-state, which caused light scattering and a decrease of the gain coefficient. The gain coefficient of FLC materials reported in the year 2003 (Figure 14) was much smaller than that of polymer materials [16].

### **4.3. Refractive index grating formation time**

The formation of a refractive index grating involves charge separation and reorientation. The index grating formation time (response time of the photorefractive effect) is affected by these two processes, and both may act as rate-determining steps. The refractive index grating formation times for the commercially available FLCs examined (SCE8 and M4851/050) were determined on the basis of the simplest single-carrier model of photorefractivity [3, 5], wherein the gain transient is exponential. The rising signal of the diffracted beam was fitted using a single exponential function:


$$\gamma\left(t\right) - 1 = \left(\gamma - 1\right) \left[1 - \exp(-t/\tau)\right]^2,\tag{4}$$

**Figure 14.** Electric field dependence of the gain coefficient for SCE8 and M4851/050 mixed with several concentrations of CDH and 0.1 wt.% TNF in a 10 μm gap cell measured at 30 °C.

where *γ*(*t*) represents the transmitted beam intensity at time *t*, divided by the initial intensity [*γ*(*t*) = I(*t*)/I0], and *τ* is the formation time. The grating formation time in SCE8/CDH/TNF is plotted as a function of the external electric field strength in Figure 15. The grating formation time shortened with an increase in the electric field strength because of the increased efficiency of charge generation. The formation time was shorter at higher temperatures, which corre‐ sponded to a decrease in the viscosity of the FLC with the increase in temperature. The formation time for SCE8 was 20 ms at 30 °C. The response time of FLC materials is thus faster than those of polymer materials, in which the typical response time is reported to be around 100 ms [5-8].

sample was obtained by only 0.2–0.4 V/μm electric field. The typical thickness of the photo‐ refractive FLC sample is 10 μm; therefore, the voltage necessary to activate the photorefractive effect is only a few volts. Figure 14 shows the electric field dependence of the gain coefficient for a mixture of FLC (SCE8)/CDH/TNF. As the strength of the external electric field increased, the gain coefficient of SCE8 doped with 0.5 wt.% to 1 wt.% CDH increased. On the other hand, the gain coefficient of SCE8 doped with 2 wt.% CDH decreased when the external electric field larger than 0.4 V/μm was applied. The same tendency was also observed for another com‐ mercially available FLC; M4851/050 (Clariant, SmC\* 65 °C SmA 70 °C N\* 74 °C I, spontaneous

**Figure 13.** Temperature dependence of the (a) gain coefficient and (b) spontaneous polarization for an FLC (SCE8) mixed with 2 wt.% CDH and 0.1 wt.% TNF. For two-beam coupling experiments, an electric field of 0.1 V/μm was

 

external electric field is increased from 0 to 0.2 V/μm due to the induced charge separation. However, when the external electric field exceeded 0.2 V/μm, a number of zigzag defects appeared in the SS-state, which caused light scattering and a decrease of the gain coefficient. The gain coefficient of FLC materials reported in the year 2003 (Figure 14) was much smaller

The formation of a refractive index grating involves charge separation and reorientation. The index grating formation time (response time of the photorefractive effect) is affected by these two processes, and both may act as rate-determining steps. The refractive index grating formation times for the commercially available FLCs examined (SCE8 and M4851/050) were determined on the basis of the simplest single-carrier model of photorefractivity [3, 5], wherein the gain transient is exponential. The rising signal of the diffracted beam was fitted using a


() ( ) *t t* <sup>2</sup>


 t

ë û (4)

gg

). The formation of an orientational grating is enhanced when the

polarization=14 nC/cm2

applied to the sample.

 

 

Γ

than that of polymer materials [16].

single exponential function:

**4.3. Refractive index grating formation time**

136 Ferroelectric Materials – Synthesis and Characterization

**Figure 15.** Electric field dependence of the index grating formation time. FLC (SCE8) mixed with 2 wt.% CDH and 0.1 wt.% TNF in a two-beam coupling experiment. ●: measured at 30 °C (T/TSmC\* - SmA = 0.95); ▪: measured at 36 °C (T/ TSmC\* - SmA = 0.97).


 
