**5. Organic-inorganic hybrid structures operating at Bragg matched regime of diffraction**

### **5.1. Organic-inorganic hybrid structure design and principle of operation**

For most practical realizations, the organic-inorganic structures required to operate at the Bragg matched regime of diffraction, for which the phase matching conditions are satisfied only in one direction. It turns out that selected inorganic photorefractive crystals possesses sufficiently large effective trap density to support efficient space-charge generation necessary to reach the Bragg regime (in comparison with conventional LC cell where the low trap density of LCs is the limitation). In Bragg regime of diffraction, the grating period Λ is comparable with the LC layer thickness (Λ ~ *L*) and the hybrid structure acts as a dynamic thick grating.

Generally, this kind of hybrid structure is assembled by photorefractive crystal substrate and a glass substrate, arranged into a cell, filled with liquid crystal or polymer-dispersed liquid crystal layer (PDLC consists of micron-sized droplets of LC molecules randomly dispersed in transparent polymer matrix [38]). The fabrication procedure is very simple and easy, without necessity of conductive layers deposition (external voltage application (and in case of PDLC no need of alignment layers and polarizers)) in contrast to the previously reported devices in Section 4.

The operation principle relays on the unique property of surface-activated photorefractive effect: the photo-generated charge carriers (inside the inorganic substrate) induce a space-charge field, which penetrate into the LC layer and interact with the LC nematic n̂ lc director. As a result, the refractive index of LC layer changes which control the light-intensity distribution by producing the diffraction grating. In this hybrid configuration, the two-beam coupling happens at both the photorefractive substrate and LC layer where the charge migration, trap density and spacecharge field come from the crystal substrate, whereas the high-beam amplification is provided by the LC layer. Hence, all the processes are controlled only by the action of light.

First, Tabiryan and Umeton theoretically proposed the idea about the surface-localized electromagnetic field in organic-inorganic hybrid structures [39]. In their concept, the photo-generated evanescent electric field combines with the LC director through the LC anisotropy. This electric space charge field plays the essential role as it acts as a driving force for LC molecules re-orientation and subsequent refractive index modulation. **Figure 7** shows the schematic presentation of the above idea.

After Tabiryan and Umeton prediction [39], detailed theory of the beam energy exchange was developed by Jones and Cook [40], according to which the coupling between the space charge field and LC director is caused by the LC static dielectric anisotropy. It predicts that maximal beam coupling occurs when the grating spacing has similar order as LC thickness; however,

#### Two-Wave Mixing in Organic-Inorganic Hybrid Structures for Dynamic Holography http://dx.doi.org/10.5772/67190 493

Besides display applications, the Raman-Nath diffraction with multiple output order beams has been successfully applied to control the fast and slow components of light propagation [36]. Different group delays have been obtained depending on the output order and frequency detuning between the pump and signal beam. Varieties of applications in interferometry, optical signal processing, precision metrology and optical sensing are demonstrated [33–37].

For most practical realizations, the organic-inorganic structures required to operate at the Bragg matched regime of diffraction, for which the phase matching conditions are satisfied only in one direction. It turns out that selected inorganic photorefractive crystals possesses sufficiently large effective trap density to support efficient space-charge generation necessary to reach the Bragg regime (in comparison with conventional LC cell where the low trap density of LCs is the limitation). In Bragg regime of diffraction, the grating period Λ is comparable with the LC layer thickness (Λ ~ *L*) and the hybrid structure acts as a dynamic thick grating. Generally, this kind of hybrid structure is assembled by photorefractive crystal substrate and a glass substrate, arranged into a cell, filled with liquid crystal or polymer-dispersed liquid crystal layer (PDLC consists of micron-sized droplets of LC molecules randomly dispersed in transparent polymer matrix [38]). The fabrication procedure is very simple and easy, without necessity of conductive layers deposition (external voltage application (and in case of PDLC no need of alignment layers and polarizers)) in contrast to the previously reported devices in Section 4.

The operation principle relays on the unique property of surface-activated photorefractive effect: the photo-generated charge carriers (inside the inorganic substrate) induce a space-charge field,

refractive index of LC layer changes which control the light-intensity distribution by producing the diffraction grating. In this hybrid configuration, the two-beam coupling happens at both the photorefractive substrate and LC layer where the charge migration, trap density and spacecharge field come from the crystal substrate, whereas the high-beam amplification is provided

First, Tabiryan and Umeton theoretically proposed the idea about the surface-localized electromagnetic field in organic-inorganic hybrid structures [39]. In their concept, the photo-generated evanescent electric field combines with the LC director through the LC anisotropy. This electric space charge field plays the essential role as it acts as a driving force for LC molecules re-orientation and subsequent refractive index modulation. **Figure 7** shows the

After Tabiryan and Umeton prediction [39], detailed theory of the beam energy exchange was developed by Jones and Cook [40], according to which the coupling between the space charge field and LC director is caused by the LC static dielectric anisotropy. It predicts that maximal beam coupling occurs when the grating spacing has similar order as LC thickness; however,

lc director. As a result, the

which penetrate into the LC layer and interact with the LC nematic n̂

schematic presentation of the above idea.

by the LC layer. Hence, all the processes are controlled only by the action of light.

**5. Organic-inorganic hybrid structures operating at Bragg matched** 

**5.1. Organic-inorganic hybrid structure design and principle of operation**

**regime of diffraction**

492 Holographic Materials and Optical Systems

**Figure 7.** Surface activated photorefractive phenomena [41]. The photo-induced space charge field (indicated with arrows) penetrates into the LC layer and reorient the LC molecules, resulting in a change of the effective refractive index.

experimentally, the maximum coupling happens at much smaller grating spacing than the LC thickness [40]. Later on, Reshetnyak et al. [41] extend the theory summarizing that the exponential gain amplification is a final product of three main components: (i) the beam interference term, (ii) the flexoelectric polarization term of LC (that have upper contribution than the LC static dielectric anisotropy, assumed in Ref. [40]) and (iii) the photo-induced space-charge term. In addition, Evans and Cook [42] performed systematic study and initiate the two necessary conditions to achieve the two-beam coupling at Bragg regime: the LC molecules must be pretilted (asymmetrically aligned) and the LC electrical polarity must be sensitive to the direction of the space-charge field. These conditions enable the refractive index grating to have the same spatial frequency as the interference pattern and make the optical amplification at Bragg regime possible. Afterward, several hybrid configurations based on ferroelectric crystals as KNbO3 and SBN:Ce assembled with nematic LCs, operating at visible spectral range has been realized [42, 43]. For example, Deer [44] demonstrated a structure based on LC layer and KNbO3 substrate, at large beam intersection angle with perfect phase shift between the interference and refractive index gratings. Up to now, only limited numbers of near infrared sensitive structures are designed using semiconductor substrates as CdTe or GaAs. The maximum gain coefficient reported in GaAs/LC cell is 18 cm−1 at Λ = 1.2 μm and 16 cm−1 at Λ ~ 1 μm for CdTe/LC cell, both of them operating at 1064 nm [45, 46].

**Figure 8** shows the formation of the space-charge field in BSO:Rh/LC structure followed by monitoring the time evolution of the Gaussian laser beam (0.5-mm waist) propagating through the hybrid device (right side) [47]. Owing to the near-infrared absorption and high photoconductivity of the inorganic crystal, illumination with 1064-nm light causes charge carriers generation and formation of photo-induced space-charge field which becomes stronger at the edges of the Gaussian beam.

The numerical simulation of the intensity (I) and the space-charge field (Esc) distributions, as well as time evolution of Gaussian beam shape passing through the hybrid structure are shown at **Figure 8**(**b** and **c**). The experimental results are in good agreement with the numerical calculations reported by Stevens and Banerjee [48], which support that Gaussian beam illumination generates notch width which is proportional to the width of the intensity

**Figure 8.** The numerical simulation of the Gaussian intensity beam distribution (a) Gaussian beam propagation through BTO:Rh/LC structure, (b) light intensity numerical distribution and (c) space charge field *Esc* numerical distribution (left) and experimental propagation of the Gaussian beam (right) through the BSO:Ru/PDLC device.

beam, created by the charge accumulation at the interface between the dark and spurious illumination.

#### **5.2. Two-beam coupling and Bragg-matched regime of diffraction**

photoconductivity of the inorganic crystal, illumination with 1064-nm light causes charge carriers generation and formation of photo-induced space-charge field which becomes stronger

The numerical simulation of the intensity (I) and the space-charge field (Esc) distributions, as well as time evolution of Gaussian beam shape passing through the hybrid structure are shown at **Figure 8**(**b** and **c**). The experimental results are in good agreement with the numerical calculations reported by Stevens and Banerjee [48], which support that Gaussian beam illumination generates notch width which is proportional to the width of the intensity

**Figure 8.** The numerical simulation of the Gaussian intensity beam distribution (a) Gaussian beam propagation through BTO:Rh/LC structure, (b) light intensity numerical distribution and (c) space charge field *Esc* numerical distribution (left)

and experimental propagation of the Gaussian beam (right) through the BSO:Ru/PDLC device.

at the edges of the Gaussian beam.

494 Holographic Materials and Optical Systems

The evidences of the space charge formation give rise for two-wave mixing experiments. Illumination with two beams leads to light-intensity interference pattern, which induces a space charge field in the photorefractive substrate expressed by [1, 41]:

$$E\_{sc} = \frac{iE\_{\rm D}}{1 + \frac{E\_{\rm D}}{E\_{\rm q}}} \tag{19}$$

where *ED* <sup>=</sup> *<sup>K</sup> k <sup>B</sup> <sup>T</sup>* \_\_\_ *<sup>e</sup>* is the diffusion field, *Eq* <sup>=</sup> (<sup>1</sup> <sup>−</sup> *N*\_*A ND*) *<sup>e</sup> <sup>N</sup>* \_\_\_\_\_\_ *<sup>D</sup>* <sup>ϵ</sup><sup>0</sup> <sup>ϵ</sup>*PR <sup>K</sup>* is the saturation field and εPR is the dielectric permittivity of the photorefractive substrate.

Once accumulated in the photorefractive layer, the space-charge field *Esc* penetrates into the LC layer with decaying evanescent component. In fact, the role of the *Esc* is to generate electric field, which reorients the nematic LC director n̂ LC outside the photorefractive region. Following the couple-wave theory [1, 11], the total electric field obeys the Poisson equation:

$$\nabla \cdot \left( \varepsilon \,\varepsilon\_0 \, . \, E\_{\kappa} + P\_{\rho\_{\text{fix}}} \right) = \begin{array}{c} 0 \\ \end{array} \tag{20}$$

where *Pflex* is the flexo-polarization term of LC layer, determined by flexo-electric coefficients according to Refs. [40, 41]. To solve Eq. (20), the authors in Ref. [43] use the relation between the electrical potential in photorefractive substrate *E* (*x*, *z*) and the electrical potential in LC layer ΨLC (*x*, *z*) expressed by *E*(*x*, *<sup>z</sup>*) <sup>=</sup> <sup>−</sup><sup>∇</sup> <sup>Ψ</sup>*LC* (*x*, *z*) and the boundary conditions between the *z* = −*L*/2 to *z* = *L*/2 planes (where *L* is the LC thickness). Detailed analysis and analytical solutions have been discussed and presented in Refs. [40–43].

The ability of organic-inorganic structures to operate at Bragg match regime of diffraction is shown at **Figure 9** where two hybrid configurations are discussed: the first one is based on Rh-doped Bi12TiO20 crystal and LC layer (BTO:Rh/LC), and the second one consists of Ru-doped Bi12SiO20 crystal and PDLC layer (BSO:Ru/PDLC). Examples of simultaneously detected behaviour of two interacting beams (linearly polarized with equal intensity [1:1 ratio]) inside the hybrid structures are shown at **Figure 9(b)** and **(c)**, respectively. As it is seen, during the two-wave mixing, a constructive and deconstructive interference occurs, which is indication for π/2 phase shift between the light pattern and the index grating pattern. In case of BSO:Ru/ PDLC structure at the beginning of the light illumination, the two beams propagate together since the PDLC layer requires time to reverse its scattering state to the transparent state and after few seconds clear depletion between two beams appear. No changes between the two interfering beams were detected on glass/LC/glass and glass/PDLC/glass reference samples.

The photo-induced space charge field *Esc* in the photorefractive substrate has been estimated assuming sinusoidal charge density distribution [1] and materials parameters from **Table 1**. By using Eq. (19), the space charge field in BSO:Ru has been estimated as a value of *Esc*(BSO:Ru) = 1.6 × 105 V/m. Taking into account the experimentally measured threshold

**Figure 9.** (a) Two-beam coupling experiment in BSO:Ru/PDLC structure and simultaneous behavior of both transmitted beams through the (b) BSO:Ru/PDLC structure and (c) BTO:Rh/LC structure. Comparison with the reference samples as glass/LC/glass and glass/PDLC/glass is also presented.


**Table 1.** Material parameters for theoretical simulations.

voltage of 20 V (for 7.3-μm droplet size) of PDLC layer, the threshold electric field is *E*th(PDLC) = 2 × 10<sup>6</sup> (V/m). Substituting the known values into the boundary condition *Esc*(BSO:Ru) × *ε*(BSO) = *Esc*(PDLC) × *ε*(PDLC), we found the required electric field to re-orient LC molecules in PDLC layer is *Esc*(PDLC) = 1.25 × 105 (V/m). Obviously, the generated *Esc* field inside BSO:Ru substrate is strong enough to penetrate into the PDLC layer and realign the LCs molecules.

For BTO:Rh/LC structure, similar procedure has been performed. The estimated space charge field in BTO:Rh substrate is about *Esc*(BTO:Rh) = 1.9 × 105 (V/m). Taking into account the experimentally measured driving voltage of LC layer as 2 V (for 12-μm thickness) and the threshold electric field as *E*th(LC) = 1.67 × 105 (V/m), the required space charge field is about *Esc*(LC) = 1.5 × 105 (V/m).

The above two examples verify that the photo-induced space charge field *Esc* created in photorefractive substrates can grow high enough to exceed the threshold electric field and penetrate into the birefringent layer. The advantage of using PDLC over the LC is no need of alignment layer (since the polymer binder defines the droplets orientations), which permits the photo-generated space-charge field to penetrate directly into the PDLC layer.

**Figure 10** shows the experimentally measured gain coefficient Г (cm−1) dependence on the grating spacing Λ (μm) when the ratio of signal-to-pump beam is 1/70. Besides, **Figure 10** shows the theoretically simulated strength of the space-charge field *Esc* displayed as a single line. For BSO:Ru/PDLC structure, the measured beam amplification value of Г = 45 cm−1 is almost three times higher than reported for similar hybrid structures using double-side photorefractive substrates as CdTe (16 cm−1) and GaAs (18 cm−1), operating at near infrared spectral range [46, 47]. In case of BTO:Rh/LC structure, Г reached almost 10 cm−1 at 1-μm grating spacing. It is assumed that large amplification effect comes from suitable doping elements (as Ru and Rh) addition in sillenite crystal structure, which provides enough density of trap levels to support accumulation of high-resolution space charge field.

**Type Symbol Value Unit**

*n*0

glass/LC/glass and glass/PDLC/glass is also presented.

496 Holographic Materials and Optical Systems

*ne*

**Table 1.** Material parameters for theoretical simulations.

BTO:Rh and BSO:Ru inorganic crystals

LC (MLC type) ∆*ε* (LC) 41.6 × *ε*<sup>0</sup> Anisotropy of NLC's

**Figure 9.** (a) Two-beam coupling experiment in BSO:Ru/PDLC structure and simultaneous behavior of both transmitted beams through the (b) BSO:Ru/PDLC structure and (c) BTO:Rh/LC structure. Comparison with the reference samples as

6.1 × 1023 for BSO:Ru

5× 1023 for BSO:Ru

*ND* 2 × 1024 for BTO:Rh

NA 1 × 1024 for BTO:Rh

*K* (LC) 5 Elastic constant of NLC

(LC) 1.51 O-ray refractive index of LC

(LC) 1.75 E-ray refractive index of LC

*ε* 46 Dielectric constant of BTO

*T* 300 K Temperature

dielectric constant

(nematic)

(nematic)

cm−3 Acceptor concentration

and BSO crystal

cm−3 Donor concentration

**Figure 10.** (a) Gain coefficient dependence on the grating spacing Λ(μm) and (b) Theoretical simulation of Esc dependence on Λ(μm) for BSO:Ru/PDLC structure.

As discussed earlier, the Debye screening length in photorefractive material need to be very small to support high concentration of effective trap density. For BSO:Ru crystal, the Debye screening length of 0.08 μm has been calculated from Eq. (7) and materials parameters in **Table 1.** Moreover, as shown in **Figure 10**, the *Esc* decreases with increasing the grating spacing from 1 to 2 μm. As the gain amplification is controlled by the space charge field, it follows the behaviour of the *Esc* on the way to decrease with increasing the grating spacing Λ. In that aspect, multi-layer structure may increase the effective interaction length and optimize the *Esc* penetration depth (however limited by scattering losses).

#### **5.3. Applications**

The prime significance of the reviewed hybrid structure is all optically controlled processes. For example, the switching ability BSO:Ru/PDLC structure is demonstrated at **Figure 11**. An image pattern (rectangular mask) is placed into the input plane of 4-f optical system, and the structure is illuminated with 1064-nm Gaussian beam. When the pump light illuminates the device, the PDLC layer transparency is changed due to the induced space charge field in the photorefractive substrate.

Therefore, by controlling the droplet size and consequently the driving voltage of the LC molecules from one side and optimizing the charge carriers' concentration in crystal matrix (providing high enough density for high resolution space charge field), the proposed structure can be further optimized. Moreover, the beam coupling can be significantly improved by addition of nanoparticles in LC layer, which affects the dielectric anisotropy and decreases the driving (threshold) voltage.

**Figure 11.** Gaussian laser beam propagating through BSO/PDLC hybrid structure and image mask (rectangular shape) evolution when the light is at "on" and "off" position (right side). All processes are controlled by near infrared light only.
