Photorefractive Smectic Liquid Crystals and Their Application to Laser Ultrasonics

1. Introduction

A hologram is formed by allowing light reflected from an object to interfere with a reference beam and recording the resulting interference pattern on a photosensitive material, such as a photopolymer. The recorded hologram functions as a diffraction grating, reconstructing the object’s image when illuminated. Because holograms encode not only the intensity but also the angle and phase of light, they can reproduce images with a three-dimensional appearance. Due to the complexity of their fabrication, holograms are commonly used as anti-counterfeiting measures on digital versatile disc (DVD) and compact disc (CD) packaging, as well as on high-denomination banknotes.

The photorefractive effect is one of the key phenomena involved in hologram formation [1]. Unlike conventional holography, which relies on photochemical reactions to record interference fringes, the photorefractive effect operates through a different mechanism [1, 2]. In this process, the photovoltaic and electro-optic effects interact to produce a refractive-index grating within the material. This effect occurs in transparent materials that exhibit both photoconductivity and the electro-optic effect. Because they do not rely on irreversible photochemical reactions, the resulting holograms are rewritable. Organic photorefractive polymers can be fabricated into large-area films, making them promising candidates for three-dimensional display technologies [3–5]. In addition, liquid crystal materials have attracted considerable attention as photorefractive media because of their high birefringence and short response times, thereby enabling the development of high-performance photorefractive liquid crystals [6, 7].

Holograms formed via the photorefractive effect exhibit functionalities such as, optical amplification and phase-conjugate wave generation [2]. Their reversible nature further enables applications in various optical devices, particularly those designed to control light propagation. Between 2008 and 2010, a series of studies by US researchers, published in Nature, drew significant attention for demonstrating clear three-dimensional holographic images using polymer-based photorefractive materials [8, 9]. These materials allow both the recording and erasure of holographic images, making them suitable for dynamic holographic displays. Potential applications include medical imaging systems in which computed tomography (CT) and magnetic resonance imaging (MRI) data can be visualized as three-dimensional holograms. Researchers have also developed prototype holographic displays that enable simultaneous multiangle viewing by recording computer-generated, multiple-exposure interference patterns (derived from images captured at different perspectives) onto photorefractive polymers using pulsed lasers [5]. Despite their excellent holographic properties, photorefractive polymers have not yet achieved widespread practical use. Limitations include relatively slow response times (on the order of 100 ms) and the requirement for high applied voltages (several kilovolts) to induce the photorefractive effect [3, 4]. Consequently, active research is also focused on liquid crystal-based photorefractive materials, which offer faster response times and are therefore expected to be more suitable for practical applications, including optical measurement devices.

2. Photorefractive effect in liquid crystals

Photorefractive liquid crystals consist of liquid crystals doped with photoconductive compounds and charge-trapping agents [6]. When laser light beams interfere within such a material in the presence of an applied external electric field, a sequence of processes occurs (Figure 1a).

In the bright regions of the interference fringes, the photoconductive compounds absorb light and generate charge carriers such as, electrons and holes or positive and negative ions. Under the applied electric field (typically on the order of several volts per micrometer), these charges begin to migrate within the liquid crystal. Negative charges are preferentially captured by the charge-trapping agents and remain localized in the bright regions, leading to a buildup of negative charge there. By contrast, positive charges drift under the applied field and accumulate in the dark regions. This spatial separation of charge creates a potential difference, or internal electric field, between the bright and dark regions. The internal electric field modifies the orientation of the liquid crystal molecules, resulting in a refractive-index grating (Figures 1b, c). Notably, this grating is phase-shifted relative to the original interference pattern, which is a defining characteristic of the photorefractive effect. The externally applied electric field enhances both the efficiency of charge separation and the magnitude of this phase shift [10]. This phase offset leads to a distinctive optical behavior. The diffraction of light by the refractive-index grating depends on the phase difference between the grating and the interference fringes. When the phase difference is π/2, one of the two interfering laser beams is preferentially diffracted in the direction of the other beam. Consequently, as the grating develops, the transmitted intensities of the two beams change in opposite directions: one decreases while the other increases symmetrically (Figure 2).

The aforementioned phenomenon is known as asymmetric energy exchange, in which one beam is amplified at the expense of the other through diffraction [3]. By contrast, conventional holograms formed via photochemical reactions produce refractive-index gratings that are in phase with the interference fringes. As a result, diffraction occurs symmetrically for both beams, and their transmitted intensities remain unchanged. Therefore, when two beams of equal intensity interfere within a sample, symmetric changes in their transmitted intensities provide strong evidence of the photorefractive effect. Because the refractive index is modulated without a corresponding change in absorbance, photorefractive materials enable the formation of volume holograms.

The photorefractive effect is typically evaluated using a two-beam coupling experiment (Figure 3). In this method, two coherent laser beams interfere within the sample, and the transmitted intensities of each beam are monitored. In the case of liquid crystals, a continuous-wave laser with an output power of only a few milliwatts is sufficient to induce the photorefractive effect.

In asymmetric energy exchange, because one beam is amplified by the other laser beam, the gain coefficient (Γ) is defined as follows:

where I is the intensity of the amplified laser light, I₀ is the intensity of the laser light before amplification, and L is the length over which interference occurs within the sample. The magnitude of the photorefractive effect is evaluated on the basis of the value of Γ. The laser beams are incident at an angle relative to the sample film’s normal to ensure that the component of the external electric field along the interference fringes remains nonzero. When evaluating the dependence of the gain coefficient on the magnitude of the applied electric field, a curve consistent with a sin²-type function is obtained if the refractive-index grating is generated by the photorefractive effect [3, 7]. This behavior arises because the phase of the refractive-index grating varies with the strength of the external electric field. As the phase shift approaches π/2, the gain coefficient increases and reaches its maximum value. Reversing the direction of the external electric field results in a corresponding reversal of the direction of optical amplification. Another important parameter is the response time, τ, which represents the time required for the refractive-index grating to form after the onset of laser interference within the material. In a two-beam coupling experiment, the amplified light intensity is fitted with an exponential function (Eq. [2]), from which the response time, τ, is determined.

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 grating formation time. This equation includes a squared term because this phenomenon involves two processes: forming an internal electric field and changing the refractive index, or the alignment of the liquid crystal.

3. Photorefractive–smectic liquid crystals

Photorefractive liquid crystal materials can be realized by mixing low-molecular-weight liquid crystals with photoconductive compounds [11]. At present, nematic [12–14] and smectic [6, 7, 15, 16] liquid crystals are the primary systems under investigation. In particular, smectic liquid crystals doped with chiral compounds exhibit ferroelectric and flexoelectric behavior, leading to a rapid response to applied electric fields [10, 17]. Liquid crystal molecules show substantial changes in refractive index even with small variations in molecular orientation. As a result, a refractive-index grating can be formed by a relatively small internal electric field. In ferroelectric liquid crystals containing photoconductive compounds, light interference can induce changes in the direction of spontaneous polarization. Because the polarization response in ferroelectric liquid crystals is intrinsically fast, the resulting photorefractive response is also rapid. A key chemical feature of ferroelectric liquid crystals is their chirality. In some systems, the liquid crystal molecules themselves are chiral, whereas in others, chirality is introduced by adding chiral dopants [18]. The interaction between these chiral components and the host liquid-crystal molecules produces a molecular assembly with reduced symmetry. Because ferroelectricity arises in structures lacking inversion symmetry, the presence of chiral compounds is essential for its manifestation. The photorefractive effect in mixtures of ferroelectric liquid crystals and photoconductive compounds has been extensively investigated [10, 11, 19]. A typical example of asymmetric energy exchange observed in a two-beam coupling experiment is shown in Figure 4.

When two laser beams interfere within the liquid crystal, the transmitted intensity of one beam increases while that of the other decreases. Even the noise components exhibit symmetric behavior, providing clear evidence of asymmetric energy exchange. The response time of such systems is typically on the order of several to tens of milliseconds, which is more than an order of magnitude faster than that of polymer-based photorefractive materials. As of ca. 2010, smectic liquid crystals exhibited gain coefficients of approximately 20 cm⁻¹ with response times of ~20 ms [6]. The photorefractive effect of ferroelectric liquid crystals was only observed within the temperature range in which they exhibit the SmC phase. This means that the photorefractive effect in ferroelectric liquid crystals is based on the response of bulk polarization (spontaneous polarization) to the photogenerated internal electric fields.

4. Photoconductive chiral dopants

Smectic liquid crystals do not exhibit the pronounced dynamic scattering observed in nematic liquid crystals, making them highly transparent and attractive for optical applications [18]. However, their higher viscosity makes uniform alignment more difficult to achieve. Alignment defects lead to light scattering, which can suppress the photorefractive effect [11]. Therefore, obtaining uniformly aligned smectic liquid crystals requires the use of photoconductive compounds with high compatibility. In practical applications such as, displays, smectic (ferroelectric) liquid crystals are not single-component systems but mixtures of multiple compounds because key properties (e.g., the temperature range of ferroelectricity, alignment behavior, and birefringence) cannot be optimized using a single material. Typically, several liquid-crystalline compounds are blended to form a base liquid crystal exhibiting the smectic C phase. With the introduction of a chiral compound, a ferroelectric liquid crystal with a chiral smectic C phase can be obtained. To further impart photorefractive functionality, a photoconductive dye is added. However, because many photoconductive dyes are not inherently liquid crystalline, their incorporation can disrupt the alignment of the host liquid crystal. To address this issue, researchers have developed photoconductive chiral dopants (Figure 5) [19].

Photoconductive chiral dopants consist of a photoconductive unit combined with a chiral structure, enabling them to integrate seamlessly into the liquid crystal host while simultaneously inducing chirality and photoconductivity. When added to a parent smectic C liquid crystal, they readily produce a photoconductive ferroelectric and/or flexoelectric liquid crystal. A representative example employs terthiophene as the photoconductive core because of its rod-like structure and favorable charge-transport properties. The photoconductivity of terthiophene-based liquid-crystalline compounds has been extensively studied by researchers such as Funahashi and coworkers [20]. These compounds exhibit both liquid crystallinity and photoconductivity, making them particularly suitable for photorefractive applications. A series of photoconductive chiral compounds was synthesized, and high-performance photorefractive liquid crystals have been reported. The liquid crystal blend shown in Figure 5 has been reported to exhibit a large gain coefficient and afast response [21]. The liquid crystal blend shown in Figure 5 was initially reported as a ferroelectric liquid crystal; however, it was later found to be flexoelectric. Figure 6 shows a typical example of asymmetric energy exchange observed in a two-beam coupling experiment using such a liquid crystal blend. Photorefractive smectic liquid crystals incorporating photoconductive chiral dopants have demonstrated remarkably high performance [15, 21], with gain coefficients exceeding 1,200 cm⁻¹ and response times shorter than 1 ms under an applied electric fieldof 2 V/μm (Figure 7).

The dielectric properties of these liquid crystal systems vary substantially depending on the structure of the introduced chiral moiety [10, 21]. Some systems exhibit ferroelectricity, whereas others show only the flexoelectric effect. Ongoing research is focused on understanding the relationships among the molecular structure of chiral dopants, the resulting dielectric properties of liquid crystal blends, and their photorefractive performance. Interestingly, flexoelectric liquid crystals have been found to exhibit larger and faster photorefractive responses than ferroelectric systems [10, 21]. This behavior is attributed to the electroclinic effect: in flexoelectric liquid crystals, the molecular tilt angle changes significantly in response to an internal electric field, whereas in ferroelectric systems, the tilt angle is relatively constrained [18]. The fast response of photorefractive smectic liquid crystals enables real-time rewriting of refractive-index gratings, allowing the formation of dynamic, or “moving,” holograms [15].

As shown in Figure 8, a dynamic hologram can be generated by projecting a video onto the liquid crystal using a spatial light modulator (SLM) and a blue laser (488 nm), and then interfering the resulting beam with a reference beam. A red laser (633 nm) is subsequently used to reconstruct the holographic image. Asymmetric energy exchange, the underlying mechanism, enables one light beam to be amplified by another. Because this phenomenon relies on holographic interference, it occurs only when the wavelength, phase, and polarization of the interacting beams are matched. This selectivity allows targeted amplification of specific optical signals.

On the basis of this principle, the feasibility of optical signal amplification at video rates was investigated using these liquid crystal systems [21]. By projecting video images onto the photorefractive liquid crystal with an SLM and illuminating them with a reference beam (Figure 9), real-time amplification of the moving image was demonstrated. Notably, this was the first example of amplifying a dynamic optical image signal in real time using only the photorefractive effect, without electronic image processing.

5. Application of photorefractive liquid crystal blends to laser ultrasonics

Asymmetric energy exchange enables the detection of phase changes in light. The laser ultrasonic method is based on detecting ultrasonic vibrations generated within an object by analyzing reflected laser light [22]. When a surface vibrates due to acoustic waves, the reflected light from that surface exhibits corresponding phase fluctuations. The direct detection of such phase changes is generally difficult; however, asymmetric energy exchange enables phase variations to be converted into measurable intensity changes.

Figure 10 illustrates the two principal optical configurations used in laser ultrasonic measurements. In the transmission-type configuration (Figure 10a), a pulsed laser and a probe (detection) beam are directed onto opposite sides of the specimen, allowing accurate measurement of the sample thickness. By contrast, in the reflection-type configuration (Figure 10b), both the pulsed laser and the probe beam are incident from the same side, making this configuration suitable for detecting internal defects and for long-distance measurements. In a typical measurement, a continuous-wave laser is first directed onto the test object. The reflected light is then guided into a photorefractive liquid crystal element, where it interferes with a reference beam, resulting in asymmetric energy exchange. A pulsed laser is subsequently used to excite ultrasonic waves within the specimen. These waves propagate through the material and eventually reach the surface, inducing minute vibrations. As a result, the phase of the reflected continuous-wave laser light is modulated, thereby altering the asymmetric energy exchange process (Figure 10c). Analysis of these intensity variations enables noncontact measurement of the specimen’s thickness and internal structure. When applied to laser ultrasonics, photorefractive liquid crystal systems offer enhanced sensitivity. The theoretical minimum detectable surface displacement is approximately one order of magnitude smaller than that achievable with conventional crystal or polymer-based systems, enabling high-precision measurements [23].

Figure 11 presents an example in which an aluminum plate is used as the test specimen. The signal generated by pulsed laser excitation appears as a change in the intensity of the reflected light after passing through the liquid crystal. The pulsed laser induces ultrasonic vibrations on the surface of the aluminum plate, including both longitudinal (compressional) waves and transverse (shear) waves. While shear waves are typically difficult to detect optically, photorefractive liquid crystal systems enable their reliable observation because shear waves, upon reflection at the surface, generate weak longitudinal components that can be detected. The thickness of the aluminum plate can be determined through the measurement of the time interval between the pulsed laser excitation and the appearance of the detected signal.

Figure 12 shows the results of such measurements for aluminum plates of various thicknesses [24]. The position of the detected signal, which originates from phase modulation induced by ultrasonic vibrations, shifts depending on the plate thickness. The thickness can be calculated using the known propagation velocities of longitudinal (6,420 m/s) and transverse (3,040 m/s) waves in aluminum. The corresponding results are summarized in Table 1.

The thickness of the aluminum plate was determined with high accuracy using both longitudinal and transverse ultrasonic waves. Figure 13b presents the results obtained by scanning, in one dimension, the surface of a sample containing a dimple formed by drilling into the aluminum plate (Figure 13a) [23]. The measured signal clearly reflects the shape of the dimple, demonstrating that an object’s surface profile can be determined using a noncontact method. Furthermore, extending the scan to two dimensions enabled a three-dimensional reconstruction of the object’s shape (Figure 13c).

Previous studies on laser ultrasonics using the photorefractive effect have employed inorganic photorefractive crystals and polymer-based materials (i.e., photoconductive polymers doped with dyes). However, these materials exhibit relatively slow photorefractive responses, necessitating measurements in vibration-free, acoustically isolated environments. When the response time is slow, even minor ambient vibrations can shift the refractive-index grating, leading to fluctuations in asymmetric energy exchange and making accurate measurements difficult. For example, environmental vibrations, such as those caused by vehicles, typically span frequencies from 0.1 Hz to several tens of hertz (corresponding to timescales from seconds to tens of milliseconds), which overlap with the response times of crystals and polymers. As a result, large-scale experimental setups equipped with vibration isolation systems have traditionally been necessary. By contrast, photorefractive liquid crystals exhibit response times in the millisecond-to-microsecond range, enabling stable measurements even in the presence of ambient vibrations. This advantage allows for simpler and more flexible optical configurations. In particular, a reflection-type configuration (Figure 10b), in which both the pulsed excitation and detection beams are incident from the same direction, can be used. Such a configuration is well-suited for inspecting objects at a distance and for probing internal structures.

Figure 14 shows the results of measurements performed using a reflection-type configuration on an aluminum plate containing an internally drilled hole [24]. Although the presence of the internal defect cannot be confirmed by visual inspection, the laser ultrasonic method successfully visualizes the upper surface of the internal cavity. This visualization demonstrates the potential of the technique for nondestructive evaluation and structural health monitoring of distant objects, such as steel bridges. Because liquid crystal elements can be fabricated over large areas, data such as those shown in Figures 13c and 14b can be acquired with a single laser pulse. With further improvements in the sensitivity of photorefractive liquid crystals, applications such as portable handheld measurement devices and noncontact medical diagnostic systems are expected to become feasible. Photorefractive liquid crystals are composite systems comprising liquid crystals and photoconductive compounds. Tailoring the molecular structures of these components enables key properties, such as, operating wavelength and sensitivity, to be tuned. The most promising applications of laser ultrasonic systems based on liquid crystals are likely to be compact, portable instruments rather than large-scale remote sensing systems. The development of such portable, noncontact measurement technologies would greatly expand their applicability, including for the inspection of high-temperature objects in metal-processing environments. Moreover, there is a growing demand for noncontact measurement techniques that can be conducted in challenging environments, such as, firefighting scenarios and nuclear power facility maintenance. In this context, photorefractive liquid crystals have the potential to extend the application of liquid crystal technology – traditionally associated with display devices – into new industrial domains, opening innovative avenues for sensing and diagnostics.

Laser ultrasonics based on the photorefractive effect have been reported for inorganic photorefractive crystals [25, 26] and polymer photorefractive materials [27]. However, in these cases, the response time for forming the photorefractive grating was slow, and the photorefractive materials required fast measurement performance free from vibration. The frequencies of vibrations caused by automobiles range from 0.1 Hz to several tens of hertz. As these frequencies are close to the response times of crystals and polymers, they are not suitable for use in laser ultrasonics. Figure 15 shows schematic diagrams of the movement of refractive-index gratings generated by the photorefractive effect under environmental vibrations. The response times of the photorefractive effect in inorganic crystals or polymers are on the order of 10 ms to 100 ms. This makes them highly susceptible to environmental vibrations (from a few tens of ms to a few seconds). The photorefractive material moves with environmental vibrations, and the refractive-index grating also moves with it (Figure 15a). On the other hand, flexoelectric smectic liquid crystals respond on the μs to ms timescale; thus, even if the liquid crystal moves due to environmental vibration, the refractive-index grating is rewritten instantaneously, and its position does not change, as shown in Figure 15b, allowing us to measure the laser ultrasonic signal without being affected by the vibration.

6. Conclusions

This chapter has reviewed current trends in research on photorefractive liquid crystal materials. Because the photorefractive effect is closely related to holography, it is often discussed in the context of three-dimensional imaging and similar applications. However, its true potential lies in its use as a functional material for sensing and measurement technologies. Since holograms are formed through the interference of light, even positional variations on the order of the optical wavelength are encoded in the refractive-index grating. When the photorefractive effect is induced by laser light reflected from an object, extremely small changes in distance can be converted into detectable variations in light intensity. This capability makes photorefractive materials particularly promising for high-precision, noncontact measurements. In urban regions such as, the Tokyo metropolitan area, aging infrastructure, including bridges and other critical structures, has become an increasingly serious issue. At present, inspection methods often rely on manual techniques, such as hammer tapping, to assess structural integrity. By contrast, the photorefractive effect could enable remote, optical detection of internal deterioration in materials such as concrete and steel, offering a safer and more efficient alternative. To realize such applications, the further development of high-performance photorefractive materials is essential. Research on photorefractive liquid crystals is still in its early stages, but further advances in material design and device engineering are expected to drive significant progress in the near future.

Acknowledgments

This work is supported by the Adaptable and Seamless Technology Transfer Program through Target-driven R&D (A-STEP) from the Japan Science and Technology Agency (JST, Grant Number JPMJTR25T7). This work was also supported by the Research Foundation of TOPY Enterprises Limited, the Precise Measurement Technology Promotion Foundation, the Japan Research Institute of Industrial Science, the Nakanishi Scholarship Foundation, the Amada Foundation, ICHJYU Industrial Science and Technology Promotion Foundation, and the Izumi Science and Technology Foundation.