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Abstract
A photorefractive effect of mixtures of flexoelectric liquid-crystal (flex LC) was investigated and applied to laser ultrasonics. Mixtures of flex LC, composed of smectic-C liquid crystals, photoconductive chiral compounds, and a sensitizer, are demonstrated to exhibit a large photorefractive effect. The experiments of a two-beam mixing with a photorefractive flexoelectric liquid crystal (PR-flex LC) show that a gain coefficient was measured as 1400 cm–1 and a response time was 960 microseconds, both with an applied electric field of 2.0 V/µm. The large gain and fast response are advantageous for remote ultrasound detection by using two-beam mixing with PR-flex LC. This remote sensing method can be used to probe the internal structure of an object or to measure the thickness of a plate object. The experimental results of acoustic time-of-flight in an aluminum (Al) plate are presented by using an adaptive two-beam interferometer with a PR-flex LC. A 3-D surface topology is shown by using laser ultrasonics with 2-D scanning of a test Al plate. With a fast response time in PR-flex LC, the system is not affected by vibrations in an industrial environment.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Laser ultrasonic testing is an excellent method for non-destructively investigating the shape and internal structure of materials without contact [1–7]. When a pulsed laser irradiates a material such as an aluminum plate, ultrasonic waves are generated on its surface, travel through it, and are reflected by cavities inside the material or its opposite surface. In detecting ultrasonic vibrations on the material surface, it is possible to determine the shape and internal defects of materials from a remote location by measuring a time-of-flight of acoustic waves. Optical interferometry and laser Doppler vibrometry have been used for ultrasonic detection [2,7] However, their sensitivity and resolution are limited, because the signal is remarkably decreased when a material has a rough surface. The photorefractive effect is expected to be used for detection of these vibrations with high sensitivity by using the two-beam mixing method [8,9] In two-beam mixing, one of the interfering beams (signal beam) is amplified by another beam (pump beam). The pump beam diffracted from a photorefractive index grating has the same propagation direction and the speckle structure reflected from an object’s surface as those of the transmitted signal beam. Two-beam mixing scheme makes it possible to detect the phase changes caused by the acoustic waves in a signal beam. [10]. An application of two-beam mixing to acoustic detection was first reported by Hall et al. using Bi12SiO20 crystals [11].
In this paper, we show the gain and time response of photorefractive flexoelectric liquid crystals (PR-flex LCs) that are applied to laser ultrasonics, constructing a high-precision laser ultrasonic non-contact measurement system. Ferroelectric liquid crystals are well known as fast-responding liquid crystals, however, they are difficult to fabricate into a uniformly aligned state because they are spontaneously polarised. Flexoelectric liquid crystals can be oriented uniformly because they are not polarised unless an electric field is applied. Under an applied electric field, flexoelectric liquid crystals respond quickly to the electric field because they exhibit bulk polarisation. A 3-D surface topology is shown by using the laser ultrasonics with 2-D scanning of a test aluminum (Al) plate. With fast response time in PR-flex LC, the system is not affected by vibrations in an industrial environment.
The mechanism of the photorefractive effect is shown in Fig. 1. The medium absorbs light in the bright part of the interference fringe and generates positive charges (holes and/or positive ions) and negative charges (electrons and/or negative ions). The mobilities of positive charges and negative charges are different in most organic mediums. The mobilities of positive charges are often larger than that of negative charges. As a result, the bright part of the interference fringe is negatively charged and the dark part is positively charged. A space–charge electric field is established between the bright and dark areas. The refractive-index grating is formed through the electro-optic effect caused by the internal electric field, demonstrating an asymmetric energy-exchange property [8].
Fig. 1. Mechanism of photorefractive effect: (a) Two beams interfere in photorefractive material; (b) Charge generation in light areas of interference fringes; (c) Electrons are trapped at trap sites in light areas; holes migrate by diffusion or drift in the presence of an external electric field and generate an internal electric field between light and dark. positions; (d) Refractive index is distributed by the internal electric field.
For general holograms based on photochemical reactions, as shown in Fig. 2(a), no special change occurs in the intensity of laser light transmitted through the hologram. However, in a photorefractive index grating, the transmission intensity of one laser beam increases as the transmission intensity of the other beam decays as shown in Fig. 2(b). If the phase of one laser changes, it produces a large change in the asymmetric energy exchange [8,12]. Thus, it can be used as a sensor for the phase change of light. In addition to inorganic crystals such as lithium niobate and barium titanate, organic photoconductive polymers are known to exhibit the photorefractive effect [12–14]. However the response time is tens to hundreds of milliseconds, and large voltages of typically 5∼7 kV in a 100 µm thick film must be applied to obtain a sufficient response. Liquid crystals possess great birefringence and fluidity, and exhibit substantial photorefractive effects [12,15–18]. The liquid crystals can be formed into thin films of 10 µm, so that the electric field necessary for the photorefractive applications is only 10∼20 V. Also the flexoelectric liquid crystals exhibit photorefractive response time of 1 ms, that is advantageous for laser ultrasonic measurements.
Fig. 2. Diffraction of light by refractive index grating: (a) Grating due to photochemical reaction; (b) Asymmetric energy exchange due to photorefractive effect.
1.1 Photorefractive liquid crystals
Liquid crystals mixed with photoconductive compounds exhibit the photorefractive effect [12]. In particular, the photorefractive effect of nematic liquid crystals [15–18], and smectic liquid crystals [19–23] that are ferroelectric liquid crystals have been extensively studied. Liquid crystals respond rapidly to photoinduced space-charge electric fields; their optical properties change significantly in response to electric fields. A PR-flex LC consists of a mixture of photoconductive chiral dye (3T-2MB) and electron trap reagent (TNF) in a smectic liquid crystal mixture as depicted in Fig. 3(a). The PR-flex LC exhibits the flexoelectric effect; it represents the induced polarization caused by orientation distortion of liquid crystal molecules. Details of the dielectric properties of this photorefractive liquid crystal mixture have already been reported in our previous paper [23]. This liquid crystal mixture does not exhibit spontaneous polarization, and no Goldstone modes are observed in the dielectric relaxation spectrum. However, the electro-optic switching of this liquid crystal responds in 850 microseconds to the application of an electric field [22], suggesting that the bulk polarization, not the dipole moment of the molecules, responds to the electric field. Therefore, it is concluded that this liquid crystal is a flexoelectric liquid crystal. PR-flex LC demonstrates a substantial photorefractive effect [23], making it possible to form the moving holograms displaying the animation [20]. Furthermore it is possible to amplify the diffracted signal intensity through the asymmetric energy exchange [21]. The capability of high-repetitive recording in holograms can be used for high-speed detection of the sonic source by laser ultrasonics and more it is possible to measure the ultrasonic sounds immune to external vibrations as will be explained in §3.2.
Fig. 3. (a) Structures of PR-flex liquid-crystal mixture. The concentration of photoconductive chiral dye (3T-2MB) is 10 wt.% and the concentration of electron trap reagent (trinitrofluorene, TNF) is 0.1 wt.%. (b) The structure of the PR-flex LC cell. (c) Schematic illustration of the p-polarized beam incidence in the two-beam mixing experiment.
1.2 Laser ultrasonic non-contact measurement using photorefractive liquid crystals
As illustrated in Fig. 4, the laser ultrasonics can be performed by using the features of asymmetric energy exchange in two-beam mixing to measure the thickness and shape of the object; it is the sound source generated by laser pulse irradiation. When the phase of two-beam interference fringes in Fig. 4 (b) is shifted by π/2 from the refractive-index grating, the intensity I1(t) of light 1 reaches its maximum value and that I2(t) of light 2 reaches its minimum value as the time lapses. Thus, light 1 is amplified by light 2 according to Eq. (1).
where Γ is the gain coefficient, and L is the interaction length in the PR-flex LC cell, assuming the absence of absorption in LC. The magnitude of the asymmetric energy exchange is evaluated by the magnitude of gain coefficient Γ. If there is a change in the phase of the light, the asymmetric energy exchange changes significantly. The signal beam holding the phase change due to acoustic vibrations in an object is amplified and that of the reference light is attenuated, both settling to a constant value. A nanosecond pulsed laser is irradiated on the object to generate ultrasonic waves at the object surface that travel through the object and are appear on the surface of the object, causing a phase shift in the object light. This causes a change in the amplification and attenuation of the light as it deviates from the conditions of asymmetric energy exchange as shown in Fig. 4(b). By measuring the time between the irradiation of the pulsed light on the object and the change in the signal beam and/or the reference pump beam, we can obtain information on the thickness of the object and the defects and structures inside it.Fig. 4. (a) Optical setup for measuring the thickness and shape of an object by laser ultrasonics; (b) Phase change due to an acoustic vibration in an object signal beam leads to changes of an interference intensity by two-beam mixing.
2. Sample preparation and experiments
A PR-flex liquid crystal was used as a photorefractive material. The structures of the compounds used in the experiments are shown in Fig. 3(a). A liquid crystalline mixture (base LC) was mixed with a photoconductive chiral compound and an electron trap reagent in order to introduce photoconductivity and flexoelectricity. The photorefractive effect with a fast response is obtained in flexoelectric liquid crystals [23]. The base LC exhibited a phase sequence of Crystal → 6.4 °C → SmC → 48.1 °C → SmA → 59.4 °C → Nematic → 67.6 °C → Isotropic. The trinitrofluorene (TNF) concentration was 0.1 wt. %. A terthiophene compound was chosen as the photoconductive chiral compound because the terthiophene moiety has a rod-like structure so that it is highly soluble in the base LC. In a LC medium, the terthiophene compound is considered to exhibit photoconductivity based on the hopping mechanism as well as the ionic conduction when its concentration exceeds 4 wt. % [22]. The concentration of the photoconductive chiral compound was 8 wt. %. The base LC, TNF, and a photoconductive chiral compound were mixed. As shown in Fig. 3(b), FLC mixture was injected into the space sandwiched between two glass plates with a spacing of 10 µm. Two glass plates were equipped with an indium tin oxide (ITO) electrode and a polyimide alignment layer.
The gain coefficient Γ in two-beam mixing was measured by using an experimental setup with a 473-nm diode-pumped laser (Cobolt 08-01, 50 mW) in Fig. 5(a). The power of the signal and pump beams was 2 mW for each beam, and both beam diameters were 0.5 mm. As shown in Fig. 2, “light 1” and “light 2” beams correspond to the signal and pump beams, respectively, those intensities are termed as I1(z) and I2(z), respectively. The small and large angles of two beams to the LC cell were 30° and 50°, respectively (Fig. 5(a)). The rubbing direction corresponds to the c-axis of the liquid crystal. The polarization of the laser beam was p-polarized and the polarization plane was coincident with the alignment direction of the liquid crystal (see Fig. 3(c)). An electric field of 0∼2 V/µm was applied to the sample from a regulated DC power supply (Kenwood DW36-1) while the change in the transmitted beam intensities were monitored by silicon PIN detectors (ET-2070, Electro-Optics Technology, Inc., response time: 30 ns) and the data recorded on an oscilloscope (IWATSU DS5514A, 100 MHz, sampling rate 1 GS/s). On-off of the beam was controlled by a mechanical shutter (AD Science Inc. Japan, 300 ms high-speed mechanical shutter LC2 with VCM-D1J controller). The experimental setup used for the laser ultrasonic measurement is shown in Fig. 5(b).
Fig. 5. (a) Experimental setup for the measurement of the gain coefficients and the response times of two-beam mixing. (b) Experimental setup used for the laser ultrasonic measurements in this study: PBS, polarizing beam splitter; λ/2, half-wave plate; λ/4, quarter-wave plate.
A linearly polarized beam from a diode-pumped laser (Cobolt, 08-01, 473 nm, continuous wave) was divided in two by a beam splitter, one of which (reference beam) is injected to the PR-flex liquid crystal sandwiched between two glass plates and the other beam is irradiated on the aluminum plate. The reflected beam from the aluminum plate is injected to the PR-flex liquid crystal and interfered with the reference beam. The laser intensity was 2 mW for each beam in front of the LC and each had a 0.5 mm diameter. The beam angles incident to the glass plane were 30° and 50° and the interference fringe interval was 1.9 µm. An electric field of 2.0 V/µmm was applied to the sample from a regulated DC power supply (Kenwood DW36-1) while the change in the transmitted beam intensities were monitored by silicon PIN detectors (PDA10A2 Fixed Gain Detector, 150 MHz max bandwidth, rise time: 2.3 ns, Thorlabs, Inc.) and the data recorded on an oscilloscope (IWATSU DS5514A, 100 MHz, sampling rate 1 GS/s, 1 µs/div). A 1064-nm Q-switched pulsed laser (Minilite II, Continuum, 5–7 ns pulse width) was used as a light pulse source. The laser ultrasonic measurement was conducted with the laser pulse intensity of 1.5 mJ/pulse. The timing of the laser pulse irradiation was controlled by a digital delay generator (Stanford research systems, model DG645). The thicknesses of aluminum plates were measured by a digital micrometer (Mitutoyo MDC-25MJ, permissible measurement error 1 µm).
3. Results and discussion
3.1 Two-beam mixing experiment on PR-flex liquid crystal
Two-beam mixing experiments were conducted on the PR-flex LC. In Fig. 6(a), we show experimental results of increasing and decreasing intensities of a signal beam I1(t) (shown in red) and a pump beam I2(t) (shown in blue) detected by upper and lower photodiodes in Fig. 2, respectively. A PR-flex LC cell is regulated at 25 °C where an electric field of 1.6 V/µm is applied to it. Two different diffractions by an index grating of a PR-flex LC sample resulted in increased transmittance of one of the beams and decreased transmittance of the other beam. The index grating is recorded in a PR-flex LC sample with a 90° phase shift from the two-beam interference fringes. The characteristics in diffraction was reversed when the polarity of the applied electric field was reversed. In this case, more than 50% of the energy of one of the laser beams was transferred to another beam. The change in transmitted intensities of the interfering laser beams was measured and the two-beam mixing gain coefficients Γ were obtained from Eq. (2) assuming Bragg diffraction [8,12].
Where D = L/cos(θ) is the interaction path for the signal beam (L = sample thickness, θ=propagation angle of the signal beam in the sample), g is the ratio of the signal beam intensities behind the sample with and without a pump beam, and m is the ratio of the beam intensities (pump/signal) in front of the sample. The gain coefficients of the samples were measured as a function of the applied electric field strength (Fig. 6(b)). The gain coefficient Γ was calculated to be 1400 cm–1 with the application of 2.0 V/µm. The time required to form the refractive-index grating in the LC was determined based on the single-carrier model of photorefractivity, in which the gain transient is exponential. The rising signal of the diffracted beam was fitted using a single exponential function:Fig. 6. (a) An experimental result of two-beam mixing for the PR-flex liquid crystal at 25 °C. An external electric field of 1.6 V was applied. (b) Electric-field dependence of the gain coefficients Γ for mixtures of the PR-flex LC measured at 23 °C. (c) Refractive index grating formation times for mixtures of the PR-flex liquid crystal measured at 23 °C. Light scattering by the liquid crystal increased significantly at the electric field strength higher than 2.0 V/µm.
The response time of the photorefractive effect affects the refractive index grating rewrite time, but not the detection of ultrasonic vibrations. When the phase of the laser light deviates from the conditions of asymmetric energy exchange, the signal due to ultrasonic vibrations is instantaneous. The refractive index grating remains unchanged and only the phase of the detected light changes, resulting in a change in the asymmetric energy exchange. Therefore, if the refractive index grating is written too fast, it is not suitable for detection. On the other hand, the refractive index grating must be constantly rewritten to ensure that the measurement is unaffected by environmental vibrations. Therefore, the response time of the photorefractive effect must be faster than the environmental vibration and slower than the fluctuation of the laser light. Considering that the range of environmental oscillations is from 0.1 Hz to several tens of Hz, a response time of 1 ms is desirable in practice. Previous reports on laser ultrasonics with crystals and polymers have not reported elimination of environmental vibration effects by speeding up the photorefractive effect. The resolution of laser ultrasonics is determined by the time resolution of the vibration signal detection. This is determined by the performance of the detector and oscilloscope. The photorefractive liquid crystals proposed in this study have few defects and low light scattering, thus providing the high sensitivity required for laser ultrasonics.
3.2 Laser ultrasonic measurement using PR-flex liquid crystal
The laser ultrasonic measurement was conducted with the set-up shown in Fig. 5(b). Two beams of a 473 nm CW laser were interfered in the PR-flex liquid crystal and asymmetric energy exchange was observed. An external electric field of 2.0 V/µm was applied to the PR-flex liquid crystal. Then, a 1064-nm laser pulse was irradiated to the aluminum plate, and the changes in the asymmetric energy exchange were examined. The distance from the front surface to the back surface of the object can be obtained by measuring the time between the pulse laser irradiation and the change in the asymmetric energy exchange. Figure 7(a) shows an experimental result using an aluminum plate as an object.
Fig. 7. (a) Measured signal in ultrasonic measurement using PR-flex liquid crystal. The thickness of the aluminum plate was 2 mm. Downward and upward arrows indicate the detection positions of longitudinal waves and transverse waves, respectively. The vertical line denotes the time when the Al plate is irradiated with the pulsed laser. (b) Multiple reflections of acoustic waves on the front and back surfaces of the Al plate. (c) The locations of the signals caused by multiple reflections of longitudinal and transverse ultrasonic waves on the surface of the Al plate. T is the time taken for the transverse wave to travel through the aluminum plate from the back to front sides and t is the time taken for the longitudinal wave.
The measurement results show many signals, caused by the repeated reflection of ultrasonic vibrations on the front and back surfaces of the aluminum plate (Fig. 7(b)). The signals were observed at the pulsed laser intensities higher than 0.6 mJ/pulse. The pulsed laser irradiation generates ultrasonic vibrations on the surface of the aluminum plate in the form of longitudinal and transverse waves. The velocities of the ultrasounds in the aluminum plate were 6420 m/s for longitudinal waves and 3040 m/s for transverse waves. Literature values were used for sound velocities in aluminum plates [24].
The signals of longitudinal ultrasonic waves are sharp and clearly observed. However, the signals of transverse waves are broad and the positions of all signals except the first one appear to deviate from the expected positions. Transverse ultrasonic waves decay quickly, so the second and subsequent reflected waves are not observed. However, when the longitudinal wave reflected on the front side transits the aluminum plate and is reflected on the back side, a transverse wave is also generated, which transmits to the front side and is detected. Then the positional relationship between the signals of the longitudinal and transverse waves is shown in Fig. 7(c). In this figure, t shows the time taken for the longitudinal wave to travel through the aluminum plate and T shows the time taken for the transverse wave to travel through the aluminum plate. The thickness of the flat plate can be obtained from the time between the neighboring longitudinal signal (=2 t) and the longitudinal ultrasound velocity (6420 m/s). However, the thickness of the plate can not be obtained from the combination of the time between the neighboring transverse signal T and the transverse ultrasound velocity (3040 m/s).
Figure 8 shows the results of the ultrasonic measurement on aluminum plates with thicknesses of 5, 3, and 2 mm. The positions of the signals are different in different thicknesses of the plate. The thicknesses of the plates obtained from the ultrasonic measurements are shown in Table 1. The results are in good agreement with the actual aluminum plate thickness, indicating that the aluminum plate thickness can be measured using this method. Figure 9 shows the measurement results using a sample with a drilled cavity in the aluminum plate (Fig. 9(a)) while changing the laser irradiation position (Fig. 9(b)).
Fig. 8. Measured signal in ultrasonic measurement using PR-flex liquid crystal. The thicknesses of the aluminum plates were 5, 3, and 2 mm. Arrows indicate the positions of longitudinal waves and transverse waves. The dashed line denotes the time when the Al plate is irradiated with the pulsed laser.
Fig. 9. (a) Photograph of the aluminum plate with a cavity. (b) 1D-scan measurement results in an aluminum plate cavity. (c) A 3D plot of the cavity on aluminum plate measured by the laser ultrasonics.
Table 1. Measured thickness of aluminum plates
The shape of the cavity in the aluminum plate appears in the signal, indicating that the shape of the object can be measured without contact. A three-dimensional image of the object shape was obtained by scanning the object in two dimensions. A total of 169 points were measured, 13 in the x-axis direction and 13 in the y-axis direction, and plotted in three dimensions (Fig. 9(c)).
The sensitivity of the two-beam interferometer recorded in a PR-flex LC of laser ultrasonics can be assessed by the magnitude of the surface displacement at the limit of detectability obtained from Eq. (4), the signal-to-noise-ratio (SNR) equation for the system [25].
It has been reported that for polymer materials, typical values are λopt = 633 nm, P = 0.00017 Js-1, α = 20 cm-1, Γ = 70 cm-1, and L = 0.1 cm, resulting in δ = 0.10 nm [25]. In this study, λopt = 473 nm, P = 0.0080 Js-1, α = 90 cm-1, Γ = 1400 cm-1, and L = 0.001 cm, resulting in δ = 0.01 nm. Thus, the sensitivity of PR-Flex LC is much greater than that in laser ultrasonics using photorefractive polymers. The resolution of laser ultrasound is determined by the time resolution of the vibration signal detection. This is determined by the performance of the detector and oscilloscope. The photorefractive liquid crystals proposed in this study have few defects and low light scattering, thus providing the high sensitivity required for laser ultrasound.
Ultrasonic testing using the photorefractive effect has been reported using inorganic photorefractive crystals [26,27] and polymer photorefractive materials [25]. However, in these cases, the response time for forming the photorefractive grating was slow, and the photorefractive materials require fast-measurement performance free from vibration. The frequencies of vibrations caused by automobiles range from 0.1 Hz to several tens of hertz, which is close to the response time of crystals and polymers, unable to detect the laser ultrasonic. However, PR-flex liquid crystals respond in microseconds to milliseconds; thus, even if the liquid crystal moves due to environmental vibration, the refractive index grating is instantly recorded, allowing us to measure the laser ultrasonic unaffected by the vibration. Figure 10 shows the schiematic diagrams for movements of refractive-index gratings by photorefractive effect in a vibration environment.
Fig. 10. Movement of refractive index grating due to the vibration: Cases for PR materials with (a) slow and (b) fast response times.
4. Conclusions
In this study, a laser ultrasonic measurement system using a flexoelectric liquid crystal mixture was demonstrated. Photorefractive flexoelectric liquid crystal (PR-flex LC) show that a gain coefficient was measured as 1400 cm–1 and a response time was 960 microseconds, both with an applied electric field of 2.0 V/mm. The flexoelectric liquid crystals do not show spontaneous polarization unless an electric field are applied so that uniformly aligned defect-free firms have been obtained in flexoelectric liquid crystals. The experimental results of acoustic time-of-flight measurements in a target aluminum (Al) plate are presented by using an adaptive two-beam interferometer with a PR-flex LC cell. The acoustic velocities in the longitudinal and transverse waves propagating through this plate can be measured by using measured time-of-flight in both waves and the thickness of Al plate. The measured velocities are compared with the nominal values with good agreement. The parameters in an adapted interferometer with a PR-flex LC are appropriate for remote ultrasonic detection immune to the vibrations in an industrial environment.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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