1. Introduction

Liquid crystals (LCs) are widely used for various applications such as electronic imaging, displays, and optoelectronics. In particular, the electro-optic (EO) devices based on LCs can be used as sensing devices because of their large EO response [1–10]. There are several methods to demonstrate the EO sensors using LC devices. Most of the methods are used a Fabry-Perot filter with LC as a sensing device [5–10] where the refractive index of the LC is changed by electric field or temperature. In general, Fabry–Perot filters with LC have been developed for use in wavelength-division-multiplexing communication systems [11,12] as they can be used as wavelength-tunable elements. The LC in the Fabry–Perot etalon is used as an active medium that can be controlled by changing the applied voltage. Therefore, it can be used as a wavelength-tunable filter. The EO sensors with LC have good stability and high resolution since they usually measure the variation of resonance peaks. On the other hand, the optical fiber EO sensors with LC have attracted much attention because of their easy integration with fiber optics [1,2,4,13]. Specially, fiber-optic-based LC devices are used as electric field sensors in the electric power industry because the molecular orientation of LCs is highly dependent on the external electric field. Most fiber-optic electric field sensors measure the transmission intensity variation, performing direct measurements of the intensity according to the applied electric fields.

When the homogeneous nematic liquid crystal (NLC) in the Fabry–Perot etalon is modulated by an electric field, the alignment of the NLC is modulated as well. Therefore, the transmission output of the NLC Fabry–Perot etalon is modulated in the spectral domain. However, measuring the transmission characteristics of the NLC in the spectral domain according to the dynamic variation in the electric field is not easy because of the slow response of the optical spectrum analyzer (OSA). If the modulation output could be displayed in the temporal domain, the transmission characteristics of the modulation response from the NLC can be measured using a high-speed photo-detector. Such temporal-domain modulation output can be realized using a high-speed wavelength-swept laser (WSL) because, for this device, emitting wavelength depends linearly on time [14].

The WSL is a promising optical source that is used in optical coherence tomography, optical fiber sensors, and optical beat source generation [14–28]. It has been developed via various methods using a narrowband wavelength scanning filter such as a rapidly rotating polygonal mirror, a diffraction grating on a galvo-scanner, and a scanning fiber Fabry–Perot tunable filter [14,21–25]. The main advantage of using the WSL for measurement is the linear relationship that exists between wavelength and time. Therefore a wavelength in the spectral domain exactly corresponds to a pulse signal in the temporal domain. This type of dynamic measurement in fiber optic sensors has been reported using this advantage of the WSL [15–18,28].

In this paper, we propose a fiber-optic electric field sensor that can measure the frequency of the dynamic variation in an electric field. A high-speed WSL is used as an optical source. Because the spectral and temporal outputs of the WSL show a correlation, the transmission output of the NLC Fabry–Perot etalon with dynamic variation in the electric field can be easily measured in the temporal domain.

2. Nematic liquid crystal Fabry-Perot etalon

Commercial 4-cyano-4'-pentylbiphenyl (5CB, from Merck) is used as an NLC. This compound exhibits nematic- phase properties in the temperature range of 24 °C to 36 °C. Figure 1 shows the cell structure of the fabricated NLC Fabry–Perot etalon. It consists of glass substrates, gold layers as the electrodes and highly reflective surfaces, polyimide layers as the planar alignment layers, and an LC layer. In order to reduce the absorption form the gold layer, it can be fabricated with the dielectric materials and indium tin oxide (ITO) [29]. The NLC is homogeneously aligned between the polyimide layers. The orientation of the NLC is aligned with the x-axis in the absence of an electric field. Because the electric field direction is parallel to the z-axis, the director is gradually reoriented along this axis as the electric field intensity increases. The thicknesses of the gold layer and the LC layer are approximately 30 nm and 30 μm, respectively.

 

Fig. 1 Structure of the NLC Fabry–Perot etalon.

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When linearly polarized input light is incident on the cell along an arbitrary direction, under no electric field, the polarization direction of the light can be represented by two orthogonal components in the homogeneously aligned NLC. One is the component perpendicular to the director orientation in the “ordinary mode” and the other is the component that is parallel to the director orientation in the “extraordinary mode.” Thus, there are two propagation modes in the homogeneous NLC Fabry–Perot etalon. In general, there are two refractive indices in the NLC: n_o (ordinary refractive index) for the ordinary mode and n_e (extraordinary refractive index) for the extraordinary mode [6].

3. Principle of operation

The condition for the appearance maximum fringe of the NLC Fabry–Perot etalon is given by

As described in section 2 as regards the properties of the NLC, the etalon can operate in the ordinary and extraordinary modes when linearly polarized input light is incident on the NLC along an arbitrary direction. While the wavelengths of the transmitted peaks of the NLC Fabry–Perot etalon do not change in the ordinary mode, they do change in the extraordinary mode according to the applied electric field. There are two methods to calculate the electric field applied to the NLC. One is to measure the wavelength difference between the peaks of the ordinary mode and the extraordinary mode while the peak of the ordinary mode remains as a reference. However, it is hard to measure this wavelength difference as the applied electric field is increased because the peaks of the ordinary and extraordinary modes cannot be distinguished when they are very close to each other. Further, the wavelengths of the transmitted peaks are shifted to the shorter-wavelength region as the applied electric field strength is increased. Eventually, the peaks no longer lie within the measurable spectral range, and the wavelength difference cannot be measured via this method. The other method involves the measurement of the wavelength difference between the peaks of any two wavelengths in the extraordinary modes. In this case, it is possible to measure the applied electric field in the measurable spectral range. The effective refractive index is calculated using two consecutive wavelengths from Eq. (2) as follows:

When the modulated electric field is applied to the NLC Fabry–Perot etalon, the wavelengths of the transmitted peaks are modulated by the same frequency as that of the field. Therefore, the wavelength difference between two consecutive wavelengths is also modulated. As previously mentioned as regards the output of the WSL, there is a linear relationship between the wavelength measurement and the time measurement because the spectral output and the temporal output are correlated. Because the modulated wavelength difference, which is measured using an OSA corresponds exactly to the modulated time difference of the pulses measured by a sampling oscilloscope, the modulation frequency of the variation can be estimated by measuring the peak position of the modulated pulses using a high-speed photodetector. Therefore, the modulation frequency of the applied electric field can be obtained by measuring the variation in the time difference $\Delta t$ in the temporal domain.

4. Experiments

Figure 2 shows the experimental setup for the dynamic measurement of the applied electric field using the NLC Fabry–Perot etalon and the WSL. The WSL with a polygon-scanner-based wavelength filter is used as an optical source. It comprises two semiconductor optical amplifiers (SOAs), two polarization controllers, an optical circulator, an optical output coupler, and a polygon-scanner-based wavelength filter. The dotted box in the figure represents the polygon-scanner-based wavelength filter [28].

 

Fig. 2 Experimental setup for electric field sensor using an NLC Fabry–Perot etalon. (SOA: semiconductor optical amplifier; NLC FP etalon: nematic liquid crystal Fabry-Perot etalon)

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The center wavelength of the WSL is approximately 1300 nm, the output power is approximately 20 mW, and the scanning bandwidth is greater than 90 nm for a scanning speed of 10 kHz. The collimated output beam of the WSL is transmitted to the NLC Fabry–Perot etalon through a linear polarizer. The input beam is linearly polarized in the direction of the extraordinary mode. Therefore, there exist only n_e modes in the transmitted wavelength peaks. The operation of the NLC Fabry–Perot etalon is controlled by an arbitrary function generator (Tabor electronics Inc., 8023) that applies the electric fields. The output of the NLC Fabry–Perot etalon is collected by a collimator and monitored using an OSA and a sampling oscilloscope. All instruments are controlled by Labview programs via a general purpose interface bus (GPIB).

In order to measure the variation in the effective refractive index of the NLC according to the applied static electric field, the wavelengths of the transmitted peaks of the NLC Fabry–Perot etalon are monitored by the OSA. Figure 3(a) shows the characteristics of wavelength tuning from the NLC Fabry–Perot etalon according to the applied electric field. The solid lines in the figure represent the wavelengths tuning from the transmitted peaks. There only exists the n_e mode of the wavelengths of the transmitted peaks in the optical spectrum because the polarization of the input beam is controlled by the linear polarizer in the direction of the extraordinary mode. Under the threshold voltage corresponding to the Freedericks transition, the wavelengths of the transmitted peaks do not shift with the applied electric field. However, above the threshold voltage, the wavelengths of the transmitted peaks begin to shift toward the shorter-wavelength region as the applied electric field increases. The threshold value of the electric field was 25 mV_rms/μm for the observed NLC cell. At electric field values of more than 150 mV_rms/μm, the shifts of the wavelengths in the transmitted peaks gradually become saturated. The inset of Fig. 3(a) shows the transmitted optical spectrum from the NLC Fabry–Perot etalon under an electric field of 10 mV_rms/μm. By selecting two consecutive wavelengths of the transmitted peaks, the effective refractive index can be calculated from Eqs. (3) and (4). The reflectivity of the gold layer and insertion loss of the NLC Fabry–Perot etalon are ~90% and ~20 dB, respectively. The measured linewidth and the free spectral range (FSR) of the transmitted peaks are ~0.8 nm and ~17 nm, respectively. Therefore the finesse of the NLC Fabry–Perot etalon is calculated with ~21.

 

Fig. 3 (a) Wavelength tuning of the NLC Fabry–Perot etalon in the extraordinary mode (Inset: optical spectrum of the NLC Fabry–Perot etalon under a field of 0.24 mV_rms/μm) and (b) effective refractive index as a function of the applied electric field.

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Figure 3(b) shows the plot of the effective refractive index of the NLC as a function of the applied electric field at room temperature of 24 °C, obtained using Eq. (3). The effective refractive index of the NLC remains at approximately 1.67 until the threshold electric field is reached. On the other hand, after the threshold electric field of 25 mV_rms/μm is surpassed, the effective refractive index decreases quickly and eventually saturates at a value of 1.51. These refractive index values agree with those reported in a previous study [30].

Next, the amplitude-modulated electric field is applied to the NLC Fabry–Perot etalon in order to measure the dynamic variation in the transmitted peaks. A sinusoidal waveform with a value of 9 V is applied to the NLC Fabry–Perot etalon as an amplitude-modulated signal. When the amplitude-modulated electric field of the proper amplitude and frequency is applied to the NLC, the wavelengths of the transmitted peaks for the extraordinary mode are modulated with the same frequency. Two consecutive wavelengths of the transmitted peaks are chosen to measure the dynamic variation. As previously mentioned, the wavelength difference between two consecutive wavelengths is also modulated. However, measuring the modulated wavelength of the transmitted peaks in the spectral domain is difficult because the response of the wavelength variation in the OSA is extremely slow compared to the modulation speed. As previously stated as regards the output of the WSL, the spectral output in the OSA and the temporal output in the sampling oscilloscope are correlated. Because the modulated wavelengths of the transmitted peaks correspond exactly to the modulated pulses in the sampling oscilloscope, the amplitude modulation frequency can be estimated by measuring the peak positions of the modulated pulses using a high-speed photodetector. Figure 4(a) shows the pulses of the transmitted peaks in the temporal domain. The pulses in the figure exactly correspond to those in the inset of Fig. 3(a). By measuring the variation in the time difference $\Delta t$ _{for two consecutive pulses in the temporal domain, the amplitude modulation frequency of the electric field applied to the NLC can be estimated. The dynamic variation signals collected by the detector are digitized using a DAQ board with a high sampling rate of 100 Msamples/s. Figure 4(b) shows the dynamic variation in the time difference for two consecutive pulses at an amplitude modulation frequency of 10 Hz. The y-axis represents the time difference between the two consecutive peaks. The time difference variation closely agrees with the amplitude modulation signal frequency of 10 Hz, as shown in Fig. 4(b).}

 

Fig. 4 (a) Pulses of the transmitted peaks in the temporal domain and (b) dynamic variation in the time difference for two consecutive pulses at an amplitude modulation frequency of 10 Hz

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Figures 5(a)-5(c) show the measured dynamic variations in the time difference for two consecutive pulses at amplitude modulation frequencies of 100 Hz, 1000 Hz, and 1500 Hz, respectively. The measured frequencies closely tally with the amplitude modulation frequencies of the applied electric field. There are asymmetric behaviors in the measured dynamic variation in Fig. 4(b) and Fig. 5(a). They are due to the difference of response time between turn on (forward voltage scan) and turn off (backward voltage scan) of the LC device [31]. Furthermore, there are some high-frequency noises in Fig. 4(b) and Fig. 5(a). These might be due to the background noise from the wavelength-swept laser. It should be solved to obtained clear response. The corresponding fast Fourier transform (FFT) spectra of the periodic outputs of Fig. 5(a)-5(c) are shown in Fig. 5(d). There are several components of the corresponding frequencies observed in the FFT spectrum. These are the higher-order components of the amplitude modulation frequencies. The signal-to-noise ratios (SNRs) of these components were determined to be more than 25 dB. Figure 5(e) shows the expanded FFT spectrum at 1000 Hz. The measured 3 dB linewidth is ~5 Hz and the deviation of the accuracy for the measured frequency is less than 0.2%.

 

Fig. 5 Measured dynamic variations in the time difference for two consecutive pulses at amplitude modulation frequencies of (a) 100 Hz, (b) 1000 Hz, (c) 1500 Hz, (d) FFT spectra corresponding to the periodic outputs shown in (a)-(c), and (e) expanded FFT spectrum at 1000 Hz.

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5. Summary

We successfully demonstrated the working of a fiber-optic dynamic electric field sensor using a nematic liquid crystal (NLC) Fabry–Perot etalon and a high-speed wavelength-swept laser (WSL). The liquid crystal (LC) used was commercial 4-cyano-4'-pentylbiphenyl that exhibits NLC properties in the temperature range of 24 °C to 36 °C. The wavelengths of the transmitted peaks in the NLC Fabry–Perot etalon depended on the applied electric field strength. The input beam was linearly polarized in the direction of the extraordinary mode. By selecting two consecutive wavelengths of the transmitted peaks, we measured the effective refractive index change according to the applied electric field. The refractive index decreased from 1.67 to 1.51 as the applied electric field increased. We also successfully measured the dynamic amplitude modulation frequencies of the applied electric field using the high-speed WSL. The dynamic amplitude modulation frequencies were obtained by measuring the variation in the time difference between two consecutive pulses in the temporal domain. The measured frequencies of dynamic modulations closely agreed with the amplitude modulation frequencies of the applied electric field. The signal-to-noise ratios (SNRs) of the measured frequencies were determined to be more than 25 dB.