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Abstract
A novel intense electric field optical sensor based on Fabry-Perot interferometer utilizing LiNbO3 crystal is proposed and demonstrated. Compared to the traditional bulk-type electric field optical sensors, this sensor unit requires only a LiNbO3 and two collimators, eliminating the need for quarter wave-plate and allowing for measurement of electric field without limitation by half wave voltage. The Vernier effect, generated by birefringence of LiNbO3, is utilized to enhance the sensitivity of electric field measurement, which does not require additional reference cavity. Both theoretical and experimental results illustrate that the wavelength shift of the sensor is linear function of the measured electric field. In the range of 0∼1010 kV/m, the sensor’s measurement sensitivity is 2.22 nm/E (V/µm) with detection limit of 1.27 × 10−2 E. Additionally, an MZI is proposed for temperature compensation, resulting in a standard deviation of spectrum variation after compensation of only 5.01 × 10−3. Applications using this sensor confirmed that it is expected to find widespread use in measurements of intense transient electric fields.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In large-scale power systems, such as ships, power grids and railways, the accurate measurement of intense electric field (E-field) is crucial to ensure safe and stable operation of equipment. However, traditional E-field sensors based on electromagnetic or capacitance dividers are rarely meet the measurement requirements due to their susceptibility to interference in intense E-field environments and the large size [1–3]. By contrast, the novel optical E-field sensor (OES) can not only overcome the aforementioned shortcomings, but also boast superior insulation, robust anti-electromagnetic interference capabilities, and rapid response times [4–7].
At present, there are two major sensing mechanisms for OES. One is based on the electro-optical effect, which can be categorized into two types: crystal bulk-type [8–11] and optical waveguide-type [12–15]. The crystal bulk-type generally consists of a crystal, two polarizers and a quarter wave-plate. The inclusion of the quarter wave-plate increases the size of the optical system and renders it easy to be affected by temperature leading to compromise long-term stability of the system. The optical waveguide-type is an integrated optical waveguide sensors based on LiNbO3 (LN) or electro-optical polymer. It has the advantages of high sensitivity, broadband frequency response and mass production. However, the bias point of such kind of sensor depends on the length of waveguide, which is difficult to adjust after the sensor is fabricated, and it is easily susceptible to temperature. The E-field measured by these two sensors is constrained by the half-wave voltage, with a maximum measurement of 450 kV/m in above references. Therefore, it is not feasible to measure more intense E-fields. Furthermore, as all aforementioned sensors employ an optical intensity modulation system, their output may be influenced by fluctuations in light source. The other one involves utilizing the inverse piezoelectric effect [16–18] to create either a Mach-Zehnder interferometer (MZI) or FBG by wrapping the optical fiber group on the PZT. This type of sensor structure leads to poor stability, unable to measure intense E-field, and too many devices to achieve miniaturization. Additionally, there are also some OESs proposed based on other principles. In 2002, Changsheng Li [19] designed an electro-optical crystal multiplier utilizing double transverse Kerr effect for E-field measurement. The sensor unit does not need the quarter wave-plate to achieve linear measurement of external E-field. In 2014, Liming Zhou [20] proposed an Fabry-Perot interferometer (FPI) voltage sensor based on the mechanism of liquid flow induced by charged particles and dielectrophoresis under electric field-induced. The power frequency AC voltage measurement results demonstrate a delay of only 0.1 ms, and the experiment proves that the OES based on FPI exhibits excellent response characteristics. In 2017, Yong Zhao [21] developed an MZI OES by filling liquid crystal in photonic crystal fiber. The experimental results showed a measurement sensitivity of 7 nW per V/m for E-fields. The above methods provide a new idea for the measurement of E-field.
In practice, the ambient temperature is often unstable, which inevitably affects sensor output. To eliminate the impact of temperature on sensor output, the common methods include software and hardware compensation [20,22] or placing two identical crystals [23,24]. However, these approaches are challenging to implement and compensate for, potentially increasing complexity within the optical system devices. Therefore, facing the demand of accurate measurement of intense E-field in variable temperature environment, it is necessary to propose a stable and reliable intense E-field sensor that is immune to temperature effects.
In this work, we proposed and demonstrated an OES based on FPI utilizing LN crystal. By combining FPI with Pockels effect, the E-field measurement is not limited by the half-wave voltage, and the measured result is unaffected by the fluctuation of light intensity. Compared with the traditional bulk-type E-field sensor, such E-field sensor unit consists of only one LN crystal and two collimators, reducing the size of the sensor unit and facilitating miniaturization. Furthermore, the Vernier effect is generated to improve the sensitivity utilizing the birefringence of the LN crystal without requiring an additional reference cavity. Experimental results show that the E-field sensitivity is of 2.22 nm/E and the resolution of 1.27 × 10−2 E. In addition, an MZI based on lateral offset fusion splicing structure are proposed to implement temperature compensate. The experimental results prove that the temperature compensation is effective. Compared to the conventional bulk-type electric field optical sensors, the proposed OES has a better application prospect.
2. Principle of operation and theoretical description
2.1 Principle of operation
The schematic diagram of the experimental setup is shown in Fig. 1. The natural light emitted by the super luminescent diode (SLD) is transformed into linearly polarized light through the polarizer. The MZI acts as temperature monitor to realize temperature compensation, which is explained detailly in section 3, thus a sinusoidal spectrum can be obtained through it. After this, the light is split into two orthogonal polarized beams through the 45° axial rotation fusion point, and enter fast axis and slow axis of polarization-maintaining fiber (PMF), respectively. Due to the birefringent effect of the LN crystal, the two beams maintain a mutually orthogonal state while propagating through the crystal. In further, each beam produces a sinusoidal spectrum in the FPI based on LN crystal, which does not interfere with the other. The axial direction of X-cut LN crystal is slightly angled from the axis of PMF on the front and rear sides, so that the two spectra combine in the optical fiber collimator at the back end of the crystal and generate Vernier effect. Finally, the sinusoidal spectrum generated by MZI and envelope spectrum are received by the optical spectrum analyzer (OSA).
2.2 Key components of the sensing setup
To achieve maximum E-field sensitivity in FPI based on LN crystal, it is crucial to utilize the highest electro-optical coefficient of LN while ensuring that the two perpendicular beams of light propagating in the crystal can be superimposed to generate Vernier effect. Therefore, this paper applies an E-field through the z axis and transmits incident light along the x axis to LN crystal for generating Pockels effect. The FPI based on LN crystal is shown in Fig. 2, the principal axis of the crystal is placed at an angle θ with the fast and slow axis of PMF on the front and rear sides. Due to the birefringent effect of LN crystal, the two linearly polarized lights will propagate along the x axis after entering the crystal through the fiber collimator, while the vibration directions are perpendicular to each other along the y and z axes, respectively. According to the Pockels effect of LN, the refractive index of lights vibrating along different principal axes are:
The RI of LN crystal no = 2.21 and ne = 2.14 at 1550 nm under room temperature. Therefore, there is a certain RI difference at the two sides of the crystal faces, the light will be reflected several times between the two faces of the crystal and produce an interference spectrum, namely FPI. According to the above analysis, there is no interference between the two beams vibrating along the y and z axis, two FPI will be formed in the crystal, whose free spectrum range (FSR) can be expressed as:
which λ=1550 nm represents the input light wavelength. L1 is the length of LN crystal. We can infer that the FSR of the two interference spectra are matched (similar but not equal). When the two light beams propagated from the crystal enter the second fiber collimator, their interference spectra will superimpose to produce Vernier effect, allowing for obtaining interference spectra with a certain magnification. The intensity of the interference light is:The change in nz is more pronounced than that of ny under the influence of E-field, as evidenced by the higher value of γ33 compared to γ13. Consequently, the FPI vibrating along the z axis exhibits greater sensitivity to E-field when compared to its counterpart vibrating along the y axis. In light of this, the former is designated as the sensing cavity while the latter serves as the reference cavity. The magnification factor M defined as:
Therefore, the expression for the FSR of the spectrum envelope can be given as:
According to Eq. (1) and (4), it induces a change in RI of crystal when an E-field (V/µm) is applied to the crystal, thus leading to a shift of the interference spectrum envelope of FPI. The variation of the envelope in response to E can be mathematically expressed as:
Actually, since the E-field affects both ny and nz, the shift of the interference spectrum envelope should be equivalent to the difference in shift of the FPI spectrum formed along the two axes. Therefore, by modifying Eq. (7) we can derive:
By substituting the LN crystal parameters into the aforementioned equation, the theoretical shift of spectrum envelope can be obtained as 2.22 nm/E. Assuming L1 = 2.28 mm, the simulation analysis results are depicted in Fig. 3. It is evident that when the interference spectrum variation of the two FPIs caused by E is 16 pm and 54 pm respectively, the envelope shift of the interference spectrum after cascade is 1.11 nm - a value which is 29 times greater than their difference.
The E-field is measured through the combination of Pockels effect and Vernier effect. The measured spectrum shift corresponds to the change in E-field, allowing for measurement of E beyond the limitations of half-wave voltage. This improves the value of E-field measurements greatly. At the same time, the integrated parallel Vernier effect configuration is realized in the crystal, which effectively enhances measurement sensitivity and reduces sensor size for conducive to miniaturization. Moreover, the parallel configuration offers the benefit of a reference signal without compromising the visibility of the sensing signal, whereas the series configuration using two sensors may result in visibility issues due to an additional interface [25].
In addition, if the polarized light beam propagates along the slow axis enters the crystal, the light intensity of FPI formed by vibration along y and z axes of LN will be inconsistent due to the angle between the main axes of LN and PMF’s main axes θ<45°, thus results in a lower fringe contrast of the interference spectrum envelope. Considering that the fringe contrast of the sensor spectrum is related to the signal-to-noise ratio (SNR) and consequently affects the limit of detection, the Vernier effect configuration need to be further optimized.
Therefore, prior to entering the collimator, PMFs axial rotation fusion splicing at an angle of 45° is performed as depicted in Fig. 1. Through a 45° fusion spliced, polarized light is able to propagate in both the fast and slow axes of PMF. This effectively resolves the issue of inconsistent light intensity between the two axes of the crystal upon re-entry, thereby enhancing fringe contrast within the spectral envelope. This step is a crucial element of both Vernier effect and sensing setup.
2.3 Temperature self-compensation using MZI
As aforementioned, an MZI is used as the temperature sensor to realize temperature compensation. It is constructed with lateral offset fusion splicing structure, where a light beam propagates in the fiber cladding and air after through the first fusion point. The beams then combine at the second offset fusion point to generate an interference spectrum with an FSR:
where nclad and nair are the RI of PMF cladding and air, respectively. L2 is the cavity length. The variation of the spectrum in response to temperature T can be mathematically expressed as:The simulation result of interference spectrum of MZI superposition FPI is shown in Fig. 4(a). The spectra of MZI and FPI can be extracted via fast Fourier transform (FFT) and band-pass filtering method. And Fig. 4(b) shows the spectrum of MZI shift with temperature.
Fig. 4. (a) Spectrum of the MZI superposition FPI, (b) wavelength variation versus temperature of MZI.
When the E or temperature T of the surrounding environment changes, the reflection spectrum of the sensor will shift accordingly. The following matrix equation can be derived:
The shift of the interference spectrum Δλ induced only by E-field after temperature compensation is thus derived:
3. Experimental setup
3.1 Sensors fabrication
An X-cut LN crystal was adopted as the E-field sensor, with light transmitting in the x direction and E-field applied in the z direction. The crystal dimensions are 5 mm × 5 mm × 2.28 mm, where the length of light transmitting is 2.28 mm. Thus, the FSR of the interference spectrum can be deduced as follows: FSRy = 0.24, FSRz = 0.25, FSRenvelope = 7.18 nm. To increase the intensity of the FPI spectrum and improve fringe contrast ratio, the y-z surface of the crystal was polished and coated with a dielectric film. Subsequently, the x-z surface is coated with silver paint to serve as the electrode and the FPI based on LN is shown in Fig. 5(a). The fabricated LN is fixed in the middle of two collimator at θ angle to complete the production of E-field sensor.
Before fabricating the MZI, 45° axial rotation fusion splicing should be finished for better fringe contrast ratio of the LN spectrum envelope. The fusion steps are as follows:
Firstly, the light source is connected to a section of PMF, and the other PMF is connected to a polarization analyzer.
Secondly, the two sections of PMF are put into the optical fiber fusion splicer, semi-automatic splicing mode was selected and the PMF is manually rotated while polarization analyzer monitoring the change of polarization extinction ratio (PER) in real time. The PER value was determined to be 45° when it approached zero indefinitely [26].
After the 45° axial rotation fusion splicing, the fringe contrast ratio of spectral envelope increased from 0.20 dBm to 0.90 dBm, as illustrated in Fig. 6(a-b). And the FSR of the interference spectrum envelope is 7.18 nm, which is consistent with theoretical analysis. The polarization state results are shown in Fig. 6(c), where the PER is 0.52 dB.
Fig. 6. Spectral envelope (a) before and (b) after 45° axial rotation fusion splicing, (c) the polarization state results of 45° axial rotation fusion splicing.
The manufacturing process of MZI based on the lateral offset fusion splicing structure has been very mature at present. As documented in Refs. [27], this compact and cost-effective structure is easy and safe to produce, thus obviating the need for detailed description in this paper. The proposed MZI is shown in Fig. 5(b), with cavity length L2 = 635 µm and FSR = 8.33 nm according to Eq. (8).
The fabricated sensors are connected in accordance with Fig. 1, and the final interference spectrum is obtained as depicted in Fig. 7(a). The FFT and band-pass filter results of the spectrum are shown in Fig. 7(b), where Peak 1 corresponds to the frequency of MZI spectrum (0.12 nm-1), while Peak 2 corresponds to that of spectrum envelope (0.14 nm-1), which is consistent with theoretical analysis. Peaks 3 represents the spectrum of FPI based on LN, wherein the peak group contains frequency components of FPI along the y axis, z axis and the spectrum fringes within the envelope. The spectra of MZI and FPI can be obtained by band-pass filtering the spectrum in Fig. 7 (a) according to the spectral results, as shown in Fig. 7 (c) and (d).
Fig. 7. (a) The total spectrum and the (b) corresponding spatial frequency spectrum, (c) The retrieved spectrum of MZI and (d) FPI based on LN Crystal.
3.2 E-field sensitivity and responsivity
The experimental test system is shown in Fig. 8, wherein the crystal is fixed between two collimators. A uniform E-field is generated by placing parallel copper plates on either side of the crystal and applying a standard voltage source.
According to Eq. (8), wavelength shift of the FPI is a linear function of the E-field, it is of interest to measure this slope or E-field sensitivity, i.e., K2 in Eq. (11). The K2 is tested by gradually increasing the E-field from 0 to 1.01 V/µm while keeping the sensor at stable room temperature (around 20°C). As shown in Fig. 9, the spectra formed by FPI along y and z axis shifted toward shorter wavelength (Δλy = 35.30 pm, Δλz = 115.39 pm), while the spectrum envelope shifted toward longer wavelength (Δλ=2.22 nm) when the sensor was supplied with increasing E-field. The latter is nearly 28 times the difference between the first two, and the inconsistency with the theoretical value is caused by the errors in the selection of spectral points. The envelope peak wavelength as a function of the E-field exhibits a good linearity, which agrees well with the theoretical prediction, suggesting an E-field sensitivity of 2.22 nm/E, as depicted in Fig. 10(a).
Fig. 9. Different spectrum shift under E-field: (a) FPI along y axis, (b) FPI along z axis, (c) spectrum envelope.
Fig. 10. (a) 1st wavelength shift versus E-field (b) 2nd wavelength shift versus E-field (c) result of AC E-field test.
For high-precision applications, the hysteresis effect is a very important indicator. Herein, it can be observed from Fig. 10(a) that the dip wavelengths during both the increasing and decreasing E-field cycle measurements are nearly consistent. The fitting equations of the increasing process and decreasing process for the E-field cycle measurement are y = 2.2185x-0.0211 and y = 2.2187x-2.2105, respectively. It can be found that there is only a slight variation in sensitivity between these two processes, with a fluctuation of just 9.02 × 10−5. This indicates that the proposed E-field sensor possesses low hysteresis effect for E-field measurements.
In addition, to test the measurement repeatability of the proposed sensor, we conducted another separate cycle measurement 72 hours later from 0 to 1.01 V/µm. The experimental results show that the proposed sensor is repeatable, as illustrated in Fig. 10(b). The calculated E-field sensitivity is stabilized at 2.22 ± 0.003 nm/E. The repeatability error is calculated to be 2.43 × 10−3. As can be seen from the figure, the sensor has also good stability.
To further verify the excellent responsivity of the FPI-based E-field sensor, we conducted tests on power frequency AC E-field (0.65 V/µm) using a photodetector and oscilloscope, and the result is shown in Fig. 10(c). It obviously indicates that the sensor can effectively reflect the power frequency AC E-field without distortion, and the peak-peak value of the amplitude change is about 31.20 mV. The experiment proves that the OES exhibits excellent response characteristics.
The aforementioned experiments demonstrate that the structure of the E-field sensor not only enhances the intensity of the measured E-field, but also improves measurement sensitivity. In order to make a proper performance assessment, we compared the proposed sensor with a few other optical E-field/voltage sensors reported in recent years, as shown in Table 1. It clearly suggests that, the proposed sensor here has the most intense E-field, more compact and more sensitivity than most of sensors. The comparison results of sensitivity are not obvious due to the prevalent use of optical amplitude modulation mode in current OESs, making it challenging to conduct an accurate comparison. In contrast, since this study measures E-field changes through detecting variations in optical frequency (wavelength), the measurement outcomes remain unaffected by light intensity amplitude and fundamentally eliminate any influence from light source fluctuations on the signal.
Table 1. Comparison of optical E-field/voltage sensors
3.3 Temperature test
The temperature sensitivities of both the MZI (i.e., K1 in Eq. (11)) and the FPI based on LN (i.e., K3 in Eq. (11)) are calculated. The temperature was changed from 30°C to 40°C with an interval of 2°C. The temperature sensitivities are 31.50 pm/°C and 647.50 pm/°C for the MZI and FPI based on LN, respectively as shown in Fig. 11.
Based on the experimental results above, a temperature compensation experiment is conducted. The sensors are subjected to E-fields of 0.21 V/µm and 0.61 V/µm respectively, while recording spectral changes from 30°C to 40°C. The results are presented in Fig. 12, where it can be observed that after temperature compensation, the standard deviation of spectrum variation is found to be 5.01 × 10−3 and 7.26 × 10−3 for E = 0.21 V/µm and E = 0.61 V/µm respectively. The results indicate that the utilization of MZI for temperature compensation yields superior performance.
Fig. 12. Results of temperature compensation test under different E-fields: (a) and (c) under E = 0.21 V/µm, (b) and (d) under E = 0.61 V/µm.
3.4 DL of the sensors
We also investigate the detection limit (DL) of the proposed sensors. As expressed in Ref. [28], the LOD of sensor is defined as below:
where R is the sensor resolution, which characterizes the minimum spectral shift that is detectable by the system using the wavelength scanning process. It has specific limitations originating from the spectral noise and amplitude noise of the measurement system.The spectral noise primarily consists of thermal-induced fluctuations and system spectral resolution. Amplitude noise will cause some random spectral deviation in the process of measuring spectral location, with its standard deviation being linearly related to full-width-half-max (FWHM) and exponentially related to SNR. The mathematical expression can be approximately expressed as:
The equation above indicates that an increase in FWHM results in higher amplitude noise. While the Vernier effect increases the sensitivity, it also enhances the FWHM of the spectrum. From this perspective, the Vernier effect has an opposite impact on DL. Reference [29] provides four explanations for the rise in DL due to Vernier effect: Firstly, the data point of the Vernier effect is based on the number of fringes in the envelope, which is typically much less than the number of data points scanned by OSA for a single interference fringe. Secondly, superimposing two interference spectra will cause more noise in the enveloping data points. Thirdly, the FWHM of the Vernier effect is relatively large, as demonstrated in Eq. (15), which can increase the standard deviation of amplitude noise. Fourthly, a lower fringe contrast ratio will result in an increased DL of the sensor.
According to Eq. (13), the E-field resolution is not only dependent on FPI, but also on MZI. Therefore, the combined spectrum (FPI and MZI) is repeatedly scanned over a period of time under the E-field-free condition, with data being recorded. Meanwhile, to further elucidate the correlation between Vernier effect and DL, a 5 mm × 5 mm × 1.12 mm LN-based FPI was included for comparison, and its combined spectrum is depicted in Fig. 13(c). According to Eq. (5), this FPI exhibits the same magnification of 29 as the above FPI (L1 = 2.28 mm), and its FSR = 14.65 nm. As there is a discernible difference in light intensity between FPI and MZI, sub-harmonics will exist in the combined interference spectrum. Since the former takes on an envelope form, these sub-harmonics also appear as envelopes. Therefore, data points should be fitted to the two adjacent minor envelope peaks at 1550 nm shown in Fig. 13(a) and (c). The results are presented in Fig. 13(b) and (d). It is evident that the resolution at 1550 nm for the two spectra is 28.30 pm and 130.40 pm, respectively. Consequently, their DL can be calculated as 1.27 × 10−2 E and 5.87 × 10−2 E, correspondingly.
Fig. 13. (a) The spectra variation around 1550 nm of FPI with L1 = 2.28 mm and (b)the fluctuation of the spectra peak, (c) the spectra variation around 1550 nm of FPI with L1 = 1.12 mm and (d) the fluctuation of the spectra peak.
The comparative experimental results above offer a viable approach to reducing the side effects of Vernier effect on DL. By increasing the cavity length at the same magnification, a smaller FWHM can be achieved, thereby reducing amplitude noise. Additionally, this method also increases envelope data points indirectly as more fringes are present within the same FSR range. However, the increase of cavity length also enlarge noise to a certain extent. Therefore, it is more effective to use specific methods to reduce noise and improve contrast such as the Vernier effect of parallel structures to obtain better fringe contrast, 45° fusion splicing and coating to improve fringe contrast, and temperature compensation method to eliminate thermal noise - all of which are employed in this paper. In conclusion, relying solely on the Vernier effect to enhance sensitivity for improving the sensor performance is not feasible as it amplifies DL along with sensitivity. In the practical design of the sensor, appropriate parameters such as cavity length and magnification should be configured in accordance with the requirements of the application scenario to achieve optimal DL.
Similarly, we conducted an investigation into the temperature DL. As the temperature resolution is solely dependent on MZI, it is only necessary to scan and record the spectrum of MZI multiple times. The experimental results are depicted in Fig. 14, with a resolution of 19.5 pm at 1550 nm. According to the above analysis, it can be calculated that the DL of temperature is 0.62 °C. Note that the DL is also dependent upon the system resolution, and can therefore be further improved by using measurement equipment with a better spectral resolution than that we used in the present experimental setup.
Fig. 14. The spectra variation around 1550 nm of (a) MZI and (b) the fluctuation of the spectra peak.
4. Conclusion
In summary, an OES based on FPI using LN crystal has been proposed and investigated in this paper. By combining the Pockels effect and Vernier effect, the E-field to be measured is not limited by half-wave voltage, and the sensitivity of E-field measurement is improved. Experimental results demonstrate a sensitivity of 2.22 nm/E (V/µm) with a DL of 1.27 × 10−2 E within the range of 0∼1010 kV/m. The Vernier effect is generated by the birefringence of LN without additional reference cavity, which reduces the size of the sensor effectively. Meanwhile, in comparison to the traditional bulk-type E-field sensor, the E-field sensor unit consists of only one LN crystal and two collimators, further reducing the size of the sensor unit and facilitating miniaturization. In addition, this paper employs an MZI for temperature compensation of the sensor with a standard deviation of spectral drift after compensation at 5.01 × 10−3. Furthermore, since the E-field measurement is achieved by detecting changes in optical frequency (wavelength), the measurement results remain unaffected by the amplitude of light intensity, which fundamentally eliminates any influence from light source fluctuation on the signal. These advantages make the proposed sensor competitive in a wide range of practical applications.
Funding
National Natural Science Foundation of China (51909048, 52271315); Fundamental Research Funds for the Central Universities (ZFQQ2970101222).
Acknowledgments
The authors wish to thank colleagues’ help for the experiment and result discussion, as well as the anonymous reviewers for their valuable suggestions.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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