# Electro-Optic Sensor for Measuring Electrostatic Fields in the Frequency Domain
## 2 Method and Experimental Results
### Proof-of-Concept Test Bench  
The results obtained with the mathematical model served to design and optimize the proof-of-principle laboratory test bench. Given the ultimate objective of the project, the test bench resembles a particle accelerator vacuum chamber as shown in Figure 14.  
The test bench consists of a 60 cm long pipe with a 45 \(\times\) 45 mm square aperture which houses the electric-field-sensing crystal (i.e., the second crystal in the previously described mathematical model) which is attached to a removable holder--annotated with a red circle in Figure 14) and shown in detail in Figure 15. The holder is installed on the horizontal wall of the pipe. The sensing crystal is a 50 mm long, unpoled and uncoated LiNbO\({}_{3}\) crystal, doped with MgO at 5% and has a cross section of 2 \(\times\) 5 mm. Figure 14: Proof-of-principle laboratory test bench. The red circle highlights the metallic holder used for the sensing crystal. Figure 13: Comparison of the two most sensitive combinations of working point and modulation amplitude. Two metal stripes attach the crystal to the metal holder, lowering the electric field intensity in the crystal. The attenuation, evaluated through numerical electrostatic simulations of the test bench, is stronger by approximately 32% compared to an equivalent dielectric holder. This effect was known during the design phase of the sensor but a metal holder was used nevertheless to ease fabrication of the test bench. Moreover, the ultimate goal of our development is to apply the proposed technique to measure the relative strength of two electric fields using two sensors placed symmetrically around the centre of the field source. As such measurements do not require knowing the absolute field intensity, the final choice was to produce the holder out of metal. The bias crystal is made from the same material as the sensing crystal but is 40 mm long, with a cross section of 3 \(\times\) 3 mm. Additionally, to improve electric contact with the PCBs, the bias crystal features a Cr-Au coating on the two sides parallel to the z-plane. The bias crystal is fixed outside of the square pipe, between two PCBs connected to a high-voltage piezo-amplifier (SVR 1000/3 from PIEZOSYSTEM JENA). The entire optical chain was assembled using off-the-shelf THORLABS components. First, a single frequency, linearly polarized, laser diode (SFL1550P) generates the laser beam which travels through a polarization-maintaining fiber to a collimator (CPF5-1550A) which maintains the laser beam's polarization. By rotating the collimator, it is possible to fix a 45\({}^{\circ}\) polarization on the input face of the bias crystals without using a dedicated polarizer. After traversing the bias crystal, the laser beam is guided in and out of the sensing crystal holder by two mirrors (PF10-03-P01) and two prisms. The laser beam then couples into a Glan-Taylor polarizer (GT10-C). Finally, a photodetector (S122C) connected to a power meter (PM100D) provides an output signal which is measured by a 10-bit oscilloscope and a signal analyzer. The SL1550P laser diode generates a single-frequency laser beam with a wavelength of 1550 nm. This choice, even if counter intuitive considering the figure of merit \(E_{\pi}\) in Equation (11), was made to minimize the creation of optically induced hole-electron pairs, since the absorption coefficient in LiNbO\({}_{3}\) is at its lowest value [21] for that wavelength. Moreover, an abundance of commercially available optical components and detectors for  
Figure 15: Sensing crystal holder. the 1550 nm wavelength commonly used by the telecommunications industry made our proof-of-principle development faster and cheaper. The electric field measured by the sensing crystal is radiated by a rigid wire, traversing the entire square pipe, to which a voltage up to 1 kV can be applied. The length of the pipe and wire are large compared to the crystal's length which enables a uniform distribution of electric field close to the sensing crystal.