# Three-Dimensional Broadband Electric Field Sensor Based on Integrated Lithium Niobate on Insulator
## 1 Introduction  
Electric field sensors (EFSs) are extensively used in atmospheric science, electromagnetic (EM) environment assessment of spacecraft and rocket launch, measurement of EM compatibility, and long-term monitoring of high-voltage transmission lines [1; 2; 3]. Due to the increasingly complicated EM environment, EM measurement with a large operation bandwidth, high-density large-scale distribution, and three-dimensional (3D) measurement capacity is urgently needed. Particularly, 3D measurement can provide EM information in three orthogonal polarization directions, which is beneficial for realizing comprehensive control of the space EM field. In order to realize distributed 3D measurement, EFSs are expected to have a large operation bandwidth and a small size, which is conducive to achieving high-accuracy measurement of broadband EM waves in free space.  
There are various EFSs to realize 3D measurement. Thereinto, EFSs based on micro-electro-mechanical systems (MEMS) are well developed in recent years due to their small size (\(<\)1 cm \(\times\) 1 cm) and high sensitivity [4; 5; 6; 7; 8]. However, the highest measurable frequency of the MEMS-based EFSs is limited to the level of kHz, which is attributed to the sensing implementation based on slow mechanical shape variation. Different from employing three EFSs with orthogonal polarization directions, EFSs with D-dot antennas naturally have the ability of 3D sensing due to the 3D shape construction [9; 10; 11; 12]. The highest measurable frequency can be up to 10 GHz. However, the size of the metal antenna is generally tens of centimeters, which leads to serious distortion of the electric field under test. Moreover, D-dot sensors cannot measure the amplitudes of the electric field in different polarization directions separately. EFSs based on lithium niobate (LN) have been extensively investigated in recent years [13; 14; 15; 16; 17; 18; 19; 20], whose theoretical operation bandwidth can reach beyond 500 GHz due to the strong linear electro-optic effect (Pockels effect) in the LN [21]. In addition, theintegrated optical waveguide fabricated on lithium niobate on insulator (LNOI) reduces the sensor size significantly. Therefore, the EFSs based on integrated LNOI waveguides have the characteristics of small size, large operation bandwidth, and undistorted measurement.  
In this paper, a 3D EFS scheme is proposed and experimentally demonstrated based on an integrated LNOI platform. The optical waveguide in the EFS has an asymmetrical Michelson interferometer (MI) architecture. Due to the round-trip optical transmission in the MI, the waveguide length in the proposed EFS is reduced to half of that based on the Mach-Zehnder interferometer (MZI). In addition, the asymmetrical MI structure helps the EFS work without any electrical power supply. In the experiment, three EFSs with specially designed antennas and modulation electrodes are fixed in a triangular-prism-type clamp to realize 3D measurement. All three sensor chips have flat responses in the frequency range of 10 MHz to 3 GHz. A \(3\times 3\) response calibration matrix is obtained and utilized to reduce the measurement error. Based on the calibration matrix, the relative error between the measurement results and the theoretical values is smaller than 5.1%.