Lithium niobate fabrication, mounting, and characterization

The LN crystals are grown with the standard Czochralski process. The congruent composition produces crystals with uniform composition and therefore minimal property variations (see US patent #5,310,448). The rods are cut to the standard longitudinal extension mode Y\(\angle\)36° orientation and are rough cut to cuboids of 20 mm × 20 mm × 94 mm.

Using a DC sputtering system in a 50 × 10−3 Torr argon background, a bonding layer of 10–100 Å thick titanium is applied to each rod face. Prior to venting, an electrical contact and sealing layer of 10–100 Å thick gold is applied. A substrate heater raises the LN to about 400 °C before and during the coating process. The coatings are applied prior to finishing and polishing the crystal OD so masking is not required. After coating, the LN is ground to rough shape using a rotating 180 grit then a 600 grit diamond sintered plate. After, the diameter is ground by hand against glass plates using 15 μm and then 9 μm aluminum oxide. Next, a lathe is used to grind with successively finer grit sizes using wet silicon carbide sand paper. Finally, a lathe was used to polish the rod using a 1-μm aluminum oxide slurry and a polyurethane pad.

Each metalized end of the LN rod has a 0.003 inch copper wire bonded to the surface via structural epoxy and silver paint. On one end, the thin wire attaches to the input signal. On the other end, the wire attaches to a field shaping toroid. Using this common high-voltage design technique, the toroids are at or near the potential of the LN rod corners and therefore spatially distribute the equipotential lines. This decreases the peak surface electric field on the LN for a given dipole moment, thereby increasing the achievable dipole moment prior to high voltage flashover. The toroids on either end of the LN are mechanically supported by alumina posts and do not contact the LN rod. The LN is suspended by two fused silica rods located at the longitudinal center of the LN rod. The fused silica rods are supported by vertical alumina rods (see supplementary Fig. 4). For tests in the vacuum chamber, the pressure is kept to less than 2 × 10−7 Torr.

To measure the crystal velocity, a Polytek OFV-5000 with OFV-552 sensor head laser Doppler vibrometer shines on one end of the LN rod. In laboratory tests, the input signal is supplied to the crystal via a Tektronics AFG3021C arbitrary function generator. The signal current is monitored by a Pearson current transformer and the voltage is directly monitored by a Lecroy 44MX 400 MHz, >125 kS s−1 oscilloscope. Waveforms are post-processed in Matlab. The modulation system is comprised of a metal modulation plate, a mechanical relay (COTO 9913), and a 60 pF capacitor. The relay coils are driven by a SRS DG645 trigger generator which is synchronized to the RF input FSK modulation signal.

Multiphysics and circuit simulation

The piezoelectric system is modeled using the FEM multi-physics software COMSOL with the MEMS toolbox29. Standard material properties are used, with the isotropic loss tangent of LN set to the effective 1/Q t found from experiment. For a given input voltage and frequency, the frequency domain response is used to calculate parameters such as peak electric fields, stress within the LN, dipole moment, velocity, and input impedance.

To model time domain problems, an equivalent circuit model is used30. This lumped element model (see supplementary Fig. 8) consists of four sub-circuits including the driver input, the piezoelectric equivalent circuit, radiative coupling, and modulation circuit. A time-varying voltage source with a 10-Ω output impedance is assumed for the input driver. The equivalent circuit follows a conventional template for piezoelectric elements while radiation impedance is characterized by parallel resistive (radiation resistance) and capacitive (output coupling) elements to ground. The modulation circuit is a capacitive network represented by a single element that is either coupled or isolated from the antenna circuit via an electrical switch. Manufacturer’s data was used for the switching time and open and closed contact resistance.

An exact analytical solution is used for the circuit model. The Laplace transform for each of the impedance elements along with the initial conditions is calculated and the circuit loop equations are found. The switch is modeled as a resistor. The inverse Laplace transform is solved with the values of the circuit elements input into the loop equations. The time dependent currents and voltages are then calculated for each element. At the end of an FSK or switch cycle, the final conditions of the circuit were then used as input conditions for subsequent simulations.

This lumped element circuit is tuned by matching the input impedance and output voltage to the frequency domain COMSOL results (see Fig. 3). The circuit solver is then used to model the transient response of the antenna during filling, discharge, and switching. supplementary Figs. 1 and 2 compare the time-dependent output voltage of the circuit model to experimental results both with and without DAM. The element values used in the circuit model are R in = 10 Ω, C in = 3.7 pF, C m = 92.12 fF, L m = 239.6041H, R = 85 Ω, C o = 1.4001 pF.

Field measurement at range

For the range measurements, a microprocessor controlled MOSFET H-bridge translates DC voltage from a battery pack into a square wave. This waveform is fed directly to the input of the piezoelectric transmitter. The waveform frequency is controlled via a Bluetooth serial connection. Lead lengths from this power processing unit to the piezoelectric transmitter were minimized (<1–2″ total) to reduce RFI.

The electric field is measured using a probe made up of a 2-cm metal stud mated to an SMA female connector. The signal is fed to a Stanford Research Systems preamplifier model SR560. A calibrated transfer function is generated by immersing the probe in the electric field generated by a 1 m x 1 m x 0.09 m parallel plate capacitor. A 3 kHz, 12 dB/octive high-pass filter is used to attenuate RFI primarily from power line harmonics. The signal is fed to a LeCroy WaveJet 354 with a 250 kHz low pass filter and a sampling rate of 250 kS s−1.

The magnetic field is measured using a 200 turn, 1.2 m diameter, air-core, 6 cm long solenoid. A grounded aluminum foil (cut at one point to ensure induced current is not shorted out) is placed around the coil to attenuate electric field pickup. The two ends of the coil are differentially fed (with a common ground referenced to the receiver shield) to a Stanford Research Systems preamplifier model SR650. The preamplifier has a 115 dB/octive bandpass filter from 29 kHz to 38 kHz. The stop band attenuation is >80 dB and the gain is set between 40 and 60 dB. The signal is measured with a Tektronix TDS5054B oscilloscope with a sampling rate of 125 kS s−1. This magnetic field received is uncalibrated and is included as a relative measurement.

For both the electric field and magnetic field data, the CW signals are measured for 4 s total. At each range data point, four repetitions are measured. Each distance measurement was repeated twice. In addition, at each point the background was measured with the input signal turned off. Data is post processed by taking the DFT of each 4-s long interval. The magnitude of the signal at the frequency of interest is both found by calculating the RMS value of the DFT within a bandwidth of 10 Hz as well as measuring the peak of the DFT. Both methods yield similar results. The SNR for all measurements is >20 dB.

To provide a baseline signal, a coil transmitter antenna was used to generate a reference magnetic field. This coil was driven at about 35.5 kHz, the approximate resonant frequency of the piezoelectric antenna. Measurements of this coil confirmed that the magnetic field dropped off as 1/r3, consistent with a magnetic dipole.

To measure the effect of RFI from the power processing unit, a wirewound resistor with a resistance approximately equal to the input impedance of the piezoelectric transmitter at resonance is attached directly to the output of the power processing unit. The voltage and frequency are tuned to the same values used in the piezoelectric transmitter measurements. The measured voltage on the receiver with just the wirewound resistor is 24 dBV below the signal when measuring just the piezoelectric transmitter (see supplementary Fig. 5). The noise floor for all the magnetic field measurements is <−90 dB V/Hz0.5.

Calculated Q A , antenna efficiency, and bandwidth-efficiency

For the calculation of Q A (angular frequency times the average stored energy in the near field divided by the radiated power), the radiation from the piezoelectric element is assumed equivalent to a simple electric dipole wire. This is supported by the similarity of the simulated piezoelectric displacement current to the current in a typical copper antenna. In addition, the measured magnetic field in the near field drops off as 1/r2, consistent with an electric dipole.

As we do not measure radiated power at the far field, to compare to other ESAs, we calculate an estimate of Q A based upon on two different formulations. Q A,min is the theoretical lowest possible Q A for a given size antenna. McLean8 shows,

$$Q_{A,{\mathrm{min}}} = \frac{1}{{ka}} + \frac{1}{{\left( {ka} \right)^3}},$$ (4)

where a is the effective antenna radius and k is the free space wavenumber. Conventionally, the length a is defined as the radius of the smallest sphere which completely encapsulates the antenna7,8. However, proximity to ground and the associated image charges produce a monopole-like antenna with double the effective length19,31. For simplicity, we assume a perfectly conducting ground plane with the full antenna length defining the radius of the enclosing sphere. With a k × a value of 7.5 × 10−5, the calculated Q A,min is 3 × 1012. This estimate is a lower bound for ESAs as it is derived from evanescent modes in the near field assuming the antenna completely fills the spherical bound. Thiele suggests that due to the inherent super-directivity of ESAs, a more accurate Q A,min derivation for dipole antennas uses the far-field radiation pattern9. The calculated Q A,min with this methodology is 3 × 1013.