Bidirectional Microwave-optical Transduction Based on Integration: Appendix C: Optical

Table of Links

• Introduction

• Results

• A. Physics and design

• B. Device characterization

• C. Bidirectional microwave-optical transduction

• D. Pulsed transduction

• Discussion

• Acknowledgments

• Appendix A: Theory

• Appendix B: Fabrication process flow

• Appendix C: Optical characterization

• Appendix D: Characterization of acoustic resonances

• Appendix E: Characterization of bidirectional transduction

• Appendix F: Optimization of optical extraction efficiency

Appendix C: Optical characterization

1. Resonance linewidths

Fitting the hybridized transmission spectrum in Fig. 2c to the coupled mode theory presented in Appendix A 1 and in Ref. [2] yields κr/(2π) = 154 MHz and κl/(2π) = 190 MHz, with κex,l/(2π) = κex,r/(2π) = 60 MHz.

2. Hybridization of optical resonances via integrated thermo-optic heaters

For the purpose of rapid characterization of the photonic molecules at room temperature, the bottom electrode of the piezoelectric actuator also serves as an integrated heater to control the relative detuning between the microrings by thermo-optic effect. As seen in Fig. 2a, we pattern Mo to make three electrical connections to the bottom electrode. The top and bottom connections are connected to ground, whereas the central connection is biased to a constant voltage. The finite resistance of Mo at room temperature leads to Joule heating as current flows through the bottom electrode, modifying the refractive index of the Si3N4 waveguide buried directly underneath.

3. Thermal response characterization through cavity-enhanced photothermal spectroscopy.

present transducer due to optical pump heating. Specifically, thermally induced refractive index change causes a shift in resonance frequency of the Si3N4 micro-ring, which is detected using cavity-enhanced pump-probe spectroscopy [12]. The intensity-modulated pump addresses a TE resonance, while the probe measures the resulting side-of-fringe modulation of another TE mode. To ascertain the physical mechanism of each cross phase modulation (XPM) process, we sweep the pump modulation frequency to leverage the separation of time scales. Seen in Supplementary Fig. 2, the response exhibits three plateaus. We associate the process at modulation frequencies ≳ 1 MHz with Kerr-induced XPM. The two slower processes at ∼ 100 kHz and ∼ 1 kHz are characteristic of photothermal XPM in quasi-freestanding microresonators such as spheres [13] and toroids [14]. Here, the former “local” time scale can be attributed to thermalization of the mode volume with the acoustic resonator, while the thermalization of the suspended structure with the rest of the chip constitutes the latter “global” time scale. Therefore, it is expected that for future cryogenic operations, employing a pulse-on time (τon) shorter than the local time scale to gate the optical pump will significantly reduce thermal occupancy in the cladding acoustic mode. The pulse repetition rate (frep) and hence pulse-off time can then be chosen based on the available cooling power.