Bidirectional Microwave-optical Transduction Based on Integration: C. Bidirectional

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

C. Bidirectional microwave-optical transduction

We measure the off-chip efficiency η tot of the microwave-to-optical (up-conversion) and optical-tomicrowave (down-conversion) processes as a function of off-chip CW input optical pump power Pin. Compared to the on-chip efficiency η oc, this efficiency also accounts for the loss channels of the microwave and optical ports. First, we study the transducer in the triply resonant configuration. For up-conversion, the optical sideband generated from the microwave input, detuned by ωin = ωm from the pump frequency, is measured via a self-calibrated heterodyne detection method. The off-chip optical output containing both the pump (ωL) and the sideband (ωs) is combined with a local oscillator (LO; ωLO) and detected. By placing the LO at a frequency ωLO = (ωL + ωs) /2 + δ such that the photodetector response is constant over a frequency span of δ, we determine the sideband power relative to the pump. Picking off a fraction of the optical output then enables the determination of its absolute power and, by extension, that of the sideband with a power meter. The measured optical sideband power is compared to that of the microwave input to yield η tot. In the case of down-conversion, the optical input is generated by modulating the phase of the pump with an electrooptic modulator (EOM) driven by a microwave source of frequency ωEOM = ωm. Only one of the resulting sidebands is admitted into the photonic molecule and transduced, as the other is far off-resonance. The converted microwave power is directly probed with an electrical spectrum analyzer (ESA). Summarized in Figs. 3a and c, bidirectional transduction processes corresponding to both the effective beam-splitter (ωL = ω−; anti-Stokes) and two-mode-squeezing (ωL = ω+; Stokes) interactions are investigated. We reach a maximal η tot of −48 dB at 21 dBm pump for each configuration. Knowing the port losses, we estimate an on-chip efficiency η oc = −41 dB (Appendix E). Accounting for the extraction efficiency η ext, we further obtain an internal conversion efficiency η int = 2 × 10−3 from Eq. 2.

Furthermore, we deviate from triple resonance to map out the transduction bandwidth. First, for a pump still resonant with one of the optical supermodes, the input microwave frequency ωin and input optical detuning (controlled by EOM drive frequency ωEOM) are varied for up- and down-conversion, respectively. Shown in Fig. 3b and d, transduction leveraging the main transduction mode exhibits a full width at half maximum (FWHM) of 25 MHz. The multimode nature of the transducer is further manifest in Fig. 3e, where the pump is in the beam-splitter configuration but slightly detuned from aˆ−. An additional transduction peak in η tot with a FWHM of 10 MHz is observed around ωin = 2π × 3.165 GHz, which corresponds to another HBAR one FSR away from the main transduction mode ωm = 2π × 3.480 GHz. The engineering degrees of freedom such as cladding and actuator thickness (HBAR FSR), and optical dispersion (supermode splitting as a function of optical wavelength) in the present system offer possibilities for frequencymultiplexed transduction.