Bidirectional Microwave-optical Transduction Based on Integration: Appendix E: Characterization

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 E: Characterization of bidirectional transduction

1. Estimation of cooperavity and single-photon coupling rate

Given the measured off-chip efficiency, the single-photon coupling rate can be estimated. The off-chip efficiency is given by

where ηprobes and ηfiber-chip denote the microwave and optical insertion losses, respectively. The on-chip efficiency can be written as

The internal efficiency

in the low-cooperativity regime, where the plus and minus signs correspond to the anti-Stokes and Stokes configurations, respectively. The optical and microwave extraction efficiencies

The single-photon cooperativity C0 is enhanced by the intracavity photons

where the pump detuning is assumed to be small. The input power in the bus waveguide Pwg is related to the power in the input fiber Pin by the fiber-chip coupling efficiency

The off-chip efficiency with respect to the microwave probe and optical fiber is thus

2. Estimation of on-chip and internal transduction efficiencies

We have achieved η tot = −48 dB at an input pump power of 21 dBm. With the losses quoted in Appendix E 1, the on-chip and internal efficiencies can be estimated. For conversion in either directions, the signal goes through the respective input and output ports exactly once, acquiring an attenuation of η probesη fiber−chip = −7 dB. We therefore have η oc = 7.9×10−5 . Knowing the extraction efficiencies ηo = 35% and ηm = 11%, we further obtain η int = 2×10−3 .