This PDF file includes:

• section S1. Balanced photodetection
  
• section S2. PT symmetry
  
• section S3. Loop length–dependent phase noise
  
• fig. S1. Block diagram of the BPD used in the experiment.
  
• fig. S2. Optical to electrical conversion at the BPD.
  
• fig. S3. Open-loop response of the OEO.
  
• fig. S4. Phase noise enhancement with a long OEO loop.

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Other Supplementary Material for this manuscript includes the following:

• movie S1 (.mp4 format). Phase noise of a 5.26 GHz signal from a PT-symmetric OEO.
  
• movie S2 (.mp4 format). Electrical spectrum of the 5.26 GHz signal.
  
• movie S3 (.mp4 format). A 10-GHz microwave signal generated by the OEO with PT symmetry.
  
• movie S4 (.mp4 format). Output of the OEO without PT symmetry.