Quantum Noise of Kramers-Kronig Receiver

Abstract

Abstrac--Kramers-Kronig (KK) receiver, which is equivalent to heterodyne detection with one single photodetector, provides an efficient method to reconstruct the complex-valued optical field by means of intensity detection given a minimum-phase signal. In this paper, quantum noise of the KK receiver is derived analytically and compared with that of the balanced heterodyne detection. We show that the quantum noise of the KK receiver keeps the radical fluctuation of the measured signal the same as that of the balanced heterodyne detection, while compressing the tangential noise to 1/3 times the radical one using the information provided by the Hilbert transform. In consequence, the KK receiver has 3/2 times the signal-to-noise ratio of balanced heterodyne detection while presenting an asymmetric distribution of fluctuations, which is also different from that of the latter. More interestingly, the projected in-phase and quadrature field operators of the retrieved signal after down conversion have a time dependent quantum noise distribution depending on the time-varying phase. This property provides a feasible scheme for controlling the fluctuation distribution according to the requirements of measurement accuracy in the specific direction. Under the condition of strong carrier wave, the fluctuations of the component requiring to be measured more accurately can be compressed to 1 / 6, which is even lower than 1/4 by measuring a coherent state. Finally, we prove the analytic conclusions by simulation results