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Optics Letters

Optical signal-to-noise ratio measurement by optical homodyne tomography

Paolo Martelli, Silvia Maria Pietralunga, Leonardo Ranzani, Rocco Siano, Mario Martinelli

Published Jan 1, 2006• 1 citation
Publisher

Abstract

An all-fiber optical homodyne tomography setup is introduced that measures the optical signal-to-noise ratio through reconstruction of the photon statistics. The scheme described has been conceived for applications to optical communications. In particular, the signal-to-noise ratio has been evaluated at lambda= 1.55 microm as a function of the received power. From the experimental data, in the case of optically amplified signals, the amplifier noise figure can be estimated.

DOI
10.1364/ol.31.000302

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An all-fiber optical homodyne tomography setup is introduced that measures the optical signal-to-noise ratio through reconstruction of the photon statistics. The scheme described has been conceived for applications to optical communications. In particular, the signal-to-noise ratio has been evaluated at lambda= 1.55 microm as a function of the received power. From the experimental data, in the case of optically amplified signals, the amplifier noise figure can be estimated.
The operational theory of homodyne detection by nonideal detectors, used in quantum tomography, was recently modified in order to incorporate the preamplification (before homodyne detection) of the input signal, thus enabling one to beat the handicap of the lower than 0.5 detector efficiency. In the present work we set expressions for the Mandel QQQ parameter and the signal-to-noise ratio in terms of the operational (measured) moments of the preamplified homodyne detection formalism. These quantities furnish important information on the statistical properties of the input signal field and the photocounts at the output. We illustrate the theory by considering several kinds of fields (for the input signal) and determine the effects of the preamplification on the output signal-to-noise ratios. Here we essentially verify that (i) the preamplification shifts the statistics towards the super-Poissonian limit, without jeopardizing the capacity of reconstructing a sub-Poissionan input signal, and (ii) the preamplification is more effective, i.e., the rate of increase of the signal-to-noise ratio of the output photocount is larger for low-efficiency detectors than for ideal ones.
Optical homodyne tomography (OHT) is a tool that allows the reconstruction of Wigner functions for each detection frequency of a propagating optical beam. It can measure probability distribution functions (PDF's) of the field amplitude for any given quadrature of interest. We demonstrate OHT for a range of classical optical states with constant and time varying modulations and show the advantage of OHT over conventional homodyne detection. The OHT simultaneously determines the signal to noise ratio in both amplitude and phase quadratures. We show that highly non-Gaussian Wigner functions can be obtained from incoherent superpositions of optical states.
The recently developed method of optical homodyne tomography (OHT) allows one to obtain the photon statistics of a single mode with single-photon resolution. Recently, we used OHT to prove the Bose Einstein distribution (BED) character of parametric fluorescence. In general, in an OHT setup, a weak signal beam is mixed on a 50/50 beamsplitter with a strong local oscillator beam of the same polarization and spatio-temporal mode. In this paper, we apply OHT to show, we believe for the first time, that ASE noise of a single mode in an EDFA is Bose-Einstein distributed.
In this paper, two models for simulating the shot noise and electronic noise performances of resonant photodetectors designed for homodyne measurements are presented. One is based on a combination of a buffer and a low-noise amplifier, and the other is based on an operational amplifier. Through the comparisons between the numerical simulation results and the experimentally obtained data, excellent agreements are achieved, which show that the models provide a highly efficient guide for the development of a high signal-to-noise ratio (SNR) resonant photodetector. Furthermore, we demonstrate a high SNR resonant photodetector for homodyne measurements at the 147 MHz optical sideband, achieving a 20.8 dB SNR of the shot noise to the electronic noise with a 2 mW optical signal input, utilizing a combination of a buffer and a low-noise amplifier. Concurrently, we have obtained another resonant photodetector at the 1.14 GHz optical sideband, which exhibits a 13 dB SNR based on an operational amplifier.