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Journal of Optics B Quantum and Semiclassical Optics

Self-homodyne tomography of a laser diode

Marco Fiorentino B, A. Conti, Alessandro Zavatta, Giovanni Giacomelli, Francesco Marin

Published Apr 1, 2000• 6 citations
Publisher

Abstract

Considerable interest is growing around self-homodyne techniques. Such techniques allow one to avoid non-unitary detection efficiencies due to inefficient mode matching of the local oscillator. Galatola et al (1991 Opt. Commun. 85 95) proposed one possible scheme of self-homodyne detection of a field with a strong coherent component involving the use of a Fabry-Perot cavity with a perfectly reflecting mirror. We extend the theory to arbitrary cavities, and we observe a remarkable agreement between the theory and the observed data. Using the same setup we performed a tomographic measure of the Wigner function of the field emitted by a laser diode.

DOI
10.1088/1464-4266/2/2/321

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Considerable interest is growing around self-homodyne techniques. Such techniques allow one to avoid non-unitary detection efficiencies due to inefficient mode matching of the local oscillator. Galatola et al (1991 Opt. Commun. 85 95) proposed one possible scheme of self-homodyne detection of a field with a strong coherent component involving the use of a Fabry-Perot cavity with a perfectly reflecting mirror. We extend the theory to arbitrary cavities, and we observe a remarkable agreement between the theory and the observed data. Using the same setup we performed a tomographic measure of the Wigner function of the field emitted by a laser diode.
Summary form only given. Considerable interest is growing around self homodyne techniques. Such techniques allow to avoid nonunitary detection efficiencies due to inefficient mode matching of the local oscillator. As proposed by Galatola et al. [1991], one possible scheme of self homodyne detection of a field with a strong coherent component involves the use of a Fabry-Perot cavity with a high reflecting rear mirror. Using this setup we are able to perform a tomographic measure of the Wigner function of the field emitted by a laser diode.
We develop a scheme to reconstruct the optical quantum state of a single-mode bright light field by using the dispersion characteristics of the empty cavity. The input field has a strong coherent component at frequency ω0, which serves as a local oscillator (LO) to measure its two-sideband mode at ω0±Ω. We control the relative phase of the 0–2π range between the LO and the two-sideband mode by scanning the cavity length, so the optical quantum state is tomographically reconstructed. In the proposed scheme the influence of the space-mode mismatch between the LO and measured mode on the quantum efficiency is eliminated, and this scheme can conveniently be used in some quantum optical systems in which LO field cannot be available.
A self-homodyne detection scheme is proposed to perform two-mode tomography on a twin-beam state at the output of a nondegenerate optical parametric amplifier. This scheme has been devised to improve the matching between the local oscillator and the signal modes, which is the main limitation to the overall quantum efficiency in conventional homodyning. The feasibility of the measurement is analyzed on the basis of Monte Carlo simulations, studying the effect of nonunit quantum efficiency on detection of the correlation and the total photon-number oscillations of the twin-beam state.
Ultimately the properties of all optical fields are contained in the density matrix that specifies their quantum mechanical state. It has only recently been demonstrated that it is possible to actually reconstruct this density matrix from measured data, and to do so with temporal resolution of a few hundred femtoseconds.[1] This technique, known as Optical Homodyne Tomography (OHT), is unfortunately restricted to the measurement of only single mode radiation. In fact it selects out from the test field only those components which overlap temporally with the local oscillator pulse mode.
Wigner function tomography is indispensable for characterizing quantum states, but its commonly used version, balanced homodyne detection, suffers from several weaknesses. First, it requires efficient detection, which is critical for measuring fragile non-Gaussian states, especially bright ones. Second, it needs a local oscillator, tailored to match the spatiotemporal properties of the state under test, and fails for multimode and broadband states. Here we propose Wigner function tomography based on optical parametric amplification followed by direct detection. The method is immune to detection inefficiency and loss, and suitable for broadband, spatially and temporally multimode quantum states. To prove the principle, we experimentally reconstruct the Wigner function of squeezed vacuum occupying a single mode of a strongly multimode state. We obtain a squeezing of −7.5±0.4dB and purity of 0.91 −0.08 +0.09 despite more than 97% loss caused mainly by filtering. Theoretically, we also consider the reconstruction of a squeezed single photon—a bright non-Gaussian state. Due to multimode parametric amplification, the method allows for simultaneous tomography of multiple modes. This makes it a powerful tool for optical quantum information processing.