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Conference on Lasers and Electro-Optics

Self-reference temporal phase reconstruction based on causality arguments in linear optical filters

Mohammad H. Asghari, José Azaña

Published Jan 1, 2012• 3 citations
Publisher

Abstract

We introduce and numerically prove a simple and general concept for direct reconstruction of the temporal phase profile of an optical signal from temporal intensity measurements at the input and output of an arbitrary linear optical filter.
DOI
10.1364/cleo_si.2012.ctu2a.8

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We introduce and numerically demonstrate a simple and general concept for direct reconstruction of the temporal phase profile of an optical signal from temporal intensity measurements at the input and output of an arbitrary linear optical filter. The concept is based on exploiting the linearity and causality properties of any physical filter. Very few restrictions need to be imposed on the optical filter response to ensure an unambiguous phase reconstruction. The filter can be specifically designed to minimize the noise influence on the measurement process.
The transmission of optical signals under the effects of cross-phase modulation (XPM) and self-phase modulation (SPM) together in pump-probe wave structure is investigated in intensity modulation-direct detection wavelength division multiplexing (IM-DD WDM) systems. A simple expression for frequency domain IM of probe channel is derived. The analytical method to determine the temporal shape of probe wave when arbitrary wave is inputted in pump channel is confirmed. The impact of channel separation and transmission rate to XPM is assessed. We find that the SPM in pump channel increase temporal intensity modulation index reflected XPM to a certain extent. The analytical result agrees well with numerical simulation.
Abstract Tunable linear-optical interferometers are a key element in the implementation of both classical and quantum information technologies. At the same time, during the production process, these systems are subject to various instrumental imperfections and it is necessary to be able to determine with what accuracy and what transformations the manufactured device is capable to reproduce. For integrated devices, such tasks are difficult to perform due to the difficulties in obtaining direct access to individual optical elements of the circuit. Existing methods for reconstructing the transfer matrix of tunable linear-optical interferometers require measuring the phases of its matrix elements at different values of control signals in the circuit, which is also an experimentally time-consuming task. However, in some cases, it is possible to construct a mathematical model of the circuit that works for any values of its control signals, measuring only partial amplitude transmission coefficients at the outputs of the circuit, which significantly simplifies reconstruction and is relevant in a number of applications. In this paper, we performed numerical and experimental approbation of the method on the example of a linear-optical interferometer with four inputs and four outputs with a universal architecture based on mixing layers. The average fidelity value of the reconstruction of the reduced transfer matrix of the optical interferometer, taking into account realistic noise in the experiment, was 99.9% and can be improved due to the proven stability of the model to them.
We demonstrate theoretical conditions for highly efficient degenerate four-wave mixing in triply resonant nonlinear (Kerr) cavities. We employ a general and accurate temporal coupled-mode analysis in which the interaction of light in arbitrary microcavities is expressed in terms of a set of coupling coefficients that we rigorously derive from the full Maxwell equations. Using the coupled-mode theory, we show that light consisting of an input signal of frequency ${\ensuremath{\omega}}_{0}\ensuremath{-}\ensuremath{\Delta}\ensuremath{\omega}$ can, in the presence of pump light at ${\ensuremath{\omega}}_{0}$, be converted with quantum-limited efficiency into an output shifted signal of frequency ${\ensuremath{\omega}}_{0}+\ensuremath{\Delta}\ensuremath{\omega}$, and we derive expressions for the critical input powers at which this occurs. We find the critical powers in the order of 10 mW, assuming very conservative cavity parameters (modal volumes  10~10 10 cubic wavelengths and quality factors  1000~1000 1000). The standard Manley-Rowe efficiency limits are obtained from the solution of the classical coupled-mode equations, although we also derive them from simple photon-counting ``quantum'' arguments. Finally, using a linear stability analysis, we demonstrate that maximal conversion efficiency can be retained even in the presence of self- and cross-phase modulation effects that generally act to disrupt the resonance condition.