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International Topical Meeting on Microwave Photonics

Time-reversal of μs-long radiofrequency signals based on approximate temporal imaging

Héloïse Linget, T. Chanelière, J.-L. Le Gouët, Anne Louchet-Chauvet, Loïc Morvan

Published Oct 1, 2013• 1 citation
Publisher

Abstract

We propose a purely analog way to time reverse optically-carried radiofrequency signals. Taking advantage of the time-space duality, we implement an approximate temporal imaging device that combines a time-lens and a single dispersive line. For military applications, this dispersive element must offer a group delay dispersion high enough to time-reverse μs-long signals. We propose to use spectral hole burning to tailor the absorption profile of erbium ions embedded in a crystalline lattice of yttrium orthosilicate. This way, we achieve a group delay dispersion 105larger than reached with km-long dispersive fibers, allowing us to extend the time-reversal process from the ns-range to the μs-range.

DOI
10.1109/mwp.2013.6724011

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We propose a purely analog way to time reverse optically-carried radiofrequency signals. Taking advantage of the time-space duality, we implement an approximate temporal imaging device that combines a time-lens and a single dispersive line. For military applications, this dispersive element must offer a group delay dispersion high enough to time-reverse μs-long signals. We propose to use spectral hole burning to tailor the absorption profile of erbium ions embedded in a crystalline lattice of yttrium orthosilicate. This way, we achieve a group delay dispersion 105larger than reached with km-long dispersive fibers, allowing us to extend the time-reversal process from the ns-range to the μs-range.
The time-reversal (TR) protocol we implement in an erbium-doped YSO crystal is based on photon echoes but avoids the storage of the signal to be processed. Unlike other approaches implying digitizing or highly dispersive optical fibers, the proposed scheme reaches the μs range and potentially offers high bandwidth, both required for RADAR applications. In this Letter, we demonstrate faithful reversal of arbitrary pulse sequences with 6 μs duration and 10 MHz bandwidth. To the best of our knowledge, this is the first demonstration of TR via linear filtering in a programmable material.
Based on the similarity of paraxial diffraction and dispersion mathematical descriptions, the temporal imaging of optical pulses combines linear dispersive filters and quadratic phase modulations operating as time lenses. We consider programming a dispersive filter near atomic resonance in rare earth ion-doped crystals, which leads to unprecedented high values of dispersive power. This filter is used in an approximate imaging scheme, combining a single time lens and a single dispersive section and operating as a time-reversing device, with potential applications in radio-frequency signal processing. This scheme is closely related to a three-pulse photon echo with chirped pulses, but the connection with temporal imaging and dispersive filtering emphasizes new features.
Temporal imaging is a technique that enables manipulation of temporal optical signals in a manner similar to manipulation of optical images in spatial domain. It uses the notion of space-time duality with dispersion phenomena playing the role of diffraction and quadratic phase modulation in time acting as a time lens. In this work we address the problem of temporal imaging of a temporally broadband squeezed light generated by a traveling-wave optical parametric amplifier or a similar device. We consider a single-lens temporal imaging system formed by two dispersive elements and a parametric temporal lens, based on a sum-frequency generation process. We derive a unitary transformation of the field operators performed by this kind of time lens. We evaluate the squeezing spectrum at the output of the single-lens imaging system and find the conditions preserving squeezing in the output field. When the efficiency factor of the temporal lens is smaller than unity, the vacuum fluctuations deteriorate squeezing at its output. For efficiency close to unity, when certain imaging conditions are satisfied, the squeezing spectrum at the output of the imaging system will be the same as that at the output of the OPA. This scheme gives the possibility of matching the coherence time of the broadband squeezed light to the response time of the photodetector. We finally discuss a temporal imaging scheme which allows to partially compensating the frequency dispersion of the OPA.
We describe the design of a temporal imaging system that simultaneously reshapes the temporal profile and converts the frequency of a photonic wave packet, while preserving its quantum state. A field lens, which imparts a temporal quadratic phase modulation, is used to correct for the residual phase caused by field curvature in the image, thus enabling temporal imaging for phase-sensitive quantum applications. We show how this system can be used for temporal imaging of time-bin entangled photonic wave packets and compare the field lens correction technique to systems based on a temporal telescope and far-field imaging. The field-lens approach removes the residual phase using four dispersive elements. The group delay dispersion DDD is constrained by the available bandwidth $\ensuremath{\Delta}\ensuremath{\nu}$ by $D>t/\ensuremath{\Delta}\ensuremath{\nu}$, where ttt is the temporal width of the wave form associated with the dispersion DDD. This is compared to the much larger dispersion $D\ensuremath{\gg}\ensuremath{\pi}{t}^{2}/8$ required to satisfy the Fraunhofer condition in the far-field approach.