Come Schnebelin

Fractional Fourier transform-based description of the Talbot effect: application to analog signal processing

The Talbot effect, or self-imaging, is a fascinating feature of Fresnel diffraction, where an input periodic wavefront is periodically recovered after specific propagation distances through free space. Interestingly, the Fresnel propagator shows a great similarity to the fractional Fourier transform (FrFT). In this paper, we provide an interpretation of the Talbot effect in the frame of the FrFT and derive simple summation formulas between the FrFT of a function and the function itself. In particular, we show that both the FrFT and the Fourier transform (FT) of any input function can be generated by coherent addition of spatially shifted replicas of the function itself, multiplied by a quadratic phase term. Transposed into the temporal domain, these results may have important applications for real-time analog computation of the FrFT/FT of arbitrary signals.

Reconfigurable photonic generation of arbitrary RF chirped waveforms based on a single CW laser

We demonstrate a novel technique for the generation of fully-reconfigurable radio frequency chirped waveforms with extremely simple hardware based on a single CW laser and a frequency-shifting loop. All the waveform parameters, namely sign and value of the chirp rate, bandwidth, repetition rate and chirp duration are fully reconfigurable by simply tuning the frequency of a MHz-range single RF tone. In addition, the envelope of the generated RFCW can be shaped arbitrarily. We experimentally report the generation of arbitrary RF chirps with time duration ranging from 1 ns to over 100 ns, bandwidth above 28 GHz, and time-bandwidth product exceeding 1000, limited only by the detection bandwidth available.

Agile photonic fractional Fourier transformation of optical and RF signals

The last 20 years have seen the spectacular emergence of optically assisted solutions for the analog generation and processing of radio-frequency (RF) signals [J. Lightwave Technol.27, 314 (2009)JLTEDG0733-872410.1109/JLT.2008.2009551]. Among these, real-time Fourier transformation (FT) is of particular importance for signal processing and filtering, but is of limited use for analyzing signals with time-dependent spectrum, especially chirped RF waveforms. On the contrary, fractional Fourier transformation (FrFT), which decomposes a waveform onto a continuous basis of linearly chirped functions, provides a generalization of FT and constitutes a valuable tool for analyzing signals with time-dependent spectrum [Signal Process.91, 1351 (2011)10.1016/j.sigpro.2010.10.008]. Here we prove a new and simple concept, enabling agile computation of the FrFT of both optical and RF signals in real time, with minimum latency time and a frequency resolution in the tens of kHz range. We demonstrate two practical applications of the technique: the absolute measurement of RF/optical chirp rates and the detection of weak chirped RF signals buried under noise. The introduced concept should be of practical interest for RF signal filtering and radar signal processing.

Reconfigurable photonic generation of broadband chirped waveforms using a single CW laser and low-frequency electronics

Broadband radio-frequency chirped waveforms (RFCWs) with dynamically tunable parameters are of fundamental interest to many practical applications. Recently, photonic-assisted solutions have been demonstrated to overcome the bandwidth and flexibility constraints of electronic RFCW generation techniques. However, state-of-the-art photonic techniques involve broadband mode-locked lasers, complex dual laser systems, or fast electronics, increasing significantly the complexity and cost of the resulting platforms. Here we demonstrate a novel concept for photonic generation of broadband RFCWs using a simple architecture, involving a single CW laser, a recirculating frequency-shifting loop, and standard low-frequency electronics. All the chirp waveform parameters, namely sign and value of the chirp rate, central frequency and bandwidth, duration and repetition rate, are easily reconfigurable. We report the generation of mutually coherent RF chirps, with bandwidth above 28 GHz, and time-bandwidth product exceeding 1000, limited by the available detection bandwidth. The capabilities of this simple platform fulfill the stringent requirements for real-world applications.Producing versatile radio-frequency chirped waveforms often requires complicated techniques. The authors use a fiber-optic frequency-shifting loop to create a low-complexity photonic chirp generator with high bandwidth and fully flexible properties for application in radar, spectroscopy, and imaging.

Acousto-optic frequency combs for heterodyne interferometry

We demonstrate the capability of a frequency shifting loop seeded with a CW laser to generate a coherent optical frequency comb. Our system produces a spectrum that contains near 1000 modes, with a frequency spacing between them easily reconfigurable in the kHz-100 MHz range, without high-speed electronics. In order to show the potentiality of this kind of frequency combs for precise spectroscopy, we report the measurement of the complex amplitude of the resonance peaks of a Fabry-Perot cavity, with sub-MHz resolution.

Agile photonic arbitrary waveform generation based on a single CW laser

We propose and demonstrate a new and extremely simple concept of reconfigurable photonic generation of arbitrary RF waveforms, based on a single CW laser and a frequency shifting loop. Our system does not require broadband light source or fast electronic generator. It is capable of generating arbitrary RF waveforms with duration ranging from 1 ns to more than 100 ns, and with dynamic performances beyond state of the art photonic AWG techniques (spectral bandwidth > 25 GHz, TBWP > 500, limited by detection). Our concept, which can be seen as spectral shaping with a resolution in the MHz range, is expected to open a wide range of applications in microwave photonics.

Agile photonic generation of arbitrary RF chirped waveforms based on a single CW laser

Photonic generation of radio-frequency (RF) chirped signals has proven an attractive solution to overcome the limitations of conventional electronic waveform generators. However most of the designs proposed so far make use of a mode-locked laser as a broadband light source, resulting in high cost and complexity [1, 2]. Here we propose a much simpler concept of photonic generation of arbitrary RF chirped waveforms based on a frequency shifting loop (FSL) seeded with a single CW laser [3]. This simple scheme enables generation of on-demand RF chirps with large bandwidth (> 100 GHz), and fully controllable chirp sign, rate and envelope. The RF chirp duration can be adjusted from a few ns to hundreds of ns, resulting in time-bandwidth products (TBWP) exceeding 1000.

Heterodyne interferometry using acousto-optic frequency combs

Optical frequency combs (OFCs) have led to an impressive number of achievements, including multi-heterodyne spectroscopy [1]. Mode-locked OFCs have been widely used due to their exceptional spectral bandwidth, but they usually require sophisticated locking methods to control the free spectral range (FSR) and the absolute frequency of the comb. A promising alternative is provided by electro-optic OFCs, where multiple mutually coherent sidebands are generated by intensity and/or phase modulation of a single stable CW laser. The comb FSR is easily reconfigurable by changing the frequency of the modulation signals. However the number of lines is typically limited to ∼10s. This quantity can be increased to 100s but at the expense of conducting spectral broadening by light propagation through a nonlinear fiber [2, 3]. Alternatively, pseudo-random EO phase modulation leads to the generation of hundreds of mutually coherent lines, but then the comb bandwidth is limited to a few GHz [4].

Agile photonic generation of arbitrary RF chirped waveforms

We demonstrate a simple platform for reconfigurable generation of arbitrary RF chirped waveforms from a single CW laser. Our scheme is capable of generating >100 GHz bandwidth chirps with a time-bandwidth product up to ∼1300.