Single-shot measurement of phase and amplitude by using a heterodyne time-lens system and ultrafast digital time-holography

Abstract

Temporal imaging systems are outstanding tools for single-shot observation of optical signals that have irregular and ultrafast dynamics. They allow long time windows to be recorded with femtosecond resolution, and do not rely on complex algorithms. However, simultaneous recording of amplitude and phase remains an open challenge for these systems.Here we present a new heterodyne time-lens arrangement that efficiently records both the amplitude and phase of complex signals, while keeping the performances of classical time-lens systems (∼ 200 fs) and field of view (tens of ps). Phase and time are encoded onto the two spatial dimensions of a camera. We demonstrate direct application of our heterodyne time lens to turbulent-like optical fields and optical rogue waves generated from nonlinear propagation of partially coherent waves inside optical fibres. We also show how this phase-sensitive time-lens system enables digital temporal holography to be performed with even higher temporal resolution (80 fs).Simultaneous measurement of the amplitude and phase of ultrafast complex optical signals is a a key question in modern optics and photonics [1][2][3][4][5][6]. This kind of detection is needed for the characterization of various fundamental phenomena such as e.g. supercontinuum [7,8], optical rogue waves (RWs) [9-11], or soliton dynamics in mode-locked lasers [12,13]. The task remains a particulary challenging open problem when femtosecond resolution and long time windows are simultaneously required. These requirements are found for exemple in the context of nonlinear statistical optics and of the characterization of random light [14] or in the study of spatio-temporal dynamics of lasers [15].In the quest for long-window and ultrafast recording tools, temporal imaging devices, such as time-lenses, are considered as promising candidates. Time-lenses enable femtosecond time evolutions to be manipulated so that they can be magnified in time [16][17][18] or spectrally encoded [10,17,19] with high fidelity. These signals evolution replica can thus be recorded using a simple GHz oscilloscope (for time-magnification systems) or a singleshot optical spectrum analyzer [10]). No special algorithms are necessary for retrieving the ultrafast power evolutions, long windows can be recorded (up to hun-dreds of picoseconds), and the method is suitable for recording continuous-wave (i.e., non-pulsed) complex signals. Recently, temporal imaging systems have thus begun to play a central role in fundamental studies dealing with nonlinear propagation of light in fibers leading for example to the emergence of rogue waves and integrable turbulence [10,11,20], where recording long temporal traces with femtosecond resolution is mandatory. Commercial devices are also available in the market (by Pi-coLuz LLC).However, a range of applications is still hampered by the need to also record the phase evolution of long and complex ultrafast optical signals. Extension of temporal imaging has been performed in this direction, by performing heterodyning ...

Rogue waves and analogies in optics and oceanography

“…Such a "time lens" exploits the mathematical equivalence of paraxial diffraction in space and linear group velocity dispersion in time [66], and combines two segments of dispersive propagation on either side of a time lens element that introduces a temporal quadratic phase [67]. The addition of an additional heterodyne detection stage can also be used to yield intensity and phase information [68].…”

“…Peregrine soliton in a wave tank (57) Draupner wave (1D propagation) in a wave tank (166) Modulation instability in optical fibre (47) Backgroundfree solitons in optical fibre (46) Rogue waves in supercontinuum generation (4) Full field measurements of turbulence and dissipative soliton transients (68,106) High order breathers in optical fibre (59) 2013 Current effects on rogue waves in a wave tank (157)…”

Effect of local Peregrine soliton emergence on statistics of random waves in the one-dimensional focusing nonlinear Schrödinger equation

“…Presence of the PSs in the spatiotemporal evolution of the partially-coherent wave in the 1-D focusing NLS governed systems is an experimentally verified fact [27][28][29]. However, the modulation instability cannot be considered as a dominating mechanism in this case.…”

Statistical Properties of the Nonlinear Stage of Modulation Instability in Fiber Optics

“…Shot-to-shot fluctuations of the optical spectra have been measured in experiments with light pulses in [20], while breather structures spontaneously emerging from noise superimposed to a continuous wave (CW) field have been reported in [22]. However, in these pioneering studies the spatio-temporal dynamics and the evolution of statistical properties of the light field along the fiber could not be recorded, since the observation was made only at the output of the fiber.From the theoretical point of view, the question of noise-driven MI enters whithin the fundamental framework of integrable turbulence, which was first introduced by V. E. Zakharov in [24] and is now a subject of extensive theoretical [19,[24][25][26][27][28][29][30] and experimental [31][32][33][34][35][36] research.In the long term evolution, the integrable turbulence is characterized by a steady state where statistical properties become invariant. Surprisingly, for initial conditions made of a plane wave with small additional noise, numerical simulations of the focusing 1DNLSE show that the long-term single-point probability density function (PDF) of the field ψ is Gaussian while the PDF of the power P = |ψ| 2 is exponential [19,28,29].…”