Pulse-resolved spectral information was obtained by extracting wavelengths far from that of the input pulse using a longpass filter and detecting the filtered light with a photodiode and a real-time digital oscilloscope. The study of optical rogue waves ultimately showed that stimulated supercontinuum generation (as described further below) provides a means of becalming such broadband sources. The initial observations occurred at the University of California, Los Angeles as part of DARPA-funded research aiming to harness supercontinuum for time-stretch A/D conversion and other applications in which stable white light sources are required (e.g., real-time spectroscopy). Consequently, these attributes are normally averaged out or hidden in time-averaged observations. These measurements revealed that the attributes of individual pulses can be markedly different from those of the ensemble average. In the experiments, radiation from a mode-locked laser (megahertz pulse train) was injected into a nonlinear optical fiber and characteristics of the output radiation were measured at the single-shot level for thousands of pulses (events). Optical rogue waves were initially reported in 2007 based on experiments investigating the stochastic properties of supercontinuum generation from a train of nearly-identical picosecond input pulses. The particulars of the analogy between extreme waves in optics and hydrodynamics may vary depending on the context, but the existence of rare events and extreme statistics in wave-related phenomena are common ground. Consequently, optical rogue waves are attractive for experimental and theoretical research and have become a highly studied phenomenon. A key practical difference is that most optical experiments can be done with a table-top apparatus, offer a high degree of experimental control, and allow data to be acquired extremely rapidly. More generally, research has exposed a number of different analogies between extreme events in optics and hydrodynamic systems. Aside from the statistical similarities, light waves traveling in optical fibers are known to obey the similar mathematics as water waves traveling in the open ocean (the nonlinear Schrödinger equation), supporting the analogy between oceanic rogue waves and their optical counterparts. Despite their infrequency, rare events wield significant influence in many systems. Such distributions also describe the probabilities of freak ocean waves and various phenomena in both the man-made and natural worlds. These probability distributions are characterized by long tails: large outliers occur rarely, yet much more frequently than expected from Gaussian statistics and intuition. These anomalous events have been shown to follow heavy-tailed statistics, also known as L-shaped statistics, fat-tailed statistics, or extreme-value statistics. In this context, optical rogue waves are characterized by an anomalous surplus in energy at particular wavelengths (e.g., those shifted to the red of the input waveform) or an unexpected peak power. The term optical rogue waves was coined to describe rare pulses of broadband light arising during the process of supercontinuum generation-a noise-sensitive nonlinear process in which extremely broadband radiation is generated from a narrowband input waveform-in nonlinear optical fiber. Optical rogue waves are rare pulses of light analogous to rogue or freak ocean waves. Rogue events reach intensities of at least 30–40 times the average value. Single-shot time traces for three different pump power levels (increasing from top to bottom) and corresponding histograms. Experimental observation of optical rogue waves.
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