Real-time measurements,rare events and photon economics

Rogue events otherwise known as outliers and black swans are singular, rare, events that carry dramatic impact. They appear in seemingly unconnected systems in the form of oceanic rogue waves, stock market crashes, evolution, and communication systems. Attempts to understand the underlying dynamics of such complex systems that lead to spectacular and often cataclysmic outcomes have been frustrated by the scarcity of events, resulting in insufficient statistical data, and by the inability to perform experiments under controlled conditions. Extreme rare events also occur in ultrafast physical sciences where it is possible to collect large data sets, even for rare events, in a short time period. The knowledge gained from observing rare events in ultrafast systems may provide valuable insight into extreme value phenomena that occur over a much slower timescale and that have a closer connection with human experience. One solution is a real-time ultrafast instrument that is capable of capturing singular and randomly occurring non-repetitive events. The time stretch technology developed during the past 13 years is providing a powerful tool box for reaching this goal. This paper reviews this technology and discusses its use in capturing rogue events in electronic signals, spectroscopy, and imaging. We show an example in nonlinear optics where it was possible to capture rare and random solitons whose unusual statistical distribution resemble those observed in financial markets. The ability to observe the true spectrum of each event in real time has led to important insight in understanding the underlying process, which in turn has made it possible to control soliton generation leading to improvement in the coherence of supercontinuum light. We also show a new class of fast imagers which are being considered for early detection of cancer because of their potential ability to detect rare diseased cells (so called rogue cells) in a large population of healthy cells.