We describe compression and expansion of the time-bandwidth product of signals and present tools to design optical data compression and expansion systems that solve bottlenecks in the real-time capture and generation of wideband data. Applications of this analog photonic transformation include more efficient ways to sample, digitize, and store optical data. Time-bandwidth engineering is enabled by the recently introduced Stretched Modulation (S M ) Distribution function, a mathematical tool that describes the bandwidth and temporal duration of signals after arbitrary phase and amplitude transformations. We demonstrate design of time-bandwidth engineering systems in both near-field and far-field regimes that employ engineered group delay (GD), and we derive closed-form mathematical equations governing the operation of such systems. These equations identify an important criterion for the maximum curvature of warped GD that must be met to achieve time-bandwidth compression. We also show application of the S M Distribution to benchmark different GD profiles and to the analysis of tolerance to system nonidealities, such as GD ripples.

Adaptive all-order dispersion compensation of ultrafast laser pulses using dynamic spectral holography

Recently, it has been shown that the intensity time-bandwidth product of optical signals can be engineered to match that of the data acquisition instrument. In particular, it is possible to slow down an ultrafast signal, resulting in compressed RF bandwidth-a similar benefit to that offered by the Time-Stretch Dispersive Fourier Transform-but with reduced temporal record length leading to time-bandwidth compression. The compression is implemented using a warped group delay dispersion leading to non-uniform time stretching of the signal's intensity envelope. Decoding requires optical phase retrieval and reconstruction of the input temporal profile, for the case where information of interest resides in the complex field. In this paper, we present results on the general behavior of the reconstruction process and its dependence on the signal-to-noise ratio. We also discuss the role of chirp in the input signal. V C 2014 AIP Publishing LLC.Capturing wide-bandwidth ultrafast signals in real-time is restricted by the time-bandwidth product of the data acquisition instrument. Here, the "product" does not refer to the uncertainty limit but rather to that imposed by the digitizer's bandwidth and record length. The time-stretch dispersive Fourier transformation (TS-DFT) has proven to be very useful in digitizing ultrafast optical signals in real-time. It has led to the discovery of optical rogue waves, 1 the study of supercontinuum noise, 2 and the detection of cancer cells in blood with one-in-a-million sensitivity. 3,4 TS-DFT allows real-time analog-to-digital conversion by reducing the intensity (envelope) bandwidth of information-carrying optical signals to match the much smaller bandwidth of the electronic digitizer. 5,6 However, it does not address the generation of big data volumes inherent in high-throughput realtime measurements. This has fueled interest in non-uniform time stretch transformations that take advantage of sparsity in physical signals to achieve both bandwidth compression as well as reduction in the temporal length. 7-10 Compared to linear time stretch achieved with TS-DFT, such transforms lead to savings in the amount of digital data required for transfer. The aim of this technique is to transform a signal such that its intensity matches not only the digitizer's bandwidth but also its temporal record length. The latter is typically limited by the digitizer's storage capacity. To be sure, reduction of digital data size also facilitates its transmission over communication networks.To this end, it was shown that it is possible to reshape the spectro-temporal profile of optical signals in the analog domain such that signal intensity's time-bandwidth product is commensurate with the acquisition instrument and the big data problem is alleviated. 7-10 The compression is achieved through a warped time-stretch dispersive Fourier transform, in which the transformation is intentionally warped using an engineered group delay (GD) dispersion profile. The transformation causes a frequency-dependent reshaping of th...

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Photonic time stretch is the key enabling technology for a wide variety of instruments with unparalleled single-shot data acquisition performance at high throughput and continuous operation. These systems have established landmark performance in spectroscopy and imaging including flow-through microscopy, velocimetry, lidar, and other measurements. The evolution of the original time-stretch technique into such diverse instruments and applications over the last 25 years has created the need for a unified theoretical framework. This paper represents the first step toward a universal mathematical model for time-stretch instruments. It shows that the "stretch factor"-the fundamental performance metric-is governed by a single canonical equation in a wide range of seemingly diverse time-stretch instruments. The paper also provides new insight into the operation of time-stretch imaging and light scattering systems. The stretch factor is derived for time-stretch systems that operate in temporal, spatial, angular, and Doppler domains. The analysis and mathematical tools provided here can facilitate understanding and analysis of such systems and help future developments in this field.