Time–bandwidth engineering

Abstract

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.

Design of Warped Stretch Transform

“…For either technology, the implemented group delay profile will have some deviations from the design. A numerical study of the tolerance to profile nonidealities is performed previously 17 . Time stretch dispersive Fourier transform maps the spectrum of the pulses in a burst-mode signal to the silent intervals in between them.…”

“…For example, direct frequency-to-time mapping can be replaced by phase retrieval 13 or coherent detection after the dispersion 14 followed by back propagation. Using warped group delay dispersion as a photonic hardware accelerator 15 , an optical signal's intensity envelope can be engineered to match the specifications of the data acquisition back-end [16][17][18] . One can slow down an ultra-fast burst of data, and at the same time, achieve data compression by exploiting sparsity in the original data 19 .…”

Ultrafast time-stretch imaging at 932 nm through a new highly-dispersive fiber

“…At a MHz line-scan rate, i.e., 7.6 MHz in this case, the extremely-high data rate is always a concern [22], and thus the real-time data processing is the bottleneck of the ultrafast diagnosis. In most previous works [6][7][8][9], the time-stretch signal has usually been recorded by >10-GHz real-time oscilloscopes, which can easily generate a data stream of >50 GS/s. Such a heavy data processing is very difficult for the state-of-the-art electrical processors, e.g., the parallel-configured field-programmable gate array (FPGA) [23].…”

“…The temporal spectrum, which is encoded with the spatial information through the wavelength-to-time mapping, can be efficiently captured in a singleshot manner and then reconstructed into 2D images through off-line data processing. In spite of the ultrahigh throughput capacity, it is also a high-data-streaming imaging modalityeasily >50 GS/s [6], which is even beyond the processing capability of the state-of-the-art electrical signal processors [8]. As a consequence, a large electrical bandwidth, typically >10 GHz, is usually required to fully interpret the spectral information [9].…”

Optical Data Compression in Time Stretch Imaging

“…Detecting rare events such as cancer cells or rogue signals requires that data be recorded continuously and for a long time to catch the rare events. The need to compress massive volumes of data in real-time has fueled interest in nonuniform time stretch transformation that takes advantage of sparsity in physical signals to achieve both bandwidth compression as well as reduction in the temporal length [1,[19][20][21][22]. 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.…”