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We are inspired by mechanical gearboxes and demonstrate its analog counterpart in optics. We use nonlinear dispersion modes as "gears" to overcome the mismatch between the ultrahigh speed of optical data and the much slower sampling rate of electronic digitizers and processors. We delineate the mathematical foundations and show its utility in ultrafast optical measurements and digital image compression., Comment: Corrected affiliation

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 (TS-DFT) - 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 is 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., Comment: Pre-print for Applied Physics Letters submission

We introduce the concept of coherent temporal imaging and its combination with the anamorphic stretch transform. The new system can measure both temporal profile of fast waveforms as well as their spectrum in real time and at high-throughput. We show that the combination of coherent detection and warped time-frequency mapping also performs time-bandwidth compression. By reducing the temporal width without sacrificing spectral resolution, it addresses the Big Data problem in real time instruments. The proposed method is the first application of the recently demonstrated Anamorphic Stretch Transform to temporal imaging. Using this method narrow spectral features beyond the spectrometer resolution can be captured. At the same time the output bandwidth and hence the record length is minimized. Coherent detection allows the temporal imaging and dispersive Fourier transform systems to operate in the traditional far field as well as in near field regimes.

A general method for compressing the modulation time-bandwidth product of analog signals is introduced and experimentally demonstrated. As one of its applications, this physics-based signal grooming performs feature-selective stretch, enabling a conventional digitizer to capture fast temporal features that were beyond its bandwidth. At the same time, the total digital data size is reduced. The compression is lossless and is achieved through a same-domain transformation of the signal's complex field, performed in the analog domain prior to digitization. Our method is inspired by operation of Fovea centralis in the human eye and by anamorphic transformation in visual arts. The proposed transform can also be performed in the digital domain as a digital data compression algorithm to alleviate the storage and transmission bottlenecks associated with "big data"., Comment: M. H. Asghari and B. Jalali, "Anamorphic transformation and its application to time-bandwidth compression," submitted on May 28th, 2013 to Applied Optics journal- Accepted. To be presented at IEEE Photonic Conference, September 2013 and in IEEE GlobalSIP, December 2013