Mohammad H. Asghari

All-optical Hilbert transformer based on a single phase-shifted fiber Bragg grating: design and analysis

A simple all-fiber design for implementing an all-optical temporal Hilbert transformer is proposed and numerically demonstrated. We show that an all-optical Hilbert transformer can be implemented using a uniform-period fiber Bragg grating (FBG) with a properly designed amplitude-only grating apodization profile incorporating a single pi phase shift in the middle of the grating length. All-optical Hilbert transformers capable of processing arbitrary optical waveforms with bandwidths up to a few hundreds of gigahertz can be implemented using feasible FBGs.

Transform-limited picosecond pulse shaping based on temporal coherence synthesization

A simple and efficient optical pulse re-shaper based on the concept of temporal coherence synthesization is proposed and analyzed in detail. Specifically, we demonstrate that an arbitrary chirp-free (transform-limited) optical pulse waveform can be synthesized from a given transform-limited Gaussian-like input optical pulse by coherently superposing a set of properly delayed replicas of this input pulse, e.g. using a conventional multi-arm interferometer. A practical implementation of this general concept based on the use of conventional concatenated two-arm interferometers is also suggested and demonstrated. This specific implementation allows the synthesis of any desired temporally-symmetric optical waveform with time features only limited by the input pulse bandwidth. A general optimization algorithm has been developed and applied for designing the system specifications (number of interferometers and relative time delays in these interferometers) that are required to achieve a desired optical pulse re-shaping operation. The required tolerances in this system have been also estimated and confirmed by numerical simulations. The proposed technique has been experimentally demonstrated by re-shaping an approximately 1-ps Gaussian-like optical pulse into various temporal shapes of practical interest, i.e. picosecond transform-limited flat-top, parabolic and triangular pulses (all centered at a wavelength of approximately 1550nm), using a simple two-stage interferometer setup. A remarkable synthesis accuracy and high energetic efficiency have been achieved for all these pulse re-shaping operations.

Experimental demonstration of optical real-time data compressiona)

We experimentally demonstrate a method for compressing the time-bandwidth product of analog signals in real-time. By performing self-adaptive stretch, this technology enables digitizers to capture waveforms beyond their bandwidth with digital data size being reduced at the same time. The compression is lossless and is achieved through a transformation of the signals complex field, performed in the analog domain prior to digitization. For proof of concept experiments, we compress the modulation bandwidth of an optical signal by 500 times. At the same time, we reduce its modulation time-bandwidth product (i.e., the record length) by 2.73 times while achieving 16 dB power efficiency improvement in comparison to the case of using conventional dispersive Fourier transform. Dispersive data compression addresses the big data problem in real-time instruments and in optical communications.

Time–bandwidth engineering

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 (SM) 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 SM Distribution to benchmark different GD profiles and to the analysis of tolerance to system nonidealities, such as GD ripples.

Discrete Anamorphic Transform for Image Compression

To deal with the exponential increase of digital data, new compression technologies are needed for more efficient representation of information. We introduce a physics-based transform that enables image compression by increasing the spatial coherency. We also present the Stretched Modulation Distribution, a new density function that provides the recipe for the proposed image compression. Experimental results show pre-compression using our method can improve the performance of JPEG 2000 format.

Complex-field measurement of ultrafast dynamic optical waveforms based on real-time spectral interferometry

Several methods are now available for single-shot measurement of the complex field (amplitude and phase profiles) of optical waveforms with resolutions down to the sub-picosecond range. As a main critical limitation, all these techniques exhibit measurement update rates typically slower than a few Hz. It would be very challenging to directly upgrade the update rate of any of these available methods beyond a few kHz. By combining spectral interferometry with dispersion-induced real-time optical Fourier transformation, here we demonstrate single-shot complex-field measurements of optical waveforms with a resolution of approximately 400 fs over a record length as long as approximately 350 ps, corresponding to a large record-length-to-resolution ratio of approximately 900. This performance is achieved at a measurement update rate of approximately 17 MHz, i.e. at least one thousand times faster than with any previous single-shot complex-field THz-bandwidth optical signal characterization method.

High-order passive photonic temporal integrators

We experimentally demonstrate, for the first time to our knowledge, an ultrafast photonic high-order (second-order) complex-field temporal integrator. The demonstrated device uses a single apodized uniform-period fiber Bragg grating (FBG), and it is based on a general FBG design approach for implementing optimized arbitrary-order photonic passive temporal integrators. Using this same design approach, we also fabricate and test a first-order passive temporal integrator offering an energetic-efficiency improvement of more than 1 order of magnitude as compared with previously reported passive first-order temporal integrators. Accurate and efficient first- and second-order temporal integrations of ultrafast complex-field optical signals (with temporal features as fast as approximately 2.5ps) are successfully demonstrated using the fabricated FBG devices.

The Anamorphic Stretch Transform: Putting the Squeeze on “Big Data”

Coping with a deluge of digital information will require more efficient ways to capture, sample and store data. One new approach works by selectively “warping” the data to provide better resolution of the fine details - while still reducing total data size.

Stereopsis-Inspired Time-Stretched Amplified Real-Time Spectrometer (STARS)

We introduce and experimentally demonstrate a single-shot real-time optical vector analyzer (OVA). This instrument combines amplified dispersive Fourier transform with stereopsis reconstruction and is inspired by binocular vision in biological eyes.

Design of all-optical high-order temporal integrators based on multiple-phase-shifted Bragg gratings

In exact analogy with their electronic counterparts, photonic temporal integrators are fundamental building blocks for constructing all-optical circuits for ultrafast information processing and computing. In this work, we introduce a simple and general approach for realizing all-optical arbitrary-order temporal integrators. We demonstrate that the N(th) cumulative time integral of the complex field envelope of an input optical waveform can be obtained by simply propagating this waveform through a single uniform fiber/waveguide Bragg grating (BG) incorporating N pi-phase shifts along its axial profile. We derive here the design specifications of photonic integrators based on multiple-phase-shifted BGs. We show that the phase shifts in the BG structure can be arbitrarily located along the grating length provided that each uniform grating section (sections separated by the phase shifts) is sufficiently long so that its associated peak reflectivity reaches nearly 100%. The resulting designs are demonstrated by numerical simulations assuming all-fiber implementations. Our simulations show that the proposed approach can provide optical operation bandwidths in the tens-of-GHz regime using readily feasible photo-induced fiber BG structures.