A simple and general technique for recovering the phase profile of a given optical waveform from temporal intensity measurements is introduced and experimentally demonstrated. The proposed method involves the measurement of the temporal intensity profiles at the input and output of a linear optical time differentiator. The signal phase profile can be unambiguously recovered from these intensity measurements using a direct and noniterative algorithm. Given that ultrafast optical differentiators can be readily implemented in all-fiber or free-space platforms, the proposed technique could be applied over time waveforms with durations ranging from the subpicosecond to the nanosecond regime.
"A differentiator is one of these essential signal processing elements which provides n-th order time derivative of the complex envelope of an arbitrary input optical pulse. In addition to signal processing purposes , a temporal differentiator can be used for ultra-fast signal generation , , and ultra-high-speed coding , . Numerous techniques have been proposed recently to implement all-optical temporal differentiators. "
[Show abstract][Hide abstract] ABSTRACT: We propose and demonstrate an optically tunable photonic fractional temporal differentiator using a tilted fiber Bragg grating written in an erbium/ytterbium (Er-Yb) co-doped fiber. Thanks to the high absorption of the Er-Yb co-doped fiber, when it is pumped the refractive index is changed, and thus the phase of a cladding mode resonant wavelength is changed continuously by continuous tuning of the pumping power. By locating the wavelength of the input light wave at the location of a cladding mode resonant wavelength, a temporal differentiator with a tunable fractional order is achieved. The proposed technique is experimentally evaluated. A temporal differentiator with a tunable fractional order is demonstrated. The use of the fractional differentiator to implement temporal differentiation of a Gaussian pulse with a bandwidth of 28 and 75 GHz is also demonstrated.
"Digital Object Identifier 10.1109/JLT.2011.2159827 A temporal photonic differentiator is a basic operator that performs real-time differentiation of an optical signal in the optical domain , which can find applications in numerous fields such as ultrafast signal generation  and pulse characterization . In general, a photonic temporal differentiation can be realized using an optical device that has a transfer function with the form , where is the differentiation order, is the optical frequency and is the optical carrier frequency of the optical signal. "
"icosecond to the nanosecond regime using ultrafast photonic differentiation, " J. Lightwave Technol. 27(21), 4623–4633 (2009). 17. P. M. Anandarajah, A. M. Clarke, C. Guignard, L. Bramerie, L. P. Barry, J. D. Harvey, and J. C. Simon, " System-performance analysis of optimized gain-switched pulse source employed in 40-and 80-Gb/s OTDM systems, " J. Lightwave Technol. 25(6), 1495–1502 (2007)"
[Show abstract][Hide abstract] ABSTRACT: We present a novel implementation of the "phase reconstruction using optical ultra fast differentiation" (PROUD) technique and apply it to characterize the time resolved chirp of a gain switched semiconductor laser. The optical temporal differentiator is a fiber based polarization interferometer. The method provides a fast and simple recovery of the instantaneous frequency from two temporal intensity measurements, obtained by changing the spectral response of the interferometer. Pulses with different shapes and durations of hundreds of picoseconds are fully characterized in amplitude and phase. The technique is validated by comparing the measured pulse spectra with the reconstructed spectra obtained from the intensity and the recovered phase.
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