Linear self-referenced complex-field characterization of fast optical signals using photonic differentiation

Automatic classification of the frequency chirp in directly modulated lasers using cross-correlation

“…While the laser output power can be directly measured using the oscilloscope, frequency deviations can be transformed in power variations using the interferometer. Alternatively, more sophisticated single-shot schemes can be implemented to measure chirp [16], such as the use of a programmable Fourier domain optical processor to realize a tunable frequency discriminator [17]. The automatic algorithm put forward here thus represents a flexible, straightforward, accurate and therefore powerful tool to determine the chirp characteristics of a directly modulated semiconductor laser, particularly attractive for the fabrication and testing of transmitters for the telecommunications industry.…”

Theoretical Analysis of Directly Modulated Reflective Semiconductor Optical Amplifier Performance Enhancement by Microring Resonator-Based Notch Filtering

“…In this manner, the desired chirp can be directly extracted in analytical form from the knowledge of the time-domain intensity profiles of the signals that enter and exit the MRR. Thus [54],…”

“…For the MRR case, however, the phase of the transmitted light undergoes a steep variation around resonance [52], which compromises the direct numerical calculation of the corresponding response and accordingly of its temporal rate of change, which provides the chirp. Instead of taking the inverse tangent function of the ratio between the imaginary and real parts of the complex-valued electric field [53], we use the relevant information that is extracted when applying the signal phase-reconstruction technique in the optical domain [54,55]. This technique allows one to unambiguously recover the instantaneous frequency deviation profile of a random repetitive data signal which is inserted in a frequency discriminator whose spectral transfer function has a linear spectral amplitude variation around the detuning position.…”

PROUD-based method for simple real-time in-line characterization of propagation-induced distortions in NRZ data signals

“…However, these techniques are typically not ideal, as these rely in the use of nonlinearities, which can prove to be a drawback in the characterization of low-power telecommunications signals. In this context, Phase Reconstruction using Optical Ultrafast Differentiation (PROUD) is a set of direct selfreferenced techniques well adapted for the characterization of lowpower telecom signals [8]- [11]. Nonetheless, to our knowledge, no results have been reported in the literature to validate the use of PROUD for signal characterization in fiber-optics propagation experiments.…”

“…Here, y+(t) and y-(t) can be obtained by inputting x(t) into two linear time-invariant frequency filters with an amplitude response that is linear with the optical frequency, i.e., with spectral transfer functions D±(ω)=±S(ω0-ω±Δω), with the same central frequencies as the carrier frequency of the input optical signal x(t), ω0, same (positive) frequency shift Δω between ω0 and the resonance frequency (i.e., frequency at which the spectral transfer function reaches zero) of the differentiator, and opposite slopes ±S. The differential output optical instantaneous power (obtained by balance photodetection of the filters outputs y+(t) and y-(t)) can be easily demonstrated to be [10], [11]:…”