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Versatile and easy to implement methods to generate arbitrary optical waveforms at high repetition rates are of considerable interest with applications in optical communications, all-optical signal processing, instrumentation systems and microwave signal manipulation. While shaping sinusoidal, Gaussian or hyperbolic secant intensity profiles is commonly achieved by means of modulators or mode-locked lasers, other pulse profiles such as parabolic, triangular or flat-top shapes still remain challenging to synthesize. In this context, several strategies were already explored. First, the linear pulse shaping is a common method to carve an initial ultrashort pulse train into the desired shape. The line-by-line shaping of a coherent frequency comb made of tens of spectral components was also investigated to generate more complex structures whereas Fourier synthesis of a few discrete frequencies spectrum was exploited to efficiently generate high-fidelity ultrafast periodic intensity profiles.
Besides linear shaping techniques, several nonlinear methods were implemented to benefit from the adiabatic evolution of the intensity pulse profile upon propagation in optical fibers. Other examples of efficient methods are based on the photonic generation involving specific Mach-Zehnder modulators, microwave photonic filters as well as frequency-to-time conversion.
In this contribution, we theoretically and experimentally demonstrate a new approach enabling the synthesis of periodic high-repetition rate pulses with various intensity profiles ranging from parabola to triangular and flat-top pulses. More precisely by linear phase and amplitude shaping of only four spectral lines is it possible to reach the targeted temporal profile. Indeed, tailoring the input symmetric spectrum only requires the determination of two physical parameters: the phase difference between the inner and outer spectral sidebands and the ratio between the amplitude of these sidebands. Therefore, a systematic bidimensional analysis provides the optimum parameters and also highlights that switching between the different waveforms is achieved by simply changing the spectral phase between the inner and outer sidebands.
We successfully validate this concept with the generation of high-fidelity ultrafast periodic waveforms at 40 GHz by shaping with a liquid cristal on insulator a four sideband comb resulting from a phase-modulated continuous wave. In order to reach higher repetition rates, we also describe a new scenario to obtain the required initial spectrum by taking advantage of the four-wave mixing process occurring in a highly nonlinear fiber. This approach is experimentally implemented at a repetition rate of 80-GHz by use of intensity and phase measurements that stress that full-duty cycle, high-quality, triangular, parabolic or flat-top profiles are obtained in full agreement with numerical simulations. The reconfigurable property of this photonic waveform generator is confirmed. Finally, the generation of bunch of shaped pulses is investigated, as well as the impact of Brillouin backscattering.
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