Real-time dynamics and cross-correlation gating spectroscopy of free-carrier Drude slow-light solitons

Abstract

Optical solitons—stable waves balancing delicately between nonlinearities and dispersive effects—have advanced the field of ultrafast optics and dynamics, with contributions spanning from supercontinuum generation to soliton fission, optical event horizons, Hawking radiation and optical rogue waves, among others. Here, we investigate picojoule soliton dynamics in silicon slow-light, photonic-bandgap waveguides under the influence of Drude-modeled, free-carrier-induced nonlinear effects. Using real-time and single-shot amplified dispersive Fourier transform spectroscopy simultaneously with high-fidelity cross-correlation frequency resolved optical gating at femtojoule sensitivity and femtosecond resolution, we examine the soliton stability limits, the soliton dynamics including free-carrier quartic slow-light scaling and acceleration, and the Drude electron–hole plasma-induced perturbations in the Cherenkov radiation and modulation instability. Our real-time single-shot and time-averaged cross-correlation measurements are matched with our detailed theoretical modeling, examining the reduced group velocity free-carrier kinetics on solitons at the picojoule scale.

Hybrid modeling approach for mode-locked laser diodes with cavity dispersion and nonlinearity

“…The split-step Fourier method has been used extensively in literature and consists of a nonlinear- and dispersion operator that act alternately upon the propagating field 36 , 37 , 45 . Here we concisely describe the implementation used in our model, for further details we refer to the literature 35 , 37 , 46 – 48 . In this work, the linear losses, nonlinear losses due to two-photon and free-carrier absorption, second- and third-order dispersion, the Raman effect and third order nonlinear interactions stemming from the Kerr nonlinearity of the silicon waveguide are included through a generalized nonlinear Schrödinger equation of the form 35 , 37 , 46 – 48 where E(z,t) is the slowly varying pulse envelope (units of ), z is the spatial variable and has the dimension of distance, represents the n-th order dispersion term and denotes the linear losses.…”

“…Here we concisely describe the implementation used in our model, for further details we refer to the literature 35 , 37 , 46 – 48 . In this work, the linear losses, nonlinear losses due to two-photon and free-carrier absorption, second- and third-order dispersion, the Raman effect and third order nonlinear interactions stemming from the Kerr nonlinearity of the silicon waveguide are included through a generalized nonlinear Schrödinger equation of the form 35 , 37 , 46 – 48 where E(z,t) is the slowly varying pulse envelope (units of ), z is the spatial variable and has the dimension of distance, represents the n-th order dispersion term and denotes the linear losses. Furthermore, the nonlinear parameter is defined as , where is the material nonlinear coefficient, is the effective mode area, c is the speed of light in vacuum, and is the two-photon absorption parameter.…”

“…Furthermore, the nonlinear parameter is defined as , where is the material nonlinear coefficient, is the effective mode area, c is the speed of light in vacuum, and is the two-photon absorption parameter. Furthermore, free-carrier absorption and dispersion are included through the free-carrier absorption coefficient , the free-carrier dispersion , and the auxiliary equation that governs the time dependence of the free-carrier density 47 , 48 where is the free-carrier lifetime in the waveguide and is the photon energy. Furthermore, the integral in Eq.…”

“…A simulation time of 100 ns (260 roundtrips) was used with a 20 fs stepsize. The model parameters are based on earlier work 48 , 52 , 53 and are listed in Table 1 . The real part of the nonlinear coefficient , with the material nonlinear coefficient and the effective mode area.…”

Improving Low-Dispersion Bandwidth of the Silicon Photonic Crystal Waveguides for Ultrafast Integrated Photonics

“…The second factor is the disordered transmission spectrum in the large group index region resulting from the wavelength-dependent insertion loss. Furthermore, the third factor is the high nonlinear absorption resulting from the slow-light enhanced two-photon absorption (TPA) and free-carriers absorption (FCA) [22]. What is more, combining with the high group index, large low-dispersion bandwidth is also vital for the ultrafast nonlinear photonics, as an ideal transform-limited Gaussian pulse with center wavelength of 1550 nm and 100 fs pulse-duration is corresponding to 35 nm spectral-width [23].…”