Nonlinear Localization of Dissipative Modulation Instability

Dynamics of temporal Kerr cavity solitons in the presence of rapid parameter inhomogeneities: From bichromatic driving to third-order dispersion

“…Equation (9) shows that the TCS velocity in the presence of two driving fields separated by angular frequency Ω is dependent upon the Fourier amplitudes of the real and imaginary parts of the adjoint neutral mode evaluated at Ω. To gain more insights, we plot these Fourier coefficients in Fig.…”

“…Coherently-driven, dispersive resonators with Kerr nonlinearity can sustain localized dissipative structures known as temporal Kerr cavity solitons (TCSs) [1][2][3]. Such solitons, also known as dissipative Kerr solitons, have attracted significant attention over the past decade due to their rich dynamics [4][5][6][7][8][9][10] as well as significance with regards to practical applications. In particular, TCSs underpin the generation of coherent microresonator optical frequency combs [11][12][13][14][15], whose many applications range from telecommunications [16] and distance measurements [17][18][19] to spectroscopy [20,21] and imaging [22].…”

Bloch Oscillations of Driven Dissipative Solitons in a Synthetic Dimension

“…1b]. They have been extensively studied in experiments in the absence of a synthetic frequency dimension (J EOM = 0) [36][37][38][39][40][41][42][43][44][45][46][47]. In what follows, we will present the first experiments that probe their behaviour when J EOM = 0, unveiling Bloch band transport phenomena whose precise features are shaped by the interplay of nonlinearity and dissipation [see Figs.…”

“…Concurrently, the nonlinear dynamics of coherentlydriven Kerr-type resonators have been extensively studied in the absence of an intra-cavity EOM (and hence without a synthetic frequency dimension) [36][37][38][39][40][41][42][43][44][45][46][47]. It is well-established that such devices can host a number of universal nonlinear phenomena [36][37][38]44], amongst which the emergence of localized dissipative structures known as temporal cavity solitons (CSs) has attracted particular attention.…”

Multiple symmetry breaking induced by weak damping in the Fermi-Pasta-Ulam-Tsingou recurrence process

“…The nonlinear stage of MI has attracted a great deal of attention as a triggering mechanism of rogue waves [17,18]. It turned out to be an incredibly rich and multi-faceted phenomenon whose understanding is slowly progressing thanks to recent efforts that range from theory [19][20][21][22][23][24][25][26][27][28][29] to experiments mainly concentrated in the areas of nonlinear optics [30][31][32][33][34][35][36][37][38][39][40][41] and hydrodynamics [33,[41][42][43][44][45]. In this context, FPUT recurrences emerge, when MI is seeded by periodic perturbations (sideband pairs), as cycles of conversion and back-conversion between the sidebands and the pump.…”