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Frequency conversion in microresonators has revolutionised modern-day nonlinear and quantum optics. Here, we present a theory of the multimode second harmonic generation in microresonators under conditions when the parametric conversion…
Microresonator-based platforms with $\chi^{(2)}$ nonlinearities have the potential to perform frequency conversion at high efficiencies and ultralow powers with small footprints. The standard doctrine for achieving high conversion…
A two dimensional model is introduced to study pattern formation, secondary instabilities and the transition to spatiotemporal chaos (weak turbulence) in parametric surface waves. The stability of a periodic standing wave state above onset…
The Eckhaus instability is a secondary instability of nonlinear spatiotemporal patterns in which high-wavenumber periodic solutions become unstable against small-wavenumber perturbations. We show in this letter that this instability can…
Experimental and theoretical studies of nonlinear frequency combs in \chi^(3) optical microresonators attracted tremendous research interest during the last decade and resulted in prototypes of solitonbased steadily working devices.…
Light states relevant to the $\chi^{(2)}$ comb generation in optical microresonators possess typically dual backgrounds for coupled first-harmonic (FH) and second-harmonic (SH) envelopes. Stability and/or instability of these backgrounds is…
Investigations of frequency combs in $\chi^{(3)}$ optical microresonators are burgeoning nowadays. Changeover to $\chi^{(2)}$ resonators promises further advances and brings new challenges. Here, the comb generation entails not only coupled…
The notion of instability of a turbulent flow is introduced in the case of a von K\'arm\'an flow thanks to the monitoring of the spatio-temporal spectrum of the velocity fluctuations, combined with projection onto suitable Beltrami modes.…
A particular interest on two-dimensional turbulence is the inverse energy cascade from small to large sales, which leads to an energy condensation accompanied by the formation of large-scale vortical structures. Indeed, such a phenomenon is…
The question of optimal spanwise-periodic modification for the stabilisation of spanwise-invariant flows is addressed. A 2nd-order sensitivity analysis is conducted for the linear temporal stability of parallel flows U0 subject to…
The plane-wave dynamics of 3*omega => (2*omega, omega) subharmonic optical parametric oscillators containing a second harmonic generator of the idler wave omega is analyzed analytically by using the meanfield approximation and numerically…
In some linearly unstable flows, secondary instability is found to have a much larger wavelength than that of the primary unstable modes, so that it cannot be recovered with a classical Floquet analysis. In this work, we apply a new…
As electronic operating frequencies increase toward the terahertz regime, new electrooptic modulators capable of low-voltage high-frequency operation must be developed to provide the necessary optical interconnects. This letter presents a…
The mechanisms governing the low-frequency unsteadiness in the shock wave/turbulent boundary layer interaction at Mach 2 are considered. The investigation is conducted based on the numerical database issued from large-eddy simulations…
In the following we consider a 2-dimensional system of ODE's containing quasiperiodic terms. The system is proposed as an extension of Mathieu-type equations to higher dimensions, with emphasis on how resonance between the internal…
A free-energy minimization approach is used to address the secular & dynamical instabilities & the bifurcations along sequences of rotating, self-gravitating fluid and stellar systems. Our approach stems from the Landau-Ginzburg theory of…
We show that arrays of $\chi^{(2)}$ nonlinear waveguides in the second harmonic generation regime are a promising source of continuous-variable entanglement. We indeed demonstrate analytically that optical arrays with odd number of…
We investigate the induced modulation instability in second-harmonic generation beyond the early stage of the linearized growth of the modulation. We find a regime of recurrence (quasi-periodic conversion and back-conversion between the…
Optical $\chi^{(2)}$ non-linearity can be used for parametric amplification and producing down-converted entangled photon pairs that have broad applications. It is known that weak non-linear media exhibit dispersion and produce a frequency…
Quadratic nonlinear processes are currently exploited for frequency comb transfer and extension from the visible and near infrared regions to other spectral ranges where direct comb generation cannot be accomplished. However, frequency comb…