Andrea Armaroli

Tunable modulational instability sidebands via parametric resonance in periodically tapered optical fibers

We analyze the modulation instability induced by periodic variations of group velocity dispersion and nonlinearity in optical fibers, which may be interpreted as an analogue of the well-known parametric resonance in mechanics. We derive accurate analytical estimates of resonant detuning, maximum gain and instability margins, significantly improving on previous literature on the subject. We also design a periodically tapered photonic crystal fiber, in order to achieve narrow instability sidebands at a detuning of 35 THz, above the Raman maximum gain peak of fused silica. The wide tunability of the resonant peaks by variations of the tapering period and depth will allow to implement sources of correlated photon pairs which are far-detuned from the input pump wavelength, with important applications in quantum optics.

Oscillatory dynamics in nanocavities with noninstantaneous Kerr response

We investigate the impact of a finite response time of Kerr nonlinearities over the onset of spontaneous oscillations (self-pulsing) occurring in a nanocavity. The complete characterization of the underlying Hopf bifurcation in the full parameter space allows us to show the existence of a critical value of the response time and to envisage different regimes of competition with bistability. The transition from a stable oscillatory state to chaos is found to occur only in cavities which are detuned far off-resonance, which turns out to be mutually exclusive with the region where the cavity can operate as a bistable switch.

Fourth-order dispersion mediated modulation instability in dispersion oscillating fibers

We investigate the role played by fourth-order dispersion on the modulation instability process in dispersion oscillating fibers. It not only leads to the appearance of instability sidebands in the normal dispersion regime (as in uniform fibers), but also to a new class of large detuned instability peaks that we ascribe to the variation of dispersion. All these theoretical predictions are experimentally confirmed.

Three-dimensional analysis of cylindrical microresonators based on the aperiodic Fourier modal method

We develop a 3D vectorial description of microresonators of the microdisk and microring types based on the aperiodic Fourier modal method. Such a rigorous coupled-wave analysis allows us to evaluate accurately the resonant wavelengths, the quality factor, and the full profile of whispering-gallery modes. The results are compared with 2D (effective index) as well as 3D finite-difference time domain calculations.

Rogue solitons in optical fibers: a dynamical process in a complex energy landscape?

Nondeterministic giant waves, denoted as rogue, killer, monster, or freak waves, have been reported in many different branches of physics. Their physical interpretation is however still debated: despite massive numerical and experimental evidence, a solid explanation for their spontaneous formation has not been identified yet. Here we propose that rogue waves [more precisely, rogue solitons (RSs)] in optical fibers may actually result from a complex dynamical process very similar to well-known mechanisms such as glass transitions and protein folding. We describe how the interaction among optical solitons produces an energy landscape in a highly dimensional parameter space with multiple quasi-equilibrium points. These configurations have the same statistical distribution of the observed rogue events and are explored during the light dynamics due to soliton collisions, with inelastic mechanisms enhancing the process. Slightly different initial conditions lead to very different dynamics in this complex geometry; a RS turns out to stem from one particularly deep quasi-equilibrium point of the energy landscape in which the system may be transiently trapped during evolution. This explanation will prove to be fruitful to the vast community interested in freak waves.

Suppression and splitting of modulational instability sidebands in periodically tapered optical fibers because of fourth-order dispersion

We study the modulational instability induced by periodic variations of group-velocity dispersion in the proximity of the zero dispersion point. Multiple instability peaks originating from parametric resonance coexist with the conventional modulation instability because of fourth-order dispersion, which in turn is suppressed by the oscillations of dispersion. Moreover, isolated unstable regions appear in the space of parameters because of imperfect phase matching. This confirms the dramatic effect of periodic tapering in the control and shaping of MI sidebands in optical fibers.

Vector modulational instability induced by parametric resonance in periodically tapered highly birefringent optical fibers

We study the modulational instability induced by periodic variations of group-velocity dispersion and nonlinear coefficients in a highly birefringent fiber. We observe, for each resonance order, the presence of two pairs of genuine vector-type sidebands, which are spectrally unbalanced between the polarization components for nonzero group-index mismatch, and one pair of balanced sidebands emerging and dominating at increasing group-index mismatch. As the conventional modulational instability manifests itself, it is partially suppressed by the proximity of these additional unstable regions.

Raman-induced temporal condensed matter physics in gas-filled photonic crystal fibers.

Raman effect in gases can generate an extremely long-living wave of coherence that can lead to the establishment of an almost perfect temporal periodic variation of the medium refractive index. We show theoretically and numerically that the equations, regulate the pulse propagation in hollow-core photonic crystal fibers filled by Raman-active gas, are exactly identical to a classical problem in quantum condensed matter physics - but with the role of space and time reversed - namely an electron in a periodic potential subject to a constant electric field. We are therefore able to infer the existence of Wannier-Stark ladders, Bloch oscillations, and Zener tunneling, phenomena that are normally associated with condensed matter physics, using purely optical means.

Collective modulation instability of multiple four-wave mixing.

We investigate the modulation instability of multiple four-wave mixing arising from a dual-frequency pump in a single-mode fiber or waveguide. By applying the Floquet theory on account of the periodic nature of four-wave mixing, we reveal a collective type of instability occurring in the anomalous dispersion regime. Our interpretation of the linear stability analysis is validated by the numerical solution of the nonlinear Schrödinger equation.

Comparative Analysis of a Planar Slotted Microdisk Resonator

We analyze a microdisk resonator of sub-micrometer radius where confinement is obtained in a vertical sandwich characterized by a central slot of lower refractive index material. The properties of the antiguiding even modes characterized by TM fields peaked in the slot are analyzed with specific reference to the resonant wavelengths, the quality factor, the mode confinement properties, and the Purcell factor. It is shown, by means of a comparative analysis, that, for a small disk radius a full vectorial approach is required in order to properly account for the hybrid nature of the modes. This reflects on the dependence of such figures of merit upon geometrical parameters of the structure.