Theory of filter-induced modulation instability in driven passive optical resonators

Abstract

We present the theory of modulation instability induced by spectrally dependent losses (optical filters) in passive driven nonlinear fiber ring resonators. Starting from an Ikeda map description of the propagation equation and boundary conditions, we derive a mean-field model-a generalized Lugiato-Lefever equation-which reproduces with great accuracy the predictions of the map. The effects on instability gain and comb generation of the different control parameters such as dispersion, cavity detuning, filter spectral position, and bandwidth are discussed.

Amplifier enhanced gain-through-filtering instability in a hybrid Kerr cavity

“…are the group velocity dispersions, γ (1,2) are the Kerr nonlinearity coefficients, and g is the unsaturated amplifier gain. As the intracavity power is relatively low, saturation is ignored.…”

“…One sideband appears near the filter frequency, while the other symmetrically emerges in relation to the pump. 1,2 Nevertheless, the inherent constraint of a low Q-factor in fiber cavities restricts the maximum achievable number of OFC lines. Inspired by recent progress in hybrid active-passive cavities, 3,4 we show a notable improvement in the efficiency of the GTF process by integrating an intracavity Erbium-doped fiber (EDF) amplifier.…”

Double-frequency-comb-like source with PM passive fibre cavity and Gain Through Filtering

“…Within the right conditions, this allows the destabilization of Modulation Instability (MI) bands at frequencies which depends on the Bragg wavelength of the filter. This process is known as Gain Through Filtering [3], and it's basically an additional degree of freedom for MI in fibre cavity. In this work, we exploit this degree of freedom for generate spectra with slightly different FSR in the two polarizations axis, creating a double-frequency-comb-like source.…”

“…In the latter case, several advantages are obtainable with a technique known as double-frequency-comb spectroscopy [2], which imply the use of two coherent frequency combs. In this work we propose a theoretical study which illustrate the formation of a double-frequency-comb-like spectrum in a single PM cavity, by exploiting a phenomenon called GTF [3]. Even if a fibre cavity does not reach the number of spectral lines of an OFC, this work is a valid physical study of the phenomenon, which can be scaled down to sizes and performances typical of micro-cavities.…”

Occurrence of gradual resonance in a finite-length granular chain driven by harmonic vibration

“…Many unique characteristics, including localized solitary wave, shock energy trapping, and wave filtering have been revealed [3][4][5][6]. Similar phenomena in many physical settings, including nonlinear optics, and ordered crystal arrays, have also been attracted extensively research attention [7][8][9][10][11][12][13][14]. Hence, further understanding the physical mechanisms of an aligned grains for controlling energy propagation, localization, and resonance could lead to new mechanical filtering and protective devices.…”