Abstract
We examine the steady state and dynamic behaviour of an optical resonator comprised of two interlinked fibre loops sharing a common pump. A coupled Ikeda map models with great accuracy the field evolution within and exchange between both fibres over a single roundtrip. We find this supports a range of rich multi-dimensional bistability in the continuous wave regime, as well as previously unseen cavity soliton states. Floquet analysis reveals that modulation and parametric instabilities occur over wider domains than in single-fibre resonators, which can be tailored by controlling the relative dispersion and resonance frequencies of the two fibre loops. Parametric instability gives birth to train of pulses with a peculiar period-doubling behavior.
Highlights
Optical resonators are complex physical platforms, exhibiting an even richer range of phenomena than single-pass nonlinear systems due to their driven-dissipative nature
Floquet analysis reveals that modulation and parametric instabilities occur over wider domains than in single-fiber resonators, which can be tailored by controlling the relative dispersion and resonance frequencies of the two fiber loops
Nonlinear optical resonators can be precisely modelled by the so-called Ikeda map [12,13], which describes separately the evolution of the electric field as it propagates through the cavity, and the boundary conditions which account for the injection of pump light and transmission of the cavity field between each round trip
Summary
Optical resonators are complex physical platforms, exhibiting an even richer range of phenomena than single-pass nonlinear systems due to their driven-dissipative nature. Cavity solitons may be generated with great efficiency in one fiber loop by weakly coupling to a much shorter loop driven with a constant pump field. While their extended mean-field model could be applied to the Möbius resonator, we choose to study the full Ikeda map as we work with a wide variety of conditions often far from resonances. First we examine steady states in the continuous-wave (time independent) limit, where the field in either fiber is independent of both the round trip number n and the intracavity time coordinate t This reveals an extended set of solutions exhibiting bistability, whose symmetry depends on the relative detuning of the two fiber loops. We derive the modulation instability (MI) spectrum by applying Flo-
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