107 research outputs found
On the statistical interpretation of optical rogue waves
Numerical simulations are used to discuss various aspects of "optical rogue
wave" statistics observed in noise-driven fiber supercontinuum generation
associated with highly incoherent spectra. In particular, we consider how long
wavelength spectral filtering influences the characteristics of the statistical
distribution of peak power, and we contrast the statistics of the spectrally
filtered SC with the statistics of both the peak power of the most red-shifted
soliton in the SC and the maximum peak power across the full temporal field
with no spectral selection. For the latter case, we show that the unfiltered
statistical distribution can still exhibit a long-tail, but the extreme-events
in this case correspond to collisions between solitons of different
frequencies. These results confirm the importance of collision dynamics in
supercontinuum generation. We also show that the collision-induced events
satisfy an extended hydrodynamic definition of "rogue wave" characteristics.Comment: Paper accepted for publication in the European Physical Journal ST,
Special Topics. Discussion and Debate: Rogue Waves - towards a unifying
concept? To appear 201
Nonlinear optics of fibre event horizons
The nonlinear interaction of light in an optical fibre can mimic the physics
at an event horizon. This analogue arises when a weak probe wave is unable to
pass through an intense soliton, despite propagating at a different velocity.
To date, these dynamics have been described in the time domain in terms of a
soliton-induced refractive index barrier that modifies the velocity of the
probe. Here, we complete the physical description of fibre-optic event horizons
by presenting a full frequency-domain description in terms of cascaded
four-wave mixing between discrete single-frequency fields, and experimentally
demonstrate signature frequency shifts using continuous wave lasers. Our
description is confirmed by the remarkable agreement with experiments performed
in the continuum limit, reached using ultrafast lasers. We anticipate that
clarifying the description of fibre event horizons will significantly impact on
the description of horizon dynamics and soliton interactions in photonics and
other systems.Comment: 7 pages, 5 figure
Theory of quadratic optical frequency combs
We present theoretical studies of optical frequency comb generation in dispersive quadratically nonlinear resonators. We introduce a mean field equation approach to model cavity enhanced second harmonic generation and find excellent agreement with recent experimental frequency comb observations. We also develop a more general approach based on a single envelope equation for both quadratic and Kerr nonlinear cavities
Singly resonant second-harmonic-generation frequency combs
We consider frequency comb generation in dispersive singly resonant second-harmonic-generation cavity
systems. Using a single temporal mean-field equation for the fundamental field that features a noninstantaneous
nonlinear response function, we model the temporal and spectral dynamics and analyze comb generation,
continuous wave bistability, and modulational instability. It is found that, owing to the significant temporal
walk-off between the fundamental and second-harmonic fields, modulational instability can occur even in the
complete absence of group-velocity dispersion. We further consider the relation of our model to a previously
proposed modal expansion approach, and present a derivation of a general system of coupled mode equations.
We show that the two models provide very similar predictions and become exactly equivalent in the limit that
absorption losses and group-velocity dispersion at the fundamental frequency are neglected. Finally, we perform
numerical simulations that show examples of the variety of comb states that are possible in phase-matched
quadratic resonators, and discuss the dynamics of the comb formation process
Nonlinear dynamics of optical frequency combs
We discuss recent advances in the modelling of optical frequency comb generation in quadratic and cubic microresonators.
Dierent time domain models are presented and compared, and their solutions are analysed by
numerical methods
Quadratic optical frequency combs: Towards a new platform for multi-octave microcombs
Optical frequency comb sources based on three-wave-mixing in quadratic nonlinear materials allow for reduced pump power threshold and extended spectral coverage. We review recent progress on quadratic optical frequency combs based on second-harmonic generation and optical parametric oscillation
Frequency comb generation in continuously pumped optical parametric oscillator
We demonstrate and theoretically explain optical frequency comb generation in a cw-pumped, doubly resonant optical parametric oscillator. Numerical simulations are in pretty good agreement with the observed comb patterns
Rogue wave generation by inelastic quasi-soliton collisions in optical fibres
Optical “rogue” waves are rare and very high intensity pulses of light that occur in optical devices such as communication fibers. They appear suddenly and can cause transmission errors and damage in optical communication systems. Indeed, the physics governing their dynamics is very similar to “monster” or “freak” waves on the Earth’s oceans, which are known to harm shipping. It is therefore important to characterize rogue wave generation, dynamics and, if possible, predictability. Here we demonstrate a simple cascade mechanism that drives the formation and emergence of rogue waves in the generalized non-linear Schrödinger equation with third-order dispersion. This generation mechanism is based on inelastic collisions of quasi-solitons and is well described by a resonant-like scattering behaviour for the energy transfer in pair-wise quasi-soliton collisions. Our theoretical and numerical results demonstrate a threshold for rogue wave emergence and the existence of a period of reduced amplitudes — a “calm before the storm” — preceding the arrival of a rogue wave event. Comparing with ultra-long time window simulations of 3.865 × 106ps we observe the statistics of rogue waves in optical fibres with an unprecedented level of detail and accuracy, unambiguously establishing the long-ranged character of the rogue wave power-distribution function over seven orders of magnitude
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