79 research outputs found
The anisotropic Kerr nonlinear refractive index of the beta-barium borate (\beta-BaB2O4) nonlinear crystal
We study the anisotropic nature of the Kerr nonlinear response in a
beta-barium borate (\beta-BaB2O4, BBO) nonlinear crystal. The focus is on
determining the relevant cubic tensor components that affect
interaction of type I cascaded second-harmonic generation. Various experiments
in the literature are analyzed and we correct the data from some of the
experiments for contributions from cascading as well as for updated material
parameters. We find that the Kerr nonlinear tensor component responsible for
self-phase modulation in cascading is considerably larger than what has been
used to date. We evaluate the impact of using such a cubic anisotropic response
in ultrafast cascading experiments.Comment: Updated version, comments on experiments from the literature welcom
Breathing dissipative solitons in optical microresonators
Dissipative solitons are self-localized structures resulting from a double
balance between dispersion and nonlinearity as well as dissipation and a
driving force. They occur in a wide variety of fields ranging from optics,
hydrodynamics to chemistry and biology. Recently, significant interest has
focused on their temporal realization in driven optical microresonators, known
as dissipative Kerr solitons. They provide access to coherent, chip-scale
optical frequency combs, which have already been employed in optical metrology,
data communication and spectroscopy. Such Kerr resonator systems can exhibit
numerous localized intracavity patterns and provide rich insights into
nonlinear dynamics. A particular class of solutions consists of breathing
dissipative solitons, representing pulses with oscillating amplitude and
duration, for which no comprehensive understanding has been presented to date.
Here, we observe and study single and multiple breathing dissipative solitons
in two different microresonator platforms: crystalline
resonator and integrated microring. We report a
deterministic route to access the breathing state, which allowed for a detailed
exploration of the breathing dynamics. In particular, we establish the link
between the breathing frequency and two system control parameters - effective
pump laser detuning and pump power. Using a fast detection, we present a direct
observation of the spatiotemporal dynamics of individual solitons, revealing
irregular oscillations and switching. An understanding of breathing solitons is
not only of fundamental interest concerning nonlinear systems close to critical
transition, but also relevant for applications to prevent breather-induced
instabilities in soliton-based frequency combs.Comment: 10 pages, 4 figure
Detuning-dependent Properties and Dispersion-induced Instabilities of Temporal Dissipative Kerr Solitons in Optical Microresonators
Temporal-dissipative Kerr solitons are self-localized light pulses sustained
in driven nonlinear optical resonators. Their realization in microresonators
has enabled compact sources of coherent optical frequency combs as well as the
study of dissipative solitons. A key parameter of their dynamics is the
effective-detuning of the pump laser to the thermally- and Kerr-shifted cavity
resonance. Together with the free spectral range and dispersion, it governs the
soliton-pulse duration, as predicted by an approximate analytical solution of
the Lugiato-Lefever equation. Yet, a precise experimental verification of this
relation was lacking so far. Here, by measuring and controlling the
effective-detuning, we establish a new way of stabilizing solitons in
microresonators and demonstrate that the measured relation linking soliton
width and detuning deviates by less than 1 % from the approximate expression,
validating its excellent predictive power. Furthermore, a detuning-dependent
enhancement of specific comb lines is revealed, due to linear couplings between
mode-families. They cause deviations from the predicted comb power evolution,
and induce a detuning-dependent soliton recoil that modifies the pulse
repetition-rate, explaining its unexpected dependence on laser-detuning.
Finally, we observe that detuning-dependent mode-crossings can destabilize the
soliton, leading to an unpredicted soliton breathing regime (oscillations of
the pulse) that occurs in a normally-stable regime. Our results test the
approximate analytical solutions with an unprecedented degree of accuracy and
provide new insights into dissipative-soliton dynamics.Comment: Updated funding acknowledgement
Generalized Nonlinear Wave Equation in Frequency Domain
We interpret the forward Maxwell equation with up to third order induced
polarizations and get so called nonlinear wave equation in frequency domain
(NWEF), which is based on Maxwell wave equation and using slowly varying
spectral amplitude approximation. The NWEF is generalized in concept as it
directly describes the electric field dynamics rather than the envelope
dynamics and because it concludes most current-interested nonlinear processes
such as three-wave mixing, four-wave-mixing and material Raman effects. We give
two sets of NWEF, one is a 1+1D equation describing the (approximated) planar
wave propagation in nonlinear bulk material and the other corresponds to the
propagation in a waveguide structure.Comment: Equation Derivation
Soliton-induced nonlocal resonances observed through high-intensity tunable spectrally compressed second-harmonic peaks
Experimental data of femtosecond thick-crystal second-harmonic generation
shows that when tuning away from phase matching, a dominating narrow spectral
peak appears in the second harmonic that can be tuned over 100's of nm by
changing the phase-mismatch parameter. Traditional theory explains this as
phase matching between a sideband in the broadband pump to its second-harmonic.
However, our experiment is conducted under high input intensities and instead
shows excellent quantitative agreement with a nonlocal theory describing
cascaded quadratic nonlinearities. This theory explains the detuned peak as a
nonlocal resonance that arises due to phase-matching between the pump and a
detuned second-harmonic frequency, but where in contrast to the traditional
theory the pump is assumed dispersion-free. As a soliton is inherently
dispersion-free, the agreement between our experiment and the nonlocal theory
indirectly proves that we have observed a soliton-induced nonlocal resonance.
The soliton exists in the self-defocusing regime of the cascaded nonlinear
interaction and in the normal dispersion regime of the crystal, and needs high
input intensities to become excited.Comment: submitted, revised versio
Soliton compression to few-cycle pulses with a high quality factor by engineering cascaded quadratic nonlinearities
We propose an efficient approach to improve few-cycle soliton compression
with cascaded quadratic nonlinearities by using an engineered multi-section
structure of the nonlinear crystal. By exploiting engineering of the cascaded
quadratic nonlinearities, in each section soliton compression with a low
effective order is realized, and high-quality few-cycle pulses with large
compression factors are feasible. Each subsequent section is designed so that
the compressed pulse exiting the previous section experiences an overall
effective self-defocusing cubic nonlinearity corresponding to a modest soliton
order, which is kept larger than unity to ensure further compression. This is
done by increasing the cascaded quadratic nonlinearity in the new section with
an engineered reduced residual phase mismatch. The low soliton orders in each
section ensure excellent pulse quality and high efficiency. Numerical results
show that compressed pulses with less than three-cycle duration can be achieved
even when the compression factor is very large, and in contrast to standard
soliton compression, these compressed pulses have minimal pedestal and high
quality factor
Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media
We interpret the purely spectral forward Maxwell equation with up to 3 order induced polarizations for pulse propagation and interactions in
quadratic nonlinear crystals. The interpreted equation, also named nonlinear
wave equation in frequency domain, includes both quadratic and cubic
nonlinearities, delayed Raman effects and anisotropic nonlinearities. The full
potential of this wave equation is demonstrated by investigating simulations of
solitons generated in the process of ultrafast cascaded second-harmonic
generation. We show that a balance in the soliton delay can be achieved due to
competition between self-steepening, Raman effects and self-steepening-like
effects from cascading originating in the group-velocity mismatch between the
pump and second harmonic. We analyze the first-order contributions, and show
that this balance can be broken to create fast or slow pulses. Through further
simulations we demonstrate few-cycle compressed solitons in extremely short
crystals, where spectral phenomena such as blue/red shifting, non-stationary
radiation in accordance with the non-local phase matching condition and
dispersive-wave generation are observed and marked, which help improving the
experimental knowledge of cascading nonlinear soliton pulse compression
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