5,139 research outputs found
Solitons in quadratic nonlinear photonic crystals
We study solitons in one-dimensional quadratic nonlinear photonic crystals
with modulation of both the linear and nonlinear susceptibilities. We derive
averaged equations that include induced cubic nonlinearities and numerically
find previously unknown soliton families. The inclusion of the induced cubic
terms enables us to show that solitons still exist even when the effective
quadratic nonlinearity vanishes and conventional theory predicts that there can
be no soliton. We demonstrate that both bright and dark forms of these solitons
are stable under propagation.Comment: 4 pages with 6 figure
Accurate switching intensities and length scales in quasi-phase-matched materials
We consider unseeded Type I second-harmonic generation in quasi-phase-matched
(QPM) quadratic nonlinear materials and derive an accurate analytical
expression for the evolution of the average intensity. The intensity-dependent
nonlinear phase mismatch due to the QPM induced cubic nonlinearity is found.
The equivalent formula for the intensity for maximum conversion, the crossing
of which changes the nonlinear phase-shift of the fundamental over a period
abruptly by , corrects earlier estimates by more than a factor of 5. We
find the crystal lengths necessary to obtain an optimal flat phase versus
intensity response on either side of this separatrix intensity.Comment: 3 pages with 3 figure
The complete modulational instability gain spectrum of nonlinear QPM gratings
We consider plane waves propagating in quadratic nonlinear slab waveguides
with nonlinear quasi-phase-matching gratings. We predict analytically and
verify numerically the complete gain spectrum for transverse modulational
instability, including hitherto undescribed higher order gain bands.Comment: 4 pages, 3 figures expanded with more explanation and mathematical
detai
Nonlocal explanation of stationary and nonstationary regimes in cascaded soliton pulse compression
We study soliton pulse compression in materials with cascaded quadratic
nonlinearities, and show that the group-velocity mismatch creates two different
temporally nonlocal regimes. They correspond to what is known as the stationary
and nonstationary regimes. The theory accurately predicts the transition to the
stationary regime, where highly efficient pulse compression is possible.Comment: 3 pages, 2 figures, published verison in Optics Letters. Contains
revised equations, including an updated mode
Limits to compression with cascaded quadratic soliton compressors
We study cascaded quadratic soliton compressors and address the physical
mechanisms that limit the compression. A nonlocal model is derived, and the
nonlocal response is shown to have an additional oscillatory component in the
nonstationary regime when the group-velocity mismatch (GVM) is strong. This
inhibits efficient compression. Raman-like perturbations from the cascaded
nonlinearity, competing cubic nonlinearities, higher-order dispersion, and
soliton energy may also limit compression, and through realistic numerical
simulations we point out when each factor becomes important. We find that it is
theoretically possible to reach the single-cycle regime by compressing
high-energy fs pulses for wavelengths in a
-barium-borate crystal, and it requires that the system is in the
stationary regime, where the phase mismatch is large enough to overcome the
detrimental GVM effects. However, the simulations show that reaching
single-cycle duration is ultimately inhibited by competing cubic nonlinearities
as well as dispersive waves, that only show up when taking higher-order
dispersion into account.Comment: 16 pages, 5 figures, submitted to Optics Expres
Plane waves in periodic, quadratically nonlinear slab waveguides: stability and exact Fourier structure
We consider the propagation of broad optical beams through slab waveguides
with a purely quadratic nonlinearity and containing linear and nonlinear
long-period quasi-phase-matching gratings. An exact Floquet analysis on the
periodic, plane-wave solution shows that the periodicity can drastically alter
the growth rate of the modulational instability but that it never completely
removes the instability. The results are confirmed by direct numerical
simulation, as well as through a simpler, approximate theory for the averaged
fields that accurately predicts the low-frequency part of the spectrum.Comment: 10 Pages, 13 figures (some in two parts) new version has some typos
removed and extra references and explanation adde
On the best compact approximation problem for operators between Lp-spaces
AbstractWe construct (for 1 < p < 2) an operator from lp into Lp which has no nearest compact operator. We also give a sufficient condition for an operator from Lp into Lp (2 < p < â) to have a best compact approximant
- âŠ