Search results for "Dispersion."
showing 10 items of 1094 documents
Covering by discrete and closed discrete sets.
2008
Say that a cardinal number $\kappa$ is \emph{small} relative to the space $X$ if $\kappa <\Delta(X)$, where $\Delta(X)$ is the least cardinality of a non-empty open set in $X$. We prove that no Baire metric space can be covered by a small number of discrete sets, and give some generalizations. We show a ZFC example of a regular Baire $\sigma$-space and a consistent example of a normal Baire Moore space which can be covered by a small number of discrete sets. We finish with some remarks on linearly ordered spaces.
Interaction between optical parabolic pulses in a Raman fiber amplifier
2009
We investigate the interaction between optical parabolic pulses in a Raman fiber amplifier. Self-similar amplification of two identical time-delayed pulses creates an oscillation which further evolves into a train of dark solitons through the combined effects of non-linearity, normal dispersion and adiabatic Raman gain. Theoretical predictions are in good agreement with experimental results.
Differential toolbox to shape dispersion behavior in photonic crystal fibers.
2006
We present an analytical procedure to compute the first derivatives of the propagation constants with respect to several structural parameters in photonic crystal fibers (PCFs). From them we can easily evaluate the same derivatives of other directly related magnitudes. The above derivatives provide the trend of the magnitude at issue, which allows us to take advantage of a gradient-based algorithm to shape the properties of the guiding structure. In this way we implement an optimization process to carry out real inverse design in PCFs. We focus our attention on designing PCFs with a specific chromatic dispersion behavior. Likewise, the same approach makes it possible to analyze their fabric…
Transmission performance ofN×160 Gbit s−1densely dispersion-managed optical fibre systems
2005
We carefully analyse the feasibility of N × 160 Gbit s−1 ultra-long haul transmissions in densely dispersion-managed (DDM) fibre systems. By using a novel analytical approach, we design highly optimized configurations of DDM fibre systems. Transmission performances of the analytically designed DDM fibre systems are evaluated using numerical simulations. We show that single-channel transoceanic transmissions at 160 Gbit s−1 may be achievable in DDM fibre systems, whereas multi-channel transmissions result in dramatically poor performances.
Modulational instability in optical fibers with arbitrary higher-order dispersion and delayed Raman response
2006
International audience; We analyse modulational instability (MI) of electromagnetic waves in a large variety of optical fibers having different refractive-index profiles. For the normal-, anomalous-, and zero-dispersion regimes of the wave propagation, we show that whenever the second-order dispersion competes with higher-order dispersion (HOD), propagation of plane waves leads to a rich variety of dynamical behaviors. Most of the richness comes from the existence of critical behaviors, which include situations in which the HOD suppresses MI in the anomalous dispersion regime, and other situations in which the HOD acts in the opposite way by inducing non-conventional MI processes in the nor…
Generalized modulational instability in multimode fibers: Wideband multimode parametric amplification
2015
In this paper intermodal modulational instability (IM-MI) is analyzed in a multimode fiber where several spatial and polarization modes propagate. The coupled nonlinear Schr\"odinger equations describing the modal evolution in the fiber are linearized and reduced to an eigenvalue problem. As a result, the amplification of each mode can be described by means of the eigenvalues and eigenvectors of a matrix that stores the information about the dispersion properties of the modes and the modal power distribution of the pump. Some useful analytical formulas are also provided that estimate the modal amplification as function of the system parameters. Finally, the impact of third-order dispersion …
Broadband dispersion compensation using inner cladding modes in photonic crystal fibers.
2012
A photonic crystal fiber is optimized for chromatic dispersion compensation by using inner cladding modes. To this end, a photonic-oriented version of the downhill-simplex algorithm is employed. The numerical results show a dispersion profile that accurately compensates the targeted dispersion curve, as well as its dispersion slope. The presented fiber has a simple structure, while radiation losses can be reduced simply by adding a few more air-hole rings. Fabrication tolerances are also considered showing how fabrication inaccuracies effects can be overridden by just adjusting the compensation length.
Acousto-optic interaction in biconical tapered fibers: shaping of the stopbands
2016
The effect of a gradual reduction of the fiber diameter on the acousto-optic (AO) interaction is reported. The experimental and theoretical study of the intermodal coupling induced by a flexural acoustic wave in a biconical tapered fiber shows that it is possible to shape the transmission spectrum, for example, substantially broadening the bandwidth of the resonant couplings. The geometry of the taper transitions can be regarded as an extra degree of freedom to design the AO devices. Optical bandwidths above 45 nm are reported in a tapered fiber with a gradual reduction of the fiber down to 70 μm diameter. The effect of including long taper transition is also reported in a double-tapered st…
Effect of wavelength dependence of nonlinearity, gain, and dispersion in photonic crystal fiber amplifiers
2005
Photonic crystal fibers are used in fiber amplifiers and lasers because of the flexibility in the design of mode area and dispersion. However, these quantities depend strongly on the wavelength. The wavelength dependence of gain, nonlinearity and dispersion are investigated here by including the wavelength dependence explicitly in the nonlinear Schr\"odinger equation for photonic crystal fibers with varying periods and hole sizes. The effect of the wavelength dependence of each parameter is studied separately as well as combined. The wavelength dependence of the parameters is shown to create asymmetry to the spectrum and chirp, but to have a moderating effect on pulse broadening. The effect…
phase-locked soliton pairs in a fiber ring laser
2002
We have experimentally observed the formation of stable pulse pairs with a π/2 phase difference in a passively mode-locked stretched-pulse fiber ring laser. We have developed a simplified theoretical model that, keeping the essential features of the experiment, reduces greatly the number of free parameters and solved it numerically. The agreement with the experimental results is excellent.