39,902 research outputs found
Exploring, tailoring, and traversing the solution landscape of a phase-shaped CARS process
Pulse shaping techniques are used to improve the selectivity of broadband CARS experiments, and to reject the overwhelming background. Knowledge about the fitness landscape and the capability of tailoring it is crucial for both fundamental insight and performing an efficient optimization of phase shapes. We use an evolutionary algorithm to find the optimal spectral phase of the broadband pump and probe beams in a background-suppressed shaped CARS process. We then investigate the shapes, symmetries, and topologies of the landscape contour lines around the optimal solution and also around the point corresponding to zero phase. We demonstrate the significance of the employed phase bases in achieving convex contour lines, suppressed local optima, and high optimization fitness with a few (and even a single) optimization parameter
Accelerated graph-based spectral polynomial filters
Graph-based spectral denoising is a low-pass filtering using the
eigendecomposition of the graph Laplacian matrix of a noisy signal. Polynomial
filtering avoids costly computation of the eigendecomposition by projections
onto suitable Krylov subspaces. Polynomial filters can be based, e.g., on the
bilateral and guided filters. We propose constructing accelerated polynomial
filters by running flexible Krylov subspace based linear and eigenvalue solvers
such as the Block Locally Optimal Preconditioned Conjugate Gradient (LOBPCG)
method.Comment: 6 pages, 6 figures. Accepted to the 2015 IEEE International Workshop
on Machine Learning for Signal Processin
Fourier Based Fast Multipole Method for the Helmholtz Equation
The fast multipole method (FMM) has had great success in reducing the
computational complexity of solving the boundary integral form of the Helmholtz
equation. We present a formulation of the Helmholtz FMM that uses Fourier basis
functions rather than spherical harmonics. By modifying the transfer function
in the precomputation stage of the FMM, time-critical stages of the algorithm
are accelerated by causing the interpolation operators to become
straightforward applications of fast Fourier transforms, retaining the
diagonality of the transfer function, and providing a simplified error
analysis. Using Fourier analysis, constructive algorithms are derived to a
priori determine an integration quadrature for a given error tolerance. Sharp
error bounds are derived and verified numerically. Various optimizations are
considered to reduce the number of quadrature points and reduce the cost of
computing the transfer function.Comment: 24 pages, 13 figure
Tailoring a coherent control solution landscape by linear transforms of spectral phase basis
Finding an optimal phase pattern in a multidimensional solution landscape becomes easier and faster if local optima are suppressed and contour lines are tailored towards closed convex patterns. Using wideband second harmonic generation as a coherent control test case, we show that a linear combination of spectral phase basis functions can result in such improvements and also in separable phase terms, each of which can be found independently. The improved shapes are attributed to a suppressed nonlinear shear, changing the relative orientation of contour lines. The first order approximation of the process shows a simple relation between input and output phase profiles, useful for pulse shaping at ultraviolet wavelengths
Applications of the wave packet method to resonant transmission and reflection gratings
Scattering of femtosecond laser pulses on resonant transmission and
reflection gratings made of dispersive (Drude metals) and dielectric materials
is studied by a time-domain numerical algorithm for Maxwell's theory of linear
passive (dispersive and absorbing) media. The algorithm is based on the
Hamiltonian formalism in the framework of which Maxwell's equations for passive
media are shown to be equivalent to the first-order equation, , where is a linear differential
operator (Hamiltonian) acting on a multi-dimensional vector built of the
electromagnetic inductions and auxiliary matter fields describing the medium
response. The initial value problem is then solved by means of a modified time
leapfrog method in combination with the Fourier pseudospectral method applied
on a non-uniform grid that is constructed by a change of variables and designed
to enhance the sampling efficiency near medium interfaces. The algorithm is
shown to be highly accurate at relatively low computational costs. An excellent
agreement with previous theoretical and experimental studies of the gratings is
demonstrated by numerical simulations using our algorithm. In addition, our
algorithm allows one to see real time dynamics of long leaving resonant
excitations of electromagnetic fields in the gratings in the entire frequency
range of the initial wide band wave packet as well as formation of the
reflected and transmitted wave fronts.Comment: 23 pages; 8 figures in the png forma
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