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A spectral method for determining the stability of periodically stationary pulses in fiber lasers is introduced. Pulse stability is characterized in terms of the spectrum (eigenvalues) of the monodromy operator, which is the linearization of the round trip operator about a periodically stationary pulse. A formula for the continuous (essential) spectrum of the monodromy operator is presented, which quantifies the growth and decay of continuous waves far from the pulse. The formula is verified by comparison with a fully numeric method for an experimental fiber laser. Finally, the effect of a saturable absorber on pulse stability is demonstrated.

A detailed investigation of the influence of quartz tuning forks (QTFs) resonance properties on the performance of quartz-enhanced photoacoustic spectroscopy (QEPAS) exploiting QTFs as acousto-electric transducers is reported. The performance of two commercial QTFs with the same resonance frequency (32.7 KHz) but different geometries and two custom QTFs with lower resonance frequencies (2.9 KHz and 7.2 KHz) were compared and discussed. The results demonstrated that the fundamental resonance frequency as well as the quality factor and the electrical resistance were strongly inter-dependent on the QTF prongs geometry. Even if the resonance frequency was reduced, the quality factor must be kept as high as possible and the electrical resistance as low as possible in order to guarantee high QEPAS performance.

We describe a new class of surface flows, diffeomorphic surface flows, induced by restricting diffeomorphic flows of the ambient Euclidean space to a surface. Different from classical surface PDE flows such as mean curvature flow, diffeomorphic surface flows are solutions of integro-differential equations in a group of diffeomorphisms. They have the potential advantage of being both topology-invariant and singularity free, which can be useful in computational anatomy and computer graphics. We first derive the Euler-Lagrange equation of the elastic energy for general diffeomorphic surface flows, which can be regarded as a smoothed version of the corresponding classical surface flows. Then we focus on diffeomorphic mean curvature flow. We prove the short-time existence and uniqueness of the flow, and study the long-time existence of the flow for surfaces of revolution. We present numerical experiments on synthetic and cortical surfaces from neuroimaging studies in schizophrenia and auditory disorders. Finally we discuss unresolved issues and potential applications.

We calculate the time shift function for collisions of pairs of pulses in different channels in a prototypical return-to-zero wavelength-division-multiplexed system with dispersion management and precompensation and postcompensation. Once the time shift function is known, the impairments that are due to collision-induced timing jitter can be rapidly determined. We characterize the shape of this function and determine how it scales with the initial pulse separation in time and with channel separation in wavelength. Finally, we apply it to the calculation of the worst-case time shift.

We describe a neural network that enhances and completes salient closed contours in images. Our work is different from all previous work in three important ways. First, like the input provided to primary visual cortex (V1) by the lateral geniculate nucleus (LGN), the input to our computation is isotropic. That is, it is composed of spots, not edges. Second, our network computes a well-defined function of the input based on a distribution of closed contours characterized by a random process. Third, even though our computation is implemented in a discrete network, its output is invariant to continuous rotations and translations of the input image.

We study four-wave mixing between pulses in two subchannels of a quasi-linear 40-Gbit/s subchannel-multiplexed system. For a pseudorandom bit string there are resonances in the mean of the ghost pulse energy and in the jitter of the energy in the marks as functions of the subchannel frequency spacing. However, away from these resonances the effect of four-wave mixing decreases as the subchannel spacing increases, permitting propagation over longer distances.