A note on the finite fractal dimension of the global attractors for dissipative nonlinear Schrödinger‐type equations

In this article, we present, throughout two basic models of damped nonlinear Schrödinger (NLS)–type equations, a new idea to bound from above the fractal dimension of the global attractors for NLS‐type equations. This could answer the following open issue: consider, for instance, the classical one‐dimensional cubic nonlinear Schrödinger equation $$u_t+i{u}_{xx}+i|u{|}^{2}u+\gamma u=f,f\in {\mathrm{??}}^2(?).$$ “How can we bound the fractal dimension of the associate global attractor without the need to assume that the external forcing term f has some decay at infinity (that is belonging to some weighted Lebesgue space)?”     

Interaction of Fluorescently Labeled Triethyleneglycol and Peptide Derivatives with β‐Cyclodextrin

A triethyleneglycol (TEG) chain, a linear peptide, and a cyclic peptide labeled with 7‐methoxycoumarin‐3‐carboxylic acid (MC) and 7‐diethylaminocoumarin‐3‐carboxylic acid (DAC) were used to thoroughly study Förster resonance energy transfer (FRET) in inclusion complexes. ¹H NMR evidence was given for the formation of a 1:1 inclusion complex between β‐cyclodextrin (β‐CD) and the fluorophore moieties of model compounds. The binding constant was 20 times higher for DAC than for MC derivatives. Molecular modeling provided additional information. The UV/Vis absorption and fluorescence properties were studied and the energy transfer process was quantified. Fluorescence quenching was particularly strong for the peptide derivatives. The presence of β‐CDs reduced the FRET efficiency slightly. Dye‐labeled peptide derivatives can thus be used to form inclusion complexes with β‐CDs and retain most of their FRET properties. This paves the way for their subsequent use in analytical devices that are designed to measure the activity of matrix metalloproteinases.     

Self-mode-locked pulsed monomode laser

We predict the existence of a new pulsed-laser operation regime, when the phases and polarizations of the two coupled cold-cavity eigenstates of a monomode solid-state laser are taken into account in the derivation of the Maxwell-Bloch equations. This monomode pulsed regime is experimentally observed, without any normal mode locking or Q switching occurring inside the cavity. We obtain close agreement between experiments and theory, even in the simple case of a Nd:YAG microchip laser, for which sech(2) pulses at nearly megahertz repetition rates are readily observed.     

Precision of degree of polarization estimation in the presence of additive Gaussian detector noise

We address the problem of degree of polarization (DOP) estimation in images limited by additive Gaussian detector noise. We derive and analyze the probability density function (PDF) of the pixelwise DOP estimate, which is shown to have significantly different statistical properties than when noise is Gamma distributed (speckle). We then determine the Cramer-Rao Lower Bound and the maximum likelihood estimator of the DOP. We deduce from this study practical solutions for characterizing and reducing the noise in these images.     

Dual-frequency single-axis laser using a lead lanthanum zirconate tantalate (PLZT) birefringent etalon for millimeter wave generation: beyond the standard limit of tunability

We demonstrate the generation of optically carried, broadly tunable, millimeter-wave signals with a dual-frequency single-axis Nd:YAG laser. A frequency difference as high as 127 GHz is reached thanks to an intracavity electro-optically tunable etalon made of lead zirconate tantalate (PLZT) ceramic. We show that the available frequency range is actually limited by the bandwidth of the amplification medium, namely, far beyond the usually accepted free spectral range value in the case of a single-axis laser. Both coarse discrete and fine continuous tunabilities are obtained with the same voltage-controlled device, opening the way to widely tunable low-phase-noise optically carried submillimeter or even terahertz sources.     

Broad-bandwidth shot-noise-limited class-A operation of a monomode semiconductor fiber-based ring laser

We demonstrate the operation of a monomode semiconductor laser with a relative intensity noise limited by the shot-noise floor, -156 dB/Hz for a typical detected photocurrent of 1 mA, over a large frequency range from 50 MHz to 18 GHz. We achieve direct control of photon lifetime to turn an initially class-B laser into a relaxation-oscillation-free class-A one while preserving strict single-mode operation. Finally, we confirm experimentally that the laser operation in the desired class-A regime allows a dramatic filtering out of the relative intensity noise.     

Existence of two coupling constants in microchip lasers

We implemented two different experimental setups to probe directly the nonlinear coupling between modes in microchip lasers. We show that, remarkably, the results can be interpreted by use of Lamb's coupling constant. In an Er, Yb:glass microchip laser, we measured C(12) = 0.80 between longitudinal modes and C(xy) = 0.95 between orthogonally linearly polarized eigenstates. The high values obtained give some physical insight into the single-frequency operation of such lasers.     

Computational polarization imaging from a single speckle image

We experimentally demonstrate that imaging of the degree of polarization (DOP) can be achieved from a single intensity image acquired under coherent illumination. This computational technique is based on the analysis of the speckle characteristics in a statistically homogeneous neighborhood of the pixel. Over a variety of samples obtained experimentally, we show that a simple calibration step allows this method to quickly and simply provide correct estimated values of the DOP, with precision in agreement with theoretical predictions. It is shown that unlike linear polarimetric contrast imaging, this method remains valid on birefringent samples.     

Minimization of the influence of passive-light contribution in active imaging of the degree of polarization

Active imaging systems that measure the degree of polarization (DOP) are often perturbed by passive light owing to ambient illumination. Passive light introduces a shot noise that combines with the noise due to the active signal to perturb estimation of the DOP. We quantitatively study its influence and show that the polarization state of active illumination can be adjusted to minimize the influence of passive light. It is thus an additional degree of freedom for optimization.