40 GHz Mode-Locked Semiconductor Lasers: Theory, Simulations and Experiment

We study both theoretically and experimentally typical operation regimes of 40 GHz monolithic mode-locked lasers. The underlying Traveling Wave Equation model reveals quantitative agreement for characteristics of the fundamental mode-locking as pulse width and repetition frequency tuning, as well as qualitative agreement with the experiments for other dynamic regimes. Especially the appearance of stable harmonic mode-locking at 80 GHz has been predicted theoretically and confirmed by measurements. Furthermore, we derive and apply a simplified Delay-Differential-Equation model which guides us to a qualitative analysis of bifurcations responsible for the appearance and the breakup of different mode-locking regimes. Higher harmonics of mode-locking are predicted by this model as well.     

Generation of low-timing-jitter femtosecond pulse trains with 2 GHz repetition rate via external repetition rate multiplication

Generation of low-timing-jitter 150 fs pulse trains at 1560 nm with 2 GHz repetition rate is demonstrated by locking a 200 MHz fundamental polarization additive-pulse mode-locked erbium fiber laser to high-finesse external Fabry-Perot cavities. The timing jitter and relative intensity noise of the repetition-rate multiplied pulse train are investigated.     

Intermediate-temperature polymorphic phase transition in KH2PO4: A synchrotron X-ray diffraction study

We have used synchrotron X-ray diffraction to investigate the structural and chemical changes undergone by polycrystalline KH₂PO₄ (KDP) upon heating within the 30-250 °C temperature interval. Our data show evidence of a polymorphic transition at T∼190 °C from the room-temperature tetragonal KDP phase to a new intermediate-temperature monoclinic KDP modification (spacegroup P2₁/m and lattice parameters a=7.590, b=6.209, c=4.530 Å, and β=107.36°). The monoclinic RDP polymorph remains stable upon further heating to 235 °C, and is isomorphic to its RbH₂PO₄ and CsH₂PO₄ counterparts.     

The effect of signal duration on the underwater detection thresholds of a harbor porpoise (Phocoena phocoena) for single frequency-modulated tonal signals between 0.25 and 160 kHz

The underwater hearing sensitivity of a young male harbor porpoise for tonal signals of various signal durations was quantified by using a behavioral psychophysical technique. The animal was trained to respond only when it detected an acoustic signal. Fifty percent detection thresholds were obtained for tonal signals (15 frequencies between 0.25-160 kHz, durations 0.5-5000 ms depending on the frequency; 134 frequency-duration combinations in total). Detection thresholds were quantified by varying signal amplitude by the 1-up 1-down staircase method. The hearing thresholds increased when the signal duration fell below the time constant of integration. The time constants, derived from an exponential model of integration [Plomp and Bouman, J. Acoust. Soc. Am. 31, 749-758 (1959)], varied from 629 ms at 2 kHz to 39 ms at 64 kHz. The integration times of the porpoises were similar to those of other mammals including humans, even though the porpoise is a marine mammal and a hearing specialist. The results enable more accurate estimations of the distances at which porpoises can detect short-duration environmental tonal signals. The audiogram thresholds presented by Kastelein et al. [J. Acoust. Soc. Am. 112, 334-344 (2002)], after correction for the frequency bandwidth of the FM signals, are similar to the results of the present study for signals of 1500 ms duration. Harbor porpoise hearing is more sensitive between 2 and 10 kHz, and less sensitive above 10 kHz, than formerly believed.     

Fluorescence monitoring of microchip capillary electrophoresis separation with monolithically integrated waveguides

Using femtosecond laser writing, optical waveguides were monolithically integrated into a commercial microfluidic lab-on-a-chip device, with the waveguides intersecting a microfluidic channel. Continuous-wave laser excitation through these optical waveguides confines the excitation window to a width of 12 microm, enabling high-resolution monitoring of the passage of different types of fluorescent analytes when migrating and being separated in the microfluidic channel by microchip capillary electrophoresis. Furthermore, we demonstrate on-chip-integrated waveguide excitation and detection of a biologically relevant species, fluorescently labeled DNA molecules, during microchip capillary electrophoresis. Well-controlled plug formation as required for on-chip integrated capillary electrophoresis separation of DNA molecules, and the combination of waveguide excitation and a low limit of detection, will enable monitoring of extremely small quantities with high spatial resolution.     

Fusion of conventional ultrasound imaging and acousto-optic sensing by use of a standard pulsed-ultrasound scanner

Acousto-optic sensing (AOS) is a dual-wave sensing technique based on the ultrasound modulation of diffuse light in a turbid medium. We experimentally demonstrate the feasibility of combining AOS and conventional ultrasound imaging by use of a commercially available pulsed-ultrasound scanner coupled with a photorefractive crystal-based optical interferometry system. Optically absorbing targets embedded in highly diffusive phantoms (mus'= 10 cm(-1)) are imaged through a thickness of 27 mm with millimeter resolution. The acousto-optic images are intrinsically coregistered with the ultrasound images.     

The validity of nonlinear geometric optics for weak solutions of conservation laws

The method of weakly nonlinear geometric optics is one of the main formal perturbation techniques used in analyzing nonlinear wave motion for hyperbolic systems. The tacit assumption in using such perturbation methods is that the corresponding solutions of the hyperbolic system remain smooth; since shock waves typically form in such solutions, these assumptions are rarely satisfied in practice. Nevertheless, in a variety of applied contexts, these methods give qualitatively reliable answers for discontinuous weak solutions. Here we give a rigorous proof for the validity of nonlinear geometric optics for general weak solutions of systems of hyperbolic conservation laws in a single space variable. The methods of proof do not mimic the formal construction of weakly nonlinear asymptotics but instead rely on structural symmetries of the approximating equations, stability estimates for intermediate asymptotic times, and the rapid decay in variation of weak solutions for large asymptotic times.Partially supported by NSF Grant No. DMS-8301135Partially supported by NSF Grant No. MCS-81-02360 and ARO Grant No. 483964-25530     

The Hamiltonian structure of general relativistic perfect fluids

We show that the evolution equations for a perfect fluid coupled to general relativity in a general lapse and shift, are Hamiltonian relative to a certain Poisson structure. For the fluid variables, a Lie-Poisson structure associated to the dual of a semi-direct product Lie algebra is used, while the bracket for the gravitational variables has the usual canonical symplectic structure. The evolution is governed by a Hamiltonian which is equivalent to that obtained from a canonical analysis. The relationship of our Hamiltonian structure with other approaches in the literature, such as Clebsch potentials, Lagrangian to Eulerian transformations, and its use in clarifying linearization stability, are discussed.Research supported in part by NSF grant MCS 81-08814(A02)Research supported in part by NSF grant MCS 81-07086     

Mathematical properties of the vacuum polarization function

This paper is an investigation of certain mathematical properties of the vacuum polarization function (s). We show that (s) is a Herglotz function, has no complex zeroes, and belongs to the class of functions called typically real. In addition, we obtain upper bounds on the higher derivatives of (s), at s=0, given that we know the value of the first derivative at that point.Research supported in part by NASA Grant NSG-8035     

Determination of a double Lie groupoid by its core diagram

In a double groupoid S, we show that there is a canonical groupoid structure on the set of those squares of S for which the two source edges are identities; we call this the core groupoid of S. The target maps from the core groupoid to the groupoids of horizontal and vertical edges of S are now base-preserving morphisms whose kernels commute, and we call the diagram consisting of the core groupoid and these two morphisms the core diagram of S. If S is a double Lie groupoid, and each groupoid structure on S satisfies a natural double form of local triviality, we show that the core diagram determines S and, conversely, that a locally trivial double Lie groupoid may be constructed from an abstractly given core diagram satisfying some natural additional conditions.

In the algebraic case, the corresponding result includes the known equivalences between crossed modules, special double groupoids with special connection (Brown and Spencer), and cat¹-groups (Loday). These cases correspond to core diagrams for which both target morphisms are (compatibly) split surjections.