Ultrashort pulse characterization with a terahertz streak camera

A phase-locked terahertz transient is exploited as an ultrafast phase gate for femtosecond optical pulses. We directly map out the group delay dispersion of a low-power near-infrared pulse by measuring the electro-optically induced polarization rotation as a function of wavelength. Our experiment covers the spectral window from 1.0 to 1.4 μm and reaches a temporal precision better than 1 fs. A quantitative analysis of the detector response confirms that this streaking technique requires no reconstruction algorithm and is also well suited for the characterization of pulses spanning more than one optical octave.     

Maassanalytische Bestimmung des Chroms

Ohne Zusammenfassung     

The spectrum of an invariant submanifold

This paper is concerned with vector fields on smooth compact manifolds. The exponential growth of solutions of the linearized equations is described by the already well-known Spectral Theorem applied to the induced linear flow on the tangent bundle. The spectrum of the tangent bundle flow is compared to the two secondary spectra obtained by first taking the spectrum of the bundle of tangent spaces to an invariant submanifold and second, the spectrum of an induced flow on an arbitrary complementary bundle to the latter. The relationship among the three spectra is studied and it is shown that whenever these secondary spectra are disjoint then an invariant complementary bundle can be found. The results have implications in the theory of perturbation of invariant manifolds. The problem is studied in the setting of skew-product dynamical systems and the results are applicable to block triangular systems of ordinary differential equations.     

Smoothness of spectral subbundles and reducibility of quasi-periodic linear differential systems

In this paper we study linear differential systems (1) $\text{x′ =}\text{A}\text{?}\text{(θ + ωt)x,}\text{where}\text{A}\text{?}\text{(θ)}\text{is an}\text{(n × n)}$ matrix-valued function defined on the k-torus T^k and (θ, t) → θ + ωt is a given irrational twist flow on T^k. First, we show that if A ? C^N(T^k), where N ? {0, 1, 2,…; ∞; ω}, then the spectral subbundles are of class C^N on T^k. Next we assume that à is sufficiently smooth on T^k and ω satisfies a suitable “small divisors” inequality. We show that if (1) satisfies the “full spectrum” assumption, then there is a quasi-periodic linear change of variables x = P(t)y that transforms (1) to a constant coefficient system y′ =By. Finally, we study the case where the matrix $\text{A}\text{?}\text{(θ + ωt)}$ in (1) is the Jacobian matrix of a nonlinear vector field $\text{?(x)}$ evaluated along a quasi-periodic solution x = φ(t) of (2) $\text{x′ = ?(x)}$. We give sufficient conditions in terms of smoothness and small divisors inequalities in order that there is a coordinate system (z, ?) defined in the vicinity of $\text{Ω = H(φ)}$, the hull of φ, so that the linearized system (1) can be represented in the form z′ = Dz, ?′ = ω, where D is a constant matrix. Our results represent substantial improvements over known methods because we do not require that à be “close to” a constant coefficient system.     

On the stability of hyperbolic attractors of systems of differential equations

We study small C¹-perturbations of systems of differential equations that have a weakly hyperbolic invariant set. We show that the weakly hyperbolic invariant set is stable even if the Lipschitz condition fails.     

A craft-project loudspeaker to serve as an educational demonstration

Moving-coil loudspeakers typify the interdisciplinary nature of acoustics: in order to reproduce sound, these devices employ principles of electricity, magnetism, mechanics, and acoustics. The widespread use of loudspeakers has made them a familiar and valuable opportunity to introduce students to acoustics. A low-cost loudspeaker project/demonstration is presented here that is built from scratch using common household items and craft supplies. A variety of educational topics may be illustrated with this device, making it appropriate for a wide range of academic levels.     

Temperature dependence of Rb 5P fine-structure transfer induced by 4He collisions

Employing ultrafast laser excitation and time-correlated single-photon counting, we have measured the fine-structure transfer between Rb 5P states induced by collisions with 4He buffer gas at temperatures up to 150 °C. The temperature dependence of the binary cross section agrees with earlier measurements. Our data show that the temperature dependence of the three-body rate is about the same as that of the binary rate. The three-body rate can be described as arising from the reduction of the rubidium fine-structure splitting due to nearby helium atoms.