3-4.5 μm continuously tunable single mode VECSEL

We present continuously tunable Vertical External Cavity Surface Emitting Lasers (VECSEL) in the mid-infrared. The structure based on IV-VI semiconductors is epitaxially grown on a Si-substrates. The VECSEL emit one single mode, which is mode hop-free tunable over 50-100nm around the center wavelength. In this work, two different devices are presented, emitting at 3.4μm and 3.9μm, respectively. The lasers operate near room temperature with thermoelectric stabilization. They are optically pumped, yielding an output power >10mWp. The axial symmetric emission beam has a half divergence angle of <3.3

5-μm vertical external-cavity surface-emitting laser (VECSEL) forspectroscopic applications

Mid-IR tunable VECSELs (Vertical External-Cavity Surface-Emitting Lasers) emitting at 4-7 μm wavelengths and suitable for spectroscopic sensing applications are described. They are realized with lead-chalcogenide (IV-VI) narrow band gap materials. The active part, a single 0.6-2-μm thick PbTe or PbSe gain layer, is grown onto an epitaxial Bragg mirror consisting of two or three Pb1−y EuyTe/BaF2 quarter-wavelength layer pairs. All layers are deposited by MBE in a single run employing a BaF2 or Si substrate, no further processing is needed. The cavity is completed with an external curved top mirror, which is again realized with an epitaxial Bragg structure. Pumping is performed optically with a 1.5-μm laser. Maximum output power for pulsed operation is currently up to >1 Wp at −173°C and >10 mW at 10°C. In continuous wave (CW) operation, 18 mW at 100 K are reached. Still higher operating temperatures and/or powers are expected with better heat-removal structures and better designs employing QW (Quantum-Wells). Advantages of mid-IR VECSELs compared to edge-emitting lasers are their very good beam quality (circular beam with 15 μm are accessible with Pb1−y XyZ (X=Sr, Eu, Sn, Z=Se, Te) and/or including Q

Appendix to "Approximating perpetuities"

An algorithm for perfect simulation from the unique solution of the distributional fixed point equation $Y=_d UY + U(1-U)$ is constructed, where $Y$ and $U$ are independent and $U$ is uniformly distributed on $[0,1]$. This distribution comes up as a limit distribution in the probabilistic analysis of the Quickselect algorithm. Our simulation algorithm is based on coupling from the past with a multigamma coupler. It has four lines of code

Multiphoton radiative recombination of electron assisted by laser field

In the presence of an intensive laser field the radiative recombination of the continuum electron into an atomic bound state generally is accompanied by absorption or emission of several laser quanta. The spectrum of emitted photons represents an equidistant pattern with the spacing equal to the laser frequency. The distribution of intensities in this spectrum is studied employing the Keldysh-type approximation, i.e. neglecting interaction of the impact electron with the atomic core in the initial continuum state. Within the adiabatic approximation the scale of emitted photon frequencies is subdivided into classically allowed and classically forbidden domains. The highest intensities correspond to emission frequencies close to the edges of classically allowed domain. The total cross section of electron recombination summed over all emitted photon channels exhibits negligible dependence on the laser field intensity.Comment: 14 pages, 5 figures (Figs.2-5 have "a" and "b" parts), Phys.Rev.A accepted for publication. Fig.2b is presented correctl

Almost uniform sampling via quantum walks

Many classical randomized algorithms (e.g., approximation algorithms for #P-complete problems) utilize the following random walk algorithm for {\em almost uniform sampling} from a state space $S$ of cardinality $N$: run a symmetric ergodic Markov chain $P$ on $S$ for long enough to obtain a random state from within $\epsilon$ total variation distance of the uniform distribution over $S$. The running time of this algorithm, the so-called {\em mixing time} of $P$, is $O(\delta^{-1} (\log N + \log \epsilon^{-1}))$, where $\delta$ is the spectral gap of $P$. We present a natural quantum version of this algorithm based on repeated measurements of the {\em quantum walk} $U_t = e^{-iPt}$. We show that it samples almost uniformly from $S$ with logarithmic dependence on $\epsilon^{-1}$ just as the classical walk $P$ does; previously, no such quantum walk algorithm was known. We then outline a framework for analyzing its running time and formulate two plausible conjectures which together would imply that it runs in time $O(\delta^{-1/2} \log N \log \epsilon^{-1})$ when $P$ is the standard transition matrix of a constant-degree graph. We prove each conjecture for a subclass of Cayley graphs.Comment: 13 pages; v2 added NSF grant info; v3 incorporated feedbac

Exact eigenvalue spectrum of a class of fractal scale-free networks

The eigenvalue spectrum of the transition matrix of a network encodes important information about its structural and dynamical properties. We study the transition matrix of a family of fractal scale-free networks and analytically determine all the eigenvalues and their degeneracies. We then use these eigenvalues to evaluate the closed-form solution to the eigentime for random walks on the networks under consideration. Through the connection between the spectrum of transition matrix and the number of spanning trees, we corroborate the obtained eigenvalues and their multiplicities.Comment: Definitive version accepted for publication in EPL (Europhysics Letters

Combinatorial Markov chains on linear extensions

We consider generalizations of Schuetzenberger's promotion operator on the set L of linear extensions of a finite poset of size n. This gives rise to a strongly connected graph on L. By assigning weights to the edges of the graph in two different ways, we study two Markov chains, both of which are irreducible. The stationary state of one gives rise to the uniform distribution, whereas the weights of the stationary state of the other has a nice product formula. This generalizes results by Hendricks on the Tsetlin library, which corresponds to the case when the poset is the anti-chain and hence L=S_n is the full symmetric group. We also provide explicit eigenvalues of the transition matrix in general when the poset is a rooted forest. This is shown by proving that the associated monoid is R-trivial and then using Steinberg's extension of Brown's theory for Markov chains on left regular bands to R-trivial monoids.Comment: 35 pages, more examples of promotion, rephrased the main theorems in terms of discrete time Markov chain

Role of electromagnetically induced transparency in resonant four-wave-mixing schemes.

Published versio

Exact field ionization rates in the barrier suppression-regime from numerical TDSE calculations

Numerically determined ionization rates for the field ionization of atomic hydrogen in strong and short laser pulses are presented. The laser pulse intensity reaches the so-called "barrier suppression ionization" regime where field ionization occurs within a few half laser cycles. Comparison of our numerical results with analytical theories frequently used shows poor agreement. An empirical formula for the "barrier suppression ionization"-rate is presented. This rate reproduces very well the course of the numerically determined ground state populations for laser pulses with different length, shape, amplitude, and frequency. Number(s): 32.80.RmComment: Enlarged and newly revised version, 22 pages (REVTeX) + 8 figures in ps-format, submitted for publication to Physical Review A, WWW: http://www.physik.tu-darmstadt.de/tqe

Boundary non-crossings of Brownian pillow

Let B_0(s,t) be a Brownian pillow with continuous sample paths, and let h,u:[0,1]^2\to R be two measurable functions. In this paper we derive upper and lower bounds for the boundary non-crossing probability \psi(u;h):=P{B_0(s,t)+h(s,t) \le u(s,t), \forall s,t\in [0,1]}. Further we investigate the asymptotic behaviour of $\psi(u;\gamma h)$ with $\gamma$ tending to infinity, and solve a related minimisation problem.Comment: 14 page