337 research outputs found
Reducing the linewidth of a diode laser below 30 Hz by stabilization to a reference cavity with finesse above 10^5
An extended cavity diode laser operating in the Littrow configuration
emitting near 657 nm is stabilized via its injection current to a reference
cavity with a finesse of more than 10^5 and a corresponding resonance linewidth
of 14 kHz. The laser linewidth is reduced from a few MHz to a value below 30
Hz. The compact and robust setup appears ideal for a portable optical frequency
standard using the Calcium intercombination line.Comment: 8 pages, 4 figures on 3 additional pages, corrected version,
submitted to Optics Letter
First Steps into Practical Engineering for Freshman Students Using MATLAB and LEGO Mindstorms Robots
Besides lectures on basic theoretical topics, contemporary teaching and learning concepts for first semester students give more and more consideration to practically motivated courses. In this context, a new first-year introductory course in practical engineering has been established in the first semester curriculum of Electrical Engineering at RWTH Aachen University, Germany. Based on a threefold learning concept, programming skills in MATLAB are taught to 309 students within a full-time block course laboratory. The students are encouraged to transfer known mathematical basics to program algorithms and real-world applications performed by 100 LEGO Mindstorms robots. A new MATLAB toolbox and twofold project tasks have been developed for this purpose by a small team of supervisors. The students are supervised by over 60 tutors at 23 institutes, and are encouraged to create their own robotics applications. We describe how the laboratory motivates the students to act and think like engineers and to solve real-world issues with limited resources. The evaluation results show that the proposed practical course concept successfully boosts students’ motivation, advances their programming skills, and encourages the peer learning process.
Ultra-precise measurement of optical frequency ratios
We developed a novel technique for frequency measurement and synthesis, based
on the operation of a femtosecond comb generator as transfer oscillator. The
technique can be used to measure frequency ratios of any optical signals
throughout the visible and near-infrared part of the spectrum. Relative
uncertainties of for averaging times of 100 s are possible. Using a
Nd:YAG laser in combination with a nonlinear crystal we measured the frequency
ratio of the second harmonic at 532 nm to the fundamental at
1064 nm, .Comment: 4 pages, 4 figure
Reconfiguration on sparse graphs
A vertex-subset graph problem Q defines which subsets of the vertices of an
input graph are feasible solutions. A reconfiguration variant of a
vertex-subset problem asks, given two feasible solutions S and T of size k,
whether it is possible to transform S into T by a sequence of vertex additions
and deletions such that each intermediate set is also a feasible solution of
size bounded by k. We study reconfiguration variants of two classical
vertex-subset problems, namely Independent Set and Dominating Set. We denote
the former by ISR and the latter by DSR. Both ISR and DSR are PSPACE-complete
on graphs of bounded bandwidth and W[1]-hard parameterized by k on general
graphs. We show that ISR is fixed-parameter tractable parameterized by k when
the input graph is of bounded degeneracy or nowhere-dense. As a corollary, we
answer positively an open question concerning the parameterized complexity of
the problem on graphs of bounded treewidth. Moreover, our techniques generalize
recent results showing that ISR is fixed-parameter tractable on planar graphs
and graphs of bounded degree. For DSR, we show the problem fixed-parameter
tractable parameterized by k when the input graph does not contain large
bicliques, a class of graphs which includes graphs of bounded degeneracy and
nowhere-dense graphs
Frequency Comb Assisted Diode Laser Spectroscopy for Measurement of Microcavity Dispersion
While being invented for precision measurement of single atomic transitions,
frequency combs have also become a versatile tool for broadband spectroscopy in
the last years. In this paper we present a novel and simple approach for
broadband spectroscopy, combining the accuracy of an optical fiber-laser-based
frequency comb with the ease-of-use of a tunable external cavity diode laser.
This scheme enables broadband and fast spectroscopy of microresonator modes and
allows for precise measurements of their dispersion, which is an important
precondition for broadband optical frequency comb generation that has recently
been demonstrated in these devices. Moreover, we find excellent agreement of
measured microresonator dispersion with predicted values from finite element
simulations and we show that tailoring microresonator dispersion can be
achieved by adjusting their geometrical properties
Fast Algorithms for Join Operations on Tree Decompositions
Treewidth is a measure of how tree-like a graph is. It has many important
algorithmic applications because many NP-hard problems on general graphs become
tractable when restricted to graphs of bounded treewidth. Algorithms for
problems on graphs of bounded treewidth mostly are dynamic programming
algorithms using the structure of a tree decomposition of the graph. The
bottleneck in the worst-case run time of these algorithms often is the
computations for the so called join nodes in the associated nice tree
decomposition.
In this paper, we review two different approaches that have appeared in the
literature about computations for the join nodes: one using fast zeta and
M\"obius transforms and one using fast Fourier transforms. We combine these
approaches to obtain new, faster algorithms for a broad class of vertex subset
problems known as the [\sigma,\rho]-domination problems. Our main result is
that we show how to solve [\sigma,\rho]-domination problems in arithmetic operations. Here, t is the treewidth, s is the
(fixed) number of states required to represent partial solutions of the
specific [\sigma,\rho]-domination problem, and n is the number of vertices in
the graph. This reduces the polynomial factors involved compared to the
previously best time bound (van Rooij, Bodlaender, Rossmanith, ESA 2009) of arithmetic operations. In particular, this removes
the dependence of the degree of the polynomial on the fixed number of
states~.Comment: An earlier version appeared in "Treewidth, Kernels, and Algorithms.
Essays Dedicated to Hans L. Bodlaender on the Occasion of His 60th Birthday"
LNCS 1216
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