821 research outputs found
Efficient Localization of Discontinuities in Complex Computational Simulations
Surrogate models for computational simulations are input-output
approximations that allow computationally intensive analyses, such as
uncertainty propagation and inference, to be performed efficiently. When a
simulation output does not depend smoothly on its inputs, the error and
convergence rate of many approximation methods deteriorate substantially. This
paper details a method for efficiently localizing discontinuities in the input
parameter domain, so that the model output can be approximated as a piecewise
smooth function. The approach comprises an initialization phase, which uses
polynomial annihilation to assign function values to different regions and thus
seed an automated labeling procedure, followed by a refinement phase that
adaptively updates a kernel support vector machine representation of the
separating surface via active learning. The overall approach avoids structured
grids and exploits any available simplicity in the geometry of the separating
surface, thus reducing the number of model evaluations required to localize the
discontinuity. The method is illustrated on examples of up to eleven
dimensions, including algebraic models and ODE/PDE systems, and demonstrates
improved scaling and efficiency over other discontinuity localization
approaches
Optical microsphere resonators: optimal coupling to high-Q whispering gallery modes
A general model is presented for coupling of high- whispering-gallery
modes in optical microsphere resonators with coupler devices possessing
discrete and continuous spectrum of propagating modes. By contrast to
conventional high-Q optical cavities, in microspheres independence of high
intrinsic quality-factor and controllable parameters of coupling via evanescent
field offer variety of regimes earlier available in RF devices. The theory is
applied to the earlier-reported data on different types of couplers to
microsphere resonators and complemented by experimental demonstration of
enhanced coupling efficiency (about 80%) and variable loading regimes with
Q>10^8 fused silica microspheres.Comment: 14 pages, 4 figure
A continuous analogue of the tensor-train decomposition
We develop new approximation algorithms and data structures for representing
and computing with multivariate functions using the functional tensor-train
(FT), a continuous extension of the tensor-train (TT) decomposition. The FT
represents functions using a tensor-train ansatz by replacing the
three-dimensional TT cores with univariate matrix-valued functions. The main
contribution of this paper is a framework to compute the FT that employs
adaptive approximations of univariate fibers, and that is not tied to any
tensorized discretization. The algorithm can be coupled with any univariate
linear or nonlinear approximation procedure. We demonstrate that this approach
can generate multivariate function approximations that are several orders of
magnitude more accurate, for the same cost, than those based on the
conventional approach of compressing the coefficient tensor of a tensor-product
basis. Our approach is in the spirit of other continuous computation packages
such as Chebfun, and yields an algorithm which requires the computation of
"continuous" matrix factorizations such as the LU and QR decompositions of
vector-valued functions. To support these developments, we describe continuous
versions of an approximate maximum-volume cross approximation algorithm and of
a rounding algorithm that re-approximates an FT by one of lower ranks. We
demonstrate that our technique improves accuracy and robustness, compared to TT
and quantics-TT approaches with fixed parameterizations, of high-dimensional
integration, differentiation, and approximation of functions with local
features such as discontinuities and other nonlinearities
Mid-Infrared ultra-high-Q resonators based on fluoride crystalline materials
Decades ago, the losses of glasses in the near infrared (near-IR) were
investigated in views of developments for optical telecommunications. Today,
properties in the mid-infrared (mid-IR) are of interest for molecular
spectroscopy applications. In particular, high-sensitivity spectroscopic
techniques based on high-finesse mid-IR cavities hold high promise for medical
applications. Due to exceptional purity and low losses, whispering gallery mode
microresonators based on polished alkaline earth metal fluoride crystals (i.e
the family, where X Ca, Mg, Ba, Sr,...) have attained
ultra-high quality (Q) factor resonances (Q10) in the near-IR and
visible spectral ranges. Here we report for the first time ultra-high Q factors
in the mid-IR using crystalline microresonators. Using an uncoated chalcogenide
(ChG) tapered fiber, light from a continuous wave quantum cascade laser (QCL)
is efficiently coupled to several crystalline microresonators at 4.4 m
wavelength. We measure the optical Q factor of fluoride crystals in the mid-IR
using cavity ringdown technique. We observe that
microresonators feature quality factors that are very close to the fundamental
absorption limit, as caused by the crystal's multiphonon absorption
(Q10), in contrast to near-IR measurements far away from these
fundamental limits. Due to lower multiphonon absorption in and
, we show that ultra-high quality factors of Q 1.4
can be reached at 4.4 m. This corresponds to an optical
finesse of 4 10, the highest value achieved for any
type of mid-IR resonator to date, and a more than 10-fold improvement over the
state-of-the-art. Such compact ultra-high Q crystalline microresonators provide
a route for narrow linewidth frequency-stabilized QCL or mid-IR Kerr comb
generation.Comment: C. Lecaplain and C. Javerzac-Galy contributed equally to this wor
Frequency combs and platicons in optical microresonators with normal GVD
We predict the existence of a novel type of the flat-top dissipative
solitonic pulses, "platicons", in microresonators with normal group velocity
dispersion (GVD). We propose methods to generate these platicons from cw pump.
Their duration may be altered significantly by tuning the pump frequency. The
transformation of a discrete energy spectrum of dark solitons of the
Lugiato-Lefever equation into a quasicontinuous spectrum of platicons is
demonstrated. Generation of similar structures is also possible with
bi-harmonic, phase/amplitude modulated pump or via laser injection locking.Comment: 9 pages, 6 figure
Octave Spanning Frequency Comb on a Chip
Optical frequency combs have revolutionized the field of frequency metrology
within the last decade and have become enabling tools for atomic clocks, gas
sensing and astrophysical spectrometer calibration. The rapidly increasing
number of applications has heightened interest in more compact comb generators.
Optical microresonator based comb generators bear promise in this regard.
Critical to their future use as 'frequency markers', is however the absolute
frequency stabilization of the optical comb spectrum. A powerful technique for
this stabilization is self-referencing, which requires a spectrum that spans a
full octave, i.e. a factor of two in frequency. In the case of mode locked
lasers, overcoming the limited bandwidth has become possible only with the
advent of photonic crystal fibres for supercontinuum generation. Here, we
report for the first time the generation of an octave-spanning frequency comb
directly from a toroidal microresonator on a silicon chip. The comb spectrum
covers the wavelength range from 990 nm to 2170 nm and is retrieved from a
continuous wave laser interacting with the modes of an ultra high Q
microresonator, without relying on external broadening. Full tunability of the
generated frequency comb over a bandwidth exceeding an entire free spectral
range is demonstrated. This allows positioning of a frequency comb mode to any
desired frequency within the comb bandwidth. The ability to derive octave
spanning spectra from microresonator comb generators represents a key step
towards achieving a radio-frequency to optical link on a chip, which could
unify the fields of metrology with micro- and nano-photonics and enable
entirely new devices that bring frequency metrology into a chip scale setting
for compact applications such as space based optical clocks
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