8,826 research outputs found
Application of a trace formula to the spectra of flat three-dimensional dielectric resonators
The length spectra of flat three-dimensional dielectric resonators of
circular shape were determined from a microwave experiment. They were compared
to a semiclassical trace formula obtained within a two-dimensional model based
on the effective index of refraction approximation and a good agreement was
found. It was necessary to take into account the dispersion of the effective
index of refraction for the two-dimensional approximation. Furthermore, small
deviations between the experimental length spectrum and the trace formula
prediction were attributed to the systematic error of the effective index of
refraction approximation. In summary, the methods developed in this article
enable the application of the trace formula for two-dimensional dielectric
resonators also to realistic, flat three-dimensional dielectric microcavities
and -lasers, allowing for the interpretation of their spectra in terms of
classical periodic orbits.Comment: 13 pages, 12 figures, 1 tabl
Experimental Observation of Localized Modes in a Dielectric Square Resonator
We investigated the frequency spectra and field distributions of a dielectric
square resonator in a microwave experiment. Since such systems cannot be
treated analytically, the experimental studies of their properties are
indispensable. The momentum representation of the measured field distributions
shows that all resonant modes are localized on specific classical tori of the
square billiard. Based on these observations a semiclassical model was
developed. It shows excellent agreement with all but a single class of measured
field distributions that will be treated separately.Comment: 6 pages, 5 figures, 1 tabl
Nonperiodic echoes from mushroom billiard hats
Mushroom billiards have the remarkable property to show one or more clear cut
integrable islands in one or several chaotic seas, without any fractal
boundaries. The islands correspond to orbits confined to the hats of the
mushrooms, which they share with the chaotic orbits. It is thus interesting to
ask how long a chaotic orbit will remain in the hat before returning to the
stem. This question is equivalent to the inquiry about delay times for
scattering from the hat of the mushroom into an opening where the stem should
be. For fixed angular momentum we find that no more than three different delay
times are possible. This induces striking nonperiodic structures in the delay
times that may be of importance for mesoscopic devices and should be accessible
to microwave experiments.Comment: Submitted to Phys. Rev. E without the appendi
Bound States in Sharply Bent Waveguides: Analytical and Experimental Approach
Quantum wires and electromagnetic waveguides possess common features since
their physics is described by the same wave equation. We exploit this analogy
to investigate experimentally with microwave waveguides and theoretically with
the help of an effective potential approach the occurrence of bound states in
sharply bent quantum wires. In particular, we compute the bound states, study
the features of the transition from a bound to an unbound state caused by the
variation of the bending angle and determine the critical bending angles at
which such a transition takes place. The predictions are confirmed by
calculations based on a conventional numerical method as well as experimental
measurements of the spectra and electric field intensity distributions of
electromagnetic waveguides
Experimental test of a trace formula for two-dimensional dielectric resonators
Resonance spectra of two-dimensional dielectric microwave resonators of
circular and square shapes have been measured. The deduced length spectra of
periodic orbits were analyzed and a trace formula for dielectric resonators
recently proposed by Bogomolny et al. [Phys. Rev. E 78, 056202 (2008)] was
tested. The observed deviations between the experimental length spectra and the
predictions of the trace formula are attributed to a large number of missing
resonances in the measured spectra. We show that by taking into account the
systematics of observed and missing resonances the experimental length spectra
are fully understood. In particular, a connection between the most long-lived
resonances and certain periodic orbits is established experimentally.Comment: 14 pages, 12 figures, 1 tabl
Deviation from Snell's Law for Beams Transmitted Near the Critical Angle: Application to Microcavity Lasers
We show that when a narrow beam is incident upon a dielectric interface near
the critical angle for total internal reflection it will be transmitted into
the far-field with an angular deflection from the direction predicted by
Snell's Law, due to a phenomenon we call "Fresnel Filtering". This effect can
be quite large for the parameter range relevant to dielectric microcavity
lasers.Comment: 4 pages, 3 figures (eps), RevTeX 3.1, to be published in Optics
Letter
Machine learning for shaft power prediction and analysis of fouling related performance deterioration
Improving operational performance and reducing fuel consumption is increasingly important for shipping companies. Ship performance degrades over time due to hull and propeller fouling; therefore assessing when fouling effects are significant enough to warrant cleaning is critical. Advancements in onboard data logging systems, combined with machine learning techniques, unlock the potential to predict fouling effects accurately and determine when to clean. This study evaluates five models for shaft power prediction: Multiple Linear Regression, Decision Tree (AdaBoost), K – Nearest Neighbours, Artificial Neural Network and Random Forest. The importance of pre-processing is highlighted, contributing to the creation of a model with lower errors than previous studies. The significance of environmental parameters was explored, with the novel integration of wave statistics to the operational dataset, and simulated power-speed curves created from predictions to identify performance deterioration due to fouling. The Random Forest model was most effective in predicting shaft power, with an error of 1.17%. The addition of ‘Days Since Clean’ and ‘Significant Wave Height’ increased prediction accuracy by 0.07% and 0.12% respectively. Simulated power-speed curves revealed a 5.2% increase in shaft power due to fouling. This study provides operators with a method to determine when to conduct hull and propeller cleaning
Electronic Structure of Copper Impurities in ZnO
We have measured the near infrared absorption, Zeeman effect, and electron spin resonance of Cu2+ ions introduced as a substitutional impurity into single-crystal ZnO. From the g values of the lowest Γ6 component of the T2 state (the ground state), gII=0.74 and g⊥=1.531, and from the g values of the Γ4Γ5 component of the E state, gII=1.63 and g⊥=0, we have determined the wave functions of Cu2+ in terms of an LCAO MO model in which overlap only with the first nearest neighbor oxygen ions is considered. These wave functions indicate that the copper 3d (t2) hole spends about 40% of its time in the oxygen orbitals, and that the copper t2 orbitals are expanded radially with respect to the e orbitals. Corroboration for the radial expansion of the t2 orbitals is obtained from an analysis of the hyperfine splitting. It is concluded from our model that the large values of the hyperfine constants, |A|=195×10^-4 cm^-1 and |B|=231×10^-4 cm^-1, are due to the contribution from the orbital motion of the t2 hole
First Experimental Observation of Superscars in a Pseudointegrable Barrier Billiard
With a perturbation body technique intensity distributions of the electric
field strength in a flat microwave billiard with a barrier inside up to mode
numbers as large as about 700 were measured. A method for the reconstruction of
the amplitudes and phases of the electric field strength from those intensity
distributions has been developed. Recently predicted superscars have been
identified experimentally and - using the well known analogy between the
electric field strength and the quantum mechanical wave function in a
two-dimensional microwave billiard - their properties determined.Comment: 4 pages, 5 .eps figure
Chaotic Scattering in the Regime of Weakly Overlapping Resonances
We measure the transmission and reflection amplitudes of microwaves in a
resonator coupled to two antennas at room temperature in the regime of weakly
overlapping resonances and in a frequency range of 3 to 16 GHz. Below 10.1 GHz
the resonator simulates a chaotic quantum system. The distribution of the
elements of the scattering matrix S is not Gaussian. The Fourier coefficients
of S are used for a best fit of the autocorrelation function if S to a
theoretical expression based on random--matrix theory. We find very good
agreement below but not above 10.1 GHz
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