Light Scarring in an Optical Fiber

Doya, Valérie; Legrand, Olivier; Mortessagne, Fabrice; Miniatura, Christian

doi:10.1103/physrevlett.88.014102

Cited by 61 publications

(51 citation statements)

References 17 publications

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“…III B, using a value of c b = 2 in Eq. (19). With this criterion, ∼420 scar functions of each one-dimensional and E 1 and E 2 symmetry classes are automatically selected, out of the whole set.…”

Section: A Calculation Of the Eigenstatesmentioning

confidence: 99%

“…Other interesting aspects of scarring, such as the role of homoclinic and heteroclinic quantized circuits [11,12], the influence of bifurcations (in systems with mixed dynamics) [13], the scarring of individual resonance eigenstates in open systems [14], and relativistic scarring [15], have also been discussed in the literature. Scars have also been experimentally observed in many different contexts, including microwave cavities [16], semiconductor nanodevices [17], optical microcavities [18], optical fibers [19], and graphene sheets [20]. Different methods have been described in the literature to systematically construct functions localized on unstable POs (hereafter called scar functions).…”

Section: Introductionmentioning

confidence: 99%

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Using basis sets of scar functions

et al. 2013

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We present a method to efficiently compute the eigenfunctions of classically chaotic systems. The key point is the definition of a modified Gram-Schmidt procedure which selects the most suitable elements from a basis set of scar functions localized along the shortest periodic orbits of the system. In this way, one benefits from the semiclassical dynamical properties of such functions. The performance of the method is assessed by presenting an application to a quartic two-dimensional oscillator whose classical dynamics are highly chaotic. We have been able to compute the eigenfunctions of the system using a small basis set. An estimate of the basis size is obtained from the mean participation ratio. A thorough analysis of the results using different indicators, such as eigenstate reconstruction in the local representation, scar intensities, participation ratios, and error bounds, is also presented.

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Section: A Calculation Of the Eigenstatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Using basis sets of scar functions

et al. 2013

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“…Classical chaos manifests itself in universal spectral quantum fluctuations that can be described by random matrix theory (RMT) [1]. While the earliest investigations of spectral correlations were confined to nuclear physics [2], during the last twenty years the universality has been tested in other areas, like optical experiments [3], quantum dots [4], and acoustic setups [5]. The (local) spectral statistics depend generically only on the underlying symmetries of the system.…”

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confidence: 99%

Spectral statistics in an open parametric billiard system

et al. 2006

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We present experimental results on the eigenfrequency statistics of a superconducting, chaotic microwave billiard containing a rotatable obstacle. Deviations of the spectral fluctuations from predictions based on Gaussian orthogonal ensembles of random matrices are found. They are explained by treating the billiard as an open scattering system in which microwave power is coupled in and out via antennas. To study the interaction of the quantum (or wave) system with its environment a highly sensitive parametric correlator is used.PACS numbers: 05.45. Mt, 03.65.Nk, 42.25.Bs Classical chaos manifests itself in universal spectral quantum fluctuations that can be described by random matrix theory (RMT) [1]. While the earliest investigations of spectral correlations were confined to nuclear physics [2], during the last twenty years the universality has been tested in other areas, like optical experiments [3], quantum dots [4], and acoustic setups [5]. The (local) spectral statistics depend generically only on the underlying symmetries of the system. In particular, they are described by the Gaussian orthogonal ensemble (GOE) of real symmetric random matrices for spinless systems with time reversal symmetry, and by the Gaussian unitary ensemble (GUE) of complex Hermitian random matrices in the absence of time reversal invariance [6]. The sensitivity of the quantum (or wave) statistical properties to fundamental symmetries is obviously of great interest. For instance, it has been utilized to derive an upper bound for the magnitude of the time or parity violating component in nuclear interactions [7,8].We investigate here spectral properties of a superconducting microwave resonator where currents are induced by the measurement process. Although we study a specific wave system, the results are expected to be of general validity in the physics of complex quantum systems (atoms, molecules, nuclei, quantum dots, ...). The influence of the flux of microwave power flowing from the feeding to the receiving antenna on the spectral properties of the system is so weak that it can only be detected through a highly sensitive diagnosis tool, in our case a parametric statistical measure. In a previous experiment, the wave system was realized by a normal conducting microwave resonator attached to a large number of antennas [9]. There, the distribution of wave functions showed significant deviations from the GOE predictions, which were attributed to the transformation of the standing waves inside the closed microwave billiard into waves propagating from an emitting antenna into a large number of exit channels [10]. The aim of the present paper is to go further into the investigation of this mechanism. We will show that deviations from GOE behaviour are already observed in a resonator with only three (or less) attached antennas, when studying spectral properties as a function of a parameter.The experiment discussed here has been performed with a superconducting microwave resonator, whose high-quality factor is typically Q = 10 5 or larg...

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“…We have presented strong evidences that these results explain previous observations of 'quasi-scared' modes in spiral microcavities and of broken time reversible symmetry. We expect that other violations of the ray-wave correspondence can be explained similarly, e.g., the observation of disproportionally many regular, scarred, and scar-like resonances [4,5,10,12,27,33,34,35,36] might be related to the creation of periodic attractors, and discrepancies in the far-field pattern [12,15] might be explained by the effect of Ff and GHs on invariant sets and their unstable manifolds. Although we focused on the case of optical microcavities, where Ff and GHs are well established effects, our main results apply likewise to acous-tic, seismic, and ultrasound waves whenever deviations from the specular reflection become relevant, e.g., when the wave length becomes comparable to the system size.…”

mentioning

confidence: 99%

Non-Hamiltonian dynamics in optical microcavities resulting from wave-inspired corrections to geometric optics

Altmann¹,

Magno²,

Hentschel³

2008

Europhys. Lett.

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We introduce and investigate billiard systems with an adjusted ray dynamics that accounts for modifications of the conventional reflection of rays due to universal wave effects. We show that even small modifications of the specular reflection law have dramatic consequences on the phase space of classical billiards. These include the creation of regions of non-Hamiltonian dynamics, the breakdown of symmetries, and changes in the stability and morphology of periodic orbits. Focusing on optical microcavities, we show that our adjusted dynamics provides the missing ray counterpart to previously observed wave phenomena and we describe how to observe its signatures in experiments. Our findings also apply to acoustic and ultrasound waves and are important in all situations where wavelengths are comparable to system sizes, an increasingly likely situation considering the systematic reduction of the size of electronic and photonic devices.

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Light Scarring in an Optical Fiber

Cited by 61 publications

References 17 publications

Using basis sets of scar functions

Using basis sets of scar functions

Spectral statistics in an open parametric billiard system

Non-Hamiltonian dynamics in optical microcavities resulting from wave-inspired corrections to geometric optics

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