Stable Oscillations of a Spatially Chaotic Wave Function in a Microstadium Laser

Harayama, Takahisa; Davis, Peter; Ikeda, Kensuke S.

doi:10.1103/physrevlett.90.063901

Cited by 92 publications

(79 citation statements)

References 11 publications

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“…The complete description of such lasing cavities requires the solution of the non-linear Maxwell-Bloch equations (see e.g. [13,14,15] and references therein). For clarity, we accept here a simplified point of view (see e.g.…”

Section: Figmentioning

confidence: 99%

Inferring periodic orbits from spectra of simply shaped microlasers

et al. 2007

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Dielectric micro-cavities are widely used as laser resonators and characterizations of their spectra are of interest for various applications. We experimentally investigate micro-lasers of simple shapes (Fabry-Perot, square, pentagon, and disk). Their lasing spectra consist mainly of almost equidistant peaks and the distance between peaks reveals the length of a quantized periodic orbit. To measure this length with a good precision, it is necessary to take into account different sources of refractive index dispersion. Our experimental and numerical results agree with the superscar model describing the formation of long-lived states in polygonal cavities. The limitations of the two-dimensional approximation are briefly discussed in connection with micro-disks.

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Section: Figmentioning

confidence: 99%

Inferring periodic orbits from spectra of simply shaped microlasers

et al. 2007

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“…Various aspects of billiard dynamics have been extensively examined during last decades [10,11,12,13,14,15,16,17,18,19]. In recent years, properties of classical billiards and their quantum-mechanical counterparts were used to explain and improve performances of devices in microelectronics and nanotechnology, especially of optical microresonators in dielectrical and polymer lasers [20,21,22,23,24,25].…”

Section: Introductionmentioning

confidence: 99%

Chaotic properties of the truncated elliptical billiards

Lopac¹,

Šimić²

2011

Communications in Nonlinear Science and Numerical Simulation

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Chaotic properties of symmetrical two-dimensional stadium-like billiards with elliptical arcs are studied numerically and analytically. For the two-parameter truncated elliptical billiard the existence and linear stability of several lowest-order periodic orbits are investigated in the full parameter space. Poincaré plots are computed and used for evaluation of the degree of chaoticity with the box-counting method. The limit of the fully chaotic behavior is identified with circular arcs. Above this limit, for flattened elliptical arcs, mixed dynamics with numerous stable elliptic islands is present, similarly as in the elliptical stadium billiards. Below this limit the full chaos extends over the whole region of elongated shapes and the existing orbits are either unstable or neutral. This is conspicuously different from the behavior in the elliptical stadium billiards, where the chaotic region is strictly bounded from both sides. To examine the mechanism of this difference, a generalization to a novel three-parameter family of boundary shapes is proposed and suggested for further evaluation.

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“…For large matrices the distribution of escape rates converges to a fixed shape profile characterized by a spectral gap related to the classical escape rate. [9,10,11]. Thus the understanding of their properties in the semiclassical limit represents an important challenge.…”

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confidence: 99%

“…The quantum operator (2) can be considered as a simplified model of chaotic microlasers where all rays with orbital momenta below some critical value determined by the refraction index escape from a microcavity [9,10,11]. The right eigenstates ψ (m) n and eigenvalues λ m = exp(−iǫ m − γ m /2) of the evolution operatorÛ are determined numerically by direct dioganalization up to a maximal value N = 22001 (only states symmetric in n are considered).…”

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confidence: 99%

“…Surprisingly, only recently it has been realized that the case of nonunitary operators describing open systems in the semiclassical limit has a number of new interesting properties and the concept of the fractal Weyl law has been introduced to describe the dependence of number of resonant Gamow eigenstates onh [4,5]. The Gamow eigenstates find important applications for decay of radioactive nuclei [6], quantum chemistry reactions [7], chaotic scattering [8] and microlasers with chaotic resonators [9,10,11]. Thus the understanding of their properties in the semiclassical limit represents an important challenge.…”

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confidence: 99%

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Fractal Weyl law for quantum fractal eigenstates

Shepelyansky

2008

Phys. Rev. E

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The properties of the resonant Gamow states are studied numerically in the semiclassical limit for the quantum Chirikov standard map with absorption. It is shown that the number of such states is described by the fractal Weyl law and their Husimi distributions closely follow the strange repeller set formed by classical orbits nonescaping in future times. For large matrices the distribution of escape rates converges to a fixed shape profile characterized by a spectral gap related to the classical escape rate. [9,10,11]. Thus the understanding of their properties in the semiclassical limit represents an important challenge.According to the fractal Weyl law [4,5] the number of Gamow eigenstates N γ , which have escape rates γ in a finite band width 0 ≤ γ ≤ γ b , scales aswhere d is a fractal dimension of a classical strange repeller formed by classical orbits nonescaping in future (or past) times. By numerical simulations it has been shown that the law (1) In view of the recent results described above I study numerically a simple model of the quantum Chirikov standard map (kicked rotator) with absorption introduced in [18] which allows to vary continuously the fractal dimension of the classical strange repeller. In this way the fractal Weyl law (1) is verified in the whole interval 1 ≤ d ≤ 2. The model also allows to establish the limiting semiclassical distribution over escape rates γ and find its links with the fractal properties of the classical strange repeller. The Chirikov standard map is a generic model of chaotic dynamics and it finds applications in various physical systems including magnetic mirror traps, accelerator beams, Rydberg atoms in a microwave field [19,20,21,22]. The quantum model has been built up in experiments with cold atoms [23]. Thus the results obtained for this model should be generic and should find applications for various systems.The quantum dynamics of the model is described by the evolution matrix:wheren = −i∂/∂θ and the operatorP projects the wave function to the states in the interval [−N/2, N/2]. The semiclassical limit corresponds to k → ∞, T → 0 with the chaos parameter K = kT = const and absorption boundary a = N/k = const. Thus N is inversely proportional to the effective Planck constant T =h ef f , it gives the number of quantum eigenstates and the number of quantum cells inside the classical phase space. The classical dynamics is described by the Chirikov standard map [19,20] in its symmetric form: n = n + k sin θ + T n 2 ,θ = θ + T 2 (n +n).Physically, the map describes a free particle propagation in presence of periodic kicks with period T (e.g. kicks of optical lattice in [23]). In this model all trajectories (and quantum probabilities) escaping the interval [−N/2, N/2] are absorbed and never return back. It is convenient to fix K = 7 so that the phase space have no visible stability

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Stable Oscillations of a Spatially Chaotic Wave Function in a Microstadium Laser

Cited by 92 publications

References 11 publications

Inferring periodic orbits from spectra of simply shaped microlasers

Inferring periodic orbits from spectra of simply shaped microlasers

Chaotic properties of the truncated elliptical billiards

Fractal Weyl law for quantum fractal eigenstates

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