Wave Chaos in Real-World Vertical-Cavity Surface-Emitting Lasers

Gensty, T.; Becker, Klaus; Fischer, Ingo; Elsäßer, Wolfgang; Degen, Christian L.; Debernardi, Pierluigi; Bava, G.P.

doi:10.1103/physrevlett.94.233901

Cited by 62 publications

(47 citation statements)

References 25 publications

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“…Since the spacing of the two Bragg mirrors is on the order of one wavelength, only one longitudinal mode of the cavity falls in the emission spectra. However, if the cross section of the cavity is large (a few tens of micron in diameter), multiple transverse modes exist, and they may produce complex field patterns (Gensty et al, 2005;Huang et al, 2002).…”

Section: Microdisks and Micropillarsmentioning

confidence: 99%

Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics

2015

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Section: Microdisks and Micropillarsmentioning

confidence: 99%

Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics

2015

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“…The coherence of broad-area VCSELs is limited by the appearance of high order transverse modes [1,2] being a manifestation of selforganization in nonequilibrium systems [3]. Particularly interesting is that these structures open also a simple access for studying the relation between wave and ray optics, quantum and classically trajectories, respectively, in billiard problems [4,5], where the reflective boundaries are created by refractive index steps determining the size of the active aperture. A further important aspect of selforganization in VCSELs stems from the fact that the ideal VCSEL is almost polarization isotropic and thus has an additional continuous phase variable leading to enhanced complexity.…”

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confidence: 99%

Coupling of Polarization and Spatial Degrees of Freedom of Highly Divergent Emission in Broad-Area Square Vertical-Cavity Surface-Emitting Lasers

Babushkin

Schulz-Ruhtenberg

Loĭko³

et al. 2008

Phys. Rev. Lett.

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“…More precisely, we numerically demonstrate the selective amplification of scar modes by positioning a gain region in the vicinity of the self-focal point of the shortest periodic orbit in the transverse motion. [5,6,7]. The violation of the ergodic hypothesis implied by the existence of scars is justified by various theoretical approaches [10] but remains mathematically uncertain [11].…”

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“…Scars deviate significantly from this ergodic behavior by exhibiting unexpected enhancement of intensity in the vicinity of the least unstable periodic orbits (PO) of the corresponding billiards. Since their numerical birth in a quantum context, scars have been experimentally observed with microwaves [2], with capillary or Faraday waves [3], in guided optics [4] and their technological interest is now clearly established [5,6,7]. The violation of the ergodic hypothesis implied by the existence of scars is justified by various theoretical approaches [10] but remains mathematically uncertain [11].…”

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confidence: 99%

Selective Amplification of Scars in a Chaotic Optical Fiber

et al. 2007

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In this letter we propose an original mechanism to select scar modes through coherent gain amplification in a multimode D-shaped fiber. More precisely, we numerically demonstrate the selective amplification of scar modes by positioning a gain region in the vicinity of the self-focal point of the shortest periodic orbit in the transverse motion. [5,6,7]. The violation of the ergodic hypothesis implied by the existence of scars is justified by various theoretical approaches [10] but remains mathematically uncertain [11].In previous works we showed that a passive optical fiber with a chaotic-billiard-shape transverse section constitutes a powerful experimental system for studying (and imaging) wave chaos [12], and particularly when scars are involved [4]. Indeed, at the output of a multimode D-shaped chaotic fiber we were able to put to evidence a scar mode associated to the shortest PO. Unfortunately, diffraction due to the finite aperture of the fiber precludes any truly selective excitation of a single mode. For an input illumination privileging the lowest order modes, a few tens of modes contribute to the optical field, and the best that one can do is to slightly enhance one of the lowest order scars. For larger orders, the increasing number of excited modes hampers the scar enhancement effect. Scar modes have also been observed in microlasers [6]. These devices are more and more present in photonics, for which high directionality and low lasing threshold are required. Scar modes constitute the cavity modes with the highest quality factors [7] and privileged directions of emission. In such lasing microcavities, boundary losses play a dominant role in the mode selection mechanism and, for a given shape, only a few efficient scar modes are supported [7]. A different selection mechanism may be found in the domain of wave propagation in random media. In this context, the amplification of localized modes is observed with random lasers (see Ref.[13] for a recent review), where they play similar to scar modes. Both types of modes rely on strong coherent effects and display common statistical features [14]. Numerical investigations recently showed that, in the localized regime, the lasing modes in a random laser just above threshold are the modes of the passive disordered system [15]. The identification between lasing and passive modes even holds when the gain region is smaller than the mode size [16]. Inspired by these results, we present an original way to achieve a selective amplification of scar modes in a highly multimode D-shaped optical fiber. More precisely, we demonstrate how scar modes can be selectively amplified by positioning a gain region in the vicinity of specific points along a short PO known to give rise to scar modes. We also illustrate the robustness of this amplification with a spatially incoherent speckle-like input.We recently showed that multimode D-shaped fibers are perfectly suited to achieve high power optical amplification [17]. In the single-mode doped core of an optical amplifier, the gui...

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Wave Chaos in Real-World Vertical-Cavity Surface-Emitting Lasers

Cited by 62 publications

References 25 publications

Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics

Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics

Coupling of Polarization and Spatial Degrees of Freedom of Highly Divergent Emission in Broad-Area Square Vertical-Cavity Surface-Emitting Lasers

Selective Amplification of Scars in a Chaotic Optical Fiber

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