Precession of morphology-dependent resonances in nonspherical droplets

Swindal, James; Leach, David H.; Chang, Richard K.; Young, K.

doi:10.1364/ol.18.000191

Cited by 49 publications

(16 citation statements)

References 10 publications

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“…Certain studies have dealt with a deformed sphere cavity with a magnitude of deformation less than 1%. 7 The MDR models 5 of a spherical or cylindrical cavity can be treated analytically, and the effect of small deformations can be included by perturbation theory. However, MDR modes in a further deformed cavity are not perturbatively related to those in the ideal spherical cavities.…”

Section: Introductionmentioning

confidence: 99%

Morphology-dependent resonant laser emission of dye-doped ellipsoidal microcavity

Juodkazis

Fujiwara

Takahashi

et al. 2002

Journal of Applied Physics

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We report a morphology-dependent resonance (MDR) laser emission of rhodamine-doped ellipsoidal microcavity of the poly(methylmethacrylate) particles. Elliptical particles showed different lasing properties: the lasing threshold, intramode spectral separation, mode intensity, and spectral position, when an excitation is pointed to the different locations on the particle. This differs from the well-understood MDR lasing in spherical microparticles.

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Section: Introductionmentioning

confidence: 99%

Morphology-dependent resonant laser emission of dye-doped ellipsoidal microcavity

Juodkazis

Fujiwara

Takahashi

et al. 2002

Journal of Applied Physics

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“…Level crossing of countercirculating modes is possible [10] but, in distinction to the relatively large spatial ''beats'' observed here, manifests itself as a fine standing-wave interference pattern with nodes lying just half an optical wavelength apart. Moreover, in experiments, countercirculating modes (of similar indices) are typically split (i.e., nondegenerate) [11][12][13] due to imperfect isotropy (broken axial symmetry). In our system, this split (10 7 Hz) is much smaller than the free spectral range (10 12 Hz); such a splitting and the type of anisotropy it originates from might therefore play only a minor role here in bringing levels close enough to cross.…”

mentioning

confidence: 99%

Static Envelope Patterns in Composite Resonances Generated by Level Crossing in Optical Toroidal Microcavities

et al. 2008

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We study level crossing in the optical whispering-gallery (WG) modes by using toroidal microcavities. Experimentally, we image the stationary envelope patterns of the composite optical modes that arise when WG modes of different wavelengths coincide in frequency. Numerically, we calculate crossings of levels that correspond with the observed degenerate modes, where our method takes into account the not perfectly transverse nature of their field polarizations. In addition, we analyze anticrossing with a large avoidance gap between modes of the same azimuthal number. Here we show experimentally and theoretically that optical resonances with a different number of wavelengths along the circumference can be tuned to cross in frequency. Modes of the same number of wavelengths, on the other hand, are shown to anticross with a large gap. Overall, diverse azimuthal and radial mode shapes are imaged, and modes with complex transverse shapes and polarizations are calculated. Using a fluorescent mode-mapping technique enabled imaging of noncircular mode patterns that signals crossing. This visual indication was hidden when we were using bare nonfluorescent cavities.Near the degeneracy region, modes exhibiting a different number of circumferential wavelengths are simultaneously excited with a single-frequency laser source to produce a standing interference envelope. Here, only modes circulating in one direction are examined. Level crossing of countercirculating modes is possible [10] but, in distinction to the relatively large spatial ''beats'' observed here, manifests itself as a fine standing-wave interference pattern with nodes lying just half an optical wavelength apart. Moreover, in experiments, countercirculating modes (of similar indices) are typically split (i.e., nondegenerate) [11][12][13] due to imperfect isotropy (broken axial symmetry). In our system, this split (10 7 Hz) is much smaller than the free spectral range (10 12 Hz); such a splitting and the type of anisotropy it originates from might therefore play only a minor role here in bringing levels close enough to cross.Optical resonators in general [14 -16] and dielectric whispering-gallery (WG) cavities [17,18] in particular have a set of discrete optical eigenfrequencies. For a geometry in which the wave equation is separable, such as a cylindrical or spherical resonator, each mode can be labeled by three integer indices. Normally, by convention, the resonance frequency increases monotonically with each mode index. In a dielectric ring, for example, a whispering-gallery mode with a fixed and small transverse mode index and a large azimuthal mode index of m 105, say, will have 105 wavelengths along the circumference and will resonate at an optical frequency higher than that of

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“…Each mode possesses a natural twofold degeneracy, which results from the two possible directions of propagation, clockwise (CW) and counterclockwise (CCW). 1 Lifting of the degeneracy can occur when a fraction of the mode energy is scattered into the oppositely oriented mode. The consequences of degeneracy lifting by distributed scattering were theoretically investigated recently.…”

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confidence: 99%

Modal coupling in traveling-wave resonators

Kippenberg¹,

Spillane²,

Vahala³

2002

Opt. Lett.

356

248

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High-Q traveling-wave-resonators can enter a regime in which even minute scattering amplitudes associated with either bulk or surface imperfections can drive the system into the so-called strong modal coupling regime. Resonators that enter this regime have their coupling properties radically altered and can mimic a narrowband ref lector. We experimentally confirm recently predicted deviations from criticality in such strongly coupled systems. Observations of resonators that had Q . Here we experimentally confirm these predictions, using high-Q ͑.10 8 ͒ microsphere resonators coupled to fiber-optic tapered waveguides. The long photon lifetimes of high-Q microsphere resonators make possible a counterintuitive effect in which minute scattering gives rise to a regime of strong modal coupling. In this regime scattering into the oppositely oriented mode is the dominant scattering process. Resonances are significantly split, and severe deviations of the critical coupling point occur. We show and observe that in certain regimes the TWR acts as a narrow-bandwidth ref lector, causing a strongly ref lected signal and vanishing waveguide transmission.In the case of a slowly varying field amplitude the degenerate modes of a TWR-waveguide system can be described by a simple coupled harmonic oscillator model, equivalent to that presented in Refs. 2 and 3:where a is the amplitude of the CCW and CW modes of the resonator and s denotes the input f ield ͑jsj 2 is the input pump power). The excitation frequency is detuned by Dv with respect to resonance frequency v 0 of the initially degenerate modes and t is the total lifetime of photons in the resonator, which is related to the quality factor by Q vt. Coupling coeff icient k denotes the coupling of the input wave to the CW mode of the resonator. The relation k p 1͞t ex associates the coupling coefficient with a corresponding lifetime, such that 1͞t 1͞t ex 1 1͞t 0 . The mutual coupling of the CCW and the CW modes is described by a (scattering) lifetime, g. The coupling of the resonator modes to the waveguide gives rise to a transmitted ͑t͒ and a ref lected ͑r͒ f ield:In a microsphere TWR, Rayleigh scattering from surface inhomogenities or density f luctuations will transfer power from the initially excited mode to all the confined and radiative modes of the resonator. The scattering to all modes other than the CW and CCW modes is included in the overall effective loss, given through the intrinsic lifetime, t 0 . The eigenmodes are symmetric and antisymmetric superpositions of the original CW and CCW modes centered about new eigenfrequencies v v 0 6 1͞2g (which have a linewidth of 1͞t). Modifications to the resonator coupling physics can be described in terms of the normalized mode-coupling parameter G ϵ t 0 ͞g. In addition, we introduce the normalized coupling coefficient K ϵ t 0 ͞t ex to facilitate the discussion.We experimentally observed the frequency splitting of a TWR mode in a tapered fiber-coupled 4 microsphere resonator. Because of the high-Q (typically exceeding 10 8 ), r...

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Precession of morphology-dependent resonances in nonspherical droplets

Cited by 49 publications

References 10 publications

Morphology-dependent resonant laser emission of dye-doped ellipsoidal microcavity

Morphology-dependent resonant laser emission of dye-doped ellipsoidal microcavity

Static Envelope Patterns in Composite Resonances Generated by Level Crossing in Optical Toroidal Microcavities

Modal coupling in traveling-wave resonators

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