Some characteristics of resonant electromagnetic modes in a dielectric sphere

Datsyuk, V. V.

doi:10.1007/bf00331893

Cited by 29 publications

(15 citation statements)

References 8 publications

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“…15,16 In a sphere the whispering-gallery Q scales as Q ϰ exp͑2 ᐉ ͒, where ᐉ is the angular mode number. 16,17 Numerical modeling confirms that the angular mode number ᐉ for the measured microtoroids is nearly unchanged compared to that of a microsphere of identical principal diameter, and the radial eigenfunctions are still well described by their microsphere counterparts. Therefore, the Q-factor is expected to approximately scale according to the whispering-gallery loss of a microsphere.…”

mentioning

confidence: 63%

Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip

Kippenberg

Spillane

Vahala

2004

Applied Physics Letters

187

124

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Optical microcavities confine light spatially and temporally and find application in a wide range of fundamental and applied studies. In many areas, the microcavity figure of merit is not only determined by photon lifetime (or the equivalent quality-factor, Q), but also by simultaneous achievement of small mode volume ͑V͒. Here we demonstrate ultra-high Q-factor small mode volume toroid microcavities on-a-chip, which exhibit a Q/V factor of more than 10 6 ͑ / n͒ −3 . These values are the highest reported to date for any chip-based microcavity. A corresponding Purcell factor in excess of 200 000 and a cavity finesse of Ͼ2.8ϫ 10 6 is achieved, demonstrating that toroid microcavities are promising candidates for studies of the Purcell effect, cavity QED or biochemical Microcavities can be characterized by two figures of merits: the temporal confinement is described by the quality factor of the mode ͑Q͒, and the spatial confinement is characterized by the mode volume ͑V͒.1 Of all optical microcavities, whispering-gallery-type microsphere resonators have obtained the highest Q factor to date (nearly 9 billion 2 ). While Q-factor figures prominently in many applications, minimizing mode volume is also important in a variety of fundamental and applied studies such as cavity quantum electrodynamics (cQED) studies, photonics and biochemical sensing. In particular, a high Q/V ratio is desirable in applications such as lasers, add-drop filters and biochemical sensors, which rely upon a large finesse. Cavities can also be used to enhance the spontaneous emission rate, a concept which is used in "single-photon on-demand" sources, 3,4 where the figure of merit is the Purcell factor, given byWafer-based cavities such as photonic crystals, 6,7 microposts, 3 or microdisks 8 typically have much smaller mode volume than microspheres, and allow wafer-scale integration and control.9 However, the Q factor of these cavities has remained significantly lower than for silica microspheres. However, recently, ultra-high-Q performance on a chip has been demonstrated using a toroid-microcavity. 10These cavities allow integration and control previously not accessible in the ultra-high-Q regime. Here we demonstrate that toroid microcavities not only allow one to obtain ultrahigh-Q, but also to achieve small mode volumes, reaching a previously inaccessible range of Q/V ratio of more than 10 6 ͑ / n͒ −3 . By variations of the principal and minor toroid diameter, the Q/V value was adjusted and the highest achieved value was Q / V m Ϸ 2.5ϫ 10 6 ͑ / n͒ −3 (for a toroid microcavity with = 1550 nm, V m Ϸ 180 m 3 , and Q Ϸ 4 ϫ 10 8 ). This result is more than one order of magnitude larger than the highest value reported so far, using photonic crystal defect cavities. 6 Further optimization of the toroid microcavity can result in yet higher values.The use of silica microtoroids allows the preservation of ultra-high-Q factors while the additional transverse spatial confinement of the optical mode over spherical cavities results in a smaller modal volum...

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mentioning

confidence: 63%

Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip

Kippenberg

Spillane

Vahala

2004

Applied Physics Letters

187

124

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“…The dotted lines shown in Fig. 2 correspond to the transverse electric (TE) WGM resonance wavelengths with a radial mode number n = 1, which have intrinsically higher quality factor than the other modes [19]. The polar mode numbers are denoted at the top of the graph.…”

Section: Resultsmentioning

confidence: 99%

“…We can thus neglect the effect of the voids on the WGM resonances if the voids locate far away from the microsphere's surface. The exact layer width of the WGM energy localization in the radial direction is given by [19,21] …”

Section: Resultsmentioning

confidence: 99%

Inner structure of ZnO microspheres fabricated via laser ablation in superfluid helium

Minowa¹,

Oguni²,

Ashida³

2017

Opt. Express

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ZnO microspheres fabricated via laser ablation in superfluid helium were found to have bubble-like voids. Even a microsphere demonstrating clear whispering gallery mode resonances in the luminescence had voids. Our analysis confirmed that the voids are located away from the surface and have negligible or little effect on the whispering gallery mode resonances since the electromagnetic energy localizes near the surface of these microspheres. The existence of the voids indicates that helium gas or any evaporated target material was present within the molten microparticles during the microsphere formation.

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“…5, particles that are of a similar size. These optical tweezers measurements are also compared with reported quality factor values from dye-doped and un-doped particles reported from a broad range of other studies [39][40][41][42][43][44][45][46][47]. The mode qualities show the expected general increase with mode number, although there is considerable variability in the absorption losses across all measurements.…”

Section: Observation Of Cavity-enhanced Fluorescence From Aerosol Dromentioning

confidence: 78%