Nonstationary nonlinear effects in optical microspheres

Fomin, Aleksey E.; Gorodetsky, M. L.; Grudinin, Ivan S.; Ilchenko, Vladimir S.

doi:10.1117/12.530657

Cited by 23 publications

(25 citation statements)

References 2 publications

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“…[10,11,12,13], where fast electronic nonlinearities competed with slower thermal nonlinearities in optically resonant devices in other materials systems, resulting in optical transmission pulsations. A similar selfpulsing behavior caused solely by thermooptical nonlinearity in fused silica microspheres has also been observed and analyzed [14].…”

Section: Introductionmentioning

confidence: 66%

Self-induced optical modulation of the transmission through a high-Q silicon microdisk resonator

Johnson¹,

Borselli²,

Painter³

2006

Opt. Express

221

186

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Direct time-domain observations are reported of a low-power, self-induced modulation of the transmitted optical power through a high-Q silicon microdisk resonator. Above a threshold input power of 60 µW the transmission versus wavelength deviates from a simple optical bistability behavior, and the transmission intensity becomes highly oscillatory in nature. The transmission oscillations are seen to consist of a train of sharp transmission dips of width approximately 100 ns and period close to 1 µs. A model of the system is developed incorporating thermal and free-carrier dynamics, and is compared to the observed behavior. Good agreement is found, and the self-induced optical modulation is attributed to a nonlinear interaction between competing free-carrier and phonon populations within the microdisk. IEEE J. Quantum Electron. 22, 873-879 (1986 , 1985). 25. G. Cocorullo and I.Rendina, "Thermo-optical modulation at 1.5 µm in silicon etalon," Electron. Lett. 28, 83-85 (1992). 26. K. J. Vahala, "Optical Microcavities," Nature (London) 424, 839-846 (2003). 27. Here we assume that the coupling to each of the standing-wave modes is identical. In general, the coupling can be different, although experimentally we have noticed only small differences in coupling. 28. R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, "Influence of nonlinear absorption on Raman amplification in silicon waveguides," Opt. Express 12, 2774-2780 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-12-2774. 29. Note that the confinement factor and effective mode volume for the two standing-wave modes are identical, hence we drop the c/s subscript. 30. For TPA with the standing wave modes one has an additional term dependent upon the product U c U s , with cross-confinement factor Γ c/s,TPA and cross-mode volume 3V c/s,TPA pre-factors. For FCA, described below, one cannot write the total absorption just in terms of products of powers of the cavity energies, but rather the mode amplitudes themselves must be explicitly used. 31. R. A. Soref and B. R. Bennett, "Electrooptical Effects in Silicon," IEEE J. Quantum Electron. 23, 123-129 (1987 (Academic Press, Boston, MA, 1985). 35. M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys.Lett. 82, 2954-2956 (2003). 36. D. K. Schroder, R. N. Thomas, and J. C. Swartz, "Free Carrier Absorption in Silicon," IEEE Trans. Electron.Dev. 25, 254-261 (1978

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Section: Introductionmentioning

confidence: 66%

Self-induced optical modulation of the transmission through a high-Q silicon microdisk resonator

Johnson¹,

Borselli²,

Painter³

2006

Opt. Express

221

186

View full text Add to dashboard Cite

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“…modulation 25,[33][34][35] . Phase noise can also be generated by optomechanical coupling [36][37][38] of optical and mechanical resonator modes, by thermal oscillations of the resonator 39 , as well as by the interaction of light with different transverse modes 27 . To shed light on the origin of the broad RF beat note, we investigated the beat note at different stages during comb formation.…”

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confidence: 99%

Universal formation dynamics and noise of Kerr-frequency combs in microresonators

et al. 2012

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Optical frequency combs allow for the precise measurement of optical frequencies and are used in a growing number of applications. The new class of Kerr-frequency comb sources, based on parametric frequency conversion in optical microresonators, can complement conventional systems in applications requiring high repetition rates such as direct comb spectroscopy, spectrometer calibration, arbitrary optical waveform generation and advanced telecommunications. However, a severe limitation in experiments working towards practical systems is phase noise, observed in the form of linewidth broadening, multiple repetition-rate beat notes and loss of temporal coherence. These phenomena are not explained by the current theory of Kerr comb formation, yet understanding this is crucial to the maturation of Kerr comb technology. Here, based on observations in crystalline MgF 2 and planar Si 3 N 4 microresonators, we reveal the universal, platformindependent dynamics of Kerr comb formation, allowing the explanation of a wide range of phenomena not previously understood, as well as identifying the condition for, and transition to, low-phase-noise performance.O ptical frequency combs [1][2][3][4] have revolutionized the field of frequency metrology and spectroscopy and are enabling components in a range of applications 5 . Recently, a novel class of frequency comb generators has been discovered 6 by coupling a continuous-wave (c.w.) laser to a high-finesse fused silica microcavity, where the Kerr nonlinearity enables (cascaded) fourwave-mixing (FWM), resulting in an optical frequency comb. These Kerr combs could complement conventional frequency combs in applications where high power per comb line (typically .100 mW) and high repetition rate (.10 GHz spacing between the comb lines) are desirable 7 , such as in astronomical spectrometer calibration [8][9][10] , direct comb spectroscopy 11 , arbitrary optical waveform generation 12,13 and advanced telecommunications. The creation of Kerr combs using microresonators has been demonstrated in crystalline CaF 2 (refs 14,15) and MgF 2 (refs 16-18) resonators, fused-silica microspheres 19 , planar high-index silica 20 and Si 3 N 4 ring resonators 21,22 , and compact fibre cavities 23 . Over recent years, a significant advance in Kerr comb technology has been achieved by demonstrating a single and well-defined radiofrequency (RF) beat note between adjacent comb lines (corresponding to the equidistant comb spacing and required for stabilizing the comb) 6,14,24 , a fully phase-stabilized Kerr comb 24 , the generation of octave-spanning spectra (required for self-referencing the comb using the f-2f scheme) 25,26 , the detection and shaping of pulses 13 , and extension of spectral coverage towards the visible 27 and midinfrared spectral regimes 18 . In addition to these experimental advances, theoretical work 28,29 has also enabled an explanation of the power distribution of Kerr combs, particularly the first comb modes appearing not necessarily adjacent to the pump. Despite these advances,...

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“…The system consists of a cavity with two WGM resonances at different wavelengths, but sharing approximately the same volume. A system of coupled equations similar to those in [13,14] is used to analyze the thermal behavior. Table 1 lists the variables and definitions.…”

Section: Theoretical Modelmentioning

confidence: 99%