Whispering Gallery Mode Oscillators and Optical Comb Generators

Matsko, Andrey B.; Savchenkov, Anatoliy A.; Liang, Wei; Ilchenko, Vladimir S.; Seidel, D.; Maleki, Lute

doi:10.1142/9789812838223_0068

Cited by 14 publications

(20 citation statements)

References 17 publications

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“…Moreover, Refs. [70,71] pointed out that the theoretical formalism so far used by researchers to describe microresonators and fiber-cavities, i.e. the non-linear coupled mode equations and the Lugiato-Lefever equation [72] respectively, can be mapped onto each other.…”

Section: Dissipative Kerr Solitons In Optical Microresonatorsmentioning

confidence: 99%

Dissipative Kerr Solitons in Optical Microresonators

Herr¹,

Gorodetsky²,

Kippenberg³

2015

Nonlinear Optical Cavity Dynamics

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This chapter describes the discovery and stable generation of temporal dissipative Kerr solitons in continuous-wave (CW) laser driven optical microresonators. The experimental signatures as well as the temporal and spectral characteristics of this class of bright solitons are discussed. Moreover, analytical and numerical descriptions are presented that do not only reproduce qualitative features but can also be used to accurately model and predict the characteristics of experimental systems. Particular emphasis lies on temporal dissipative Kerr solitons with regard to optical frequency comb generation where they are of particular importance. Here, one example is spectral broadening and selfreferencing enabled by the ultra-short pulsed nature of the solitons. Another example is dissipative Kerr soliton formation in integrated on-chip microresonators where the emission of a dispersive wave allows for the direct generation of unprecedentedly broadband and coherent soliton spectra with smooth spectral envelope.

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Section: Dissipative Kerr Solitons In Optical Microresonatorsmentioning

confidence: 99%

Dissipative Kerr Solitons in Optical Microresonators

Herr¹,

Gorodetsky²,

Kippenberg³

2015

Nonlinear Optical Cavity Dynamics

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“…The similarity of the approaches was shown in [75]. A proper optimization of numerical algorithm makes the numerical evaluation time equivalent for the LL and ODE approaches [123].…”

Section: Lugiato-lefever (Forced Damped Nonlinear Schrödinger) Equationmentioning

confidence: 93%

“…They are described by the same equations [62,[75][76][77]. They are sustained due to continuous wave pumping and are phase locked to the pump (this is true for the case of coherent, not chaotic, oscillations) [12,78].…”

Section: Resonant Oscillationmentioning

confidence: 99%

“…The approach is especially convenient for studying generation of extremely short pulses [134]. A generalized LL equation that takes into account higher order dispersion was introduced in [75,135]. Raman scattering as well as self-steepening terms were added to this equation in [136][137][138].…”

Section: Lugiato-lefever (Forced Damped Nonlinear Schrödinger) Equationmentioning

confidence: 99%

“…The suggestion [75,76] that the Kerr comb generation can be analyzed using a driven damped nonlinear Schrödinger equation or the Lugiato-Lefever equation (LL) has made feasible application of numerous results of earlier studies of this equation, as well as the insight provided by the study of physical systems described by this equation to the optical microcavity case. Among others, LL equation has a number of dynamic solutions including the so called Kuznetsov-Ma (KM) solitons [215][216][217] and Akhmediev breathers (AB) [218,219].…”

Section: Breathersmentioning

confidence: 99%

See 2 more Smart Citations

On Frequency Combs in Monolithic Resonators

2016

Self Cite

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Optical frequency combs have become indispensable in astronomical measurements, biological fingerprinting, optical metrology, and radio frequency photonic signal generation. Recently demonstrated microring resonator-based Kerr frequency combs point the way towards chip scale optical frequency comb generator retaining major properties of the lab scale devices. This technique is promising for integrated miniature radiofrequency and microwave sources, atomic clocks, optical references and femtosecond pulse generators. Here we present Kerr frequency comb development in a historical perspective emphasizing its similarities and differences with other physical phenomena. We elucidate fundamental principles and describe practical implementations of Kerr comb oscillators, highlighting associated solved and unsolved problems.

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Asymptotic stability for spectrally stable Lugiato-Lefever solitons in periodic waveguides

Stanislavova

Stefanov

2018

Journal of Mathematical Physics

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We consider the Lugiato-Lefever model of optical fibers in the periodic context. Spectrally stable periodic steady states were constructed recently in the studies of Delcey and Haragus [Philos. Trans. R. Soc., A 376, 20170188 (2018)]; [Rev. Roumaine Math. Pures Appl. (to be published)]; and Hakkaev et al. (e-print arXiv:1806.04821). The spectrum of the linearization around such solitons consists of simple eigenvalues 0, −2α < 0, while the rest of it is a subset of the vertical line {μ:Rμ=−α}. Assuming such a property abstractly, we show that the linearized operator generates a C0 semigroup and, more importantly, the semigroup obeys (optimal) exponential decay estimates. Our approach is based on the Gearhart-Prüss theorem, where the required resolvent estimates may be of independent interest. These results are applied to the proof of asymptotic stability with phase of the steady states.

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Whispering Gallery Mode Oscillators and Optical Comb Generators

Cited by 14 publications

References 17 publications

Dissipative Kerr Solitons in Optical Microresonators

Dissipative Kerr Solitons in Optical Microresonators

On Frequency Combs in Monolithic Resonators

Asymptotic stability for spectrally stable Lugiato-Lefever solitons in periodic waveguides

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