Time-Domain Dynamics and Stability Analysis of Optoelectronic Oscillators Based on Whispering-Gallery Mode Resonators

We propose a detailed stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs in whispering gallery mode resonators pumped in the normal dispersion regime. We analyze the spatial bifurcation structure of the stationary states depending on two parameters that are experimentally tunable, namely the pump power and the cavity detuning. Our study demonstrates that the non-trivial equilibria play an important role in this bifurcation map, as their associated eigenvalues undergo critical bifurcations that are foreshadowing the existence of localized spatial structures. In particular, we show that in the normal dispersion regime, dark cavity solitons can emerge in the system, and thereby generate a Kerr comb. We also show how these solitons can coexist in the resonator as long as they do not interact with each other. The Kerr combs created by these (sets of) dark solitons are also analyzed, and their stability is discussed as well.

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“…[18] and used in ref. [19] for optical resonators, the dimensionless external pump field intensity can be explicitly defined as:…”

Section: The Modelmentioning

confidence: 99%

Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes

et al. 2014

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“…The add-drop configuration uses one coupler to pump the resonator (quality factor Q ext,t ) and another to retrieve the comb signal at the drop port (quality factor Q ext,d ). This configuration allows to obtain an output signal that is truly proportional to the intra-cavity field, but on the other hand, it has the disadvantage to increase the coupling losses because Q [40][41][42]). For crystalline WGMRs, the coupling is generally performed using a tapered fiber or a prism coupling.…”

Section: The Experimental Systemmentioning

confidence: 99%

“…The output fields can explicitly be expressed as A out = √︀ ∆ω ext,t A − A in in the add-through configuration and as A out = √︀ ∆ω ext,d A in the add-drop configuration [40]. It is also useful to note that the intracavity and output fields A and A out can be, respectively, rescaled to E = √︀ Ω L /T FSR A and E out = √︀ Ω L A out , which have a square modulus in units of watts.…”

Section: Spatiotemporal Model: the Lugiato-lefever Equation (Lle)mentioning

confidence: 99%

Kerr optical frequency combs: theory, applications and perspectives

Chembo

2016

Nanophotonics

139

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Abstract:The optical frequency comb technology is one of the most important breakthrough in photonics in recent years. This concept has revolutionized the science of ultra-stable lightwave and microwave signal generation. These combs were originally generated using ultrafast mode-locked lasers, but in the past decade, a simple and elegant alternative was proposed, which consisted in pumping an ultra-high-Q optical resonator with Kerr nonlinearity using a continuous-wave laser. When optimal conditions are met, the intracavity pump photons are redistributed via four-wave mixing to the neighboring cavity modes, thereby creating the so-called Kerr optical frequency comb. Beyond being energy-efficient, conceptually simple, and structurally robust, Kerr comb generators are very compact devices (millimetric down to micrometric size) which can be integrated on a chip. They are, therefore, considered as very promising candidates to replace femtosecond mode-locked lasers for the generation of broadband and coherent optical frequency combs in the spectral domain, or equivalently, narrow optical pulses in the temporal domain. These combs are, moreover, expected to provide breakthroughs in many technological areas, such as integrated photonics, metrology, optical telecommunications, and aerospace engineering. The purpose of this review article is to present a comprehensive survey of the topic of Kerr optical frequency combs. We provide an overview of the main theoretical and experimental results that have been obtained so far. We also highlight the potential of Kerr combs for current or prospective applications, and discuss as well some of the open challenges that are to be met at the fundamental and applied level.

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“…For example, if one wants to use the data of temperature per unit time today to predict the average temperature tomorrow one can observe a series of data today to make tomorrow's predictions. Coillet et al (2013) successfully applied the time domain methods to analyze optoelectronic oscillators based on whispering-gallery mode resonators. Szurley et al (2013) successfully applied the time domain technique to enhance binaural speech.…”

Section: A Time Domain Datamentioning

confidence: 99%

Flexibly-bounded Rationality

2015

Causality, Correlation and Artificial Intelligence for Rational Decision Making

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This chapter describes the theory of flexibly-bounded rationality which extends the theory of bounded rationality. Specifically, it is viewed that a decision making process which encompasses three components, information collection and analysis, the correlation, and the causal machines. Rational decision making entails utilizing information which is imperfect and incomplete jointly with human brain which is erratic on making decisions. The theory of bounded rationality prescribes making this decision despite the fact that the information is incomplete and imperfect and that the human brain is inconsistent and the decision is made within the bounds of these limitations. The theory of flexibly-bounded rationality entails using signal processing to filter noise and outliers in the data and using the correlation machine to complete missing information and artificial intelligence to make more reliable decisions. Flexibly-bounded rationality is applied to condition monitoring and HIV diagnosis problems and it is found to enlarge the bounds within which rational decision making process is employed and, thus, rises the probability of making accurate decisions than the theory of bounded rationality. 147 Causality, Correlation and Artificial Intelligence for Rational Decision Making Downloaded from www.worldscientific.com by UNIVERSITY OF BIRMINGHAM LIBRARY -INFORMATION SERVICES on 03/21/15. For personal use only. Causality, Correlation and Artificial Intelligence for Rational Decision Making Downloaded from www.worldscientific.com by UNIVERSITY OF BIRMINGHAM LIBRARY -INFORMATION SERVICES on 03/21/15. For personal use only.

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Time-Domain Dynamics and Stability Analysis of Optoelectronic Oscillators Based on Whispering-Gallery Mode Resonators

Cited by 45 publications

References 29 publications

Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes

Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes

Kerr optical frequency combs: theory, applications and perspectives

Flexibly-bounded Rationality

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