Single envelope equation modeling of multi-octave comb arrays in microresonators with quadratic and cubic nonlinearities

Hansson, Tobias; Léo, François; Erkintalo, Miro; Anthony, Jessienta; Coen, Stéphane; Ricciardi, I.; Rosa, M. De; Wabnitz, Stefan

doi:10.1364/josab.33.001207

Cited by 42 publications

(30 citation statements)

References 42 publications

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“…In this work, we review our development of the theory of OFC generation in quadratic cavities and microresonators, based on time-domain nonlinear evolution equations with different levels of complexity [7][8][9][10]. To validate our theory, we show that an excellent agreement between the theory and the experimental results is achieved.…”

Section: Introductionmentioning

confidence: 89%

Theory of quadratic optical frequency combs

Hansson

Léo

Erkintalo

et al. 2016

2016 18th International Conference on Transparent Optical Networks (ICTON)

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We present theoretical studies of optical frequency comb generation in dispersive quadratically nonlinear resonators. We introduce a mean field equation approach to model cavity enhanced second harmonic generation and find excellent agreement with recent experimental frequency comb observations. We also develop a more general approach based on a single envelope equation for both quadratic and Kerr nonlinear cavities. Keywords: nonlinear optics, parametric processes, parametric oscillators, optical resonators. INTRODUCTIONThe generation of an optical frequency comb (OFC) by means of a nonlinear microresonator shows promise for enabling chip scale devices that can complement current comb sources based on bulk mode-locked lasers [1]. Microresonator-based OFC sources can provide a direct link between optical and microwave frequencies and have a host of potential applications to metrology, including ultra-precise optical clocks, biomedical and environmental spectroscopy, microwave photonics and multi-user coherent optical communications.A substantial boost to the advancement of the theory and numerical modelling of Kerr microresonator OFCs has been provided by the realization that one can model the dynamics of the system using a time-domain description. This approach is based on the mean-field driven and damped nonlinear Schrödinger equation [2], which was earlier derived for coherently pumped passive fiber cavities [3].Most research to date has focused on coherently pumped cubic Kerr nonlinear microresonators, where the physical principle of OFC generation is cascade four-wave mixing activated by modulation instability. However, modulation instabilities and pulse trains can also be obtained from quadratic nonlinear cavities [4], that could allow frequency comb generation in wavelength ranges where pump sources are unavailable, in particular in the mid-infrared. At the same time, quadratic comb sources can also lead to a substantial decrease in the required pump power level and allow for chip scale integration.In fact, recent experiments have demonstrated the possibility of achieving OFC generation through the singly resonant cavity second harmonic process [5,6]. In this work, we review our development of the theory of OFC generation in quadratic cavities and microresonators, based on time-domain nonlinear evolution equations with different levels of complexity [7][8][9][10]. To validate our theory, we show that an excellent agreement between the theory and the experimental results is achieved.

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Section: Introductionmentioning

confidence: 89%

Theory of quadratic optical frequency combs

Hansson

Léo

Erkintalo

et al. 2016

2016 18th International Conference on Transparent Optical Networks (ICTON)

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“…The experimental observation of χ (2) combs in cavity SHG has motivated the development of theoretical models that can quantitatively describe the comb dynamics and provide in-depth insights into the underlying physics [17][18][19][20]. A particularly attractive feature of quadratic resonators is that they can permit the generation of frequency combs in spectral regions far from the pump frequency.…”

Section: Introductionmentioning

confidence: 99%

“…For example, phase-matched SHG can allow for the generation of visible frequency combs using near-infrared pump lasers. On the other hand, numerical simulations [19] suggest that the inverse process (degenerate parametric down-conversion) could similarly allow for direct generation of frequency combs in the elusive mid-IR region.…”

Section: Introductionmentioning

confidence: 99%

Frequency comb generation in continuously pumped optical parametric oscillator

Mosca

Parisi

Ricciardi

et al. 2017

Frontiers in Optics 2017

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Continuously pumped passive nonlinear cavities can be harnessed for the creation of novel optical frequency combs. While most research activities have focused on third-order 'Kerr' nonlinear interactions, recent studies have shown that frequency comb formation can also occur via secondorder nonlinear effects. Here, we extend the study of such quadratic combs to optical parametric oscillator (OPO) configurations, demonstrating that optical frequency combs can be generated in a continuously pumped OPO, in the parametric region around half of the pump frequency. We also numerically model the comb formation dynamics using a single time-domain mean field equation, and obtain simulation results that are in good agreement with experimentally observed spectra. Moreover, the analysis of the coherence properties of the simulated spectra shows the existence of correlated and phase-locked combs. Our work paves the way for a new class of frequency comb sources that could enable straightforward access to new spectral regions, such as the mid-infrared, and stimulate novel applications of frequency combs.

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“…6 In a nonlinear cavity that is phase matched for second-harmonic generation (SHG), the generated harmonic power can reach the threshold for parametric oscillation leading to an internally pumped optical parametric oscillator (IP-OPO), which triggers a cascade of secondary three-wave processes, eventually forming frequency combs around the fundamental frequency (FF) and its second harmonic (SH). A lower threshold, thus a higher efficiency, can be achieved by exploiting materials with a strong quadratic coupling constant and maintaining a phase matching relation between the interacting fields over a sufficiently long interaction path.…”

Section: Introductionmentioning

confidence: 99%

Directional quasi-phase matching AlGaAs waveguide microresonators for efficient generation of quadratic frequency combs

et al. 2017

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Optical frequency combs currently represent enabling components in a wide number of fast-growing research fields, from frequency metrology to precision spectroscopy, from synchronization of telecommunication systems to environmental and biomedical spectrometry. As recently demonstrated, quadratic nonlinear media are a promising platform for optical frequency combs generation, through the onset of an internally pumped optical parametric oscillator in cavity enhanced second-harmonic generation systems. We present here a proposal for quadratic frequency comb generation in AlGaAs waveguide resonators. Based on the crystal symmetry properties of the AlGaAs material, quasi-phase matching can be realized in curved geometries (directional quasi-phase matching), thus ensuring efficient optical frequency conversion. We propose a novel design of AlGaAs waveguide resonators with strongly reduced total losses, compatible with long-path, high-quality resonators. By means of a numerical study, we predict efficient frequency comb generation with threshold powers in the microwatt range, paving the way for the full integration of frequency comb synthesizers in photonic circuits.

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Single envelope equation modeling of multi-octave comb arrays in microresonators with quadratic and cubic nonlinearities

Cited by 42 publications

References 42 publications

Theory of quadratic optical frequency combs

Theory of quadratic optical frequency combs

Frequency comb generation in continuously pumped optical parametric oscillator

Directional quasi-phase matching AlGaAs waveguide microresonators for efficient generation of quadratic frequency combs

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