Frequency-comb formation in doubly resonant second-harmonic generation

Year: 2016

Authors: Leo F., Hansson T., Ricciardi I., De Rosa M., Coen S., Wabnitz S., Erkintalo M.

Autors Affiliation: The Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, The University of Auckland, Auckland 1142, New Zealand; Department of Applied Physics, Chalmers University of Technology, SE-41296 Goteborg, Sweden; Dipartimento di Ingegneria dell’Informazione, Universita di Brescia, via Branze 38, 25123 Brescia, Italy; CNR-INO, Istituto Nazionale di Ottica, Via Campi Flegrei 34, 80078 Pozzuoli (NA), Italy

Abstract: We theoretically study the generation of optical frequency combs and corresponding pulse trains in doubly resonant intracavity second-harmonic generation (SHG). We find that, despite the large temporal walk-off characteristic of realistic cavity systems, the nonlinear dynamics can be accurately and efficiently modeled using a pair of coupled mean-field equations. Through rigorous stability analysis of the system’s steady-state continuous-wave solutions, we demonstrate that walk-off can give rise to an unexplored regime of temporal modulation instability. Numerical simulations performed in this regime reveal rich dynamical behaviors, including the emergence of temporal patterns that correspond to coherent optical frequency combs. We also demonstrate that the two coupled equations that govern the doubly resonant cavity behavior can, under typical conditions, be reduced to a single mean-field equation akin to that describing the dynamics of singly-resonant-cavity SHG [F. Leo et al., Phys. Rev. Lett. 116, 033901 (2016)]. This reduced approach allows us to derive a simple expression for the modulation instability gain, thus permitting us to acquire significant insight into the underlying physics. We anticipate that our work will have a wide impact on the study of frequency combs in emerging doubly resonant cavity SHG platforms, including quadratically nonlinear microresonators.

Journal/Review: PHYSICAL REVIEW A

Volume: 93 (4)      Pages from: 043831-1  to: 043831-12

More Information: We acknowledge the Marsden Fund of The Royal Society of New Zealand, Rutherford Discovery Fellowships of The Royal Society of New Zealand, the Swedish Research Council (Grant No. 2013-7508), the Finnish Cultural Foundation, and the Ministero dell\’Istruzione, dell\’Universita e della Ricerca (Grant No. 2012BFNWZ2 and Progetto Premiale QUANTOM-Quantum Opto-Mechanics) for financial support.
KeyWords: Cavity resonators; Dynamics; Modulation; Natural frequencies; Nonlinear equations; Nonlinear optics; Optical frequency conversion; Optical materials, Dynamical behaviors; Intracavity second-harmonic generation; Mean field equation; Modulation instabilities; Optical frequency combs; Simple expression; Stability analysis; Temporal modulations, Harmonic generation
DOI: 10.1103/PhysRevA.93.043831

Citations: 56
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