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Ricciardi I, Maddaloni P, De Natale P, Erkintalo M, Hansson T, Arie A, Wabnitz S, De Rosa M. Optical frequency combs in dispersion-controlled doubly resonant second-harmonic generation. OPTICS EXPRESS 2022; 30:45694-45704. [PMID: 36522969 DOI: 10.1364/oe.472424] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2022] [Accepted: 10/27/2022] [Indexed: 06/17/2023]
Abstract
We report on the experimental realization and a systematic study of optical frequency comb generation in doubly resonant intracavity second harmonic generation (SHG). The efficiency of intracavity nonlinear processes usually benefits from the increasing number of resonating fields. Yet, achieving the simultaneous resonance of different fields may be technically complicated, all the more when a phase matching condition must be fulfilled as well. In our cavity we can separately control the resonance condition for the fundamental and its second harmonic, by simultaneously acting on an intracavity dispersive element and on a piezo-mounted cavity mirror, without affecting the quasi-phase matching condition. In addition, by finely adjusting the laser-to-cavity detuning, we are able to observe steady comb emission across the whole resonance profile, revealing the multiplicity of comb structures, and the substantial role of thermal effects on their dynamics. Lastly, we report the results of numerical simulations of comb dynamics, which include photothermal effects, finding a good agreement with the experimental observations. Our system provides a framework for exploring the richness of comb dynamics in doubly resonant SHG systems, assisting the design of chip-scale quadratic comb generators.
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Smirnov S, Andryushkov V, Podivilov E, Sturman B, Breunig I. Soliton based χ (2) combs in high-Q optical microresonators. OPTICS EXPRESS 2021; 29:27434-27449. [PMID: 34615159 DOI: 10.1364/oe.432529] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2021] [Accepted: 07/29/2021] [Indexed: 06/13/2023]
Abstract
Investigations of the frequency combs in χ(3) microresonators have passed a critical point when the soliton based regimes are well established and realized on different platforms. For χ(2) microresonators, where the first harmonic (FH) and second harmonic (SH) envelopes are coupled via the SH generation and optical parametric oscillation, the comb-soliton studies are just starting. Here we report on a vast accessible dual χ(2) soliton-comb family in high-Q microresonators with the SH and FH combs centered at the pump frequency ωp and its half ωp/2. Vicinity of the point of equal FH and SH group velocities λc, available via proper radial poling, is found to be the most advantageous for the generation of spectrally broad dual FH-SH combs. Our predictions as applied to lithium niobate resonators include the dependence of comb and dissipative soliton parameters on the pump power, the deviation λp - λc, the modal quality factors and frequency detunings, and the necessary parameters of radial poling of the resonator. These predictions form a solid basis for the realization of χ(2) frequency combs.
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Szabados J, Amiune N, Sturman B, Breunig I. Fine structure of second-harmonic resonances in χ (2) optical microresonators. OPTICS EXPRESS 2021; 29:13925-13936. [PMID: 33985119 DOI: 10.1364/oe.424617] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2021] [Accepted: 04/15/2021] [Indexed: 06/12/2023]
Abstract
Owing to the discrete frequency spectrum of whispering gallery resonators (WGRs), the resonance and phase-matching conditions for the interacting waves in the case of second-harmonic generation (SHG) cannot generally be fulfilled simultaneously. To account for this, we develop a model describing SHG in WGRs with non-zero frequency detunings at both the pump and second-harmonic frequencies. Our model predicts strong distortions of the line shape of pump and second-harmonic resonances for similar linewidths at both frequencies; for much larger linewidths at the second-harmonic frequency, this behavior is absent. Furthermore, it describes the SHG efficiency as a function of detuning. Experimentally, one can change the WGR eigenfrequencies, and thus the relative detuning between pump and second-harmonic waves by a number of means, for example electro-optically and thermally. Using a lithium niobate WGR, we show an excellent quantitative agreement for the SHG efficiency between our experimental results and the model. Also, we show the predicted distortions of the pump and second-harmonic resonances to be absent in the lithium niobate WGR but present in a cadmium silicon phosphide WGR, as expected from the linewidths of the resonances involved.
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Mas Arabí C, Parra-Rivas P, Hansson T, Gelens L, Wabnitz S, Leo F. Localized structures formed through domain wall locking in cavity-enhanced second-harmonic generation. OPTICS LETTERS 2020; 45:5856-5859. [PMID: 33057302 DOI: 10.1364/ol.399658] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2020] [Accepted: 09/22/2020] [Indexed: 06/11/2023]
Abstract
We analyze the formation of localized structures in cavity-enhanced second-harmonic generation. We focus on the phase-matched limit, and consider that fundamental and generated waves have opposite signs of group velocity dispersion. We show that these states form due to the locking of domain walls connecting two stable homogeneous states of the system, and undergo collapsed snaking. We study the impact of temporal walk-off on the stability and dynamics of these localized states.
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Smirnov S, Sturman B, Podivilov E, Breunig I. Walk-off controlled self-starting frequency combs in χ (2) optical microresonators. OPTICS EXPRESS 2020; 28:18006-18017. [PMID: 32680002 DOI: 10.1364/oe.395360] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2020] [Accepted: 05/22/2020] [Indexed: 06/11/2023]
Abstract
Investigations of frequency combs in χ(3) optical microresonators are burgeoning nowadays. Changeover to χ(2) resonators promises further advances and brings new challenges. Here, the comb generation entails not only coupled first and second harmonics (FHs and SHs) and two dispersion coefficients but also a substantial difference in the group velocities - the temporal walk-off. We predict walk-off controlled highly stable comb generation, which is drastically different from that known in the χ(3) case. This includes the general notion of antiperiodic states; formation of localized coherent antiperiodic steady states (solitons), where the FH and SH envelopes move with a common velocity without shape changes; characterization of a new vast family of antiperiodic solitons; and the dependence of comb spectra on the pump power and the group velocity difference.
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Szabados J, Puzyrev DN, Minet Y, Reis L, Buse K, Villois A, Skryabin DV, Breunig I. Frequency Comb Generation via Cascaded Second-Order Nonlinearities in Microresonators. PHYSICAL REVIEW LETTERS 2020; 124:203902. [PMID: 32501070 DOI: 10.1103/physrevlett.124.203902] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2020] [Accepted: 05/06/2020] [Indexed: 06/11/2023]
Abstract
Optical frequency combs are revolutionizing modern time and frequency metrology. In the past years, their range of applications has increased substantially, driven by their miniaturization through microresonator-based solutions. The combs in such devices are typically generated using the third-order χ^{(3)} nonlinearity of the resonator material. An alternative approach is making use of second-order χ^{(2)} nonlinearities. While the idea of generating combs this way has been around for almost two decades, so far only few demonstrations are known, based either on bulky bow-tie cavities or on relatively low-Q waveguide resonators. Here, we present the first such comb that is based on a millimeter-sized microresonator made of lithium niobate, that allows for cascaded second-order nonlinearities. This proof-of-concept device comes already with pump powers as low as 2 mW, generating repetition-rate-locked combs around 1064 and 532 nm. From the nonlinear dynamics point of view, the observed combs correspond to Turing roll patterns.
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Affiliation(s)
- Jan Szabados
- Laboratory for Optical Systems, Department of Microsystems Engineering-IMTEK, University of Freiburg, Georges-Köhler-Allee 102, 79110 Freiburg, Germany
| | - Danila N Puzyrev
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
| | - Yannick Minet
- Laboratory for Optical Systems, Department of Microsystems Engineering-IMTEK, University of Freiburg, Georges-Köhler-Allee 102, 79110 Freiburg, Germany
- Gisela and Erwin Sick Chair of Micro-optics, Department of Microsystems Engineering-IMTEK, University of Freiburg, Georges-Köhler-Allee 102, 79110 Freiburg, Germany
| | - Luis Reis
- Laboratory for Optical Systems, Department of Microsystems Engineering-IMTEK, University of Freiburg, Georges-Köhler-Allee 102, 79110 Freiburg, Germany
| | - Karsten Buse
- Laboratory for Optical Systems, Department of Microsystems Engineering-IMTEK, University of Freiburg, Georges-Köhler-Allee 102, 79110 Freiburg, Germany
- Fraunhofer Institute for Physical Measurement Techniques IPM, Heidenhofstraße 8, 79110 Freiburg, Germany
| | - Alberto Villois
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
| | - Dmitry V Skryabin
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
| | - Ingo Breunig
- Laboratory for Optical Systems, Department of Microsystems Engineering-IMTEK, University of Freiburg, Georges-Köhler-Allee 102, 79110 Freiburg, Germany
- Fraunhofer Institute for Physical Measurement Techniques IPM, Heidenhofstraße 8, 79110 Freiburg, Germany
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Hendry I, Trainor LS, Xu Y, Coen S, Murdoch SG, Schwefel HGL, Erkintalo M. Experimental observation of internally pumped parametric oscillation and quadratic comb generation in a χ (2) whispering-gallery-mode microresonator. OPTICS LETTERS 2020; 45:1204-1207. [PMID: 32108806 DOI: 10.1364/ol.385751] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2019] [Accepted: 01/29/2020] [Indexed: 06/10/2023]
Abstract
We report on the experimental observation of internally pumped parametric oscillation in a high-$\!Q$Q lithium niobate microresonator under conditions of natural phase matching. Specifically, launching near-infrared pump light around 1060 nm into a $ z $z-cut congruent lithium niobate microresonator, we observe the generation of optical sidebands around the input pump under conditions where second-harmonic generation is close to natural phase matching. We find that a wide range of different sideband frequency shifts can be generated by varying the experimental parameters. Under particular conditions, we observe the cascaded generation of several sidebands around the pump-the first steps of optical frequency comb generation via cavity-enhanced second-harmonic generation.
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Ricciardi I, Mosca S, Parisi M, Leo F, Hansson T, Erkintalo M, Maddaloni P, De Natale P, Wabnitz S, De Rosa M. Optical Frequency Combs in Quadratically Nonlinear Resonators. MICROMACHINES 2020; 11:E230. [PMID: 32102284 PMCID: PMC7074798 DOI: 10.3390/mi11020230] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/17/2020] [Revised: 02/17/2020] [Accepted: 02/19/2020] [Indexed: 11/17/2022]
Abstract
Optical frequency combs are one of the most remarkable inventions in recent decades. Originally conceived as the spectral counterpart of the train of short pulses emitted by mode-locked lasers, frequency combs have also been subsequently generated in continuously pumped microresonators, through third-order parametric processes. Quite recently, direct generation of optical frequency combs has been demonstrated in continuous-wave laser-pumped optical resonators with a second-order nonlinear medium inside. Here, we present a concise introduction to such quadratic combs and the physical mechanism that underlies their formation. We mainly review our recent experimental and theoretical work on formation and dynamics of quadratic frequency combs. We experimentally demonstrated comb generation in two configurations: a cavity for second harmonic generation, where combs are generated both around the pump frequency and its second harmonic and a degenerate optical parametric oscillator, where combs are generated around the pump frequency and its subharmonic. The experiments have been supported by a thorough theoretical analysis, aimed at modelling the dynamics of quadratic combs, both in frequency and time domains, providing useful insights into the physics of this new class of optical frequency comb synthesizers. Quadratic combs establish a new class of efficient frequency comb synthesizers, with unique features, which could enable straightforward access to new spectral regions and stimulate novel applications.
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Affiliation(s)
- Iolanda Ricciardi
- CNR-INO, Istituto Nazionale di Ottica, Via Campi Flegrei 34, I-80078 Pozzuoli (NA), Italy; (I.R.); (S.M.); (M.P.); (P.M.); (S.W.)
- INFN, Istituto Nazionale di Fisica Nucleare, Sez. di Napoli, Complesso Universitario di M.S. Angelo, Via Cintia, 80126 Napoli, Italy
| | - Simona Mosca
- CNR-INO, Istituto Nazionale di Ottica, Via Campi Flegrei 34, I-80078 Pozzuoli (NA), Italy; (I.R.); (S.M.); (M.P.); (P.M.); (S.W.)
| | - Maria Parisi
- CNR-INO, Istituto Nazionale di Ottica, Via Campi Flegrei 34, I-80078 Pozzuoli (NA), Italy; (I.R.); (S.M.); (M.P.); (P.M.); (S.W.)
| | - François Leo
- OPERA-photonics, Université libre de Bruxelles, 50 Avenue F. D. Roosevelt, CP 194/5, B-1050 Bruxelles, Belgium;
| | - Tobias Hansson
- Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden;
| | - Miro Erkintalo
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Auckland 1142, New Zealand;
- Physics Department, The University of Auckland, Auckland 1142, New Zealand
| | - Pasquale Maddaloni
- CNR-INO, Istituto Nazionale di Ottica, Via Campi Flegrei 34, I-80078 Pozzuoli (NA), Italy; (I.R.); (S.M.); (M.P.); (P.M.); (S.W.)
- INFN, Istituto Nazionale di Fisica Nucleare, Sez. di Napoli, Complesso Universitario di M.S. Angelo, Via Cintia, 80126 Napoli, Italy
| | - Paolo De Natale
- CNR-INO, Istituto Nazionale di Ottica, Largo E. Fermi 6, I-50125 Firenze, Italy;
| | - Stefan Wabnitz
- CNR-INO, Istituto Nazionale di Ottica, Via Campi Flegrei 34, I-80078 Pozzuoli (NA), Italy; (I.R.); (S.M.); (M.P.); (P.M.); (S.W.)
- Dipartimento di Ingegneria dell’Informazione, Elettronica e Telecomunicazioni, Sapienza Università di Roma- Via Eudossiana 18, I-00184 Roma, Italy
- Department of Physics, Novosibirsk State University, 1 Pirogova Street, Novosibirsk 630090, Russia
| | - Maurizio De Rosa
- CNR-INO, Istituto Nazionale di Ottica, Via Campi Flegrei 34, I-80078 Pozzuoli (NA), Italy; (I.R.); (S.M.); (M.P.); (P.M.); (S.W.)
- INFN, Istituto Nazionale di Fisica Nucleare, Sez. di Napoli, Complesso Universitario di M.S. Angelo, Via Cintia, 80126 Napoli, Italy
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Villois A, Kondratiev N, Breunig I, Puzyrev DN, Skryabin DV. Frequency combs in a microring optical parametric oscillator. OPTICS LETTERS 2019; 44:4443-4446. [PMID: 31517901 DOI: 10.1364/ol.44.004443] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2019] [Accepted: 08/11/2019] [Indexed: 06/10/2023]
Abstract
We report the soliton frequency comb generation in microring optical parametric oscillators operating in the downconversion regime and with the simultaneous presence of the χ(2) and Kerr nonlinearities. The combs are studied considering a typical geometry of a bulk LiNbO3 toroidal resonator with the normal group velocity dispersion spanning an interval between the pump and the downconverted signal. We have identified critical power signaling a transition between the relatively low pump power predominantly χ(2) combs and the high pump power ones shaped by the competition between the χ(2) and Kerr nonlinearities.
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