1
|
Opačak N, Schneider B, Faist J, Schwarz B. Impact of higher-order dispersion on frequency-modulated combs. OPTICS LETTERS 2024; 49:794-797. [PMID: 38359184 DOI: 10.1364/ol.509529] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2023] [Accepted: 01/11/2024] [Indexed: 02/17/2024]
Abstract
Frequency-modulated (FM) combs form spontaneously in free-running semiconductor lasers and possess a vast potential for spectroscopic applications. Despite recent progress in obtaining a conclusive theoretical description, experimental FM combs often exhibit non-ideal traits, which prevents their widespread use. Here we explain this by providing a clear theoretical and experimental study of the impact of the higher-order dispersion on FM combs. We reveal that spectrally dependent dispersion is detrimental for comb performance and leads to a decreased comb bandwidth and the appearance of spectral holes. These undesirable traits can be mended by applying a radio frequency modulation of the laser bias. We show that electrical injection-locking of the laser leads to a significant increase of the comb bandwidth, a uniform-like spectral amplitudes, and the rectification of the instantaneous frequency to recover a nearly linear frequency chirp of FM combs.
Collapse
|
2
|
Seitner L, Popp J, Heckelmann I, Vass RE, Meng B, Haider M, Faist J, Jirauschek C. Backscattering-Induced Dissipative Solitons in Ring Quantum Cascade Lasers. PHYSICAL REVIEW LETTERS 2024; 132:043805. [PMID: 38335338 DOI: 10.1103/physrevlett.132.043805] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2023] [Revised: 10/25/2023] [Accepted: 11/27/2023] [Indexed: 02/12/2024]
Abstract
Ring quantum cascade lasers have recently gained considerable attention, showing ultrastable frequency comb and soliton operation, thus opening a way to integrated spectrometers in the midinfrared and terahertz fingerprint regions. Thanks to a self-consistent Maxwell-Bloch model, we demonstrate, in excellent agreement with the experimental data, that a small but finite coupling between the counterpropagating waves arising from distributed backscattering is essential to stabilize the soliton solution.
Collapse
Affiliation(s)
- Lukas Seitner
- TUM School of Computation, Information and Technology, Technical University of Munich (TUM), 85748 Garching, Germany
| | - Johannes Popp
- TUM School of Computation, Information and Technology, Technical University of Munich (TUM), 85748 Garching, Germany
| | - Ina Heckelmann
- Institute for Quantum Electronics, Eidgenössische Technische Hochschule Zürich, 8092 Zurich, Switzerland
| | - Réka-Eszter Vass
- Institute for Quantum Electronics, Eidgenössische Technische Hochschule Zürich, 8092 Zurich, Switzerland
- Physik-Institut, Universität Zürich, 8057 Zurich, Switzerland
| | - Bo Meng
- Institute for Quantum Electronics, Eidgenössische Technische Hochschule Zürich, 8092 Zurich, Switzerland
- State Key Laboratory of Luminescence and Applications, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, People's Republic of China
| | - Michael Haider
- TUM School of Computation, Information and Technology, Technical University of Munich (TUM), 85748 Garching, Germany
| | - Jérôme Faist
- Institute for Quantum Electronics, Eidgenössische Technische Hochschule Zürich, 8092 Zurich, Switzerland
| | - Christian Jirauschek
- TUM School of Computation, Information and Technology, Technical University of Munich (TUM), 85748 Garching, Germany
- TUM Center for Quantum Engineering (ZQE), 85748 Garching, Germany
| |
Collapse
|
3
|
Kazakov D, Letsou TP, Beiser M, Zhi Y, Opačak N, Piccardo M, Schwarz B, Capasso F. Active mid-infrared ring resonators. Nat Commun 2024; 15:607. [PMID: 38242868 PMCID: PMC10799048 DOI: 10.1038/s41467-023-44628-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2023] [Accepted: 12/20/2023] [Indexed: 01/21/2024] Open
Abstract
High-quality optical ring resonators can confine light in a small volume and store it for millions of roundtrips. They have enabled the dramatic size reduction from laboratory scale to chip level of optical filters, modulators, frequency converters, and frequency comb generators in the visible and the near-infrared. The mid-infrared spectral region (3-12 μm), as important as it is for molecular gas sensing and spectroscopy, lags behind in development of integrated photonic components. Here we demonstrate the integration of mid-infrared ring resonators and directional couplers, incorporating a quantum cascade active region in the waveguide core. It enables electrical control of the resonant frequency, its quality factor, the coupling regime and the coupling coefficient. We show that one device, depending on its operating point, can act as a tunable filter, a nonlinear frequency converter, or a frequency comb generator. These concepts extend to the integration of multiple active resonators and waveguides in arbitrary configurations, thus allowing the implementation of purpose-specific mid-infrared active photonic integrated circuits for spectroscopy, communication, and microwave generation.
Collapse
Affiliation(s)
- Dmitry Kazakov
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA.
| | - Theodore P Letsou
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02142, USA
| | - Maximilian Beiser
- Institute of Solid State Electronics, TU Wien, 1040, Vienna, Austria
| | - Yiyang Zhi
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
- UC Berkeley, Berkeley, CA, 94720, USA
| | - Nikola Opačak
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
- Institute of Solid State Electronics, TU Wien, 1040, Vienna, Austria
| | - Marco Piccardo
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
- Department of Physics, Instituto Superior Técnico, Universidade de Lisboa, 1049-001, Lisbon, Portugal
- Instituto de Engenharia de Sistemas e Computadores - Microsistemas e Nanotecnologias (INESC MN), 1000-029, Lisbon, Portugal
| | - Benedikt Schwarz
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
- Institute of Solid State Electronics, TU Wien, 1040, Vienna, Austria
| | - Federico Capasso
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA.
| |
Collapse
|
4
|
Opačak N, Kazakov D, Columbo LL, Beiser M, Letsou TP, Pilat F, Brambilla M, Prati F, Piccardo M, Capasso F, Schwarz B. Nozaki-Bekki solitons in semiconductor lasers. Nature 2024; 625:685-690. [PMID: 38267681 DOI: 10.1038/s41586-023-06915-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2023] [Accepted: 11/29/2023] [Indexed: 01/26/2024]
Abstract
Optical frequency-comb sources, which emit perfectly periodic and coherent waveforms of light1, have recently rapidly progressed towards chip-scale integrated solutions. Among them, two classes are particularly significant-semiconductor Fabry-Perót lasers2-6 and passive ring Kerr microresonators7-9. Here we merge the two technologies in a ring semiconductor laser10,11 and demonstrate a paradigm for the formation of free-running solitons, called Nozaki-Bekki solitons. These dissipative waveforms emerge in a family of travelling localized dark pulses, known within the complex Ginzburg-Landau equation12-14. We show that Nozaki-Bekki solitons are structurally stable in a ring laser and form spontaneously with tuning of the laser bias, eliminating the need for an external optical pump. By combining conclusive experimental findings and a complementary elaborate theoretical model, we reveal the salient characteristics of these solitons and provide guidelines for their generation. Beyond the fundamental soliton circulating inside the ring laser, we demonstrate multisoliton states as well, verifying their localized nature and offering an insight into formation of soliton crystals15. Our results consolidate a monolithic electrically driven platform for direct soliton generation and open the door for a research field at the junction of laser multimode dynamics and Kerr parametric processes.
Collapse
Affiliation(s)
- Nikola Opačak
- Institute of Solid State Electronics, TU Wien, Vienna, Austria.
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA.
| | - Dmitry Kazakov
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
| | - Lorenzo L Columbo
- Dipartimento di Elettronica e Telecomunicazioni, Politecnico di Torino, Turin, Italy
| | | | - Theodore P Letsou
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Florian Pilat
- Institute of Solid State Electronics, TU Wien, Vienna, Austria
| | - Massimo Brambilla
- Dipartimento di Fisica Interateneo and CNR-IFN, Università e Politecnico di Bari, Bari, Italy
| | - Franco Prati
- Dipartimento di Scienza e Alta Tecnologia, Università dell'Insubria, Como, Italy
| | - Marco Piccardo
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
- Department of Physics, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal
- Instituto de Engenharia de Sistemas e Computadores - Microsistemas e Nanotecnologias (INESC MN), Lisbon, Portugal
| | - Federico Capasso
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
| | - Benedikt Schwarz
- Institute of Solid State Electronics, TU Wien, Vienna, Austria.
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA.
| |
Collapse
|
5
|
Heckelmann I, Bertrand M, Dikopoltsev A, Beck M, Scalari G, Faist J. Quantum walk comb in a fast gain laser. Science 2023; 382:434-438. [PMID: 37883562 DOI: 10.1126/science.adj3858] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2023] [Accepted: 09/07/2023] [Indexed: 10/28/2023]
Abstract
Synthetic lattices in photonics enable the exploration of light states in new dimensions, transcending phenomena common only to physical space. We propose and demonstrate a quantum walk comb in synthetic frequency space formed by externally modulating a ring-shaped semiconductor laser with ultrafast recovery times. The initially ballistic quantum walk does not dissipate into low supermode states of the synthetic lattice; instead, the state stabilizes in a broad frequency comb, unlocking the full potential of the synthetic frequency lattice. Our device produces a low-noise, nearly flat broadband comb (reaching 100 per centimeter bandwidth) and offers a promising platform to generate broadband, tunable, and stable frequency combs.
Collapse
Affiliation(s)
- Ina Heckelmann
- Institute of Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland, and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | - Mathieu Bertrand
- Institute of Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland, and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | - Alexander Dikopoltsev
- Institute of Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland, and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | - Mattias Beck
- Institute of Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland, and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | - Giacomo Scalari
- Institute of Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland, and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | - Jérôme Faist
- Institute of Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland, and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| |
Collapse
|
6
|
Micheletti P, Senica U, Forrer A, Cibella S, Torrioli G, Frankié M, Beck M, Faist J, Scalari G. Terahertz optical solitons from dispersion-compensated antenna-coupled planarized ring quantum cascade lasers. SCIENCE ADVANCES 2023; 9:eadf9426. [PMID: 37315137 DOI: 10.1126/sciadv.adf9426] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2022] [Accepted: 05/08/2023] [Indexed: 06/16/2023]
Abstract
Quantum cascade lasers (QCLs) constitute an intriguing opportunity for the generation of on-chip optical dissipative Kerr solitons (DKSs). Originally demonstrated in passive microresonators, DKSs were recently observed in mid-infrared ring QCL paving the way for their achievement even at longer wavelengths. To this end, we realized defect-free terahertz ring QCLs featuring anomalous dispersion leveraging on a technological platform based on waveguide planarization. A concentric coupled waveguide approach is implemented for dispersion compensation, while a passive broadband bullseye antenna improves the device power extraction and far field. Comb spectra featuring sech2 envelopes are presented for free-running operation. The presence of solitons is further supported by observing the highly hysteretic behavior, measuring the phase difference between the modes, and reconstructing the intensity time profile highlighting the presence of self-starting 12-picosecond-long pulses. These observations are in very good agreement with our numeric simulations based on a Complex Ginzburg-Landau Equation (CGLE).
Collapse
Affiliation(s)
- Paolo Micheletti
- Institute for Quantum Electronics, ETH-Zürich, 8093 Zürich, Switzerland
| | - Urban Senica
- Institute for Quantum Electronics, ETH-Zürich, 8093 Zürich, Switzerland
| | - Andres Forrer
- Institute for Quantum Electronics, ETH-Zürich, 8093 Zürich, Switzerland
| | - Sara Cibella
- CNR-Istituto di Fotonica e Nanotecnologie, Rome, Italy
| | | | - Martin Frankié
- Institute for Quantum Electronics, ETH-Zürich, 8093 Zürich, Switzerland
| | - Mattias Beck
- Institute for Quantum Electronics, ETH-Zürich, 8093 Zürich, Switzerland
| | - Jérôme Faist
- Institute for Quantum Electronics, ETH-Zürich, 8093 Zürich, Switzerland
| | - Giacomo Scalari
- Institute for Quantum Electronics, ETH-Zürich, 8093 Zürich, Switzerland
| |
Collapse
|
7
|
Hillbrand J, Bertrand M, Wittwer V, Opačak N, Kapsalidis F, Gianella M, Emmenegger L, Schwarz B, Südmeyer T, Beck M, Faist J. Synchronization of frequency combs by optical injection. OPTICS EXPRESS 2022; 30:36087-36095. [PMID: 36258545 DOI: 10.1364/oe.456775] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2022] [Accepted: 08/24/2022] [Indexed: 06/16/2023]
Abstract
Optical frequency combs based on semiconductor lasers are a promising technology for monolithic integration of dual-comb spectrometers. However, the stabilization of offset frequency fceo remains a challenging feat due the lack of octave-spanning spectra. In a dual-comb configuration, the uncorrelated jitter of the offset frequencies leads to a non-periodic signal resulting in broadened beatnotes with a limited signal-to-noise ratio (SNR). Hence, expensive data acquisition schemes and complex signal processing are currently required. Here, we show that the offset frequencies of two frequency combs can be synchronized by optical injection locking, which allows full phase-stabilization when combined with electrical injection locking of both repetition frequencies frep. A single comb line isolated via an optical Vernier filter serves as Master oscillator for injection locking. The resulting dual-comb signal is periodic and stable over thousands of periods. This enables coherent averaging using analog electronics, which increases the SNR and reduces the data size by one and three orders of magnitude, respectively. The presented method will enable fully phase-stabilized dual-comb spectrometers by leveraging on integrated optical filters and provides access for comparing and stabilizing fceo to narrow-linewidth optical references.
Collapse
|
8
|
Humbard L, Burghoff D. Analytical theory of frequency-modulated combs: generalized mean-field theory, complex cavities, and harmonic states. OPTICS EXPRESS 2022; 30:5376-5401. [PMID: 35209502 DOI: 10.1364/oe.445570] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2021] [Accepted: 12/22/2021] [Indexed: 06/14/2023]
Abstract
Frequency-modulated (FM) combs with a linearly-chirped frequency and nearly constant intensity occur naturally in certain laser systems; they can be most succinctly described by a nonlinear Schrödinger equation with a phase potential. In this work, we perform a comprehensive analytical study of FM combs in order to calculate their salient properties. We develop a general procedure that allows mean-field theories to be constructed for arbitrary sets of master equations, and as an example consider the case of reflective defects. We derive an expression for the FM chirp of arbitrary Fabry-Perot cavities-important for most realistic lasers-and use perturbation theory to show how they are affected by finite gain bandwidth and linewidth enhancment in fast gain media. Lastly, we show that an eigenvalue formulation of the laser's dynamics can be useful for characterizing all of the stable states of the laser: the fundamental comb, the continuous-wave solution, and the harmonic states.
Collapse
|