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Si M, Huang Y, Ruan M, Shen B, Xu Z, Yu T, Wang X, Chen Y. Relativistic-guided stable mode of few-cycle 20 µm level infrared radiation. OPTICS EXPRESS 2023; 31:40202-40209. [PMID: 38041326 DOI: 10.1364/oe.503814] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Accepted: 10/30/2023] [Indexed: 12/03/2023]
Abstract
The generation of intense infrared radiation with a wavelength greater than 10 µm is limited by the optical materials in traditional methods or the laser-plasma parameters of plasma-bubble methods. In this study, we propose a new method for generating an intense longitudinal radiation field of tens of GV/m. By utilizing the oscillations of the electron film on the inner surface of the micro-tube, excited by the relativistic electron beam propagating within it, it is possible to obtain tunable long-wavelength few-cycle infrared radiation, ranging from 20 to 30 µm and even longer. The radiation source is guided entirely by a relativistic electron beam and formed a stable TM propagation mode in the micro-tube. This opens up new opportunities for applications of the relativistic intensity infrared radiation to high-field physics, shorter attosecond pulses generation and charged particle acceleration.
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2
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Liang Q, Chan YC, Toscano J, Bjorkman KK, Leinwand LA, Parker R, Nozik ES, Nesbitt DJ, Ye J. Breath analysis by ultra-sensitive broadband laser spectroscopy detects SARS-CoV-2 infection. J Breath Res 2023; 17:10.1088/1752-7163/acc6e4. [PMID: 37016829 PMCID: PMC10930087 DOI: 10.1088/1752-7163/acc6e4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 03/23/2023] [Indexed: 04/06/2023]
Abstract
Rapid testing is essential to fighting pandemics such as coronavirus disease 2019 (COVID-19), the disease caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Exhaled human breath contains multiple volatile molecules providing powerful potential for non-invasive diagnosis of diverse medical conditions. We investigated breath detection of SARS-CoV-2 infection using cavity-enhanced direct frequency comb spectroscopy (CE-DFCS), a state-of-the-art laser spectroscopic technique capable of a real-time massive collection of broadband molecular absorption features at ro-vibrational quantum state resolution and at parts-per-trillion volume detection sensitivity. Using a total of 170 individual breath samples (83 positive and 87 negative with SARS-CoV-2 based on reverse transcription polymerase chain reaction tests), we report excellent discrimination capability for SARS-CoV-2 infection with an area under the receiver-operating-characteristics curve of 0.849(4). Our results support the development of CE-DFCS as an alternative, rapid, non-invasive test for COVID-19 and highlight its remarkable potential for optical diagnoses of diverse biological conditions and disease states.
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Affiliation(s)
- Qizhong Liang
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, CO 80309, United States of America
- Department of Physics, University of Colorado, Boulder, CO 80309, United States of America
| | - Ya-Chu Chan
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, CO 80309, United States of America
- Department of Chemistry, University of Colorado, Boulder, CO 80309, United States of America
| | - Jutta Toscano
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, CO 80309, United States of America
- Department of Physics, University of Colorado, Boulder, CO 80309, United States of America
- Present address: Department of Chemistry, University of Basel, Klingelbergstrasse 80, 4056 Basel, Switzerland
| | - Kristen K Bjorkman
- BioFrontiers Institute, University of Colorado, Boulder, CO 80303, United States of America
| | - Leslie A Leinwand
- BioFrontiers Institute, University of Colorado, Boulder, CO 80303, United States of America
- Department of Molecular Cellular and Developmental Biology, University of Colorado, Boulder, CO 80303, United States of America
| | - Roy Parker
- BioFrontiers Institute, University of Colorado, Boulder, CO 80303, United States of America
- Department of Biochemistry and HHMI, University of Colorado, Boulder, CO 80303, United States of America
| | - Eva S Nozik
- Cardiovascular Pulmonary Research Laboratories, Departments of Pediatrics and Medicine, and Division of Pediatric Critical Care Medicine, University of Colorado Anschutz Medical Campus, Aurora, CO 80045, United States of America
| | - David J Nesbitt
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, CO 80309, United States of America
- Department of Physics, University of Colorado, Boulder, CO 80309, United States of America
- Department of Chemistry, University of Colorado, Boulder, CO 80309, United States of America
| | - Jun Ye
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, CO 80309, United States of America
- Department of Physics, University of Colorado, Boulder, CO 80309, United States of America
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3
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Cui Y, Huang H, Bai Y, Du W, Chen M, Zhou B, Jovanovic I, Galvanauskas A. Long-wave-infrared pulse production at 11 µm via difference-frequency generation driven by femtosecond mid-infrared all-fluoride fiber laser. OPTICS LETTERS 2023; 48:1890-1893. [PMID: 37221792 DOI: 10.1364/ol.480010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2022] [Accepted: 02/25/2023] [Indexed: 05/25/2023]
Abstract
We present an ultrafast long-wave infrared (LWIR) source driven by a mid-infrared fluoride fiber laser. It is based on a mode-locked Er:ZBLAN fiber oscillator and a nonlinear amplifier operating at 48 MHz. The amplified soliton pulses at ∼2.9 µm are shifted to ∼4 µm via the soliton self-frequency shifting process in an InF3 fiber. LWIR pulses with an average power of 1.25-mW centered at 11 µm with a spectral bandwidth of ∼1.3 µm are produced through difference-frequency generation (DFG) of the amplified soliton and its frequency-shifted replica in a ZnGeP2 crystal. Soliton-effect fluoride fiber sources operating in the mid-infrared for driving DFG conversion to LWIR enable higher pulse energies than with near-infrared sources, while maintaining relative simplicity and compactness, relevant for spectroscopy and other applications in LWIR.
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4
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Liu M, Gray RM, Costa L, Markus CR, Roy A, Marandi A. Mid-infrared cross-comb spectroscopy. Nat Commun 2023; 14:1044. [PMID: 36828826 PMCID: PMC9957991 DOI: 10.1038/s41467-023-36811-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Accepted: 02/16/2023] [Indexed: 02/26/2023] Open
Abstract
Dual-comb spectroscopy has been proven beneficial in molecular characterization but remains challenging in the mid-infrared region due to difficulties in sources and efficient photodetection. Here we introduce cross-comb spectroscopy, in which a mid-infrared comb is upconverted via sum-frequency generation with a near-infrared comb of a shifted repetition rate and then interfered with a spectral extension of the near-infrared comb. We measure CO2 absorption around 4.25 µm with a 1-µm photodetector, exhibiting a 233-cm-1 instantaneous bandwidth, 28000 comb lines, a single-shot signal-to-noise ratio of 167 and a figure of merit of 2.4 × 106 Hz1/2. We show that cross-comb spectroscopy can have superior signal-to-noise ratio, sensitivity, dynamic range, and detection efficiency compared to other dual-comb-based methods and mitigate the limits of the excitation background and detector saturation. This approach offers an adaptable and powerful spectroscopic method outside the well-developed near-IR region and opens new avenues to high-performance frequency-comb-based sensing with wavelength flexibility.
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Affiliation(s)
- Mingchen Liu
- Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Robert M Gray
- Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Luis Costa
- Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Charles R Markus
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Arkadev Roy
- Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Alireza Marandi
- Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA.
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5
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Elkhazraji A, Shakfa MK, Lamperti M, Hakimov K, Djebbi K, Gotti R, Gatti D, Marangoni M, Farooq A. High-resolution molecular fingerprinting in the 11.6-15 µm range by a quasi-CW difference-frequency-generation laser source. OPTICS EXPRESS 2023; 31:4164-4178. [PMID: 36785391 DOI: 10.1364/oe.480107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Accepted: 01/02/2023] [Indexed: 06/18/2023]
Abstract
We report an approach for high-resolution spectroscopy using a widely tunable laser emitting in the molecular fingerprint region. The laser is based on difference-frequency generation (DFG) in a nonlinear orientation-patterned GaAs crystal. The signal laser, a CO2 gas laser, is operated in a kHz-pulsed mode while the pump laser, an external-cavity quantum cascade laser, is finely mode-hop-free tuned. The idler radiation covers a spectral range of ∼11.6-15 µm with a laser linewidth of ∼ 2.3 MHz. We showcase the versatility and the potential for molecular fingerprinting of the developed DFG laser source by resolving the absorption features of a mixture of several species in the long-wavelength mid-infrared. Furthermore, exploiting the wide tunability and resolution of the spectrometer, we resolve the broadband absorption spectrum of ethylene (C2H4) over ∼13-14.2 µm and quantify the self-broadening coefficients of some selected spectral lines.
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6
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Generation of 8–20 μm Mid-Infrared Ultrashort Femtosecond Laser Pulses via Difference Frequency Generation. PHOTONICS 2022. [DOI: 10.3390/photonics9060372] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Mid-infrared (MIR) ultrashort laser pulses have a wide range of applications in the fields of environmental monitoring, laser medicine, food quality control, strong-field physics, attosecond science, and some other aspects. Recent years have seen great developments in MIR laser technologies. Traditional solid-state and fiber lasers focus on the research of the short-wavelength MIR region. However, due to the limitation of the gain medium, they still cannot cover the long-wavelength region from 8 to 20 µm. This paper summarizes the developments of 8–20 μm MIR ultrafast laser generation via difference frequency generation (DFG) and reviews related theoretical models. Finally, the feasibility of MIR power scaling by nonlinear-amplification DFG and methods for measuring the power of DFG-based MIR are analyzed from the author’s perspective.
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Santamaria L, Di Sarno V, Aiello R, De Rosa M, Ricciardi I, De Natale P, Maddaloni P. Infrared Comb Spectroscopy of Buffer-Gas-Cooled Molecules: Toward Absolute Frequency Metrology of Cold Acetylene. Int J Mol Sci 2020; 22:E250. [PMID: 33383699 PMCID: PMC7795711 DOI: 10.3390/ijms22010250] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2020] [Revised: 12/18/2020] [Accepted: 12/24/2020] [Indexed: 11/20/2022] Open
Abstract
We review the recent developments in precision ro-vibrational spectroscopy of buffer-gas-cooled neutral molecules, obtained using infrared frequency combs either as direct probe sources or as ultra-accurate optical rulers. In particular, we show how coherent broadband spectroscopy of complex molecules especially benefits from drastic simplification of the spectra brought about by cooling of internal temperatures. Moreover, cooling the translational motion allows longer light-molecule interaction times and hence reduced transit-time broadening effects, crucial for high-precision spectroscopy on simple molecules. In this respect, we report on the progress of absolute frequency metrology experiments with buffer-gas-cooled molecules, focusing on the advanced technologies that led to record measurements with acetylene. Finally, we briefly discuss the prospects for further improving the ultimate accuracy of the spectroscopic frequency measurement.
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Affiliation(s)
- Luigi Santamaria
- Agenzia Spaziale Italiana, Contrada Terlecchia, 75100 Matera, Italy;
| | - Valentina Di Sarno
- Consiglio Nazionale delle Ricerche-Istituto Nazionale di Ottica, Via Campi Flegrei 34, 80078 Pozzuoli, Italy; (V.D.S.); (R.A.); (M.D.R.); (I.R.)
- Istituto Nazionale di Fisica Nucleare, Sez. di Napoli, Complesso Universitario di M.S. Angelo, Via Cintia, 80126 Napoli, Italy
| | - Roberto Aiello
- Consiglio Nazionale delle Ricerche-Istituto Nazionale di Ottica, Via Campi Flegrei 34, 80078 Pozzuoli, Italy; (V.D.S.); (R.A.); (M.D.R.); (I.R.)
- Istituto Nazionale di Fisica Nucleare, Sez. di Napoli, Complesso Universitario di M.S. Angelo, Via Cintia, 80126 Napoli, Italy
| | - Maurizio De Rosa
- Consiglio Nazionale delle Ricerche-Istituto Nazionale di Ottica, Via Campi Flegrei 34, 80078 Pozzuoli, Italy; (V.D.S.); (R.A.); (M.D.R.); (I.R.)
- Istituto Nazionale di Fisica Nucleare, Sez. di Napoli, Complesso Universitario di M.S. Angelo, Via Cintia, 80126 Napoli, Italy
| | - Iolanda Ricciardi
- Consiglio Nazionale delle Ricerche-Istituto Nazionale di Ottica, Via Campi Flegrei 34, 80078 Pozzuoli, Italy; (V.D.S.); (R.A.); (M.D.R.); (I.R.)
- Istituto Nazionale di Fisica Nucleare, Sez. di Napoli, Complesso Universitario di M.S. Angelo, Via Cintia, 80126 Napoli, Italy
| | - Paolo De Natale
- Consiglio Nazionale delle Ricerche-Istituto Nazionale di Ottica, Largo E. Fermi 6, 50125 Firenze, Italy;
- Istituto Nazionale di Fisica Nucleare, Sez. di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy
| | - Pasquale Maddaloni
- Consiglio Nazionale delle Ricerche-Istituto Nazionale di Ottica, Via Campi Flegrei 34, 80078 Pozzuoli, Italy; (V.D.S.); (R.A.); (M.D.R.); (I.R.)
- Istituto Nazionale di Fisica Nucleare, Sez. di Napoli, Complesso Universitario di M.S. Angelo, Via Cintia, 80126 Napoli, Italy
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Hillbrand J, Opačak N, Piccardo M, Schneider H, Strasser G, Capasso F, Schwarz B. Mode-locked short pulses from an 8 μm wavelength semiconductor laser. Nat Commun 2020; 11:5788. [PMID: 33188222 PMCID: PMC7666187 DOI: 10.1038/s41467-020-19592-1] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2020] [Accepted: 10/11/2020] [Indexed: 11/13/2022] Open
Abstract
Quantum cascade lasers (QCL) have revolutionized the generation of mid-infrared light. Yet, the ultrafast carrier transport in mid-infrared QCLs has so far constituted a seemingly insurmountable obstacle for the formation of ultrashort light pulses. Here, we demonstrate that careful quantum design of the gain medium and control over the intermode beat synchronization enable transform-limited picosecond pulses from QCL frequency combs. Both an interferometric radio-frequency technique and second-order autocorrelation shed light on the pulse dynamics and confirm that mode-locked operation is achieved from threshold to rollover current. Furthermore, we show that both anti-phase and in-phase synchronized states exist in QCLs. Being electrically pumped and compact, mode-locked QCLs pave the way towards monolithically integrated non-linear photonics in the molecular fingerprint region beyond 6 μm wavelength. Producing pulses in the mid-IR often requires bulky sources and has been inaccessible with compact and versatile quantum cascade lasers (QCLs). Here, the authors demonstrate actively mode-locked, mid-IR QCL operation at room temperature.
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Affiliation(s)
- Johannes Hillbrand
- Institute of Solid State Electronics, TU Wien, Guß, Vienna, Austria. .,Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA.
| | - Nikola Opačak
- Institute of Solid State Electronics, TU Wien, Guß, Vienna, Austria
| | - Marco Piccardo
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA.,CNST - Fondazione Istituto Italiano di Tecnologia, Via Pascoli 70/3, 20133, Milano, Italy
| | - Harald Schneider
- Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany
| | | | - 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, Guß, Vienna, Austria. .,Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA.
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9
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Cao Q, Kärtner FX, Chang G. Towards high power longwave mid-IR frequency combs: power scalability of high repetition-rate difference-frequency generation. OPTICS EXPRESS 2020; 28:1369-1384. [PMID: 32121849 DOI: 10.1364/oe.28.001369] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2019] [Accepted: 12/01/2019] [Indexed: 06/10/2023]
Abstract
Frequency combs in the mid-IR wavelength are usually implemented by difference-frequency generation (DFG) that mixes pump pulses and signal pulses. Different from most optical parametric amplifiers that operate at a typical low repetition rate of <0.1 MHz, mid-IR frequency combs require that pump/signal pulse repetition rate must be at least as high as tens of MHz (normally >30 MHz). The DFG mixing high repetition rate (HRR) pulses limits the allowed pulse energy to prevent crystal damage. In this paper, we numerically investigate HRR DFG with a focus on the energy scalability of idler pulses. We show that HRR DFG-unlike optical parametric amplifiers-may operate in the linear regime, in which the idler pulse energy scales linearly with respect to the pump/signal pulse energy. Our simulation results suggest an efficient approach to energy scaling the idler mid-IR pulses in a HRR DFG: increase the signal pulse energy to the same level as the pump pulse energy. We also show that DFG seeded by pump/signal pulses at ∼2-µm range benefits from reduced group-velocity mismatch and exhibits better idler energy scalability. For example, 44.2-nJ pulses at 9.87 µm can be achieved by mixing 500-nJ, 2.0-µm pump pulses and 100-nJ, 2.508-µm signal pulses in a 2-mm-thick GaSe crystal. At the end of this paper, we show that such high-energy signal pulses can be derived from the pump pulses using a recently invented fiber-optic method. Therefore, implementation of high-power (>2 W) longwave mid-IR frequency combs is practically feasible.
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10
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Iwakuni K, Bui TQ, Niedermeyer JF, Sukegawa T, Ye J. Comb-resolved spectroscopy with immersion grating in long-wave infrared. OPTICS EXPRESS 2019; 27:1911-1921. [PMID: 30732237 DOI: 10.1364/oe.27.001911] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2018] [Accepted: 12/31/2018] [Indexed: 06/09/2023]
Abstract
We have developed a dispersive spectrometer by using a compact immersion grating for direct frequency comb spectroscopy in the long-wave infrared region of 8-10 μm for the first time. A frequency resolution of 460 MHz is achieved, which is the highest reported in this wavelength region with a dispersive spectrometer. We also demonstrate individual comb mode-resolved imaging by cavity filtering and apply this to obtain spectra of both simple and complex molecular spectra. These results indicate that the immersion grating spectrometer offers the next advancement for sensitive, high-resolution spectroscopy of transient and large/complex molecules when combined with cavity enhancement and cooling techniques.
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11
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Changala PB, Weichman ML, Lee KF, Fermann ME, Ye J. Rovibrational quantum state resolution of the C 60 fullerene. Science 2019; 363:49-54. [PMID: 30606838 DOI: 10.1126/science.aav2616] [Citation(s) in RCA: 48] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2018] [Accepted: 11/08/2018] [Indexed: 11/02/2022]
Abstract
The unique physical properties of buckminsterfullerene, C60, have attracted intense research activity since its original discovery. Total quantum state-resolved spectroscopy of isolated C60 molecules has been of particularly long-standing interest. Such observations have, to date, been unsuccessful owing to the difficulty in preparing cold, gas-phase C60 in sufficiently high densities. Here we report high-resolution infrared absorption spectroscopy of C60 in the 8.5-micron spectral region (1180 to 1190 wave number). A combination of cryogenic buffer-gas cooling and cavity-enhanced direct frequency comb spectroscopy has enabled the observation of quantum state-resolved rovibrational transitions. Characteristic nuclear spin statistical intensity patterns confirm the indistinguishability of the 60 carbon-12 atoms, while rovibrational fine structure encodes further details of the molecule's rare icosahedral symmetry.
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Affiliation(s)
- P Bryan Changala
- JILA, National Institute of Standards and Technology and University of Colorado, Department of Physics, University of Colorado, Boulder, CO 80309, USA.
| | - Marissa L Weichman
- JILA, National Institute of Standards and Technology and University of Colorado, Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - Kevin F Lee
- IMRA America, Inc., Ann Arbor, MI 48105, USA
| | | | - Jun Ye
- JILA, National Institute of Standards and Technology and University of Colorado, Department of Physics, University of Colorado, Boulder, CO 80309, USA.
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12
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Bui TQ, Changala PB, Bjork BJ, Yu Q, Wang Y, Stanton JF, Bowman J, Ye J. Spectral analyses of trans- and cis-DOCO transients via comb spectroscopy. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1484949] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Thinh Q. Bui
- JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO, USA
| | - P. Bryan Changala
- JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO, USA
| | - Bryce J. Bjork
- JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO, USA
| | - Qi Yu
- Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, Atlanta, GA, USA
| | - Yimin Wang
- Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, Atlanta, GA, USA
| | - John F. Stanton
- Department of Chemistry, University of Florida, Gainesville, FL, USA
| | - Joel Bowman
- Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, Atlanta, GA, USA
| | - Jun Ye
- JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO, USA
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