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Allerbeck J, Kuttruff J, Bobzien L, Huberich L, Tsarev M, Schuler B. Efficient and Continuous Carrier-Envelope Phase Control for Terahertz Lightwave-Driven Scanning Probe Microscopy. ACS PHOTONICS 2023; 10:3888-3895. [PMID: 38027247 PMCID: PMC10655500 DOI: 10.1021/acsphotonics.3c00555] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Indexed: 12/01/2023]
Abstract
The fundamental understanding of quantum dynamics in advanced materials requires precise characterization at the limit of spatiotemporal resolution. Ultrafast scanning tunneling microscopy is a powerful tool combining the benefits of picosecond time resolution provided by single-cycle terahertz (THz) pulses and atomic spatial resolution of a scanning tunneling microscope (STM). For the selective excitation of localized electronic states, the transient field profile must be tailored to the energetic structure of the system. Here, we present an advanced THz-STM setup combining multi-MHz repetition rates, strong THz near fields, and continuous carrier-envelope phase (CEP) control of the transient waveform. In particular, we employ frustrated total internal reflection as an efficient and cost-effective method for precise CEP control of single-cycle THz pulses with >60% field transmissivity, high pointing stability, and continuous phase shifting of up to 0.75 π in the far and near field. Efficient THz generation and dispersion management enable peak THz voltages at the tip-sample junction exceeding 20 V at 1 MHz and 1 V at 41 MHz. The system comprises two distinct THz generation arms, which facilitate individual pulse shaping and amplitude modulation. This unique feature enables the flexible implementation of various THz pump-probe schemes, thereby facilitating the study of electronic and excitonic excited-state propagation in nanostructures and low-dimensional materials systems. Scalability of the repetition rate up to 41 MHz, combined with a state-of-the-art low-temperature STM, paves the way toward the investigation of dynamical processes in atomic quantum systems at their native length and time scales.
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Affiliation(s)
- Jonas Allerbeck
- nanotech@surfaces
Laboratory, Empa, Swiss Federal Laboratories
for Materials Science and Technology, Überlandstrasse 129, 8600 Dübendorf, Switzerland
| | - Joel Kuttruff
- Department
of Physics, University of Konstanz, Universitätsstrasse 10, 78464 Konstanz, Germany
| | - Laric Bobzien
- nanotech@surfaces
Laboratory, Empa, Swiss Federal Laboratories
for Materials Science and Technology, Überlandstrasse 129, 8600 Dübendorf, Switzerland
| | - Lysander Huberich
- nanotech@surfaces
Laboratory, Empa, Swiss Federal Laboratories
for Materials Science and Technology, Überlandstrasse 129, 8600 Dübendorf, Switzerland
| | - Maxim Tsarev
- Department
of Physics, University of Konstanz, Universitätsstrasse 10, 78464 Konstanz, Germany
| | - Bruno Schuler
- nanotech@surfaces
Laboratory, Empa, Swiss Federal Laboratories
for Materials Science and Technology, Überlandstrasse 129, 8600 Dübendorf, Switzerland
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2
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Stoyanov L, Stefanov A, Dreischuh A, Paulus GG. Gouy phase of Bessel-Gaussian beams: theory vs. experiment. OPTICS EXPRESS 2023; 31:13683-13699. [PMID: 37157251 DOI: 10.1364/oe.480761] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
It is well-known that the wave of a freely propagating Gaussian beam experiences an additional π phase shift compared to a plane wave. This phase shift, known as the Gouy phase, has significant consequences in, e.g., nonlinear optics, since the nonlinear processes require high peak intensity and phase matching of the focused beams. Hence, determining and controlling the Gouy phase is crucial in many fields of modern optics and photonics. Here, we develop an analytical model for the Gouy phase of long-range Bessel-Gaussian beams obtained by annihilating highly charged optical vortices. The model accounts for the influence of the relevant experimental parameters (topological charge, radius-to-width ratio of the initial ring-shaped beam, and focal length of the Fourier-transforming lens). We find an evolution of the Gouy phase varying nearly linearly with propagation distance and confirm this result experimentally.
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3
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Yavorsky MA, Kozhaev MA, Fedorov AY, Vikulin DV, Barshak EV, Berzhansky VN, Lyashko SD, Kapralov PO, Belotelov VI. Topological Faraday Effect for Optical Vortices in Magnetic Films. PHYSICAL REVIEW LETTERS 2023; 130:166901. [PMID: 37154644 DOI: 10.1103/physrevlett.130.166901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2022] [Accepted: 03/17/2023] [Indexed: 05/10/2023]
Abstract
Here we experimentally demonstrate the topological Faraday effect-the polarization rotation caused by the orbital angular momentum of light. It is found that the Faraday effect of the optical vortex beam passing through a transparent magnetic dielectric film differs from the Faraday effect for a plane wave. The additional contribution to the Faraday rotation depends linearly on the topological charge and radial number of the beam. The effect is explained in terms of the optical spin-orbit interaction. These findings underline the importance of using the optical vortex beams for studies of magnetically ordered materials.
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Affiliation(s)
- M A Yavorsky
- V.I. Vernadsky Crimean Federal University, Vernadsky Prospekt, 4, Simferopol, 295007, Crimea
| | - M A Kozhaev
- Russian Quantum Center, Skolkovo, Moscow Region 143025, Russia
| | - A Yu Fedorov
- Russian Quantum Center, Skolkovo, Moscow Region 143025, Russia
- Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region 141701, Russia
| | - D V Vikulin
- V.I. Vernadsky Crimean Federal University, Vernadsky Prospekt, 4, Simferopol, 295007, Crimea
| | - E V Barshak
- V.I. Vernadsky Crimean Federal University, Vernadsky Prospekt, 4, Simferopol, 295007, Crimea
| | - V N Berzhansky
- V.I. Vernadsky Crimean Federal University, Vernadsky Prospekt, 4, Simferopol, 295007, Crimea
| | - S D Lyashko
- V.I. Vernadsky Crimean Federal University, Vernadsky Prospekt, 4, Simferopol, 295007, Crimea
| | - P O Kapralov
- Russian Quantum Center, Skolkovo, Moscow Region 143025, Russia
- Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region 141701, Russia
| | - V I Belotelov
- V.I. Vernadsky Crimean Federal University, Vernadsky Prospekt, 4, Simferopol, 295007, Crimea
- Russian Quantum Center, Skolkovo, Moscow Region 143025, Russia
- Photonic and Quantum Technologies School, Faculty of Physics, Lomonosov Moscow State University, Leninskie gori, 119991 Moscow, Russia
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4
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Intensity-dependent self-induced dual-color laser phase modulation and its effect on terahertz generation. Sci Rep 2021; 11:498. [PMID: 33436751 PMCID: PMC7804029 DOI: 10.1038/s41598-020-80105-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2020] [Accepted: 12/16/2020] [Indexed: 11/16/2022] Open
Abstract
Powerful, broadband terahertz (THz) pulses and its application attract an exponential growth of interests. Dual-color laser filamentation in gases is one of the promising THz sources because of the scalability of the THz energy and wavelength with input parameters. But the additional phase induced by the nonlinearities associated with high intensities cannot be neglected because it may result in modulation of the THz waves. We investigate the influences of the infrared pump energy and air dispersion on the terahertz generation in dual-color laser filament. We observe that optimum dual-color laser relative phase of the THz generation undergoes a linear shift with increasing pump energy due to the intensity-induced refractive index change. This phase shift is verified by the spectral broadening of a two-color laser affected by the same mechanism. The result improves our understanding of the theoretical framework for a higher power THz source.
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5
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Pelchat-Voyer S, Piché M. Clarifications on the Gouy phase of radially polarized laser beams. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2020; 37:1496-1504. [PMID: 32902441 DOI: 10.1364/josaa.400805] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2020] [Accepted: 08/11/2020] [Indexed: 06/11/2023]
Abstract
The Gouy phase, which describes how a field accumulates an additional phase shift around the focus compared to a spherical wave, is investigated for the strongly focused TM01 beam in free space. It is shown, using both analytical and numerical solutions, that when the effects of the edges of focusing optics are small, the complete variation of the on-axis Gouy phase of the longitudinal electric field is 2π. It is true even in the strongly focused limit. Moreover, we show, using an appropriate effective wavevector, how to retrieve the Gouy phase when the diffraction caused by the edges is dominant at the focus. We further investigate the off-axis Gouy phase of the TM01 beam and show that any slight variation from the optical axis causes a variation of the Gouy phase of the longitudinal electric field to reduce to π.
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6
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Jolly SW. On the importance of frequency-dependent beam parameters for vacuum acceleration with few-cycle radially polarized laser beams. OPTICS LETTERS 2020; 45:3865-3868. [PMID: 32667305 DOI: 10.1364/ol.394493] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2020] [Accepted: 06/03/2020] [Indexed: 06/11/2023]
Abstract
Tightly focused, ultrashort radially polarized laser beams have a large longitudinal field, which provides a strong motivation for direct particle acceleration and manipulation in a vacuum. The broadband nature of these beams means that chromatic properties of propagation and focusing are important to consider. We show via single-particle simulations that using the correct frequency-dependent beam parameters is imperative, especially as the pulse duration decreases to the few-cycle regime. The results with different spatio-spectral amplitude profiles show either a drastic increase or decrease of the final accelerated electron energy depending on the shape, motivating both proper characterization and potentially a route to optimization.
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7
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Brennecke S, Eicke N, Lein M. Gouy's Phase Anomaly in Electron Waves Produced by Strong-Field Ionization. PHYSICAL REVIEW LETTERS 2020; 124:153202. [PMID: 32357055 DOI: 10.1103/physrevlett.124.153202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2019] [Revised: 03/17/2020] [Accepted: 03/31/2020] [Indexed: 06/11/2023]
Abstract
Ionization of atoms by strong laser fields produces photoelectron momentum distributions that exhibit modulations due to the interference of outgoing electron trajectories. For a faithful modeling, it is essential to include previously overlooked phase shifts occurring when trajectories pass through focal points. Such phase shifts are known as Gouy's phase anomaly in optics or as Maslov phases in semiclassical theory. Because of Coulomb focusing in three dimensions, one out of two trajectories in photoelectron holography goes through a focal point as it crosses the symmetry axis in momentum space. In addition, there exist observable Maslov phases already in two dimensions. Clustering algorithms enable us to implement a semiclassical model with the correct preexponential factor that affects both the weight and the phase of each trajectory. We also derive a simple rule to relate two-dimensional and three-dimensional models for linear polarization. It explains the shifted interference fringes and weaker high-energy yield in three dimensions. The results are in excellent agreement with solutions of the time-dependent Schrödinger equation.
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Affiliation(s)
- Simon Brennecke
- Leibniz Universität Hannover, Institut für Theoretische Physik, Appelstraße 2, 30167 Hannover, Germany
| | - Nicolas Eicke
- Leibniz Universität Hannover, Institut für Theoretische Physik, Appelstraße 2, 30167 Hannover, Germany
| | - Manfred Lein
- Leibniz Universität Hannover, Institut für Theoretische Physik, Appelstraße 2, 30167 Hannover, Germany
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8
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Zhang Y, Zille D, Hoff D, Wustelt P, Würzler D, Möller M, Sayler AM, Paulus GG. Observing the Importance of the Phase-Volume Effect for Few-Cycle Light-Matter Interactions. PHYSICAL REVIEW LETTERS 2020; 124:133202. [PMID: 32302186 DOI: 10.1103/physrevlett.124.133202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2019] [Revised: 02/25/2020] [Accepted: 03/10/2020] [Indexed: 06/11/2023]
Abstract
The spatially dependent phase distribution of focused few-cycle pulses, i.e., the focal phase, is much more complex than the well-known Gouy phase of monochromatic beams. As the focal phase is imprinted on the carrier-envelope phase (CEP), for accurate modeling and interpretation of CEP-dependent few-cycle laser-matter interactions, both the coupled spatially dependent phase and intensity distributions must be taken into account. In this Letter, we demonstrate the significance of the focal phase effect via comparison of measurements and simulations of CEP-dependent photoelectron spectra. Moreover, we demonstrate the impact of this effect on few-cycle light-matter interactions as a function of their nonlinear intensity dependence to answer the general question: if, when, and how much should one be concerned about the focal phase?
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Affiliation(s)
- Yinyu Zhang
- Institute of Optics and Quantum Electronics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743 Jena, Germany and Helmholtz Institute Jena, Fröbelstieg 3, 07743 Jena, Germany
| | - Danilo Zille
- Institute of Optics and Quantum Electronics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743 Jena, Germany and Helmholtz Institute Jena, Fröbelstieg 3, 07743 Jena, Germany
| | - Dominik Hoff
- Institute of Optics and Quantum Electronics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743 Jena, Germany and Helmholtz Institute Jena, Fröbelstieg 3, 07743 Jena, Germany
| | - Philipp Wustelt
- Institute of Optics and Quantum Electronics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743 Jena, Germany and Helmholtz Institute Jena, Fröbelstieg 3, 07743 Jena, Germany
| | - Daniel Würzler
- Institute of Optics and Quantum Electronics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743 Jena, Germany and Helmholtz Institute Jena, Fröbelstieg 3, 07743 Jena, Germany
| | - Max Möller
- Institute of Optics and Quantum Electronics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743 Jena, Germany and Helmholtz Institute Jena, Fröbelstieg 3, 07743 Jena, Germany
| | - A M Sayler
- Institute of Optics and Quantum Electronics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743 Jena, Germany and Helmholtz Institute Jena, Fröbelstieg 3, 07743 Jena, Germany
| | - Gerhard G Paulus
- Institute of Optics and Quantum Electronics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743 Jena, Germany and Helmholtz Institute Jena, Fröbelstieg 3, 07743 Jena, Germany
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9
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Debrah DA, Stewart GA, Basnayake G, Tisch JWG, Lee SK, Li W. Direct in-situ single-shot measurements of the absolute carrier-envelope phases of ultrashort pulses. OPTICS LETTERS 2019; 44:3582-3585. [PMID: 31305577 DOI: 10.1364/ol.44.003582] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2019] [Accepted: 06/20/2019] [Indexed: 06/10/2023]
Abstract
Many important physical processes such as nonlinear optics and coherent control are highly sensitive to the absolute carrier-envelope phase (CEP) of driving ultrashort laser pulses. This makes the measurement of CEP immensely important in relevant fields. Even though relative CEPs can be measured with a few existing technologies, the estimate of the absolute CEP is not straightforward and always requires theoretical inputs. Here, we demonstrate a novel in-situ technique based on angular streaking that can achieve such a goal without complicated calibration procedures. Single-shot measurements of the absolute CEP have been achieved with an estimated precision of 0.19 radians.
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10
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Application of Quasi-Phase Matching Concept for Enhancement of High-Order Harmonics of Ultrashort Laser Pulses in Plasmas. APPLIED SCIENCES-BASEL 2019. [DOI: 10.3390/app9081701] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Novel methods of coherent short-wavelength sources generation require thorough analysis for their further amendments and practical implementations. In this work, we report on the quasi-phase matching (QPM) of high-order harmonics generation during the propagation of single- and two-color femtosecond pulses through multi-jet plasmas, which allows the enhancement of groups of harmonics in different ranges of extreme ultraviolet. The role of the number of coherent zones; sizes of plasma jets and the distance between them; plasma formation conditions, and the characteristics of the fundamental radiation on the harmonic efficiency at quasi-phase matching (QPM) conditions are analyzed. We demonstrate the ~40× enhancement factor of the maximally-enhanced harmonic with respect to the one generated at ordinary conditions in the imperforated plasma.
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11
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Saito N, Ishii N, Kanai T, Itatani J. All-optical characterization of the two-dimensional waveform and the Gouy phase of an infrared pulse based on plasma fluorescence of gas. OPTICS EXPRESS 2018; 26:24591-24601. [PMID: 30469572 DOI: 10.1364/oe.26.024591] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2018] [Accepted: 08/26/2018] [Indexed: 06/09/2023]
Abstract
The characterization of the temporal waveform of few-cycle laser pulses is an indispensable part in strong-field physics and attosecond science. Recently, a simple waveform-characterization technique called TIPTOE (tunneling ionization with a perturbation for the time-domain observation of an electric field) has been demonstrated for measuring linearly polarized few-cycle pulses. We theoretically and experimentally show that TIPTOE can be extended to resolve more characteristics of an optical waveform: the two-dimensional polarization and the Gouy phase. Based on the plasma fluorescence of a gaseous medium, we achieve all-optical and spatially resolved measurements of the waveform of an infrared pulse. This detection method enables the remote characterization of a waveform without the need to place an apparatus near the focal point of the laser beam. The proposed approach represents a simple and powerful method for conducting waveform diagnostics on few-cycle laser sources.
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12
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Bancelin S, Van der Kolk JN, Quigley AS, Pinsard M, Veres SP, Kreplak L, Ramunno L, Légaré F. Gouy phase shift measurement using interferometric second-harmonic generation. OPTICS LETTERS 2018; 43:1958-1961. [PMID: 29714771 DOI: 10.1364/ol.43.001958] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2018] [Accepted: 03/22/2018] [Indexed: 06/08/2023]
Abstract
We report on a simple way to directly measure the Gouy phase shift of a strongly focused laser beam. This is accomplished by using a recent technique, namely, interferometric second-harmonic generation. We expect that this method will be of interest in a wide range of research fields, from high-harmonic and attosecond pulse generation to femtochemistry and nonlinear microscopy.
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13
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Zhang Y, Guo X, Han L, Li P, Liu S, Cheng H, Zhao J. Gouy phase induced polarization transition of focused vector vortex beams. OPTICS EXPRESS 2017; 25:25725-25733. [PMID: 29041237 DOI: 10.1364/oe.25.025725] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2017] [Accepted: 10/03/2017] [Indexed: 06/07/2023]
Abstract
We propose a common criterion for the effect of Gouy phase on the distinct polarization transition of focused vector vortex beams (VVBs). Such polarization transition is strongly dependent on the parity of the smaller modulus between VVB's polarization order and topological charge. Significantly, the cross polarization transitions are observed at areas where the two spin components with equi-intensity are exactly overlapping and the Gouy phase difference (GPD) between them equals to (2k + 1)π, k is an integer. As a whole, the focal field shows radially variant polarization distributions resulting from the unequal intensity proportion of the two spin components. This polarization transition holds potential in modifying the patterns of periodic surface structure induced by femtosecond vector beams.
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14
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Liebmann M, Treffer A, Bock M, Elsaesser T, Grunwald R. Spectral anomalies and Gouy rotation around the singularity of ultrashort vortex pulses. OPTICS EXPRESS 2017; 25:26076-26088. [PMID: 29041269 DOI: 10.1364/oe.25.026076] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2017] [Accepted: 10/06/2017] [Indexed: 06/07/2023]
Abstract
Spectral anomalies of femtosecond pulses with orbital angular momentum were studied in the vicinity of singularities. Bessel-Gauss (BG) beams were generated with mode-locked Ti:sapphire oscillators and dispersion-compensated diffractive axicons acting as spiral phase plates (SPPs). High-resolution two-dimensional spectral mapping was performed with a scanning fiber probe. Progressive rotation of the most pronounced features, known as "spectral eyes", in the maps of spectral moments was found at increasing propagation distance. The phenomenon is explained by a wavelength-dependent Gouy phase shift of interfering spectral components in the twisted wavefront. Spatial "spectral switching" was detected for few-cycle pulses. Possible improvements of selectivity are proposed.
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15
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Fangming Y, Yan W, Lijuan M. Study on the volatilization inhibition performance and mechanism of monolayer during the leakage process of ammonia solution. CAN J CHEM ENG 2017. [DOI: 10.1002/cjce.22960] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Yang Fangming
- School of Marine Science and Technology; Tianjin University; Tianjin, 300072 P. R. China
| | - Wu Yan
- College of Chemical Engineering and Materials Science; Tianjin University of Science & Technology; Tianjin, 300457 P. R. China
| | - Ma Lijuan
- School of chemistry and Materials Science; Shanxi Normal University; Linfen, Shanxi, 041000 P. R. China
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16
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Schlaepfer F, Ludwig A, Lucchini M, Kasmi L, Volkov M, Gallmann L, Keller U. Gouy phase shift for annular beam profiles in attosecond experiments. OPTICS EXPRESS 2017; 25:3646-3655. [PMID: 28241577 DOI: 10.1364/oe.25.003646] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Attosecond pump-probe measurements are typically performed by combining attosecond pulses with more intense femtosecond, phase-locked infrared (IR) pulses because of the low average photon flux of attosecond light sources based on high-harmonic generation (HHG). Furthermore, the strong absorption of materials at the extreme ultraviolet (XUV) wavelengths of the attosecond pulses typically prevents the use of transmissive optics. As a result, pump and probe beams are typically recombined geometrically with a center-hole mirror that reflects the larger IR beam and transmits the smaller XUV, which leads to an annular beam profile of the IR. This modification of the IR beam can affect the pump-probe measurements because the propagation that follows the reflection on the center-hole mirror can strongly deviate from that of an ideal Gaussian beam. Here we present a detailed experimental study of the Gouy phase of an annular IR beam across the focus using a two-foci attosecond beamline and the RABBITT (reconstruction of attosecond beating by interference of two-photon transitions) technique. Our measurements show a Gouy phase shift of the truncated beam as large as 2π and a corresponding rate of 50 as/mm time delay change across the focus in a RABBITT measurement. These results are essential for attosecond pump-probe experiments that compare measurements of spatially separated targets.
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17
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Furch FJ, Giree A, Morales F, Anderson A, Wang Y, Schulz CP, Vrakking MJJ. Close to transform-limited, few-cycle 12 µJ pulses at 400 kHz for applications in ultrafast spectroscopy. OPTICS EXPRESS 2016; 24:19293-19310. [PMID: 27557209 DOI: 10.1364/oe.24.019293] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Non-collinear optical parametric amplification has become the leading technology for amplifying few-cycle carrier-envelope phase (CEP) stable pulses to high energy at extreme repetition rates. In this work, a parametric amplifier system devoted to ultrafast photoionization experiments with coincidence detection is reported. The amplifier delivers CEP-stable few-cycle pulses with an average power of 5 W, and operates at repetition rates between 400 and 800 kHz. Close to transform-limited compression of the few-cycle pulses is achieved with minimized spatio-temporal distortions. Potential limitations introduced by spatio-temporal couplings to applications in attosecond science are analyzed. In particular, it is shown that pulse front tilt resulting from non-collinear amplification can considerably reduce the asymmetry in stereo above threshold ionization (stereo-ATI) experiments.
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18
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Meng C, Lü Z, Huang Y, Wang X, Chen W, Zhang D, Zhao Z, Yuan J. In situ spatial mapping of Gouy phase slip with terahertz generation in two-color field. OPTICS EXPRESS 2016; 24:12301-12309. [PMID: 27410145 DOI: 10.1364/oe.24.012301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We establish a one-to-one mapping between the local phase slip and the spatial position near the focus by scanning a thin jet along the propagation direction of laser beams. The measurement shows that the optimal phase of terahertz can be utilized to characterize in situ the spatially dependent relative phase of the two-color field. We also investigate the role of the Gouy phase shift on terahertz generation from two-color laser-induced plasma. The result is of critical importance for phase-dependent applications of two-color laser-field, including high-order harmonic and terahertz generation.
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19
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Major B, Nemes D, Porras MA, Horváth ZL, Kovács AP. Carrier-envelope phase changes in the focal region: propagation effects measured by spectral interferometry. APPLIED OPTICS 2015; 54:10717-10724. [PMID: 26837041 DOI: 10.1364/ao.54.010717] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Spectral interferometric measurements are presented that show how wave propagation affects the carrier-envelope phase (CEP) of an ultrashort pulse in the focal region and results in variations that are different from the Gouy phase shift. Wavelength-dependent properties of the input beam are investigated and are seen to influence how the CEP is altered. The measured CEP changes show characteristics similar to the variations predicted by theory.
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20
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Artoni M, Zavatta A. Large phase-by-phase modulations in atomic interfaces. PHYSICAL REVIEW LETTERS 2015; 115:113005. [PMID: 26406829 DOI: 10.1103/physrevlett.115.113005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2015] [Indexed: 06/05/2023]
Abstract
Phase-resonant closed-loop optical transitions can be engineered to achieve broadly tunable light phase shifts. Such a novel phase-by-phase control mechanism does not require a cavity and is illustrated here for an atomic interface where a classical light pulse undergoes radian level phase modulations all-optically controllable over a few micron scale. It works even at low intensities and hence may be relevant to new applications of all-optical weak-light signal processing.
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Affiliation(s)
- M Artoni
- European Laboratory for Nonlinear Spectroscopy (LENS), I-50019 Sesto Fiorentino, Firenze, Italy
- Istituto Nazionale di Ottica (INO-CNR), I-50125 Firenze, Italy
- Department of Engineering and Information Technology, Brescia University, I-25133 Brescia, Italy
| | - A Zavatta
- Istituto Nazionale di Ottica (INO-CNR), I-50125 Firenze, Italy
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21
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Pang X, Fischer DG, Visser TD. Wavefront spacing and Gouy phase in presence of primary spherical aberration. OPTICS LETTERS 2014; 39:88-91. [PMID: 24365829 DOI: 10.1364/ol.39.000088] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We study the Gouy phase of a scalar wavefield that is focused by a lens suffering from primary spherical aberration. It is found that the Gouy phase has different behaviors at the two sides of the intensity maximum. This results in a systematic increase of the successive wavefront spacings around the diffraction focus. Since all lenses have some amount of spherical aberration, this observation has implications for optical calibration and metrology.
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22
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Kling NG, Betsch KJ, Zohrabi M, Zeng S, Anis F, Ablikim U, Jochim B, Wang Z, Kübel M, Kling MF, Carnes KD, Esry BD, Ben-Itzhak I. Carrier-envelope phase control over pathway interference in strong-field dissociation of H2+. PHYSICAL REVIEW LETTERS 2013; 111:163004. [PMID: 24182264 DOI: 10.1103/physrevlett.111.163004] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2013] [Indexed: 06/02/2023]
Abstract
The dissociation of an H2+ molecular-ion beam by linearly polarized, carrier-envelope-phase-tagged 5 fs pulses at 4×10(14) W/cm2 with a central wavelength of 730 nm was studied using a coincidence 3D momentum imaging technique. Carrier-envelope-phase-dependent asymmetries in the emission direction of H+ fragments relative to the laser polarization were observed. These asymmetries are caused by interference of odd and even photon number pathways, where net zero-photon and one-photon interference predominantly contributes at H+ + H kinetic energy releases of 0.2-0.45 eV, and net two-photon and one-photon interference contributes at 1.65-1.9 eV. These measurements of the benchmark H2+ molecule offer the distinct advantage that they can be quantitatively compared with ab initio theory to confirm our understanding of strong-field coherent control via the carrier-envelope phase.
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Affiliation(s)
- Nora G Kling
- J. R. Macdonald Laboratory, Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA
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23
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Guzzinati G, Schattschneider P, Bliokh KY, Nori F, Verbeeck J. Observation of the Larmor and Gouy rotations with electron vortex beams. PHYSICAL REVIEW LETTERS 2013; 110:093601. [PMID: 23496708 DOI: 10.1103/physrevlett.110.093601] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2012] [Indexed: 05/14/2023]
Abstract
Electron vortex beams carrying intrinsic orbital angular momentum (OAM) are produced in electron microscopes where they are controlled and focused by using magnetic lenses. We observe various rotational phenomena arising from the interaction between the OAM and magnetic lenses. First, the Zeeman coupling, proportional to the OAM and magnetic field strength, produces an OAM-independent Larmor rotation of a mode superposition inside the lens. Second, when passing through the focal plane, the electron beam acquires an additional Gouy phase dependent on the absolute value of the OAM. This brings about the Gouy rotation of the superposition image proportional to the sign of the OAM. A combination of the Larmor and Gouy effects can result in the addition (or subtraction) of rotations, depending on the OAM sign. This behavior is unique to electron vortex beams and has no optical counterpart, as Larmor rotation occurs only for charged particles. Our experimental results are in agreement with recent theoretical predictions.
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Affiliation(s)
- Giulio Guzzinati
- EMAT, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium
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24
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Wang X, Sun W, Cui Y, Ye J, Feng S, Zhang Y. Complete presentation of the Gouy phase shift with the THz digital holography. OPTICS EXPRESS 2013; 21:2337-2346. [PMID: 23389213 DOI: 10.1364/oe.21.002337] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Three dimensional information of the Gouy phase shift in a converging spherical terahertz (THz) beam is directly observed by using a THz balanced electro-optic holographic imaging system. The major properties of the Gouy phase shift are presented, including the longitudinal and transverse distributions, relationships with the frequency and the f-number, influence on the THz polarization. The imaging technique supplies an accurate and comprehensive measurement method for observing and understanding the Gouy phase shift.
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Affiliation(s)
- Xinke Wang
- Department of Physics, Capital Normal University, Beijing Key Lab for Terahertz Spectroscopy and Imaging, Key Laboratory of Terahertz Optoelectronics, Ministry of Education, No.105 XiSanHuan BeiLu, Beijing 100048, China
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25
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Laban DE, Palmer AJ, Wallace WC, Gaffney NS, Notermans RPMJW, Clevis TTJ, Pullen MG, Jiang D, Quiney HM, Litvinyuk IV, Kielpinski D, Sang RT. Extreme ultraviolet interferometer using high-order harmonic generation from successive sources. PHYSICAL REVIEW LETTERS 2012; 109:263902. [PMID: 23368563 DOI: 10.1103/physrevlett.109.263902] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2012] [Indexed: 06/01/2023]
Abstract
We present a new interferometer technique whereby multiple extreme ultraviolet light pulses are generated at different positions within a single laser focus (i.e., from successive sources) with a highly controllable time delay. The interferometer technique is tested with two generating media to create two extreme ultraviolet light pulses with a time delay between them. The delay is found to be a consequence of the Gouy phase shift. Ultimately the apparatus is capable of accessing unprecedented time scales by allowing stable and repeatable delays as small as 100 zs.
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Affiliation(s)
- D E Laban
- ARC Centre of Excellence for Coherent X-Ray Science, Griffith University, Brisbane, Queensland 4111, Australia
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26
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Bai Y, Song L, Xu R, Li C, Liu P, Zeng Z, Zhang Z, Lu H, Li R, Xu Z. Waveform-controlled terahertz radiation from the air filament produced by few-cycle laser pulses. PHYSICAL REVIEW LETTERS 2012; 108:255004. [PMID: 23004609 DOI: 10.1103/physrevlett.108.255004] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2012] [Indexed: 06/01/2023]
Abstract
Waveform-controlled terahertz (THz) radiation is of great importance due to its potential application in THz sensing and coherent control of quantum systems. We demonstrated a novel scheme to generate waveform-controlled THz radiation from air plasma produced when carrier-envelope-phase (CEP) stabilized few-cycle laser pulses undergo filamentation in ambient air. We launched CEP-stabilized 10 fs-long (~1.7 optical cycles) laser pulses at 1.8 μm into air and found that the generated THz waveform can be controlled by varying the filament length and the CEP of driving laser pulses. Calculations using the photocurrent model and including the propagation effects well reproduce the experimental results, and the origins of various phase shifts in the filament are elucidated.
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Affiliation(s)
- Ya Bai
- State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, People's Republic of China
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27
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Kremer M, Fischer B, Feuerstein B, de Jesus VLB, Sharma V, Hofrichter C, Rudenko A, Thumm U, Schröter CD, Moshammer R, Ullrich J. Electron localization in molecular fragmentation of H2 by carrier-envelope phase stabilized laser pulses. PHYSICAL REVIEW LETTERS 2009; 103:213003. [PMID: 20366033 DOI: 10.1103/physrevlett.103.213003] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2009] [Indexed: 05/29/2023]
Abstract
Fully differential data for H2 dissociation in ultrashort (6 fs, 760 nm), linearly polarized, intense (0.44 PW/cm{2}) laser pulses with a stabilized carrier-envelope phase (CEP) were recorded with a reaction microscope. Depending on the CEP, the molecular orientation, and the kinetic energy release (KER), we find asymmetric proton emission at low KERs (0-3 eV), basically predicted by Roudnev and Esry, and much stronger than reported by Kling et al. Wave packet propagation calculations reproduce the salient features and discard, together with the observed KER-independent electron asymmetry, the first ionization step to be the reason for the asymmetric proton emission.
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Affiliation(s)
- Manuel Kremer
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany
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28
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Porras MA, Dombi P. Freezing the carrier-envelope phase of few-cycle light pulses about a focus. OPTICS EXPRESS 2009; 17:19424-19434. [PMID: 19997162 DOI: 10.1364/oe.17.019424] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
We study the effects of dispersive media and structures on the carrier-envelope phase (CEP) shift of focused few-cycles pulses. For phase-sensitive interactions with matter requiring focusing in vacuum, the variation of the CEP through the focal region can be significantly slow down by inserting a dispersive slab of adequate thickness between the focusing system and the focus. The focal CEP shift can also be slow down in experiments requiring focusing in a dispersive medium by a suitable choice of the dispersive propagation distance up to the focus.
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Affiliation(s)
- Miguel A Porras
- Departamento de Física Aplicada, Universidad Politécnica de Madrid, Rios Rosas 21, ES-28003 Madrid, Spain.
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29
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Gopal R, Simeonidis K, Moshammer R, Ergler T, Dürr M, Kurka M, Kühnel KU, Tschuch S, Schröter CD, Bauer D, Ullrich J, Rudenko A, Herrwerth O, Uphues T, Schultze M, Goulielmakis E, Uiberacker M, Lezius M, Kling MF. Three-dimensional momentum imaging of electron wave packet interference in few-cycle laser pulses. PHYSICAL REVIEW LETTERS 2009; 103:053001. [PMID: 19792493 DOI: 10.1103/physrevlett.103.053001] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2009] [Indexed: 05/28/2023]
Abstract
Using a reaction microscope, three-dimensional (3D) electron (and ion) momentum (P) spectra have been recorded for carrier-envelope-phase (CEP) stabilized few-cycle ( approximately 5 fs), intense ( approximately 4 x 10(14) W/cm2) laser pulses (740 nm) impinging on He. Preferential emission of low-energy electrons (E(e)<15 eV) to either hemisphere is observed as a function of the CEP. Clear interference patterns emerge in P space at CEPs with maximum asymmetry, interpreted as attosecond interferences of rescattered and directly emitted electron wave packets by means of a simple model.
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Affiliation(s)
- R Gopal
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany
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30
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Liu Y, Houard A, Durand M, Prade B, Mysyrowicz A. Maker fringes in the Terahertz radiation produced by a 2-color laser field in air. OPTICS EXPRESS 2009; 17:11480-11485. [PMID: 19582063 DOI: 10.1364/oe.17.011480] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
The terahertz radiation produced by a 2-color femtosecond laser scheme strongly saturates and develops an oscillatory behavior with increasing power of the driving femtosecond laser pulses. This is explained by the formation of a plasma channel due to filamentation. Due to dispersion inside the filament and the Gouy phase shift, the phase difference between the 800 nm and 400 nm pulses varies along this plasma emitter. As a result, the local THz radiations generated along the filament interfere destructively or constructively, which manifests itself in the form of Maker fringes.
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Affiliation(s)
- Y Liu
- Laboratoire d'Optique Appliquée, ENSTA, Ecole Polytechnique, CNRS UMR 7639, Palaiseau 91761, France
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31
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Baumann SM, Kalb DM, MacMillan LH, Galvez EJ. Propagation dynamics of optical vortices due to Gouy phase. OPTICS EXPRESS 2009; 17:9818-9827. [PMID: 19506631 DOI: 10.1364/oe.17.009818] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We study the propagation of off-axis vortices in a paraxial beam formed by two collinear Laguerre-Gauss beams. We show that the vortices move about the beam axis as the light propagates resulting in a rotation of the beam's transverse profile. This rotation is explained by the Gouy phase acquired by the component beams. Experimental measurements of the angular position of the vortices are in good agreement with a two-mode theory.
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Affiliation(s)
- S M Baumann
- Department of Physics and Astronomy, Colgate University Hamilton, New York 13346, USA
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32
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Porras MA. Characterization of the electric field of focused pulsed Gaussian beams for phase-sensitive interactions with matter. OPTICS LETTERS 2009; 34:1546-1548. [PMID: 19448816 DOI: 10.1364/ol.34.001546] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
The electric field of arbitrarily focused few-femtosecond pulsed Gaussian beams is characterized for their phase-sensitive interaction with matter. In the case of a transversally extended interaction region, the electric field is blurred, but effective values of the carrier-envelope phase and carrier frequency can still be defined.
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Affiliation(s)
- Miguel A Porras
- Departamento de Física Aplicada, Universidad Politécnica de Madrid, Rios Rosas 21, ES-28003 Madrid, Spain.
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33
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Camacho RM, Dixon PB, Glasser RT, Jordan AN, Howell JC. Realization of an all-optical zero to pi cross-phase modulation jump. PHYSICAL REVIEW LETTERS 2009; 102:013902. [PMID: 19257193 DOI: 10.1103/physrevlett.102.013902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2008] [Indexed: 05/27/2023]
Abstract
We report on the experimental demonstration of an all-optical pi cross-phase modulation jump. By performing a preselection, an optically induced unitary transformation, and then a postselection on the polarization degree of freedom, the phase of the output beam acquires either a zero or pi phase shift (with no other possible values). The postselection results in optical loss in the output beam. An input state may be chosen near the resulting phase singularity, yielding a pi phase shift even for weak interaction strengths. The scheme is experimentally demonstrated using a coherently prepared dark state in a warm atomic cesium vapor.
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Affiliation(s)
- Ryan M Camacho
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA.
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34
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35
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Görbe M, Osvay K, Grebing C, Steinmeyer G. Isochronic carrier-envelope phase-shift compensator. OPTICS LETTERS 2008; 33:2704-2706. [PMID: 19015715 DOI: 10.1364/ol.33.002704] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
A concept for orthogonal control of phase and group delay inside a laser cavity by a specially designed compensator assembly is discussed. Similar to the construction of variable polarization retarder, this assembly consists of two thin wedge prisms made from appropriately chosen optical materials. Being shifted as a whole, the assembly allows changing the phase delay with no influence on the cavity round-trip time, whereas relative shifting of the prisms enables adjustment of the latter. This scheme is discussed theoretically and verified experimentally, indicating a factor 30 reduction of the influence on the repetition rate compared to the commonly used silica wedge pair. For a 2pi adjustment of the carrier-envelope phase shift, single-pass timing differences are reduced to the single-femtosecond regime. With negligible distortions of timing and dispersion, the described compensator device greatly simplifies carrier-envelope phase control and experiments in extreme nonlinear optics.
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Affiliation(s)
- Mihaly Görbe
- Department of Optics and Quantum Electronics, University of Szeged, Szeged, Hungary
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36
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Kawase D, Miyamoto Y, Takeda M, Sasaki K, Takeuchi S. Observing quantum correlation of photons in Laguerre-Gauss modes using the Gouy phase. PHYSICAL REVIEW LETTERS 2008; 101:050501. [PMID: 18764380 DOI: 10.1103/physrevlett.101.050501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2008] [Indexed: 05/26/2023]
Abstract
The effect of the Gouy phase, which is one of the geometrical phases of photons, is observed through quantum correlation in Laguerre-Gaussian (LG) modes. In an experiment, the relative phase of two different LG modes of measurement basis states is manipulated via the Gouy phase, and the observed coincidence count rates agree well with theoretical predictions. This result suggests that the Gouy phase can be used as a new tool to manipulate multidimensional photonic quantum states.
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Affiliation(s)
- Daisuke Kawase
- Research Institute for Electronic Science, Hokkaido University, Sapporo, Japan
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37
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Lin Q, Zheng J, Becker W. Subcycle pulsed focused vector beams. PHYSICAL REVIEW LETTERS 2006; 97:253902. [PMID: 17280354 DOI: 10.1103/physrevlett.97.253902] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2006] [Indexed: 05/13/2023]
Abstract
An accurate description of a subcycle pulsed beam (SCPB) is presented based on the complex-source model. The fields are exact solutions of Maxwell's equations and applicable to a focused pulsed beam with a pulse duration down to and below one cycle of the carrier wave and with arbitrary polarization state. Depending on the pulse duration, the pulse is blueshifted, and its wings are chirped. This effect, which we refer to as "self-induced blueshift" goes beyond the carrier-envelope description. The corresponding phase is a temporal analog of the Gouy phase. The energy gain of a relativistic electron swept over by an SCPB is very sensitive to the proper form chosen to describe the pulse.
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Affiliation(s)
- Qiang Lin
- Institute of Optics, Department of Physics, Zhejiang University, Hangzhou 310027, China.
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38
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Verhoef AJ, Fernández A, Lezius M, O'Keeffe K, Uiberacker M, Krausz F. Few-cycle carrier envelope phase-dependent stereo detection of electrons. OPTICS LETTERS 2006; 31:3520-2. [PMID: 17099770 DOI: 10.1364/ol.31.003520] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
The spatial distribution of electrons emitted from atoms by few-cycle optical fields is known to be dependent on the carrier envelope phase, i.e., the phase of the field with respect to the pulse envelope. With respect to Paulus et al. [Phys. Rev. Lett.91, 253004 (2003)] we propose a greatly simplified device to measure and control the carrier envelope phase of few-cycle pulses with an accuracy of better than pi/10 based on this principle. We compared different schemes to control the carrier envelope phase of our pulses.
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Affiliation(s)
- Aart J Verhoef
- Max-Planck Institut für Quantenoptik, Garching, Germany.
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39
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Varin C, Piché M, Porras MA. Analytical calculation of the longitudinal electric field resulting from the tight focusing of an ultrafast transverse-magnetic laser beam. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2006; 23:2027-38. [PMID: 16835663 DOI: 10.1364/josaa.23.002027] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
A purely time-domain approach is proposed for the propagation of vectorial ultrafast beams in free space beyond the paraxial and the slowly varying envelope approximations. As an example of application of this method, we describe in detail the vectorial properties of an ultrafast tightly focused transverse-magnetic (TM(01)) beam, where special attention is given to the longitudinal electric field component. We show that for spot sizes at the waist comparable to the wavelength, the beam diverges more rapidly than expected from paraxial theory. A consequence of this phenomenon is a faster decrease of the amplitude of the longitudinal field away from the waist and a faster evolution of the axial Gouy phase shift in the vicinity of the focus. It has been observed that the phase of the beam has an overall variation of 2pi from z=-infinity to infinity, independent of the beam spot size at the waist and pulse duration.
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Affiliation(s)
- Charles Varin
- Centre d'Optique, Potonique et Laser, Université Laval, Québec, Canada
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40
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Nakajima T, Watanabe S. Effects of the carrier-envelope phase in the multiphoton ionization regime. PHYSICAL REVIEW LETTERS 2006; 96:213001. [PMID: 16803232 DOI: 10.1103/physrevlett.96.213001] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2005] [Indexed: 05/10/2023]
Abstract
We theoretically investigate the effects of the carrier-envelope phase of few-cycle laser pulses in the multiphoton ionization regime. For atoms with low ionization potential, total ionization yield barely exhibits phase dependence, as expected. However, population of some bound states clearly shows phase dependence. This implies that the measurement of the carrier-envelope phase would be possible through the photoemission between bound states without energy-and-angle-resolved photoelectron detection. The considered scheme could be particularly useful to measure the carrier-envelope phase for a light source without an amplifier, such as a laser oscillator, which cannot provide sufficient pulse energy to induce tunneling ionization.
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Affiliation(s)
- Takashi Nakajima
- Institute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan
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41
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Yang J, Winful HG. Generalized eikonal treatment of the Gouy phase shift. OPTICS LETTERS 2006; 31:104-6. [PMID: 16419892 DOI: 10.1364/ol.31.000104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
We use a generalized refractive index that includes diffraction effects to show that the Gouy phase shift can be seen as an intensity averaged optical path difference between the generalized eikonal and the geometrical eikonal. This approach generalizes previous treatments to include the effects of phase distortion and confirms the role of transverse spatial confinement in the Gouy shift.
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Affiliation(s)
- Jun Yang
- Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan 48109, USA.
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42
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Kolomenskii AA, Jerebtsov SN, Schuessler HA. Focal transformation and the Gouy phase shift of converging one-cycle surface acoustic waves excited by femtosecond laser pulses. OPTICS LETTERS 2005; 30:2019-21. [PMID: 16092252 DOI: 10.1364/ol.30.002019] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
We studied the changes of the pulse shape and the phase of the spectral components in converging-surface acoustic wave pulses. These pulses were excited with a femtosecond laser by a thermoelastic mechanism. To produce converging acoustic pulses, the laser beam was focused with an axicon in a circle on the surface of an aluminum sample. During propagation through the focus, the shape of the pulses of the normal surface velocity changed from two to three polar. The absolute value of the phase of the spectral components experienced a change close to pi/2 rad (Gouy phase shift) after passage of the focal region. These observations were confirmed by analytical and numerical calculations based on the two-dimensional wave equation for surface acoustic waves.
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Affiliation(s)
- A A Kolomenskii
- Department of Physics, Texas A&M University, College Station, Texas 77843-4242, USA.
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43
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Tritschler T, Hof KD, Klein MW, Wegener M. Variation of the carrier-envelope phase of few-cycle laser pulses owing to the Gouy phase: a solid-state-based measurement. OPTICS LETTERS 2005; 30:753-755. [PMID: 15832928 DOI: 10.1364/ol.30.000753] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
The carrier-envelope phase of a laser pulse has recently become an important quantity in extreme nonlinear optics. Because of the topological Gouy phase, it changes while the pulse propagates through the focus of a lens. This variation is measured by a simple solid-state-based approach. The experimental results are analyzed by comparison with simple analytical model calculations.
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Affiliation(s)
- T Tritschler
- Institut für Angewandte Physik, Universität Karlsruhe (TH), Wolfgang-Gaede-Strasse 1, 76131 Karlsruhe, Germany.
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44
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Varin C, Piché M, Porras MA. Acceleration of electrons from rest to GeV energies by ultrashort transverse magnetic laser pulses in free space. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:026603. [PMID: 15783437 DOI: 10.1103/physreve.71.026603] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2004] [Indexed: 05/24/2023]
Abstract
In this paper we describe a laser acceleration scheme where an electron is accelerated from rest to GeV energies by the longitudinal electric field of an ultrashort transverse magnetic ( TM01 ) optical pulse. The on-axis longitudinal electric field of the pulse is obtained from the free-space divergence equation beyond the so-called slowly-varying-envelope approximation. The instantaneous electron dynamics is studied; numerical simulations predict net energy gains in the GeV range for laser intensities reaching 10(22) W/ cm(2) .
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Affiliation(s)
- Charles Varin
- Centre d'Optique, Photonique et Laser, Université Laval, Sainte-Foy, Québec, Canada G1K 7P4.
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45
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Shverdin MY, Walker DR, Yavuz DD, Yin GY, Harris SE. Generation of a single-cycle optical pulse. PHYSICAL REVIEW LETTERS 2005; 94:033904. [PMID: 15698269 DOI: 10.1103/physrevlett.94.033904] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2004] [Indexed: 05/24/2023]
Abstract
We make use of coherent control of four-wave mixing to the ultraviolet as a diagnostic and describe the generation of a periodic optical waveform where the spectrum is sufficiently broad that the envelope is approximately a single-cycle in length, and where the temporal shape of this envelope may be synthesized by varying the coefficients of a Fourier series. Specifically, using seven sidebands, we report the generation of a train of single-cycle optical pulses with a pulse width of 1.6 fs, a pulse separation of 11 fs, and a peak power of 1 MW.
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Affiliation(s)
- M Y Shverdin
- Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
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