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Zeyen M, Affolter L, Ahmed MA, Graf T, Kara O, Kirch K, Marszalek M, Nez F, Ouf A, Pohl R, Rajamohanan S, Yzombard P, Antognini A, Schuhmann K. Pound-Drever-Hall locking scheme free from Trojan operating points. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2023; 94:013001. [PMID: 36725577 DOI: 10.1063/5.0130508] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2022] [Accepted: 12/13/2022] [Indexed: 06/18/2023]
Abstract
The Pound-Drever-Hall (PDH) technique is a popular method for stabilizing the frequency of a laser to a stable optical resonator or, vice versa, the length of a resonator to the frequency of a stable laser. We propose a refinement of the technique yielding an "infinite" dynamic (capture) range so that a resonator is correctly locked to the seed frequency, even after large perturbations. The stable but off-resonant lock points (also called Trojan operating points), present in conventional PDH error signals, are removed by phase modulating the seed laser at a frequency corresponding to half the free spectral range of the resonator. We verify the robustness of our scheme experimentally by realizing an injection-seeded Yb:YAG thin-disk laser. We also give an analytical formulation of the PDH error signal for arbitrary modulation frequencies and discuss the parameter range for which our PDH locking scheme guarantees correct locking. Our scheme is simple as it does not require additional electronics apart from the standard PDH setup and is particularly suited to realize injection-seeded lasers and injection-seeded optical parametric oscillators.
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Affiliation(s)
- Manuel Zeyen
- Institute for Particle Physics and Astrophysics, ETH, 8093 Zurich, Switzerland
| | - Lukas Affolter
- Institute for Particle Physics and Astrophysics, ETH, 8093 Zurich, Switzerland
| | - Marwan Abdou Ahmed
- Institut für Strahlwerkzeuge, Universität Stuttgart, Pfaffenwaldring 43, 70569 Stuttgart, Deutschland
| | - Thomas Graf
- Institut für Strahlwerkzeuge, Universität Stuttgart, Pfaffenwaldring 43, 70569 Stuttgart, Deutschland
| | - Oguzhan Kara
- Institute for Particle Physics and Astrophysics, ETH, 8093 Zurich, Switzerland
| | - Klaus Kirch
- Institute for Particle Physics and Astrophysics, ETH, 8093 Zurich, Switzerland
| | | | - François Nez
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, 75252 Paris Cedex 05, France
| | - Ahmed Ouf
- QUANTUM, Institute of Physics, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany
| | - Randolf Pohl
- QUANTUM, Institute of Physics, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany
| | - Siddharth Rajamohanan
- QUANTUM, Institute of Physics, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany
| | - Pauline Yzombard
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, 75252 Paris Cedex 05, France
| | - Aldo Antognini
- Institute for Particle Physics and Astrophysics, ETH, 8093 Zurich, Switzerland
| | - Karsten Schuhmann
- Institute for Particle Physics and Astrophysics, ETH, 8093 Zurich, Switzerland
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2
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Chen C, Gao C, Wang Q. Injection-seeded 10 kHz repetition rate Er:YAG solid-state laser with single-frequency pulse energy more than 1 mJ. OPTICS EXPRESS 2022; 30:16044-16052. [PMID: 36221457 DOI: 10.1364/oe.458583] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2022] [Accepted: 04/19/2022] [Indexed: 06/16/2023]
Abstract
We report a single-frequency Q-switched Er:YAG all-solid-state laser with a pulse repetition rate of up to 10 kHz. The single-frequency feature is ensured by injecting the seed laser into a Q-switched ring cavity, and the pulse repetition rate is increased by combing the Pound-Drever-Hall method and optical feedback. Peak power of 4.12 kW with an average pulse energy of 1.35 mJ single-frequency 1645 nm laser pulses is achieved at a pulse repetition rate of 10 kHz, which matches an average power of 13.5 W.
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3
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Zhang Y, Huang L, Duan X, Gong Z, Tian T, Ma Y, Xu AJ. Tm 3+: Bi 4Si 3O 12 crystal as a promising laser material near 2 μm: growth, spectroscopic properties and laser performance. OPTICS EXPRESS 2021; 29:29138-29148. [PMID: 34615030 DOI: 10.1364/oe.435229] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2021] [Accepted: 08/12/2021] [Indexed: 06/13/2023]
Abstract
We report on the crystal growth, spectroscopic properties and laser performance of Tm3+-doped Bi4Si3O12 (BSO) crystal. The crystal was grown by the vertical Bridgeman method. The spectroscopic properties are investigated based on absorption and luminescence spectroscopy. Judd - Ofelt (JO) analysis is performed to calculate the spontaneous emission probabilities, branching ratio and the radiative lifetimes. The absorption spectrum, emission spectrum and gain cross-section spectra of Tm3+: BSO crystal are determined for the 2 μm transition. Luminescence decay kinetic of 3F4 upper level was analysed in detail. The continuous-wave 2 μm laser with a maximum output power of 650 mW and a slope efficiency of 29.7% is demonstrated for the first time. The beam quality factor (M2) of Tm3+: BSO laser was about 1.03 at the maximum output level.
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4
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Chen C, Wang Q, Huang S, Zhang X, Wang K, Gao M, Gao C. Single-frequency Q-switched Er:YAG laser with high frequency and energy stability via the Pound-Drever-Hall locking method. OPTICS LETTERS 2020; 45:3745-3748. [PMID: 32630944 DOI: 10.1364/ol.396501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2020] [Accepted: 05/25/2020] [Indexed: 06/11/2023]
Abstract
We present an injection-seeding Q-switched 1645 nm Er:YAG ceramic laser with high frequency stability and energy stability by combining the injection-seeding technique and Pound-Drever-Hall technique. 10.31 mJ single-frequency pulses with optimal frequency stability (525 kHz) and relative energy stability (0.52%) at a high pulse repetition rate of 1 kHz are obtained. To the best of our knowledge, this is the highest frequency stability and energy stability so far in a high pulse repetition frequency, large pulse energy, single-frequency Q-switched Er-doped solid laser. This single frequency laser with high stability provides an excellent light source for a coherent lidar system.
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Wang X, Hu J, Xu J, Sun Y, Xia H, Tu C. Sb 2Te 3 as the saturable absorber for the ∼2.0 μm passively Q-switched solid state pulsed laser. RSC Adv 2019; 9:29312-29316. [PMID: 35528397 PMCID: PMC9071807 DOI: 10.1039/c9ra05209g] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2019] [Accepted: 09/09/2019] [Indexed: 11/29/2022] Open
Abstract
We demonstrated a passively Q-switched Tm:YAP solid state pulsed laser based on an Sb2Te3 saturable absorber. This saturable absorber was prepared by a facile hydrothermal method. The maximum pulse energy was up to 5.366 μJ at the absorbed pump power of 6.6 W. The corresponding pulse width, output power and repetition rate were 533 ns, 542 mW and 101 kHz, respectively. The results indicated that the hydrothermally synthesized Sb2Te3 nanosheet was a promising saturable absorber for near-infrared pulsed lasers. We demonstrated a passively Q-switched Tm:YAP solid state pulsed laser based on an Sb2Te3 saturable absorber.![]()
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Affiliation(s)
- Xihu Wang
- Key Laboratory of Functional Materials and Devices for Informatics of Anhui Educational Institutions, Department of Physics, Fuyang Normal University Fuyang Anhui 236037 China
| | - Jinyu Hu
- Key Laboratory of Functional Materials and Devices for Informatics of Anhui Educational Institutions, Department of Physics, Fuyang Normal University Fuyang Anhui 236037 China
| | - Jinlong Xu
- School of Electronic Science and Engineering, Collaborative Innovation Center of Advanced Microstructures, Nanjing University Nanjing 210093 China
| | - Yijian Sun
- School of Metallurgy and Chemical Engineering, Jiangxi University of Science and Technology Ganzhou Jiangxi 341000 China
| | - Houping Xia
- College of Physics and Optoelectronics Technology, Baoji University of Arts and Sciences Baoji Shaanxi 721016 PR China
| | - Chaoyang Tu
- Key Laboratory of Optoelectronic Materials Chemistry and Physics of CAS, Fujian Institute of Research on the Structure of Matter, CAS Fuzhou Fujian 350002 China
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Yao Y, Li X, Song R, Cui N, Liu S, Zhang H, Li D, Wang Q, Xu Y, He J. The energy band structure analysis and 2 μm Q-switched laser application of layered rhenium diselenide. RSC Adv 2019; 9:14417-14421. [PMID: 35519303 PMCID: PMC9064133 DOI: 10.1039/c9ra02311a] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2019] [Accepted: 04/25/2019] [Indexed: 12/16/2022] Open
Abstract
In this paper, we prepared a high-quality multilayer ReSe2 saturable absorber with a liquid-phase exfoliation method and characterized its saturable absorption properties around 2 μm.
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Affiliation(s)
- Yongping Yao
- College of Electronic and Information Engineering
- Shandong University of Science and Technology
- Qingdao 266590
- China
| | - Xiaowen Li
- Key Laboratory of Micro-nano Measurement-Manipulation and Physics
- Ministry of Education
- Department of Applied Physics
- Beihang University
- Beijing 100191
| | - Rengang Song
- College of Electrical, Engineering and Automation
- Shandong University of Science and Technology
- Qingdao
- China
- College of Electronic and Information Engineering
| | - Na Cui
- College of Electronic and Information Engineering
- Shandong University of Science and Technology
- Qingdao 266590
- China
| | - Shande Liu
- College of Electrical, Engineering and Automation
- Shandong University of Science and Technology
- Qingdao
- China
- College of Electronic and Information Engineering
| | - Huiyun Zhang
- College of Electronic and Information Engineering
- Shandong University of Science and Technology
- Qingdao 266590
- China
| | - Dehua Li
- College of Electronic and Information Engineering
- Shandong University of Science and Technology
- Qingdao 266590
- China
| | - Qiangguo Wang
- College of Electronic and Information Engineering
- Shandong University of Science and Technology
- Qingdao 266590
- China
| | - Yan Xu
- College of Electrical, Engineering and Automation
- Shandong University of Science and Technology
- Qingdao
- China
- College of Electronic and Information Engineering
| | - Jingliang He
- State Key Laboratory of Crystal Materials
- Shandong University
- Jinan 250100
- China
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7
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Lemmerz C, Lux O, Reitebuch O, Witschas B, Wührer C. Frequency and timing stability of an airborne injection-seeded Nd:YAG laser system for direct-detection wind lidar. APPLIED OPTICS 2017; 56:9057-9068. [PMID: 29131193 DOI: 10.1364/ao.56.009057] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2017] [Accepted: 10/16/2017] [Indexed: 06/07/2023]
Abstract
We report on the design and performance of the laser deployed in the airborne demonstrator Doppler wind lidar for the Aeolus mission of the European Space Agency (ESA). The all-solid-state, diode-pumped and frequency-tripled Nd:YAG laser is realized as a master oscillator power amplifier (MOPA) system, generating 60 mJ of single-frequency pulses at 355 nm wavelength, 50 Hz repetition rate and 20 ns pulse duration. For the measurement of the Doppler frequency shift over several accumulated laser shots, the frequency stability of the laser is of crucial importance. Injection-seeding, in combination with an active cavity control based on the Ramp-Delay-Fire technique, provides a pulse-to-pulse frequency stability of 0.25 MHz measured at 1064 nm under laboratory conditions. This value increases to 0.31 MHz for airborne operation in a vibration environment that has been characterized by multiple acceleration sensors during different flight conditions. In addition, a pure Ramp-Fire setting was tested for comparison leading to a frequency stability of 0.16 MHz both in airborne operation and on ground. The laser cavity control electronics also have to provide a trigger signal for the lidar detection electronics, about 60 μs prior to the expected laser pulse emission and with high timing stability. An in-flight timing stability of below 100 ns was measured decreasing to 20 ns for a shorter pre-trigger time of 10 μs.
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8
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Liu X, Yang K, Zhao S, Li T, Luan C, Guo X, Zhao B, Zheng L, Su L, Xu J, Bian J. Growth and lasing performance of a Tm,Y:CaF 2 crystal. OPTICS LETTERS 2017; 42:2567-2570. [PMID: 28957286 DOI: 10.1364/ol.42.002567] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2017] [Accepted: 06/05/2017] [Indexed: 06/07/2023]
Abstract
A Tm3+ ion and Y3+ ion co-doped CaF2 crystal was grown and characterized, in which spectral and lasing performance was presented for the first time, to the best of our knowledge. Under diode end-pumping, in a continuous-wave regime, maximum output power of 453 mW was delivered under an absorption pump power of 2.5 W, corresponding to an optical-to-optical conversion efficiency of 17.9% and a slope efficiency of 21%. With a birefringent quartz plate, wavelength-tunable operation with a tunable range of more than 190 nm was realized. The results show that Tm,Y:CaF2 is a promising laser crystal operating in a spectral region ranging from 1850 nm to 2050 nm.
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9
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Yao B, Shi H, Dai T, Shen Z, Ju Y, Cai G, Wang Y. Diode-pumped acousto-optical cavity-dumped Tm:YAP laser at 1989 nm. APPLIED OPTICS 2014; 53:6816-6819. [PMID: 25322388 DOI: 10.1364/ao.53.006816] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2014] [Accepted: 09/06/2014] [Indexed: 06/04/2023]
Abstract
In this paper, we demonstrated a diode-pumped acousto-optical cavity-dumped Tm:YAP laser for the first time. The pulses were coupled out of the lateral surface of the cavity when radio frequency signal was loaded on the acousto-optical modulator. A maximum output power of 1.28 W was obtained with pump power of 40.3 W at a repetition rate of 200 kHz, corresponding to a slope efficiency of 4.7%. The output pulse width of the cavity-dumped Tm:YAP laser was constant at 43 ns, and the wavelength was 1989.8 nm.
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10
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Feng T, Yang K, Zhao S, Zhao J, Qiao W, Li T, Zheng L, Xu J. Broadly wavelength tunable acousto-optically Q-switched Tm:Lu2SiO5 laser. APPLIED OPTICS 2014; 53:6119-6122. [PMID: 25322086 DOI: 10.1364/ao.53.006119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2014] [Accepted: 08/13/2014] [Indexed: 06/04/2023]
Abstract
A broadly wavelength tunable acousto-optically Q-switched Tm:Lu2SiO5 (Tm:LSO) laser is presented for the first time, to our best knowledge. The emission wavelength was tuned in a broad spectral region over 111 nm ranging from 1959 to 2070 nm. A shortest pulse duration of 345 ns with beam quality of M(2)≤1.65 was obtained at pulse repetition frequency (PRF) of 1 kHz, corresponding to a maximum single pulse energy of 0.26 mJ and peak power of 0.75 kW. The experimental results indicated that Tm:LSO crystal has outstanding potential for obtaining broadly wavelength tunable and low-PRF laser pulses at 2 μm.
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11
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Wagner G, Behrendt A, Wulfmeyer V, Späth F, Schiller M. High-power Ti:sapphire laser at 820 nm for scanning ground-based water-vapor differential absorption lidar. APPLIED OPTICS 2013; 52:2454-2469. [PMID: 23670775 DOI: 10.1364/ao.52.002454] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2012] [Accepted: 02/22/2013] [Indexed: 06/02/2023]
Abstract
The Ti:sapphire (TISA) laser transmitter of the mobile, three-dimensional-scanning water-vapor differential absorption lidar (DIAL) of the University of Hohenheim is described in detail. The dynamically-stable, unidirectional ring resonator contains a single Brewster-cut TISA crystal, which is pumped from both sides with 250 Hz using a diode-pumped frequency-doubled Nd:YAG laser. The resonator is injection seeded and actively frequency-stabilized using a phase-sensitive technique. The TISA laser is operating near 820 nm, which is optimum for ground-based water-vapor DIAL measurements. An average output power of up to 6.75 W with a beam quality factor of M2<2 is reached. The pointing stability is <13 μrad (rms), the depolarization <1%. The overall optical-optical conversion efficiency is up to 19%. The pulse length is 40 ns with a pulse linewidth of <157 MHz. The short- and long-term frequency stabilities are 10 MHz (rms). A spectral purity of 99.9% was determined by pointing to a stratus cloud in low-elevation scanning mode with a cloud bottom height of ≈2.4 km.
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Affiliation(s)
- Gerd Wagner
- Institute of Physics and Meteorology (IPM), University of Hohenheim (UHOH), Stuttgart 70599, Germany.
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12
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Bai Y, Ren D, Zhao W, Qu Y, Qian L, Chen Z. Heterodyne Doppler velocity measurement of moving targets by mode-locked pulse laser. OPTICS EXPRESS 2012; 20:764-768. [PMID: 22274421 DOI: 10.1364/oe.20.000764] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
In this study, heterodyne detection is adopted to measure the velocity of a target simulated by a rapidly rotating plate by using a mode-locked pulse laser as the resource. The coherent beat frequency of the signal light reflected by target and local oscillation light occurred on the surface of the detector. Then the waveform of beat frequency was processed by filtering to obtain the Doppler frequency shift of the signal light induced by target. With this frequency shift, the velocity of target could be obtained by calculation. Results indicate that the measurement has a high precision. The error on average is within 0.4 m/s.
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Affiliation(s)
- Yan Bai
- National Key Laboratory of Tunable Laser Technology, Harbin Institute of Technology, Harbin, China
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13
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Yao B, Tian Y, Li G, Wang Y. InGaAs/GaAs saturable absorber for diode-pumped passively Q-switched dual-wavelength Tm:YAP lasers. OPTICS EXPRESS 2010; 18:13574-13579. [PMID: 20588489 DOI: 10.1364/oe.18.013574] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
We demonstrate the first use of InGaAs/GaAs as a saturable absorber in the Q-switching of a diode pumped Tm(3+) doped laser operating at the wavelengths of 1940 nm and 1986 nm. The influence of the semiconductor saturable absorber's (SESA) position and thermal lens effect on the Q-switch characteristics was investigated. With a pump power of 35 W, the maximum pulse energy of 28.1 microJ with a pulse width of 447 ns at the pulse repetition frequency (PRF) of 43.7 kHz was obtained by selecting the appropriate position of the SESA.
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Affiliation(s)
- Baoquan Yao
- National Key Laboratory of Tunable Laser Technology, Harbin Institute of Technology, Harbin, China.
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Wulfmeyer V, Janjić T. Twenty-Four-Hour Observations of the Marine Boundary Layer Using Shipborne NOAA High-Resolution Doppler Lidar. ACTA ACUST UNITED AC 2005. [DOI: 10.1175/jam2296.1] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
Abstract
Shipborne observations obtained with the NOAA high-resolution Doppler lidar (HRDL) during the 1999 Nauru (Nauru99) campaign were used to study the structure of the marine boundary layer (MBL) in the tropical Pacific Ocean. During a day with weak mesoscale activity, diurnal variability of the height of the convective MBL was observed using HRDL backscatter data. The observed diurnal variation in the MBL height had an amplitude of about 250 m. Relations between the MBL height and in situ measurements of sea surface temperature as well as latent and sensible heat fluxes were examined. Good correlation was found with the sea surface temperature. The correlation with the latent heat flux was lower, and practically no correlation between the MBL height and the sensible heat and buoyancy fluxes could be detected. Horizontal wind profiles were measured using a velocity–azimuth display scan of HRDL velocity data. Strong wind shear at the top of the MBL was observed in most cases. Comparison of these results with GPS radiosonde data shows discrepancies in the wind intensity and direction, which may be due to different observation times and locations as well as due to multipath effects at the ship’s platform. Vertical wind profiles corrected for ship’s motion were used to derive vertical velocity variance and skewness profiles. Motion compensation had a significant effect on their shape. Normalized by the convective velocity scale and by the top of the mixed layer zi, the variance varied between 0.45 and 0.65 at 0.4z/zi and decreased to 0.2 at 1.0z/zi. The skewness ranged between 0.3 and 0.8 in the MBL and showed in almost all cases a maximum between 1.0z/zi and 1.1z/zi. These profiles revealed the existence of another turbulent layer above the MBL, which was probably driven by wind shear and cloud condensation processes.
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Affiliation(s)
- Volker Wulfmeyer
- Institut für Physik und Meteorologie, Universität Hohenheim, Stuttgart, Germany
| | - Tijana Janjić
- School of Engineering and Science, International University Bremen, Bremen, Germany
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Ostermeyer M, Kappe P, Menzel R, Wulfmeyer V. Diode-pumped Nd:YAG master oscillator power amplifier with high pulse energy, excellent beam quality, and frequency-stabilized master oscillator as a basis for a next-generation lidar system. APPLIED OPTICS 2005; 44:582-590. [PMID: 15726956 DOI: 10.1364/ao.44.000582] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
A pulsed, diode-laser-pumped Nd:YAG master oscillator power amplifier (MOPA) in rod geometry, frequency stabilized with a modified Pound-Drever-Hall scheme is presented. The apparatus delivers 33-ns pulses with a maximum pulse energy of 0.5 J at 1064 nm. The system was set up in two different configurations for repetition rates of 100 or 250 Hz. The beam quality was measured to be 1.5 times the diffraction limit at a pulse energy of 405 mJ and a repetition rate of 100 Hz. At 250 Hz with the same pulse energy, the M2 was better than 2.1. The radiation is frequency converted with an efficiency of 50% to 532 nm. This MOPA system will be the pump laser of transmitters for a variety of high-end, scanning lidar systems.
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Affiliation(s)
- Martin Ostermeyer
- Institute of Physics, University of Potsdam, Potsdam 14469, Germany.
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