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Ishii H, Otomo K, Chang CP, Yamasaki M, Watanabe M, Yokoyama H, Nemoto T. All-synchronized picosecond pulses and time-gated detection improve the spatial resolution of two-photon STED microscopy in brain tissue imaging. PLoS One 2023; 18:e0290550. [PMID: 37616194 PMCID: PMC10449175 DOI: 10.1371/journal.pone.0290550] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2023] [Accepted: 08/09/2023] [Indexed: 08/26/2023] Open
Abstract
Super-resolution in two-photon excitation (2PE) microscopy offers new approaches for visualizing the deep inside the brain functions at the nanoscale. In this study, we developed a novel 2PE stimulated-emission-depletion (STED) microscope with all-synchronized picosecond pulse light sources and time-gated fluorescence detection, namely, all-pulsed 2PE-gSTED microscopy. The implementation of time-gating is critical to excluding undesirable signals derived from brain tissues. Even in a case using subnanosecond pulses for STED, the impact of time-gating was not negligible; the spatial resolution in the image of the brain tissue was improved by approximately 1.4 times compared with non time-gated image. This finding demonstrates that time-gating is more useful than previously thought for improving spatial resolution in brain tissue imaging. This microscopy will facilitate deeper super-resolution observation of the fine structure of neuronal dendritic spines and the intracellular dynamics in brain tissue.
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Affiliation(s)
- Hirokazu Ishii
- Exploratory Research Center on Life and Living Systems (ExCELLS), National Institutes of Natural Sciences, Okazaki, Japan
- National Institute for Physiological Sciences (NIPS), National Institutes of Natural Sciences, Okazaki, Japan
- School of Life Science, The Graduate University for Advanced Studies (SOKENDAI), Okazaki, Japan
| | - Kohei Otomo
- Exploratory Research Center on Life and Living Systems (ExCELLS), National Institutes of Natural Sciences, Okazaki, Japan
- National Institute for Physiological Sciences (NIPS), National Institutes of Natural Sciences, Okazaki, Japan
- Graduate School of Medicine, Juntendo University, Tokyo, Japan
| | - Ching-Pu Chang
- Exploratory Research Center on Life and Living Systems (ExCELLS), National Institutes of Natural Sciences, Okazaki, Japan
- National Institute for Physiological Sciences (NIPS), National Institutes of Natural Sciences, Okazaki, Japan
- Faculty of Medicine, Hokkaido University, Sapporo, Japan
| | | | | | - Hiroyuki Yokoyama
- New Industry Creation Hatchery Center (NICHe), Tohoku University, Sendai, Japan
| | - Tomomi Nemoto
- Exploratory Research Center on Life and Living Systems (ExCELLS), National Institutes of Natural Sciences, Okazaki, Japan
- National Institute for Physiological Sciences (NIPS), National Institutes of Natural Sciences, Okazaki, Japan
- School of Life Science, The Graduate University for Advanced Studies (SOKENDAI), Okazaki, Japan
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2
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Notsuka Y, Kurihara M, Hashimoto N, Harada Y, Takahashi E, Yamaoka Y. Improvement of spatial resolution in photoacoustic microscopy using transmissive adaptive optics with a low-frequency ultrasound transducer. OPTICS EXPRESS 2022; 30:2933-2948. [PMID: 35209424 DOI: 10.1364/oe.446309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2021] [Accepted: 12/27/2021] [Indexed: 06/14/2023]
Abstract
Maintaining a high spatial resolution in photoacoustic microscopy (PAM) of deep tissues is difficult due to large aberration in an objective lens with high numerical aperture and photoacoustic wave attenuation. To address the issue, we integrate transmission-type adaptive optics (AO) in high-resolution PAM with a low-frequency ultrasound transducer (UT), which increases the photoacoustic wave detection efficiency. AO improves lateral resolution and depth discrimination in PAM, even for low-frequency ultrasound waves by focusing a beam spot in deep tissues. Using the proposed PAM, we increased the lateral resolution and depth discrimination for blood vessels in mouse ears.
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3
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Focusing new light on brain functions: multiphoton microscopy for deep and super-resolution imaging. Neurosci Res 2021; 179:24-30. [PMID: 34861295 DOI: 10.1016/j.neures.2021.11.011] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Accepted: 11/29/2021] [Indexed: 11/21/2022]
Abstract
Multiphoton microscopy has become a powerful tool for visualizing neurobiological phenomena such as the dynamics of individual synapses and the functional activities of neurons. Owing to its near-infrared excitation laser wavelength, multiphoton microscopy achieves greater penetration depth and is less invasive than single-photon excitation. Here, we review the principles of two-photon microscopy and its technical limitations (penetration depth and spatial resolution) on brain tissue imaging. We then describe the technological improvements of two-photon microscopy that enable deeper imaging with higher spatial resolution for investigating unrevealed brain functions.
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Abstract
Fluorescence microscopy has long been a valuable tool for biological and medical imaging. Control of optical parameters such as the amplitude, phase, polarization and propagation angle of light gives fluorescence imaging great capabilities ranging from super-resolution imaging to long-term real-time observation of living organisms. In this review, we discuss current fluorescence imaging techniques in terms of the use of tailored or structured light for the sample illumination and fluorescence detection, providing a clear overview of their working principles and capabilities.
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Affiliation(s)
- Jialei Tang
- CREOL, The College of Optics and Photonics, University of Central Florida, Orlando, Florida, USA
- These authors contributed equally to this work
| | - Jinhan Ren
- CREOL, The College of Optics and Photonics, University of Central Florida, Orlando, Florida, USA
- These authors contributed equally to this work
| | - Kyu Young Han
- CREOL, The College of Optics and Photonics, University of Central Florida, Orlando, Florida, USA
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5
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Ishii H, Otomo K, Hung JH, Tsutsumi M, Yokoyama H, Nemoto T. Two-photon STED nanoscopy realizing 100-nm spatial resolution utilizing high-peak-power sub-nanosecond 655-nm pulses. BIOMEDICAL OPTICS EXPRESS 2019; 10:3104-3113. [PMID: 31467771 PMCID: PMC6706030 DOI: 10.1364/boe.10.003104] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2019] [Revised: 05/05/2019] [Accepted: 05/27/2019] [Indexed: 05/16/2023]
Abstract
We developed two-photon excitation stimulated emission depletion (STED) nanoscopy using high-peak-power sub-nanosecond 655-nm pulses. The STED pulse exhibited ideal optical properties and sufficient pulse energy to realize a 70-nm spatial resolution in the compact setup with electrically controllable components. For biological applications, we screened suitable fluorescent dyes or proteins and realized the sub-100 nm spatial resolution imaging of presynaptic protein clusters in fixed primary cultured neurons without severe photobleaching. We expect this method to enable visualization of ultrastructures and the cluster dynamics of biomolecules representing physiological functions in living cells and tissue.
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Affiliation(s)
- Hirokazu Ishii
- Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan
| | - Kohei Otomo
- Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan
- Graduate School of Information Science and Technology, Hokkaido University, Kita 14 Nishi 9, Kita-ku, Sapporo 060-0814, Japan
| | - Jui-Hung Hung
- New Industry Creation Hatchery Center (NICHe), Tohoku University, 6-6-10, Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan
| | - Motosuke Tsutsumi
- Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan
| | - Hiroyuki Yokoyama
- New Industry Creation Hatchery Center (NICHe), Tohoku University, 6-6-10, Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan
- Graduate School of Engineering, Tohoku University, 6-6-05, Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan
| | - Tomomi Nemoto
- Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan
- Graduate School of Information Science and Technology, Hokkaido University, Kita 14 Nishi 9, Kita-ku, Sapporo 060-0814, Japan
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6
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Otomo K, Hibi T, Fang YC, Hung JH, Tsutsumi M, Kawakami R, Yokoyama H, Nemoto T. Advanced easySTED microscopy based on two-photon excitation by electrical modulations of light pulse wavefronts. BIOMEDICAL OPTICS EXPRESS 2018; 9:2671-2680. [PMID: 30258682 PMCID: PMC6154199 DOI: 10.1364/boe.9.002671] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2017] [Revised: 03/22/2018] [Accepted: 04/06/2018] [Indexed: 05/28/2023]
Abstract
We developed a compact stimulated emission depletion (STED) two-photon excitation microscopy that utilized electrically controllable components. Transmissive liquid crystal devices inserted directly in front of the objective lens converted the STED light into an optical vortex while leaving the excitation light unaffected. Light pulses of two different colors, 1.06 and 0.64 μm, were generated by laser diode-based light sources, and the delay between the two pulses was flexibly controlled so as to maximize the fluorescence suppression ratio. In our experiments, the spatial resolution of this system was up to three times higher than that obtained without STED light irradiation, and we successfully visualize the fine microtubule network structures in fixed mammalian cells without causing significant photo-damage.
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Affiliation(s)
- Kohei Otomo
- Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan
- Graduate School of Information Science and Technology, Hokkaido University, Kita 14 Nishi 9, Kita-ku, Sapporo 060-0814, Japan
| | - Terumasa Hibi
- Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan
| | - Yi-Cheng Fang
- New Industry Creation Hatchery Center (NICHe), Tohoku University, Aramaki-Aoba 6-6-10, Aoba-ku, Sendai 980-8579, Japan
| | - Jui-Hung Hung
- New Industry Creation Hatchery Center (NICHe), Tohoku University, Aramaki-Aoba 6-6-10, Aoba-ku, Sendai 980-8579, Japan
| | - Motosuke Tsutsumi
- Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan
| | - Ryosuke Kawakami
- Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan
- Graduate School of Information Science and Technology, Hokkaido University, Kita 14 Nishi 9, Kita-ku, Sapporo 060-0814, Japan
| | - Hiroyuki Yokoyama
- New Industry Creation Hatchery Center (NICHe), Tohoku University, Aramaki-Aoba 6-6-10, Aoba-ku, Sendai 980-8579, Japan
| | - Tomomi Nemoto
- Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan
- Graduate School of Information Science and Technology, Hokkaido University, Kita 14 Nishi 9, Kita-ku, Sapporo 060-0814, Japan
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Toda K, Isobe K, Namiki K, Kawano H, Miyawaki A, Midorikawa K. Interferometric temporal focusing microscopy using three-photon excitation fluorescence. BIOMEDICAL OPTICS EXPRESS 2018; 9:1510-1519. [PMID: 29675298 PMCID: PMC5905902 DOI: 10.1364/boe.9.001510] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2017] [Revised: 02/06/2018] [Accepted: 02/14/2018] [Indexed: 06/08/2023]
Abstract
Super-resolution microscopy has become a powerful tool for biological research. However, its spatial resolution and imaging depth are limited, largely due to background light. Interferometric temporal focusing (ITF) microscopy, which combines structured illumination microscopy and three-photon excitation fluorescence microscopy, can overcome these limitations. Here, we demonstrate ITF microscopy using three-photon excitation fluorescence, which has a spatial resolution of 106 nm at an imaging depth of 100 µm with an excitation wavelength of 1060 nm.
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Affiliation(s)
- Keisuke Toda
- RIKEN Center for Advanced Photonics, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
- Graduate School of Science and Engineering, Saitama University, 255 Shimo-Okubo, Sakura, Saitama 338-8570, Japan
| | - Keisuke Isobe
- RIKEN Center for Advanced Photonics, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
- JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan
| | - Kana Namiki
- Laboratory for Cell Function Dynamics, RIKEN Brain Science Institute, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Hiroyuki Kawano
- Laboratory for Cell Function Dynamics, RIKEN Brain Science Institute, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Atsushi Miyawaki
- RIKEN Center for Advanced Photonics, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
- Laboratory for Cell Function Dynamics, RIKEN Brain Science Institute, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Katsumi Midorikawa
- RIKEN Center for Advanced Photonics, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
- Graduate School of Science and Engineering, Saitama University, 255 Shimo-Okubo, Sakura, Saitama 338-8570, Japan
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Tanabe A, Hibi T, Ipponjima S, Matsumoto K, Yokoyama M, Kurihara M, Hashimoto N, Nemoto T. Transmissive liquid-crystal device for correcting primary coma aberration and astigmatism in biospecimen in two-photon excitation laser scanning microscopy. JOURNAL OF BIOMEDICAL OPTICS 2016; 21:121503. [PMID: 27624000 DOI: 10.1117/1.jbo.21.12.121503] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2016] [Accepted: 08/15/2016] [Indexed: 05/24/2023]
Abstract
All aberrations produced inside a biospecimen can degrade the quality of a three-dimensional image in two-photon excitation laser scanning microscopy. Previously, we developed a transmissive liquid-crystal device to correct spherical aberrations that improved the image quality of a fixed-mouse-brain slice treated with an optical clearing reagent. In this study, we developed a transmissive device that corrects primary coma aberration and astigmatism. The motivation for this study is that asymmetric aberration can be induced by the shape of a biospecimen and/or by a complicated refractive-index distribution in a sample; this can considerably degrade optical performance even near the sample surface. The device’s performance was evaluated by observing fluorescence beads. The device was inserted between the objective lens and microscope revolver and succeeded in improving the spatial resolution and fluorescence signal of a bead image that was originally degraded by asymmetric aberration. Finally, we implemented the device for observing a fixed whole mouse brain with a sloping surface shape and complicated internal refractive-index distribution. The correction with the device improved the spatial resolution and increased the fluorescence signal by ?2.4×. The device can provide a simple approach to acquiring higher-quality images of biospecimens.
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Affiliation(s)
- Ayano Tanabe
- Hokkaido University, Graduate School of Information Science and Technology, N14W9, Kita-Ward, Sapporo, Hokkaido 060-0814, JapanbHokkaido University, Research Institute for Electronic Science, N20W10, Kita-Ward, Sapporo, Hokkaido 001-0020, JapancCitizen Holdings Co., Ltd., 840, Shimotomi, Tokorozawa, Saitama 359-8511, Japan
| | - Terumasa Hibi
- Hokkaido University, Research Institute for Electronic Science, N20W10, Kita-Ward, Sapporo, Hokkaido 001-0020, Japan
| | - Sari Ipponjima
- Hokkaido University, Graduate School of Information Science and Technology, N14W9, Kita-Ward, Sapporo, Hokkaido 060-0814, JapanbHokkaido University, Research Institute for Electronic Science, N20W10, Kita-Ward, Sapporo, Hokkaido 001-0020, Japan
| | - Kenji Matsumoto
- Citizen Holdings Co., Ltd., 840, Shimotomi, Tokorozawa, Saitama 359-8511, Japan
| | - Masafumi Yokoyama
- Citizen Holdings Co., Ltd., 840, Shimotomi, Tokorozawa, Saitama 359-8511, Japan
| | - Makoto Kurihara
- Citizen Holdings Co., Ltd., 840, Shimotomi, Tokorozawa, Saitama 359-8511, Japan
| | - Nobuyuki Hashimoto
- Citizen Holdings Co., Ltd., 840, Shimotomi, Tokorozawa, Saitama 359-8511, Japan
| | - Tomomi Nemoto
- Hokkaido University, Graduate School of Information Science and Technology, N14W9, Kita-Ward, Sapporo, Hokkaido 060-0814, JapanbHokkaido University, Research Institute for Electronic Science, N20W10, Kita-Ward, Sapporo, Hokkaido 001-0020, Japan
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Tanabe A, Hibi T, Ipponjima S, Matsumoto K, Yokoyama M, Kurihara M, Hashimoto N, Nemoto T. Correcting spherical aberrations in a biospecimen using a transmissive liquid crystal device in two-photon excitation laser scanning microscopy. JOURNAL OF BIOMEDICAL OPTICS 2015; 20:101204. [PMID: 26244766 DOI: 10.1117/1.jbo.20.10.101204] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2015] [Accepted: 05/18/2015] [Indexed: 05/24/2023]
Abstract
Two-photon excitation laser scanning microscopy has enabled the visualization of deep regions in a biospecimen. However, refractive-index mismatches in the optical path cause spherical aberrations that degrade spatial resolution and the fluorescence signal, especially during observation at deeper regions. Recently, we developed transmissive liquid-crystal devices for correcting spherical aberration without changing the basic design of the optical path in a conventional laser scanning microscope. In this study, the device was inserted in front of the objective lens and supplied with the appropriate voltage according to the observation depth. First, we evaluated the device by observing fluorescent beads in single- and two-photon excitation laser scanning microscopes. Using a 25× water-immersion objective lens with a numerical aperture of 1.1 and a sample with a refractive index of 1.38, the device recovered the spatial resolution and the fluorescence signal degraded within a depth of 0.6 mm. Finally, we implemented the device for observation of a mouse brain slice in a two-photon excitation laser scanning microscope. An optical clearing reagent with a refractive index of 1.42 rendered the fixed mouse brain transparent. The device improved the spatial resolution and the yellow fluorescent protein signal within a depth of 0-0.54 mm.
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Affiliation(s)
- Ayano Tanabe
- Hokkaido University, Research Institute for Electronic Science, N20W10, Kita-Ward, Sapporo, Hokkaido 001-0020, JapanbHokkaido University, Graduate School of Information Science and Technology, N14W9, Kita-Ward, Sapporo, Hokkaido 060-0814, JapancCitizen Ho
| | - Terumasa Hibi
- Hokkaido University, Research Institute for Electronic Science, N20W10, Kita-Ward, Sapporo, Hokkaido 001-0020, JapanbHokkaido University, Graduate School of Information Science and Technology, N14W9, Kita-Ward, Sapporo, Hokkaido 060-0814, Japan
| | - Sari Ipponjima
- Hokkaido University, Research Institute for Electronic Science, N20W10, Kita-Ward, Sapporo, Hokkaido 001-0020, JapanbHokkaido University, Graduate School of Information Science and Technology, N14W9, Kita-Ward, Sapporo, Hokkaido 060-0814, Japan
| | - Kenji Matsumoto
- Citizen Holdings Co. Ltd., 840, Shimotomi, Tokorozawa, Saitama 359-8511, Japan
| | - Masafumi Yokoyama
- Citizen Holdings Co. Ltd., 840, Shimotomi, Tokorozawa, Saitama 359-8511, Japan
| | - Makoto Kurihara
- Citizen Holdings Co. Ltd., 840, Shimotomi, Tokorozawa, Saitama 359-8511, Japan
| | - Nobuyuki Hashimoto
- Citizen Holdings Co. Ltd., 840, Shimotomi, Tokorozawa, Saitama 359-8511, Japan
| | - Tomomi Nemoto
- Hokkaido University, Research Institute for Electronic Science, N20W10, Kita-Ward, Sapporo, Hokkaido 001-0020, JapanbHokkaido University, Graduate School of Information Science and Technology, N14W9, Kita-Ward, Sapporo, Hokkaido 060-0814, Japan
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Otomo K, Hibi T, Kozawa Y, Nemoto T. STED microscopy—super-resolution bio-imaging utilizing a stimulated emission depletion. Microscopy (Oxf) 2015; 64:227-36. [DOI: 10.1093/jmicro/dfv036] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2015] [Accepted: 06/08/2015] [Indexed: 11/13/2022] Open
Affiliation(s)
- Kohei Otomo
- Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita, Sapporo 001-0020, Japan
| | - Terumasa Hibi
- Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita, Sapporo 001-0020, Japan
- Graduate School of Information Science and Technology, Hokkaido University, Kita 14 Nishi 9, Kita, Sapporo 060-0814, Japan
| | - Yuichi Kozawa
- Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan
| | - Tomomi Nemoto
- Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita, Sapporo 001-0020, Japan
- Graduate School of Information Science and Technology, Hokkaido University, Kita 14 Nishi 9, Kita, Sapporo 060-0814, Japan
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Saito K, Tanabe T, Oyama Y. Concept of annular vector beam generation at terahertz wavelengths via a nonlinear parametric process. APPLIED OPTICS 2015; 54:2769-2775. [PMID: 25967188 DOI: 10.1364/ao.54.002769] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2014] [Accepted: 03/03/2015] [Indexed: 06/04/2023]
Abstract
In this paper, we describe our theoretical investigation and calculations for a terahertz (THz)-wave profile generated by difference frequency mixing (DFM) of focused, cylindrically symmetric, and polarized optical vector beams. Using vector diffraction theory, the second-order nonlinear polarization was estimated from the electric field components of the optical pump beams penetrating uniaxial, birefringent nonlinear optics (NLO) crystals, GaSe and CdSe. The approximate beam patterns of the THz waves were simulated using DFM formulation. The intensity patterns of the THz waves for GaSe and CdSe showed sixfold symmetry and cylindrical symmetry, respectively, based on the nonlinear susceptibility tensor of the crystals. As the phase-matching angle θ(PM) was constant with respect to the c axis of the NLO crystals, an annular vector beam with a narrow width was expected.
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