coefficient form partial differential equations (pde) module Search Results


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Coefficient Form Pde, supplied by COMSOL Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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Weak Form Pde Interface, supplied by COMSOL Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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a Experimentally measured and theoretically predicted SBS threshold enhancement over FM-only excitation increases with distance d in of the focused input beam to fiber axis (inset; spot size ≈3.4 μm). Dots: mean enhancement of experimental data, error bars: standard deviation, solid curve: theoretical prediction including mode-dependent loss, mode coupling, and polarization mixing. The effective numbers of excited modes at different d in are estimated theoretically (see , sec. , for more details). b Calculated Brillouin scattering strength \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}_{{{{{{{{\rm{B}}}}}}}}}^{(m,l)}(\Omega )$$\end{document} g B ( m , l ) ( Ω ) for two optical modes HE 11 and HE 24 (each mode profile displays the horizontal field component). Intramodal and intermodal Brillouin scattering have peaks at different Stokes frequencies Ω, and the corresponding acoustic modes are displayed above the peaks. c Calculated Brillouin gain spectrum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${G}_{{{{{{{{\rm{B}}}}}}}}}^{(m)}(\Omega )$$\end{document} G B ( m ) ( Ω ) for FM-only excitation (green) is narrower than multimode excitation with on-axis focusing of input light (blue). Off-axis focusing increases the number of excited modes and further broadens the Brillouin gain spectrum (red); the resulting decrease in peak gain enhances the SBS threshold. Optical and acoustic modes are calculated using Wave Optics and <t>Coefficient</t> Form <t>PDE</t> modules, respectively, in COMSOL .
Wave Optics Module, supplied by COMSOL Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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a Experimentally measured and theoretically predicted SBS threshold enhancement over FM-only excitation increases with distance d in of the focused input beam to fiber axis (inset; spot size ≈3.4 μm). Dots: mean enhancement of experimental data, error bars: standard deviation, solid curve: theoretical prediction including mode-dependent loss, mode coupling, and polarization mixing. The effective numbers of excited modes at different d in are estimated theoretically (see , sec. , for more details). b Calculated Brillouin scattering strength \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}_{{{{{{{{\rm{B}}}}}}}}}^{(m,l)}(\Omega )$$\end{document} g B ( m , l ) ( Ω ) for two optical modes HE 11 and HE 24 (each mode profile displays the horizontal field component). Intramodal and intermodal Brillouin scattering have peaks at different Stokes frequencies Ω, and the corresponding acoustic modes are displayed above the peaks. c Calculated Brillouin gain spectrum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${G}_{{{{{{{{\rm{B}}}}}}}}}^{(m)}(\Omega )$$\end{document} G B ( m ) ( Ω ) for FM-only excitation (green) is narrower than multimode excitation with on-axis focusing of input light (blue). Off-axis focusing increases the number of excited modes and further broadens the Brillouin gain spectrum (red); the resulting decrease in peak gain enhances the SBS threshold. Optical and acoustic modes are calculated using Wave Optics and <t>Coefficient</t> Form <t>PDE</t> modules, respectively, in COMSOL .
Comsol Multiphysics, supplied by COMSOL Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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partial differential equation (pde) coefficient form  (COMSOL Inc)
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a Experimentally measured and theoretically predicted SBS threshold enhancement over FM-only excitation increases with distance d in of the focused input beam to fiber axis (inset; spot size ≈3.4 μm). Dots: mean enhancement of experimental data, error bars: standard deviation, solid curve: theoretical prediction including mode-dependent loss, mode coupling, and polarization mixing. The effective numbers of excited modes at different d in are estimated theoretically (see , sec. , for more details). b Calculated Brillouin scattering strength \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}_{{{{{{{{\rm{B}}}}}}}}}^{(m,l)}(\Omega )$$\end{document} g B ( m , l ) ( Ω ) for two optical modes HE 11 and HE 24 (each mode profile displays the horizontal field component). Intramodal and intermodal Brillouin scattering have peaks at different Stokes frequencies Ω, and the corresponding acoustic modes are displayed above the peaks. c Calculated Brillouin gain spectrum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${G}_{{{{{{{{\rm{B}}}}}}}}}^{(m)}(\Omega )$$\end{document} G B ( m ) ( Ω ) for FM-only excitation (green) is narrower than multimode excitation with on-axis focusing of input light (blue). Off-axis focusing increases the number of excited modes and further broadens the Brillouin gain spectrum (red); the resulting decrease in peak gain enhances the SBS threshold. Optical and acoustic modes are calculated using Wave Optics and <t>Coefficient</t> Form <t>PDE</t> modules, respectively, in COMSOL .
Partial Differential Equation (Pde) Coefficient Form, supplied by COMSOL Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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coefficient form partial differential (pde) equation toolbox  (COMSOL Inc)
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a Experimentally measured and theoretically predicted SBS threshold enhancement over FM-only excitation increases with distance d in of the focused input beam to fiber axis (inset; spot size ≈3.4 μm). Dots: mean enhancement of experimental data, error bars: standard deviation, solid curve: theoretical prediction including mode-dependent loss, mode coupling, and polarization mixing. The effective numbers of excited modes at different d in are estimated theoretically (see , sec. , for more details). b Calculated Brillouin scattering strength \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}_{{{{{{{{\rm{B}}}}}}}}}^{(m,l)}(\Omega )$$\end{document} g B ( m , l ) ( Ω ) for two optical modes HE 11 and HE 24 (each mode profile displays the horizontal field component). Intramodal and intermodal Brillouin scattering have peaks at different Stokes frequencies Ω, and the corresponding acoustic modes are displayed above the peaks. c Calculated Brillouin gain spectrum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${G}_{{{{{{{{\rm{B}}}}}}}}}^{(m)}(\Omega )$$\end{document} G B ( m ) ( Ω ) for FM-only excitation (green) is narrower than multimode excitation with on-axis focusing of input light (blue). Off-axis focusing increases the number of excited modes and further broadens the Brillouin gain spectrum (red); the resulting decrease in peak gain enhances the SBS threshold. Optical and acoustic modes are calculated using Wave Optics and <t>Coefficient</t> Form <t>PDE</t> modules, respectively, in COMSOL .
Coefficient Form Partial Differential (Pde) Equation Toolbox, supplied by COMSOL Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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general coefficient form partial differential equation (pde)  (COMSOL Inc)
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a Experimentally measured and theoretically predicted SBS threshold enhancement over FM-only excitation increases with distance d in of the focused input beam to fiber axis (inset; spot size ≈3.4 μm). Dots: mean enhancement of experimental data, error bars: standard deviation, solid curve: theoretical prediction including mode-dependent loss, mode coupling, and polarization mixing. The effective numbers of excited modes at different d in are estimated theoretically (see , sec. , for more details). b Calculated Brillouin scattering strength \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}_{{{{{{{{\rm{B}}}}}}}}}^{(m,l)}(\Omega )$$\end{document} g B ( m , l ) ( Ω ) for two optical modes HE 11 and HE 24 (each mode profile displays the horizontal field component). Intramodal and intermodal Brillouin scattering have peaks at different Stokes frequencies Ω, and the corresponding acoustic modes are displayed above the peaks. c Calculated Brillouin gain spectrum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${G}_{{{{{{{{\rm{B}}}}}}}}}^{(m)}(\Omega )$$\end{document} G B ( m ) ( Ω ) for FM-only excitation (green) is narrower than multimode excitation with on-axis focusing of input light (blue). Off-axis focusing increases the number of excited modes and further broadens the Brillouin gain spectrum (red); the resulting decrease in peak gain enhances the SBS threshold. Optical and acoustic modes are calculated using Wave Optics and <t>Coefficient</t> Form <t>PDE</t> modules, respectively, in COMSOL .
General Coefficient Form Partial Differential Equation (Pde), supplied by COMSOL Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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pde interface  (COMSOL Inc)
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a Experimentally measured and theoretically predicted SBS threshold enhancement over FM-only excitation increases with distance d in of the focused input beam to fiber axis (inset; spot size ≈3.4 μm). Dots: mean enhancement of experimental data, error bars: standard deviation, solid curve: theoretical prediction including mode-dependent loss, mode coupling, and polarization mixing. The effective numbers of excited modes at different d in are estimated theoretically (see , sec. , for more details). b Calculated Brillouin scattering strength \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}_{{{{{{{{\rm{B}}}}}}}}}^{(m,l)}(\Omega )$$\end{document} g B ( m , l ) ( Ω ) for two optical modes HE 11 and HE 24 (each mode profile displays the horizontal field component). Intramodal and intermodal Brillouin scattering have peaks at different Stokes frequencies Ω, and the corresponding acoustic modes are displayed above the peaks. c Calculated Brillouin gain spectrum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${G}_{{{{{{{{\rm{B}}}}}}}}}^{(m)}(\Omega )$$\end{document} G B ( m ) ( Ω ) for FM-only excitation (green) is narrower than multimode excitation with on-axis focusing of input light (blue). Off-axis focusing increases the number of excited modes and further broadens the Brillouin gain spectrum (red); the resulting decrease in peak gain enhances the SBS threshold. Optical and acoustic modes are calculated using Wave Optics and <t>Coefficient</t> Form <t>PDE</t> modules, respectively, in COMSOL .
Pde Interface, supplied by COMSOL Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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a Experimentally measured and theoretically predicted SBS threshold enhancement over FM-only excitation increases with distance d in of the focused input beam to fiber axis (inset; spot size ≈3.4 μm). Dots: mean enhancement of experimental data, error bars: standard deviation, solid curve: theoretical prediction including mode-dependent loss, mode coupling, and polarization mixing. The effective numbers of excited modes at different d in are estimated theoretically (see , sec. , for more details). b Calculated Brillouin scattering strength \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}_{{{{{{{{\rm{B}}}}}}}}}^{(m,l)}(\Omega )$$\end{document} g B ( m , l ) ( Ω ) for two optical modes HE 11 and HE 24 (each mode profile displays the horizontal field component). Intramodal and intermodal Brillouin scattering have peaks at different Stokes frequencies Ω, and the corresponding acoustic modes are displayed above the peaks. c Calculated Brillouin gain spectrum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${G}_{{{{{{{{\rm{B}}}}}}}}}^{(m)}(\Omega )$$\end{document} G B ( m ) ( Ω ) for FM-only excitation (green) is narrower than multimode excitation with on-axis focusing of input light (blue). Off-axis focusing increases the number of excited modes and further broadens the Brillouin gain spectrum (red); the resulting decrease in peak gain enhances the SBS threshold. Optical and acoustic modes are calculated using Wave Optics and <t>Coefficient</t> Form <t>PDE</t> modules, respectively, in COMSOL .
Multiphysics 5.4, supplied by COMSOL Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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a Experimentally measured and theoretically predicted SBS threshold enhancement over FM-only excitation increases with distance d in of the focused input beam to fiber axis (inset; spot size ≈3.4 μm). Dots: mean enhancement of experimental data, error bars: standard deviation, solid curve: theoretical prediction including mode-dependent loss, mode coupling, and polarization mixing. The effective numbers of excited modes at different d in are estimated theoretically (see , sec. , for more details). b Calculated Brillouin scattering strength \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}_{{{{{{{{\rm{B}}}}}}}}}^{(m,l)}(\Omega )$$\end{document} g B ( m , l ) ( Ω ) for two optical modes HE 11 and HE 24 (each mode profile displays the horizontal field component). Intramodal and intermodal Brillouin scattering have peaks at different Stokes frequencies Ω, and the corresponding acoustic modes are displayed above the peaks. c Calculated Brillouin gain spectrum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${G}_{{{{{{{{\rm{B}}}}}}}}}^{(m)}(\Omega )$$\end{document} G B ( m ) ( Ω ) for FM-only excitation (green) is narrower than multimode excitation with on-axis focusing of input light (blue). Off-axis focusing increases the number of excited modes and further broadens the Brillouin gain spectrum (red); the resulting decrease in peak gain enhances the SBS threshold. Optical and acoustic modes are calculated using Wave Optics and <t>Coefficient</t> Form <t>PDE</t> modules, respectively, in COMSOL .
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a Experimentally measured and theoretically predicted SBS threshold enhancement over FM-only excitation increases with distance d in of the focused input beam to fiber axis (inset; spot size ≈3.4 μm). Dots: mean enhancement of experimental data, error bars: standard deviation, solid curve: theoretical prediction including mode-dependent loss, mode coupling, and polarization mixing. The effective numbers of excited modes at different d in are estimated theoretically (see , sec. , for more details). b Calculated Brillouin scattering strength \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}_{{{{{{{{\rm{B}}}}}}}}}^{(m,l)}(\Omega )$$\end{document} g B ( m , l ) ( Ω ) for two optical modes HE 11 and HE 24 (each mode profile displays the horizontal field component). Intramodal and intermodal Brillouin scattering have peaks at different Stokes frequencies Ω, and the corresponding acoustic modes are displayed above the peaks. c Calculated Brillouin gain spectrum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${G}_{{{{{{{{\rm{B}}}}}}}}}^{(m)}(\Omega )$$\end{document} G B ( m ) ( Ω ) for FM-only excitation (green) is narrower than multimode excitation with on-axis focusing of input light (blue). Off-axis focusing increases the number of excited modes and further broadens the Brillouin gain spectrum (red); the resulting decrease in peak gain enhances the SBS threshold. Optical and acoustic modes are calculated using Wave Optics and Coefficient Form PDE modules, respectively, in COMSOL .

Journal: Nature Communications

Article Title: Mitigating stimulated Brillouin scattering in multimode fibers with focused output via wavefront shaping

doi: 10.1038/s41467-023-42806-1

Figure Lengend Snippet: a Experimentally measured and theoretically predicted SBS threshold enhancement over FM-only excitation increases with distance d in of the focused input beam to fiber axis (inset; spot size ≈3.4 μm). Dots: mean enhancement of experimental data, error bars: standard deviation, solid curve: theoretical prediction including mode-dependent loss, mode coupling, and polarization mixing. The effective numbers of excited modes at different d in are estimated theoretically (see , sec. , for more details). b Calculated Brillouin scattering strength \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}_{{{{{{{{\rm{B}}}}}}}}}^{(m,l)}(\Omega )$$\end{document} g B ( m , l ) ( Ω ) for two optical modes HE 11 and HE 24 (each mode profile displays the horizontal field component). Intramodal and intermodal Brillouin scattering have peaks at different Stokes frequencies Ω, and the corresponding acoustic modes are displayed above the peaks. c Calculated Brillouin gain spectrum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${G}_{{{{{{{{\rm{B}}}}}}}}}^{(m)}(\Omega )$$\end{document} G B ( m ) ( Ω ) for FM-only excitation (green) is narrower than multimode excitation with on-axis focusing of input light (blue). Off-axis focusing increases the number of excited modes and further broadens the Brillouin gain spectrum (red); the resulting decrease in peak gain enhances the SBS threshold. Optical and acoustic modes are calculated using Wave Optics and Coefficient Form PDE modules, respectively, in COMSOL .

Article Snippet: Optical and acoustic modes are calculated using Wave Optics and Coefficient Form PDE modules, respectively, in COMSOL .

Techniques: Standard Deviation