Scattering Amplitude of Surface Plasmon Polariton Excited by a Finite Grating
Unusual optical properties of laser-ablated metal surfaces arise from the excitation of local plasmon resonances in nano- and microstructures produced by laser-processing and from the mutual interaction of those structures through surface plasmon polariton (SPP) waves. This interaction provides a sy...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Nanomaterials |
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| Online Access: | https://www.mdpi.com/2079-4991/13/14/2091 |
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| author | Anton V. Dyshlyuk Alexey Proskurin Andrey A. Bogdanov Oleg B. Vitrik |
| author_facet | Anton V. Dyshlyuk Alexey Proskurin Andrey A. Bogdanov Oleg B. Vitrik |
| author_sort | Anton V. Dyshlyuk |
| collection | DOAJ |
| description | Unusual optical properties of laser-ablated metal surfaces arise from the excitation of local plasmon resonances in nano- and microstructures produced by laser-processing and from the mutual interaction of those structures through surface plasmon polariton (SPP) waves. This interaction provides a synergistic effect, which can make the optical properties of the composite nanostructure drastically different from the properties of its elements. At the same time, the prediction and analysis of these properties are hampered by the complexity of the analytical solution to the problem of SPP excitation by surface objects of arbitrary configuration. Such a problem can be reduced to a simpler one if one considers the geometry of a structured surface as a superposition of harmonic Fourier components. Therefore, the analytical solution to the problem of surface plasmon polariton excitation through the scattering of light by a sinusoidally perturbed plasmonic metal/vacuum boundary becomes very important. In this work, we show that this problem can be solved using a well-known method for calculating guided-mode amplitudes in the presence of current sources, which is used widely in the waveguide theory. The calculations are carried out for the simplest 2D cases of (1) a sinusoidal current of finite length and (2) a finite-length sinusoidal corrugation on a plasmonic metal surface illuminated by a normally incident plane wave. The analytical solution is compared with the results of numerical simulations. It is shown that, in the first case, the analytical and numerical solutions agree almost perfectly. In the second case, the analytical solution correctly predicts the optimum height of the corrugation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>x</mi><mi>opt</mi></msub></semantics></math></inline-formula>, providing the maximum SPP excitation efficiency. At the same time, the analytical and numerical values of the SPP amplitude agree very well when the corrugation height <i>x</i> turns out to be <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>x</mi><mo>≪</mo><msub><mi>x</mi><mi>opt</mi></msub></mrow></semantics></math></inline-formula> or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>x</mi><mo>≫</mo><msub><mi>x</mi><mi>opt</mi></msub></mrow></semantics></math></inline-formula> (at least up to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><msub><mi>x</mi><mi>opt</mi></msub></mrow></semantics></math></inline-formula>); at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>x</mi><mo>=</mo><msub><mi>x</mi><mi>opt</mi></msub></mrow></semantics></math></inline-formula>, the mismatch of those does not exceed 25%. The limitations of the analytical model leading to such a mismatch are discussed. We believe that the presented approach is useful for modeling various phenomena associated with SPP excitation. |
| first_indexed | 2024-03-11T00:46:18Z |
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| id | doaj.art-c7889093a40146ea9a69e0c3047f7bb2 |
| institution | Directory Open Access Journal |
| issn | 2079-4991 |
| language | English |
| last_indexed | 2024-03-11T00:46:18Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
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| series | Nanomaterials |
| spelling | doaj.art-c7889093a40146ea9a69e0c3047f7bb22023-11-18T20:45:51ZengMDPI AGNanomaterials2079-49912023-07-011314209110.3390/nano13142091Scattering Amplitude of Surface Plasmon Polariton Excited by a Finite GratingAnton V. Dyshlyuk0Alexey Proskurin1Andrey A. Bogdanov2Oleg B. Vitrik3Institute of Automation and Control Processes, Far Eastern Branch of the Russian Academy of Sciences, Vladivostok 690041, RussiaSchool of Physics and Engineering, ITMO University, St. Petersburg 197101, RussiaSchool of Physics and Engineering, ITMO University, St. Petersburg 197101, RussiaInstitute of Automation and Control Processes, Far Eastern Branch of the Russian Academy of Sciences, Vladivostok 690041, RussiaUnusual optical properties of laser-ablated metal surfaces arise from the excitation of local plasmon resonances in nano- and microstructures produced by laser-processing and from the mutual interaction of those structures through surface plasmon polariton (SPP) waves. This interaction provides a synergistic effect, which can make the optical properties of the composite nanostructure drastically different from the properties of its elements. At the same time, the prediction and analysis of these properties are hampered by the complexity of the analytical solution to the problem of SPP excitation by surface objects of arbitrary configuration. Such a problem can be reduced to a simpler one if one considers the geometry of a structured surface as a superposition of harmonic Fourier components. Therefore, the analytical solution to the problem of surface plasmon polariton excitation through the scattering of light by a sinusoidally perturbed plasmonic metal/vacuum boundary becomes very important. In this work, we show that this problem can be solved using a well-known method for calculating guided-mode amplitudes in the presence of current sources, which is used widely in the waveguide theory. The calculations are carried out for the simplest 2D cases of (1) a sinusoidal current of finite length and (2) a finite-length sinusoidal corrugation on a plasmonic metal surface illuminated by a normally incident plane wave. The analytical solution is compared with the results of numerical simulations. It is shown that, in the first case, the analytical and numerical solutions agree almost perfectly. In the second case, the analytical solution correctly predicts the optimum height of the corrugation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>x</mi><mi>opt</mi></msub></semantics></math></inline-formula>, providing the maximum SPP excitation efficiency. At the same time, the analytical and numerical values of the SPP amplitude agree very well when the corrugation height <i>x</i> turns out to be <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>x</mi><mo>≪</mo><msub><mi>x</mi><mi>opt</mi></msub></mrow></semantics></math></inline-formula> or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>x</mi><mo>≫</mo><msub><mi>x</mi><mi>opt</mi></msub></mrow></semantics></math></inline-formula> (at least up to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><msub><mi>x</mi><mi>opt</mi></msub></mrow></semantics></math></inline-formula>); at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>x</mi><mo>=</mo><msub><mi>x</mi><mi>opt</mi></msub></mrow></semantics></math></inline-formula>, the mismatch of those does not exceed 25%. The limitations of the analytical model leading to such a mismatch are discussed. We believe that the presented approach is useful for modeling various phenomena associated with SPP excitation.https://www.mdpi.com/2079-4991/13/14/2091surface plasmon polaritonsSPPSPP excitationnanostructured substrates |
| spellingShingle | Anton V. Dyshlyuk Alexey Proskurin Andrey A. Bogdanov Oleg B. Vitrik Scattering Amplitude of Surface Plasmon Polariton Excited by a Finite Grating Nanomaterials surface plasmon polaritons SPP SPP excitation nanostructured substrates |
| title | Scattering Amplitude of Surface Plasmon Polariton Excited by a Finite Grating |
| title_full | Scattering Amplitude of Surface Plasmon Polariton Excited by a Finite Grating |
| title_fullStr | Scattering Amplitude of Surface Plasmon Polariton Excited by a Finite Grating |
| title_full_unstemmed | Scattering Amplitude of Surface Plasmon Polariton Excited by a Finite Grating |
| title_short | Scattering Amplitude of Surface Plasmon Polariton Excited by a Finite Grating |
| title_sort | scattering amplitude of surface plasmon polariton excited by a finite grating |
| topic | surface plasmon polaritons SPP SPP excitation nanostructured substrates |
| url | https://www.mdpi.com/2079-4991/13/14/2091 |
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