Self-consistent Equation Method for Solving Problems of Wave Diffraction on Scatter Systems
The paper considers one of the numerical methods to solve problems of scattering electromagnetic waves on the systems formed by parallel-oriented cylindrical elements – two-dimensional photonic crystals. The method is based on the classical partition approach used for solving the wave equation. Тhe...
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| Format: | Article |
| Language: | Russian |
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MGTU im. N.È. Baumana
2021-04-01
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| Series: | Matematika i Matematičeskoe Modelirovanie |
| Subjects: | |
| Online Access: | https://www.mathmelpub.ru/jour/article/view/243 |
| _version_ | 1811232504164646912 |
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| author | A. Yu. Vetluzhsky |
| author_facet | A. Yu. Vetluzhsky |
| author_sort | A. Yu. Vetluzhsky |
| collection | DOAJ |
| description | The paper considers one of the numerical methods to solve problems of scattering electromagnetic waves on the systems formed by parallel-oriented cylindrical elements – two-dimensional photonic crystals. The method is based on the classical partition approach used for solving the wave equation. Тhe method principle is to represent the field as the sum of the primary field and the unknown secondary field scattered on the medium elements. The mathematical expression for the latter is written as the infinite series according to elementary wave functions with unknown coefficients. In particular, the N elements-scattered field is found as the sum of N diffraction series in which one of the series is composed of the wave functions of one body and the wave functions in the remaining series are expressed in terms of the eigenfunctions of the first body using addition theorems. Further, to meet the boundary conditions, on the surface of each element, we obtain systems of linear algebraic equations with the infinite number of unknowns – the required expansion coefficients, which are solved by standard methods. A feature of the method is the use of analytical expressions to describe diffraction on a single element of the system. In contrast to most numerical methods, this approach allows one to obtain information on the amplitude-phase or spectral characteristics of the field only at the local points of the structure. The high efficiency of this method stems from the fact that there is no need to determine the field parameters in the entire area of space occupied by the multi-element system under consideration. The paper compares the calculated results of the transmission spectra of two-dimensional photonic crystals using the considered method with the experimental data and numerical results, obtained by other approaches, and demonstrates their good agreement. |
| first_indexed | 2024-04-12T11:03:58Z |
| format | Article |
| id | doaj.art-d551b3149b0f465cb74822084b121d18 |
| institution | Directory Open Access Journal |
| issn | 2412-5911 |
| language | Russian |
| last_indexed | 2024-04-12T11:03:58Z |
| publishDate | 2021-04-01 |
| publisher | MGTU im. N.È. Baumana |
| record_format | Article |
| series | Matematika i Matematičeskoe Modelirovanie |
| spelling | doaj.art-d551b3149b0f465cb74822084b121d182022-12-22T03:35:52ZrusMGTU im. N.È. BaumanaMatematika i Matematičeskoe Modelirovanie2412-59112021-04-0106283610.24108/mathm.0620.0000243155Self-consistent Equation Method for Solving Problems of Wave Diffraction on Scatter SystemsA. Yu. Vetluzhsky0Institute of Physical Materials Science, Siberian Branch of the Russian Academy of Sciences, Ulan-UdeThe paper considers one of the numerical methods to solve problems of scattering electromagnetic waves on the systems formed by parallel-oriented cylindrical elements – two-dimensional photonic crystals. The method is based on the classical partition approach used for solving the wave equation. Тhe method principle is to represent the field as the sum of the primary field and the unknown secondary field scattered on the medium elements. The mathematical expression for the latter is written as the infinite series according to elementary wave functions with unknown coefficients. In particular, the N elements-scattered field is found as the sum of N diffraction series in which one of the series is composed of the wave functions of one body and the wave functions in the remaining series are expressed in terms of the eigenfunctions of the first body using addition theorems. Further, to meet the boundary conditions, on the surface of each element, we obtain systems of linear algebraic equations with the infinite number of unknowns – the required expansion coefficients, which are solved by standard methods. A feature of the method is the use of analytical expressions to describe diffraction on a single element of the system. In contrast to most numerical methods, this approach allows one to obtain information on the amplitude-phase or spectral characteristics of the field only at the local points of the structure. The high efficiency of this method stems from the fact that there is no need to determine the field parameters in the entire area of space occupied by the multi-element system under consideration. The paper compares the calculated results of the transmission spectra of two-dimensional photonic crystals using the considered method with the experimental data and numerical results, obtained by other approaches, and demonstrates their good agreement.https://www.mathmelpub.ru/jour/article/view/243numerical methodsdiffractionscatteringphotonic crystalstransmission spectra |
| spellingShingle | A. Yu. Vetluzhsky Self-consistent Equation Method for Solving Problems of Wave Diffraction on Scatter Systems Matematika i Matematičeskoe Modelirovanie numerical methods diffraction scattering photonic crystals transmission spectra |
| title | Self-consistent Equation Method for Solving Problems of Wave Diffraction on Scatter Systems |
| title_full | Self-consistent Equation Method for Solving Problems of Wave Diffraction on Scatter Systems |
| title_fullStr | Self-consistent Equation Method for Solving Problems of Wave Diffraction on Scatter Systems |
| title_full_unstemmed | Self-consistent Equation Method for Solving Problems of Wave Diffraction on Scatter Systems |
| title_short | Self-consistent Equation Method for Solving Problems of Wave Diffraction on Scatter Systems |
| title_sort | self consistent equation method for solving problems of wave diffraction on scatter systems |
| topic | numerical methods diffraction scattering photonic crystals transmission spectra |
| url | https://www.mathmelpub.ru/jour/article/view/243 |
| work_keys_str_mv | AT ayuvetluzhsky selfconsistentequationmethodforsolvingproblemsofwavediffractiononscattersystems |