Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources
The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media. We show that such unified approach leads to explicit expressions for the field amplitudes and simple relations for the...
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| Дата: | 2012 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2012
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148687 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources / G. Burlak, V. Rabinovich // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 57 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1486872019-02-19T01:28:03Z Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources Burlak, G. Rabinovich, V. The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media. We show that such unified approach leads to explicit expressions for the field amplitudes and simple relations for the field eigenfrequencies and the retardation time that become the coupled variables. The main features of the technique are illustrated by examples of the moving source fields in the plasma and the Cherenkov radiation. It is emphasized that the deeper insight to the wave effects in dispersive case already requires the explicit formulation of the dispersive material model. As the advanced application we have considered the Doppler frequency shift in a complex single-resonant dispersive metamaterial (Lorenz) model where in some frequency ranges the negativity of the real part of the refraction index can be reached. We have demonstrated that in dispersive case the Doppler frequency shift acquires a nonlinear dependence on the modulating frequency of the radiated particle. The detailed frequency dependence of such a shift and spectral behavior of phase and group velocities (that have the opposite directions) are studied numerically. 2012 Article Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources / G. Burlak, V. Rabinovich // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 57 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 78A25; 78A35 DOI: http://dx.doi.org/10.3842/SIGMA.2012.096 http://dspace.nbuv.gov.ua/handle/123456789/148687 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media. We show that such unified approach leads to explicit expressions for the field amplitudes and simple relations for the field eigenfrequencies and the retardation time that become the coupled variables. The main features of the technique are illustrated by examples of the moving source fields in the plasma and the Cherenkov radiation. It is emphasized that the deeper insight to the wave effects in dispersive case already requires the explicit formulation of the dispersive material model. As the advanced application we have considered the Doppler frequency shift in a complex single-resonant dispersive metamaterial (Lorenz) model where in some frequency ranges the negativity of the real part of the refraction index can be reached. We have demonstrated that in dispersive case the Doppler frequency shift acquires a nonlinear dependence on the modulating frequency of the radiated particle. The detailed frequency dependence of such a shift and spectral behavior of phase and group velocities (that have the opposite directions) are studied numerically. |
| format |
Article |
| author |
Burlak, G. Rabinovich, V. |
| spellingShingle |
Burlak, G. Rabinovich, V. Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Burlak, G. Rabinovich, V. |
| author_sort |
Burlak, G. |
| title |
Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources |
| title_short |
Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources |
| title_full |
Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources |
| title_fullStr |
Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources |
| title_full_unstemmed |
Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources |
| title_sort |
time-frequency integrals and the stationary phase method in problems of waves propagation from moving sources |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148687 |
| citation_txt |
Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources / G. Burlak, V. Rabinovich // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 57 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:31:12Z |
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2023-05-20T17:31:12Z |
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