### Abstract

The theory and experimental applications of optical Airy beams are in active development recently. The Airy beams are characterised by very special properties: they are non-diffractive and propagate along parabolic trajectories. Among the striking applications of the optical Airy beams are optical micro-manipulation implemented as the transport of small particles along the parabolic trajectory, Airy-Bessel linear light bullets, electron acceleration by the Airy beams, plasmonic energy routing. The detailed analysis of the mathematical aspects as well as physical interpretation of the electromagnetic Airy beams was done by considering the wave as a function of spatial coordinates only, related by the parabolic dependence between the transverse and the longitudinal coordinates. Their time dependence is assumed to be harmonic. Only a few papers consider a more general temporal dependence where such a relationship exists between the temporal and the spatial variables. This relationship is derived mostly by applying the Fourier transform to the expressions obtained for the harmonic time dependence or by a Fourier synthesis using the specific modulated spectrum near some central frequency. Spatial-temporal Airy pulses in the form of contour integrals is analysed near the caustic and the numerical solution of the nonlinear paraxial equation in time domain shows soliton shedding from the Airy pulse in Kerr medium. In this paper the explicitly time dependent solutions of the electromagnetic problem in the form of time-spatial pulses are derived in paraxial approximation through the Green's function for the paraxial equation. It is shown that a Gaussian and an Airy pulse can be obtained by applying the Green's function to a proper source current. We emphasize that the processes in time domain are directional, which leads to unexpected conclusions especially for the paraxial approximation.

Original language | English |
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Title of host publication | PIERS proceedings Moscow |

Subtitle of host publication | Progress In Electromagnetics Research Symposium |

Publisher | Electromagnetics Academy |

Pages | 460-463 |

Number of pages | 4 |

ISBN (Print) | 978-1-934142-22-6 |

Publication status | Published - 12 Nov 2012 |

Event | Progress in Electromagnetics Research Symposium - Moscow, Russian Federation Duration: 19 Aug 2012 → 23 Aug 2012 |

### Publication series

Name | Progress in electromagnetics research symposium |
---|---|

Publisher | Electromagnetics Academy |

ISSN (Print) | 1559-9450 |

### Conference

Conference | Progress in Electromagnetics Research Symposium |
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Abbreviated title | PIERS 2012 Moscow |

Country | Russian Federation |

City | Moscow |

Period | 19/08/12 → 23/08/12 |

### Fingerprint

### Cite this

*PIERS proceedings Moscow: Progress In Electromagnetics Research Symposium*(pp. 460-463). (Progress in electromagnetics research symposium). Electromagnetics Academy.

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*PIERS proceedings Moscow: Progress In Electromagnetics Research Symposium.*Progress in electromagnetics research symposium, Electromagnetics Academy, pp. 460-463, Progress in Electromagnetics Research Symposium, Moscow, Russian Federation, 19/08/12.

**Green's function for paraxial equation.** / Nerukh, Alexander G.; Zolotariov, D.A.; Nerukh, D.A.; Georgiev, Georgi N.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Green's function for paraxial equation

AU - Nerukh, Alexander G.

AU - Zolotariov, D.A.

AU - Nerukh, D.A.

AU - Georgiev, Georgi N.

PY - 2012/11/12

Y1 - 2012/11/12

N2 - The theory and experimental applications of optical Airy beams are in active development recently. The Airy beams are characterised by very special properties: they are non-diffractive and propagate along parabolic trajectories. Among the striking applications of the optical Airy beams are optical micro-manipulation implemented as the transport of small particles along the parabolic trajectory, Airy-Bessel linear light bullets, electron acceleration by the Airy beams, plasmonic energy routing. The detailed analysis of the mathematical aspects as well as physical interpretation of the electromagnetic Airy beams was done by considering the wave as a function of spatial coordinates only, related by the parabolic dependence between the transverse and the longitudinal coordinates. Their time dependence is assumed to be harmonic. Only a few papers consider a more general temporal dependence where such a relationship exists between the temporal and the spatial variables. This relationship is derived mostly by applying the Fourier transform to the expressions obtained for the harmonic time dependence or by a Fourier synthesis using the specific modulated spectrum near some central frequency. Spatial-temporal Airy pulses in the form of contour integrals is analysed near the caustic and the numerical solution of the nonlinear paraxial equation in time domain shows soliton shedding from the Airy pulse in Kerr medium. In this paper the explicitly time dependent solutions of the electromagnetic problem in the form of time-spatial pulses are derived in paraxial approximation through the Green's function for the paraxial equation. It is shown that a Gaussian and an Airy pulse can be obtained by applying the Green's function to a proper source current. We emphasize that the processes in time domain are directional, which leads to unexpected conclusions especially for the paraxial approximation.

AB - The theory and experimental applications of optical Airy beams are in active development recently. The Airy beams are characterised by very special properties: they are non-diffractive and propagate along parabolic trajectories. Among the striking applications of the optical Airy beams are optical micro-manipulation implemented as the transport of small particles along the parabolic trajectory, Airy-Bessel linear light bullets, electron acceleration by the Airy beams, plasmonic energy routing. The detailed analysis of the mathematical aspects as well as physical interpretation of the electromagnetic Airy beams was done by considering the wave as a function of spatial coordinates only, related by the parabolic dependence between the transverse and the longitudinal coordinates. Their time dependence is assumed to be harmonic. Only a few papers consider a more general temporal dependence where such a relationship exists between the temporal and the spatial variables. This relationship is derived mostly by applying the Fourier transform to the expressions obtained for the harmonic time dependence or by a Fourier synthesis using the specific modulated spectrum near some central frequency. Spatial-temporal Airy pulses in the form of contour integrals is analysed near the caustic and the numerical solution of the nonlinear paraxial equation in time domain shows soliton shedding from the Airy pulse in Kerr medium. In this paper the explicitly time dependent solutions of the electromagnetic problem in the form of time-spatial pulses are derived in paraxial approximation through the Green's function for the paraxial equation. It is shown that a Gaussian and an Airy pulse can be obtained by applying the Green's function to a proper source current. We emphasize that the processes in time domain are directional, which leads to unexpected conclusions especially for the paraxial approximation.

UR - http://www.scopus.com/inward/record.url?scp=84868516022&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84868516022

SN - 978-1-934142-22-6

T3 - Progress in electromagnetics research symposium

SP - 460

EP - 463

BT - PIERS proceedings Moscow

PB - Electromagnetics Academy

ER -