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Cherenkov radiation in a planarly layered waveguide in the case of polarized waves

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Abstract

In the present work, we consider an isotropic planarly layered waveguide in the case of polarized waves, and calculate the Green’s function associated with a motionless unit point source in the stationary state. On the basis of the Green’s function, we approach the dynamical problem of a point source that is in uniform motion in the waveguide. The mathematical description of the transverse electric and transverse magnetic waves generated by the moving point source is given in the form of double oscillatory integrals of the time and the frequency. Then these integrals are written in terms of a large parameter \(\lambda >0\) in order to apply the stationary phase method. This gives asymptotic formulas for the electromagnetic field as \(\lambda \rightarrow \infty \). The calculation of the stationary points of the phase leads us to the condition that guarantees the existence of Cherenkov radiation in the waveguide. Finally, the analysis here presented is applied to some numerical examples, which are worked with an algorithm based on the spectral parameter power series method.

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Notes

  1. The values of \(n_{1}\) and \(n_{2}\) may be associated to crystalline materials such as \(\mathrm{SiO}_{2}\) at 446.5 nm wavelength, and Si at 1357 nm wavelength, respectively. These materials typically are used in integrated optics.

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Authors and Affiliations

  1. Posgrado en Tecnología Avanzada, SEPI UPIITA-IPN, Av. Instituto Politénico Nacional 2580, Col. Barrio la Laguna Ticomán, 07340, Ciudad de México, Mexico

    Víctor Barrera-Figueroa

  2. Departamento de Telecomunicaciones, SEPI ESIME-IPN, Av. Instituto Politénico Nacional S/N, Col. Lindavista, 07738, Ciudad de México, Mexico

    Vladimir S. Rabinovich

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  1. Víctor Barrera-Figueroa
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  2. Vladimir S. Rabinovich
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Correspondence to Víctor Barrera-Figueroa.

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To 60th birthday anniversary of Prof. Dr. Sergei Grudsky.

Research was partially supported by the National System of Investigators of Mexico (SNI). The work of V. Barrera-Figueroa was partially supported by the SIBE Program of the IPN. The work of V. S. Rabinovich was partially supported by the Conacyt Project 000000000179872.

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Barrera-Figueroa, V., Rabinovich, V.S. Cherenkov radiation in a planarly layered waveguide in the case of polarized waves. Bol. Soc. Mat. Mex. 22, 431–459 (2016). https://doi.org/10.1007/s40590-016-0107-9

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  • DOI: https://doi.org/10.1007/s40590-016-0107-9

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