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<p>We derive an explicit analytical expression for the distribution of longitudinal component of the canonical energy flux vector near the initial plane (in the near field). We consider a nonparaxial light beam with linear polarization and with an amplitude of the plane waves spectrum in the form of a circle. This distribution has the shape of an ellipse elongated along the direction of the linear polarization vector. If the plane waves spectrum includes evanescent waves, then in the near field, a reverse canonical energy flux arises. This reverse flux almost coincides with the first side lobe of the intensity distribution in the near field. The reverse flux arises near intensity zeros. Computer simulations is performed using two independent methods: plane-wave spectral decomposition and Rayleigh-Sommerfeld integral. The simulation results agree with theoretical predictions.</p>

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Reverse canonical energy flux in a nonparaxial linearly polarized beam near the initial plane

  • 期刊论文

  • 发表日期：

    2026年1月2日

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  • V. V. Kotlyar,
  • A. A. Kovalev,
  • A. G. Nalimov

摘要

We derive an explicit analytical expression for the distribution of longitudinal component of the canonical energy flux vector near the initial plane (in the near field). We consider a nonparaxial light beam with linear polarization and with an amplitude of the plane waves spectrum in the form of a circle. This distribution has the shape of an ellipse elongated along the direction of the linear polarization vector. If the plane waves spectrum includes evanescent waves, then in the near field, a reverse canonical energy flux arises. This reverse flux almost coincides with the first side lobe of the intensity distribution in the near field. The reverse flux arises near intensity zeros. Computer simulations is performed using two independent methods: plane-wave spectral decomposition and Rayleigh-Sommerfeld integral. The simulation results agree with theoretical predictions.