Electromagnetic Vortices. Группа авторов

Using the integral identity [21, eq. (7.421‐4)]

      (1.A.16)

      we find I from Eq. (1.A.8) and the far‐field expression from Eq. (1.A.9):

      (1.A.17)

      where Ψ = k₀w_g sin θ. For the definition of w_g refer to the first paragraph of the appendix and Figure 1.A.1. The previous discussion refers to the far‐field where the radiation integral can be found in closed form. The near‐field calculation using the Fresnel–Kirchhoff diffraction integral [24] was carried out numerically in Section 1.2 and the results are shown in Figure 1.7.

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