Electromagnetic Vortices. Группа авторов. Читать онлайн. Newlib. NEWLIB.NET

Автор: Группа авторов
Издательство: John Wiley & Sons Limited
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Жанр произведения: Физика
Год издания: 0
isbn: 9781119662877
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      we find the expression of the far‐field integrals:

      (1.A.6)upper L Subscript theta Baseline equals minus 2 pi cosine theta sine phi left-parenthesis negative j right-parenthesis Superscript l Baseline e Superscript negative italic j l phi Baseline upper I

      (1.A.7)upper L Subscript phi Baseline equals minus 2 pi cosine phi left-parenthesis negative j right-parenthesis Superscript l Baseline e Superscript negative italic j l phi Baseline upper I comma

      where

      and Jl(⋅) is the lth order Bessel function of the first kind [21]. The expression of the far‐field electric field can be written as [122, eqs. 6‐122b, 6‐122c]:

      (1.A.10)integral Subscript 0 Superscript delta Baseline italic z upper J 0 left-parenthesis z right-parenthesis italic d z equals delta upper J 1 left-parenthesis delta right-parenthesis comma

      (1.A.11)ModifyingAbove upper E With right-arrow Subscript italic f f Superscript italic upper A upper D Baseline left-parenthesis r comma theta comma phi right-parenthesis equals StartFraction italic j k 0 upper E 0 Superscript italic upper A upper D Baseline a squared e Superscript minus italic j k 0 r Baseline Over 2 r EndFraction left-parenthesis ModifyingAbove theta With ampersand c period circ semicolon cosine phi minus ModifyingAbove phi With ampersand c period circ semicolon cosine theta sine phi right-parenthesis StartFraction upper J 1 left-parenthesis k 0 a sine theta right-parenthesis Over k 0 a sine theta EndFraction period

      Special Case 2: Tapered‐aperture Distribution. A physically meaningful and mathematically simple model for aperture‐like antennas with uniform phase distribution is the two‐parameter (2P) model [22, eq. (16)]:

      (1.A.13)ModifyingAbove upper E With right-arrow Subscript italic f f Superscript 2 upper P Baseline left-parenthesis r comma theta comma phi right-parenthesis equals StartFraction italic j k 0 a squared e Superscript minus italic j k 0 r Baseline Over 4 r EndFraction left-parenthesis ModifyingAbove theta With ampersand c period circ semicolon cosine phi minus ModifyingAbove phi With ampersand c period circ semicolon cosine theta sine phi right-parenthesis left-bracket upper C normal upper Lamda 1 left-parenthesis italic k a sine theta right-parenthesis plus left-parenthesis 1 minus upper C right-parenthesis normal upper Lamda Subscript upper P plus 1 Baseline left-parenthesis italic k a sine theta right-parenthesis right-bracket comma

      where

      (1.A.14)normal upper Lamda Subscript upper P plus 1 Baseline left-parenthesis zeta right-parenthesis equals 2 Superscript upper P plus 1 Baseline normal upper Gamma left-parenthesis upper P plus 1 right-parenthesis StartFraction upper J Subscript upper P plus 1 Baseline left-parenthesis zeta right-parenthesis Over zeta Superscript upper P plus 1 Baseline EndFraction comma

      Special Case 3: Laguerre–Gaussian beam. The aperture field of the