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5.11: Diffraction Pattern for Pentagonal Point Scatterers

  • Page ID
    150536
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    Establish mask geometry:

    \[ \begin{matrix} R = 2 & m = 1 .. A & \Theta_m = \frac{2 \pi m}{A} & x_m = R \sin ( \Theta_m) & y_m = R \cos ( \Theta_m) \end{matrix} \nonumber \]

    Fourier transform of position wave function (mask geometry) into the momentum representation:

    \[ \Phi (p_x,~p_y) = \frac{1}{ 2 \pi \sqrt{A}} \sum_{m = 1}^{A} ( exp(-ip_xx_m) exp (-i p_y y_m)) \nonumber \]

    Display mask geometry and diffraction pattern: \( A \equiv 5\)

    \[ \begin{matrix} N = 100 & \Delta p = 12 & j = 0 .. N & k = 0 .. N & px_j = - \Delta p + \frac{2 \Delta p j}{N} & py_k = - \Delta p + \frac{2 \Delta p~ k}{N} \end{matrix} \nonumber \]

    \[ \text{Diffraction Pattern}_{j,~k} = \left( \left| \Phi (px_j,~py_k ) \right| \right)^2 \nonumber \]

    Screen Shot 2019-05-09 at 12.09.05 PM.png


    This page titled 5.11: Diffraction Pattern for Pentagonal Point Scatterers is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Frank Rioux via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.