Lateral Scattering Tests: M-discontinuity test (alpha = 0.410, Alsop fig. 13)

A. Figures (Models for the different cases are given in section B below)

A.1.a Reflection coefficients for backward and forward coefficients

A.1.b Reflection and Transmission coefficients for backward and forward coefficients for Case 4 (see email)

A.2. Transmission coefficients for backward and forward coefficients.

A.3.a Unaccounted energy for backward and forward propagation.

A.3.b Unaccounted energy for backward and forward propagation for Case 4

The energies for FORward propagation at longer periods are larger (negative) than those for backward propagation (p

The unaccounted energy for FORward propagation was computed using eqn (13) of Paper Ic. and similarly, the formula for BACKWARD PROPAGATION is given by the equation below.

\begin{eqnarray*}
   {{\mbox{$\mathcal{F}$}_{i} - \mbox{$\mathcal{F}$}_{scattered}}\over
    {\mbox{$\mathcal{F}$}_{i}}}                                            & = &
    1 \,-\, \sum_{j=1}^{16} {{\bar{U}_{j}}\over{\bar{U}_{i}}} 
        \,{{\mbox{$\bar\mathcal{I}$}_{j}}\over{\mbox{$\bar\mathcal{I}$}_{i}}} 
        \,\raisebox{-2pt}{\scriptsize $w$ \normalsize}\!R_{\,i j}^{\,2}
      \,-\, \sum_{j=1}^{16} {{U_{j}}\over{\bar{U}_{i}}} 
        \,{{{\mbox{$\mathcal{I}$}}_{j}}\over{\mbox{$\bar\mathcal{I}$}_{i}}} 
        \,\raisebox{-2pt}{\scriptsize $w$ \normalsize}\!T_{\,i j}^{\,2} \ .
\end{eqnarray*}

B. Models

B.1 Case 1

B.2 Case 2 and 3.

B.3 Case 4

C. A Parameter

C.1 The ratio of    \bar{vI}_1 / vI_1    and    \bar{KvJ}_1 / KvJ_1     .