= Flat-space anisotropic beam shear focusing
{title2=$A=1-\lambda^2,\quad \sigma^2=(1-\lambda^2)^{-2}$}
In flat spacetime take a twist-free beam's two screen Jacobi factors to be $1+\lambda$ and $1-\lambda$. They solve the zero-curvature <geodesic deviation> equation. Their product is the displayed area, and subtracting the trace from their optical matrix gives the displayed nonnegative shear. Direct differentiation yields $(A^{1/2})''=-(1-\lambda^2)^{-3/2}=-\sigma^2A^{1/2}$, an explicit check of the focusing sign.
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