Oblique coupling of parallel Hertzian dipoles ($P_L=P{\left(\frac{3}{2}{\sin }^2\theta \right)}^2{\left(\frac{\lambda }{4\pi r}\right)}^2$)

For lossless parallel Hertzian transmitting and receiving dipoles separated by distance $r$ at angle $\theta$ to their common axis, directional gains are each $G=3{\sin }^2\theta /2$. The emitted polarization matches the receiving axis's transverse projection. Matched-load power is therefore $P_L=P[3{\sin }^2\theta /2{]}^2[\lambda /(4\pi r){]}^2$. One angular factor describes transmission and the other reception. This assumes reciprocal ideal dipoles, conjugate matching, far-field separation and negligible dissipative loss.