Scalar wave intensity ($I=|E{|}^2$)

For a scalar complex wave amplitude $E$, the squared-amplitude scalar wave intensity convention is $I=E{E}^{\ast }$. It is nonnegative and unchanged by multiplying $E$ by a unit-modulus wave phase factor. This convention is useful in paraxial propagation and phase screen models. Conversion to physical energy flux also depends on the field variable and medium; an arbitrary superposition need not have its full flux determined by this scalar alone. For a random field, $⟨I⟩$ is the mean wave intensity, whereas $|⟨E⟩{|}^2$ is the squared coherent field; these generally differ.