And as such f ( r → → , t ) = α α ( ω ω ) E ( r → → , t ) ∇ ∇ E ( r → → , t ) = 1 2 α α ( ω ω ) ∇ ∇ E 2 ( r → → , t ) and thus f ( r → → ) = ∇ ∇ [ 1 2 α α ( ω ω ) E 2 ( r → → , t ) ¯ ¯ ] = ∇ ∇ [ 1 4 α α ( ω ω ) E 2 ( r → → ) ] , and as such we have V e . d = − − 1 4 α α ( ω ω ) E 2 ( r → → ) .