Both of these results can be substituted into the expression for the electric field to obtain the final expression E ( z , t ) = { E 0 e i ( k 0 z − − ω ω t ) − − ( n − − 1 n + 1 ) E 0 e − − i ( k 0 z + ω ω t ) z < 0 ( 2 n + 1 ) E 0 e i ( n k 0 z − − ω ω t ) z > 0.