You assume that the screen is perfectly absorbing when you use this field. By uses this field you are assuming that the electromagnetic field pass through the material without reflection. Furthermore, you are assuming that you don't have field in the another side of the surface. $$ \textbf{E}=E_0e^{i(kx-\omega t+\delta)} \hat{\textbf{y}}, \ \ x<0 $$ $$ \textbf{B}=\frac{E_0}{c}e^{i(kx-\omega t+\delta)} \hat{\textbf{z}}, \ \ x<0 $$ $$ \textbf{E}=0 \ \ and \ \ \textbf{B}=0, \ \ when \ \ x>0 $$ For example, if your screen is perfectly reflective, then you need to use the superposition of the incoming field and the outgoing field (reflected), getting twice of your result. If your screen is perfectly transparent, then you need to use the field in the two side of the surface, getting zero.
You can deduce from Maxwell equation plus boundary conditions, the full electromagnetic field. This full electromagnetic field tells you if you have or not a reflection and so forth. For example, if your screen is made by a perfect conductor, then you get a perfect reflection.
You are interest in the pressure of this wave, the force in the screen oscillates very fast. Then you define the pressure in this way.