Zero-order and first-order theory of the formation of space-charge gratings in photoconductive polymers

When a photoconducting polymer is illuminated by light with an intensity that varies sinusoidally with position, the space-charge electric field, hole density, ionized photosensitizer density, hole trap density, and other properties, will also vary with position. We derive an expression for the zero-order Fourier component of the hole density and a linear system of equations for the first-order Fourier component of a number of variables. The system of equations is solved for the steady-state first-order Fourier component of the electric field for the case in which hole untrapping is negligible or no hole traps are present. Next, the equations are simplified for the case in which the initial trap density is far greater than the density of holes, and for the case of no hole traps. Finally, we compare the zero-order hole density and first-order electric field calculated from our equations to values obtained by Fourier transforming the results of numerical calculations.