  We have modeled laser-induced transient current waveforms in radiation
coplanar grid detectors. Poisson's equation has been solved by finite element
method and currents induced by photo-generated charge were obtained using
Shockley-Ramo theorem. The spectral response on a radiation flux has been
modeled by Monte-Carlo simulations. We show 10$\times$ improved spectral
resolution of coplanar grid detector using differential signal sensing. We
model the current waveform dependence on doping, depletion width, diffusion and
detector shielding and their mutual dependence is discussed in terms of
detector optimization. The numerical simulations are successfully compared to
experimental data and further model simplifications are proposed. The space
charge below electrodes and a non-homogeneous electric field on a coplanar grid
anode are found to be the dominant contributions to laser-induced transient
current waveforms.
