This work is devoted to describing the mechanisms underlying the response of mouse cortical networks to two variants of ChR-assisted photostimulation of the parvalbumin-positive interneurons (PV). In the first part, we investigate the effects of the ReaChR optogenetic photostimulation of PV neurons in the anterolateral motor cortex (ALM) and in the barrel cortex (S1) on the population average responses of principal excitatory cells (PCs) and PV interneurons. ReaChR allows for a uniform stimulation of the neurons upon broadly extended regions (up to a few mm). After extending the theory of balanced networks to networks with multiple inhibitory populations, we investigate the connectivity patterns that are essential in accounting for these effects. We show that the average responses of PCs and PV neurons in ALM layer 2/3 and layer 5 can be accounted for by a four-population network with connectivity similar to that reported in the primary visual cortex. We propose an alternative network architecture to robustly account for these responses in S1. In the second part, we examine the effects of the ChR2 optogenetic stimulation of PV neurons in the mouse barrel cortex on the spatial profile of the responses of PCs and PV neurons. ChR2 allows for stimulation of the neurons upon very localized regions (a few hundred microns). We investigate these effects in two-population network models where the probability of connection between the neurons decay exponentially with distance. We show that for stimulation of strong enough intensity, the activity of the excitatory neurons is suppressed on a characteristic length that non-linearly depends on the radius of the perturbation.