Your photodetectors have no diode characteristics. It looks like a resistor with light sensing. What device structure is it? And the active material for light sensing?
I-V plot illustrates a linear current as a function of bias voltage at each illumination intensities , it is a behavior of an ohmic contact (photoresistance), the importance of this results that the linear behavior.
I am not sure if I understand correctly, but the peculiarity is voltage generation by illuminated low ohmic structure (just a few ohms in fact).
I recall something like that was already observed in 1920..1930s or so, it is caused by the fact that
1) illumination is always asymmetric in terms vs the contacts (especially if it is top/bottom contacts)
2) Electron /hole diffusion coefficients are quite different.
3) The combinations of 1 and 2 result is electrons 'pushed' by light from the more illuminated one contact toward another one, thus generating the voltage.
I would like to propose that you give the structure of your detector to and how its electrode. The I-V characteristics shown point out a reverse biased photo diode.
So, i would assume that the biasing of the diode is reversed. I mean the diode is froward biased in the third quadrant and the second quadrant.