Noise Photodiode and Laser

We have measured the dark noise and the laser noise by means of Photodiode 12595. The measured was done in the following condition:
T Chiller = 16.5 °C
Laser Power Supply: in the Lab (used long cable)
Power of the Laser (OUT): Maximum.
Power of the Laser on the photodiode: 74 mW (Vdc measured = 2.66 V).
We have used (in the lab) the pre-amplifier+power supply of the VIGO (Label 2, G=1057).
We have also tried to use another power supply (AGILENT) for the VIGO pre-amplificator in order to reduce the peaks to 50 Hz, but the amplitude of the peaks to 50 Hz are the same.
In the next figure the dark noise in the lab:




Here we report the laser noise and the saturation curve (Voltage vs Power):






In the next figure the different between noise calculated in different time and place:

From the shape of the red curve in the last graph added by Maurizio, I think that the measurement was taken with the laser in pulsed mode (the modulation peak at 2.5kHz and its harmonics are clearly visible). The comparison should be made with a graph taken with the laser operated in CW mode.

I also think that a fair comparison should be made by plotting the RIN.

It seems to me that we should concentrate on a smaller span (10kHz seems too much), maybe 3.2kHz is enough and would give us a better resolution at low frequencies.