This is an interesting problem! What I think would be the best way would be to use a White light source to give you the range of noise from 400 nm to 750 nm then use an optical fiber amplifier provide gain according to your distribution. The Optical Fiber Amplifier allows you to load a gain profile from a text file that you could populate from the relative powers of the spectrum you attached. Then you could either modify the power of the light source or the peak gain of the optical fiber to get the desired power levels.