Caustics describe an effect of specular photon transmission and are not affected by the glass reflectivity. The specular values of the transmitting object, in this case the glass, control the appearance of the caustics. Reducing the specular color values produces less photon transmission and more subtle effects. This lower rate of transmission also seems to increase the required render time.

A value of RGB 0.000 (black) for the specularity produces no transmission of photons through the material and therefore will produce no caustic effects.

Photons passing thrugh the glass will pick up the specular colour as they are transmitted so changing the RGB value of the glass specularity will change both the colour of the glass and the colour of the caustic effects. This is not actually changing the photon energy colour at emission which can be adjusted in the light property editor.

The specular decay value controls the size of the highlight and has no visible affect on the caustics.