Simple mixing of the frequencies does not result in the desired modulation. In AM Radio the signal frequency is first mixed with the carrier frequency and the mixture is pushed through a bandpass filter.  In Optical AM, both the signal frequency, and the carrier frequency are first passed through separate bandpass filters, then both results are mixed to produce the modulation. The Optical color filters are really bandpass filters as they allow a range of wavelengths through, rather than a single wavelength of light.

On the right is what happens when you switch the projector filters.  You get an image composed of the original image's complementary colors.