Are there specific microwave antennas for digital and analog signal transmission?
No. There's no physical difference between digital signals and analog signals on the air. Both are converted to analog voltages.

The only things about the electrical system that attaches to the antenna that matter for an antenna are


center frequency
bandwidth 
impedance


Selling an antenna "for digital transmissions" is like selling a car to "transport green apples". The color of apples doesn't have anything to do with their transportability. The question whether the data that is modulated onto a microwave signal is analog or digital has nothing to do with their bandwidth, center frequency or the device's impedance.