I say "yes" in the case of plane-parallel mirror substrate and "no" for wedge substrate.

Thank you Eugene, we are focused on plano-concave mirror and the front side coating technique may be e-beam evaporation (because its cheap). So AR coating makes any significant role in performance?

Hi Muhammed,

I assume you mean HR coating if you want to obtain a 99.93% reflection on the back mirror? I don't know which wavelength you're aiming at but these HR coatings normally consist of combinations of high and low index coatings (e.g. SiO2-Si3N4, SiO2-Ta2O5). There is good software to calculate these coatings for your specific wavelength (TF_calc, Filmstar, McLeod). Very often the commercial companies who deliver you the mirrors will use this software if you give them the specs (wavelength, reflectance, polarisation, etc). For a 99.93% reflectance my guess is you will need 5-6 stacks of the material combinations I mentioned. For AR coatings the same software is used and there you probably need a single thin film (e.g SiO2) or a single combination of SiO2 and Ta2O5, depending on central wavelength and wavelength window. 

I don't think you care about AR coating the outer surfaces - an unnecessary expense.

You have four surfaces - uncoated front surface, first curved HR surface, second curved HR surface, uncoated back surface.

Say you couple 1mW into your cavity so you have 1mW after passing through the first HR surface. The transmission through the second HR coated surface will be 0.07% of this, then you have 4% reflection off the back surface, then you pass through the second HR surface again at 0.07% and out through the uncoated surface at 96% transmission -  so you have about 2uW due to reflection off back surface compared with a little less than 1mW for the main internal cavity.

I don't think that's important. Ask Stable Laser Systems (http://www.stablelasers.com) if they have an AR coating on the external surfaces of their high-finesses cavities just to be sure.