Acoustic treatment for side glass doors / please, need ideas.

Very easy and not expensive either. Buy white or room darkrening pleated shades. You can pull them up and down like blinds and they certainly soften the acoustics of a hard glass door. They look nice too. 

In addition to shades please consider adding something to damp the glass. The Marigo 40mm VTS Tuning dots are ideal for this purpose
http://marigoaudio.com/tuning-dots/

If for for some reason you decide against drapes I have also had very good results addressing room acoustics with a lot of glass using the Synergistic Research ART system (the resonating bowls). This gets pretty expensive fast but it works well and looks very nice

if you check out my room (similar size to yours) you will see both of these methods applied to a large window (plus I also hung ASC panels on it as well)

Thanks folkfreak for your ideas, in other situation I can consider them but I need to make the room nice also so I think I need to go with the shades.
roxy54, sorry about my english but when you mention pleated shades you mean the ones that have a design that looks like a v regular and then inverted right?, basically no flat. What about thickness? material? any link of something that you recommend? thanks again both for the input.

Pleated shades or a roller blind will have little to no effect as they are in practice acoustically transparent. It may ameliorate some of the excess HF but that’s about it. If you really want an acoustic impact you will need heavy lined drapes. I’m sure your significant other won’t mind the tuning dots so do think about them, they may foul the action of a sliding door however as they are quite thick

One other thought is to do as I did and use the ASC sound planks or GIK panels others suggest

I have them attached via velcro (hook/eye) tape. You can leave the velcro on the glass but only attach the planks when you are listening seriously. Again it’s going to end up costing you but this would work and be flexible