If you are connecting to SQL Server using SQL authentication, I don't think SQL Server knows the AD user. You would have to get that information by querying the Windows (using a Powershell script invoked using xp_cmdshell, for example) or adding AD as a linked server (http://www.sqlservercentral.com/Forums/Topic265745-149-1.aspx#bm909492)
I have not done either of these, so I am unable to add more color. I am sure that if there is a better way, someone else would chime in.