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You dont need to call amybody, you dont have to do anything, you will be at the Non Sida area of the airport, it is ok to shoot there. I work there, I know the rules.
While this is true for any public property, it's never a bad idea to just give a heads up, or be friendly and try and reach out to them beforehand, especially considering the high security nature of airports. Wouldn't hurt to have the Airport Authority message any security detail that you'll be there and you're NOT a crazy.