By 540 BC, Cyrus had captured Susiana and its capital, Susa.

Cyrus probably incorporated the subnations of Syria, Judea, and Arabia Petraea when he conquered Babylon.

Actually, according to Herodotus, Syria, Judea and Arabia (which probably formed the country of Lydia at the time Croesus lost his kingdom to Cyrus), was the first country he conquered after he'd subdued the Medes and his immediate naeighbours with the exception of the remnant of the Assyrian Empire which was holed up in Babylon. It was only after this that he started to really extend his borders to the east...

;)

BTW, by 'Neo-Babylonian Empire', do you mean the remnants of the Assyrian Empire, whose capital had finally been conquered by Cyaxares, and which had holed up in their final stronghold: Babylon?

:)