In the late Roman/early Byzantine world, a halo represented power rather than sanctity. See, for example, the Missorium of Theodosius, c. 388, a large silver plate on which the Emperor Theodosius is shown with a halo; he is also significantly larger than the other figures in order to show his power. http://www.shafe.co.uk/crystal/images/lshaf/Missorium_of_Theodosius.jpg

This tradition continues in Byzantium, whereas in the West the halo comes to mean only holiness. Until the late 11th century, however, there are two kinds of halos, the round one familiar to us today and a square one to indicate that the person was alive when the image was painted. A good example is Abbot Desiderius of Montecassino (d. 1087), who is shown donating his church. http://erogianpi.altervista.org/wp-content/uploads/2012/11/formis62.jpg

For early representations of angels without halos in a Christian context, see Therese Martin, “The Development of Winged Angels in Early Christian Art,” Espacio, Tiempo y Forma, 14 (2001), pp. 11-30. http://dialnet.unirioja.es/servlet/articulo?codigo=1035410