and the relative rotations of the resulting interference patterns observed if perfect u201c undoing u201d of the geometric phase has been accomplished then no rotations of the interference pattern should be observed however if there has been any attempt to eavesdrop e g by evanescent field coupling or introduction of intervening taps additional phase variations will be imparted onto the lg 0 1 mode compared with the lg 0 0 modes in that case it will be found that at the receiver end it is no longer possible simply to negate the phase differences between the two modes and that will be evidence of an attempt to eavesdrop in a third example embodiment of the invention fig8 at its transmitter end the apparatus is again the same as that of the first example embodiment however a second portion 160 similar to portion 30 for degenerating the orbital angular momentum modes is provided at the receiver end fig9 in portion 160 the light from the receiver end of the fibre 130 is imaged onto a copy of the cgh used to originally create the two modes of light the second cgh diffracts the light in the same way as the first and the resulting diffracted orders are shone onto a power beam splitting cube bs 3 stops are again used to select particular diffracted orders with the first path selecting the undiffracted 0 th order of the lg 0 0 mode whilst the second path selects the u2212 1 st order of.