M. Bachmann et al., GENERAL SELF-IMAGING PROPERTIES IN N X N MULTIMODE INTERFERENCE COUPLES INCLUDING PHASE-RELATIONS, Applied optics, 33(18), 1994, pp. 3905-3911
Self-imaging properties of generalized N x N multimode interference co
uplers are derived. Positions, amplitudes, and phases of the self-imag
es are directly related to the lengths and widths of the coupler by so
lving the eigenmode superposition equation analytically for any arbitr
ary length. Devices of length (MIN) 3L(c), where M is the multiple occ
urrence of the N self-images, are analyzed in detail. The general form
alism is applied to practical N x N couplers used in integrated optics
, and simple phase relations are obtained.