Self-imaging properties of generalized N × N multimode interference couplers are derived. Positions, amplitudes, and phases of the self-images are directly related to the lengths and widths of the coupler by solving the eigenmode superposition equation analytically for any arbitrary length. Devices of length (M/N) 3L c , where M is the multiple occurrence of the N self-images, are analyzed in detail. The general formalism is applied to practical N × N couplers used in integrated optics, and simple phase relations are obtained.
© 1994 Optical Society of America
Original Manuscript: June 1, 1993
Revised Manuscript: October 20, 1993
Published: June 20, 1994
M. Bachmann, P. A. Besse, and H. Melchior, "General self-imaging properties in N × N multimode interference couplers including phase relations," Appl. Opt. 33, 3905-3911 (1994)