Launching efficiencies of the HE(1m) modes in a selffocusing optical fiber waveguide

The launching efficiencies of the HE(1m) modes and the over-all launching efficiency are calculated for the cases in which a self-focusing optical fiber is excited axially by a TEM(0n) beam mode or by a beam consisting of several beam modes. It is shown that, when the fiber is excited by a TEM(00) mode whose spot size s is very large compared with the characteristic spot size s(0) of the fiber, the HEM(1m) modes are almost equally excited and that, if s is matched to s(0), the over-all launching efficiency is nearly 100%. The over-all launching efficiency as well as the launching efficiencies of the HE(1m) modes decrease considerably when the fiber is excited by a beam containing the TEM(01) mode that is out of phase with the TEM(00) mode. The effect of the off-axis excitation by a TEM(00) mode on the over-all launching efficiency is also examined.