Impulse response of a self-focusing optical fiber

By using wave optics method, analytical expressions are derived for the impulse response of a self-focusing optical fiber with a core whose index profile is described by the second- and the fourth-order terms of the radial distance. Two cases are considered: (1) where all the possible propagating modes are equally excited; (2) where only the modes with no azimuthal variations are equally or unequally excited. It is shown that the shape and the rms width of the impulse response depend strongly on the fourth-order coefficient of the index distribution and on the excitation conditions. Comparison is also made between the results obtained from the wave optics method and those obtained from the ray optics method, and both results are found to be identical.