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Modal losses and design of modal irradiance patterns in an optical fiber by the complex scaled (t, t ′ method

The combination of complex scaling with the (t, t′) representation of the time-dependent Schrodinger equation [ J. Chem. Phys.99, 4590 ( 1993)] permits the design of graded-index multimode fiber to control the distribution of power among the modes. The differential modal losses are associated with the imaginary parts of the complex eigenvalues of a complex scaled Floquet-type operator. Although the illustrative numerical calculations are given here for the case in which the index of refraction is periodically varied along the fiber axis, the method is applicable for a more general coordinate-dependent index-of-refraction case.