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It is shown that it is possible to couple a laser beam and its frequency-doubled daughter into a multimode optical fiber through the four-wave mixing nonlinear process and generate a new wavelength. The frequency-doubled daughter can be generated in an external crystal with a large second order nonlinearity. It is argued that while this possibility is within the design parameter range of conventional multimode optical fibers, it necessitates a lower-bound for the core-cladding refractive index contrast of the multimode optical fiber

Four-Wave Mixing of a Laser and Its Frequency-Doubled Version in a Multimode Optical Fiber