Abstract

When a Ge-doped fiber is irradiated with intense visible light launched simultaneously in two different modes, the beating of the modes induces a permanent refractive-index grating through the photosensitivity of the fiber.^1,2 This grating subsequently permits mode coupling at the irradiation wavelength between the two writing modes but also between other modes at different wavelengths, provided that phase matching is satisfied i.e., that the beating period of the modes is the same as that of the grating.³ The refractive-index change for this type of grating is not a constant across the core of the fiber but depends on the transverse coordinates τ and ϕ. From the expression of the coupling coefficient, we find that mode coupling is permittted only if the modes satisfy specific selection rules. For example, a grating written with the x-polarized LP₀₁ and LP₁₁^even modes has a cos ϕ dependence and will not couple the x-polarized LP₀₁ and LP₁₁^odd modes at a wavelength different from the irradiation wavelength, since the x- and y-polarized LP₁₁^even modes have slightly different propagation constants. This is true even in a circular fiber, where one must consider the exact nondegenerate EH and HE modes. Therefore the mode coupling depends on the polarization and on the wavelength of the incident light. Mode coupling can also be allowed between modes having a different transverse profile from that of the writing modes, and there are different possibilities of obtaining phase-matched mode coupling in the IR (e.g., at diode laser wavelengths) when using a grating written with visible light around 500 nm, where the photosensitivity of the fiber is strongest.³ Mode coupling is also allowed if the refractive-index change is constant across the core but only between modes having the same value of l, i.e., they have the same angular dependence. It is therefore possible to induce an intermodal coupler by externally exposing the fiber to periodic UV light, as was done for Bragg gratings.⁴

© 1990 Optical Society of America