The most straightforward way to mitigate nonlinearities, for a given total power, is to increase the size of the optical distribution, or beam size. In a bulk optical system this is always possible, though at the expense of size and cost. But in a waveguide such as an optical fiber, increasing the beam size requires finer and finer control over the index distribution if it is to operate in a single transverse mode. There are practical limits to this control, and current high-power fiber amplifiers typically sacrifice mode purity for mode size, relying on bending to preferentially attenuate the higher-order modes with respect to the fundamental. If the higher-order modes persist, the result is a degradation in beam quality and pointing stability.
Jauregui et al. investigate a mechanism by which the modes are directly coupled, such that the fundamental mode feeds coherently into higher-order modes with propagation in the fiber. That mechanism is the coupling by a periodic perturbation of the fiber properties, or grating. Such a grating will efficiently couple two modes provided that its grating vector is equal to the difference of the propagation vectors of those modes, a condition known as phase-matching. In this work, the grating is assumed to be due to variations in the gain medium, which are generated, through local saturation of the gain (spatial hole burning), by the interference pattern of the propagating light itself. As such, it automatically satisfies the phase-matching condition, regardless of the details of the initial light distribution.
Previous work had considered the effects of spatially varying hole burning brought on by modal interference, the main interest having been the relative gain seen by the various modes: to the extent that the fundamental fails to fully saturate the gain, other modes can take advantage of the remainder. While this is a cooperative effect, with the amplification of a given mode depending on all the others, it differs from coherent mode coupling in that there is no direct flow of power between modes. Some other researchers have made this point explicit, developing the equations describing gain in a multimode fiber. In that work, both differential gain and mode coupling by the gain grating are considered; the latter is shown to be negligible because the phase-matching condition is not satisfied. As for a nonlinear index grating, an intensity-dependent index (Kerr effect) is assumed and then dropped from the analysis because its effect is small. In contrast, Jauregui et al. consider the situation in which the nonlinear refractive index cannot be ignored. They suppose—without worrying too much about its microscopic origins—that the index will depend linearly on amplifier inversion, thus producing the phase-matching grating.
They show that the consequences of such a grating can be dramatic. For typical very large mode fiber amplifiers and with the index difference they assume, they see roughly half of the power transferred from the fundamental to the next higher mode, at power levels of only a few hundred watts. It will be interesting to see the origin and scale of the index grating more fully explored, and detailed comparisons made to experimental results.
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