Taming Light Bullets in the Hollow-Fiber Compressor

The hollow-fiber compressor can probably be considered the most widespread compression tool for generating few-cycle pulses to date. While linear optics of hollow capillaries has been already explored in the 1960s by Marcatili and Schmeltzer in a completely analytical fashion [1], there has only been little analytic follow-up work to complement their approach and include nonlinear optical effects. In order to determine the modes of an optical waveguide, one typically encounters an eigenvalue problem of a differential operator [2], i.e., each discrete solution of this problem propagates at specific phase velocity inside the waveguide. For the spatial problem encountered in hollow-fiber compression, Marcatili and Schmeltzer already indicated that hollow fibers are highly susceptible to losses, which dramatically increase with mode number [1]. In other words, the propagation in a hollow fiber can be sufficiently described by only including three or four modes. This finding dramatically simplifies solution of the eigenvalue problem, allowing to expand the equations in
$k\perp$
and converting the problem into solution of an algebraic problem.