Mode conversion in nonlinear waveguides stimulated by the longitudinal   bi-harmonic refractive index modulation
  We study specific features of resonant mode conversion in nonlinear waveguides stimulated by the bi-harmonic longitudinal modulation of its parameters, which includes changes of the waveguide depth as well as its bending (in the one-dimensional case) or spiraling (in the two-dimensional case). We demonstrate the possibility of simultaneous excitation of higher-order modes of different parities and topologies with controllable energy weights. The output mode composition is highly sensitive to the variation in the input power and detuning from the resonant modulation frequency. 
Yaroslav V. Kartashov, Victor A. Vysloukh
physics.optics nlin.PS