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Wave modes induced by cross-phase reshaping of a probe photon in the guidingstructure of a periodic train of temporal pulses are investigated theoreticallywith emphasis on exact solutions to the wave equation for the probe. The studyhas direct connection with recent advances on the issue of light control bylight, the focus being on the trapping of a low-power probe by a temporalsequence of periodically matched high-power pulses of a dispersion-managedoptical fiber. The problem is formulated in terms of the nonlinear opticalfiber equation with averaged dispersion, coupled to a linear equation for theprobe including a cross-phase modulation term. Shape-preserving modes which arerobust against the dispersion are shown to be induced in the probe, they form afamily of mutually orthogonal solitons the characteristic features of which aredetermined by the competition between the self-phase and cross-phase effects.Considering a specific context of this competition, the theory predicts twodegenerate modes representing a train of bright signals and one mode whichdescribes a train of dark signals. When the walk-off between the pump and probeis taken into consideration, these modes have finite-momentum envelopes andnone of them is totally transparent vis-\`a-vis the optical pump soliton.

Fundamental modes of a trapped probe photon in optical fibers conveying periodic pulse trains