one or more input ports, wherein at least one input port is adapted to accept multiple wavelength-division-multiplexed (WDM) channels;

two or more sections of nonlinear medium coupled to the one or more input ports, wherein each section of nonlinear medium comprises a section of highly non-linear material and one periodic group delay device (PGDD);

wherein, in each section of nonlinear medium, a group delay is accumulated between center frequencies of adjacent WDM channels, an absolute value of the group delay accumulated between the center frequencies of the adjacent channels is substantially higher than an absolute value of a group delay accumulated between any two frequency components of either one of the adjacent channels,

wherein, for each section of nonlinear medium, an absolute value of the group delay slope in picoseconds per nanometer in a portion of the region between center frequencies of two of the adjacent channels is substantially higher than an absolute value of a group delay slope in picoseconds per nanometer within a bandwidth of either of the same two adjacent channels; and

one or more output ports coupled to the two or more sections of nonlinear medium, wherein at least one output port is adapted for simultaneous 2R regeneration of the multiple WDM channels, wherein 2R regeneration includes re-amplification and nonlinear-optical re-shaping, wherein at least one output port of the optical processor is adapted to substantially accumulate large amounts of intra-channel nonlinear-optical effects while suppressing nonlinear interactions among different WDM channels.