Reconstruction of nonlinear wave propagation

An optical system, comprising:

• a nonlinear optical medium configured to receive a first waveform and yield a second waveform;
• a processor configured so as to obtain information about two of said nonlinear optical medium, first waveform, and second waveform and generate characterization of the remaining one of said nonlinear optical medium, first waveform, and second waveform, said generated characterization comprising numerical propagation of one of said first and second waveforms through said nonlinear optical medium.

A computer-readable medium containing machine-executable instructions that, if executed by a device having one or more processors, causes the device to perform operations comprising:

• obtaining a digital representation of a measured output waveform resulting from propagation of an input waveform through a nonlinear medium;
• and
• computationally propagating said digital representation of said measured output waveform through said nonlinear medium so as to reconstruct a digital representation of said input waveform, said computational propagation depending on one or more properties of said nonlinear medium, information about said one or more properties stored in said computer-readable medium or accessible by said machine-executable instructions.

An apparatus, comprising:

• a nonlinear element configured so as to provide a nonlinear propagation environment for a wave passing therethrough, said nonlinear element dimensioned to receive an input and yield an output;
• and
• a computer-readable medium containing instructions that calculates one of said input and output if given the other, said calculation achieved numerically in an iterative manner using one or more parameters that characterize said nonlinear propagation environment.