The amplitude and phase evolution of ultrashort pulses in a bimodal waveguide structure has been studied with a time-resolved photon scanning tunneling microscope (PSTM). When waveguide modes overlap in time intriguing phase patterns are observed. Phase singularities, arising from interference between different modes, are normally expected at equidistant intervals determined by the difference in effective index for the two modes. However, in the pulsed experiments the distance between individual singularities is found to change not only within one measurement frame, but even depends strongly on the reference time. To understand this observation it is necessary to take into account that the actual pulses generating the interference signal change shape upon propagation through a dispersive medium. This implies that the spatial distribution of phase singularities contains direct information on local dispersion characteristics. At the same time also the mode profiles, wave vectors, pulse lengths, and group velocities of all excited modes in the waveguide are directly measured. The combination of these parameters with an analytical model for the time-resolved PSTM measurements shows that the unique spatial phase information indeed gives a direct measure for the group velocity dispersion of individual modes. As a result interesting and useful effects, such as pulse compression, pulse spreading, and pulse reshaping become accessible in a local measurement.
Phys. Rev. E

Gersen, H., van Dijk, E. M. H. P., Korterik, J. P., van Hulst, N. F., & Kuipers, K. (2004). Phase mapping of ultrashort pulses in bimodal photonic structures: a window on local group velocity dispersion. Phys. Rev. E, 70(Article number: 66609), 1–12. doi:10.1103/physreve.70.066609