Superluminal space-to-time mapping in grating-assisted co-directional couplers

A superluminal space-to-time mapping process is reported and numerically validated in grating-assisted (GA) co-directional couplers, e.g. fiber/waveguide long-period gratings (LPGs). We demonstrate that under weak-coupling conditions, the amplitude and phase of the grating complex apodization profile of a GA co-directional coupling device can be directly mapped into the device's temporal impulse response. In contrast to GA counter-directional couplers, this mapping occurs with a space-to-time scaling factor that is much higher than the propagation speed of light in vacuum. This phenomenon opens up a promising new avenue to overcome the fundamental time-resolution limitations of present in-fiber and on-chip optical waveform generation (shaping) and processing devices, which are intrinsically limited by the achievable spatial resolution of fabrication technologies. We numerically demonstrate the straightforward application of the phenomenon for synthesizing customized femtosecond-regime complex optical waveforms using readily feasible fiber LPG designs, e.g. with sub-centimeter resolutions.