Fig. 3: Illustration of Temporal Phase Modulation (TPM) process for the special case of a time lens.

The device implementing a phase transformation changes in optical path length over time from the perspective of the incoming signal. The optical wave profile at three different time locations along the enveloped optical carrier is shown above the input. After implementing the quadratic TPM, shown in black dotted lines, the optical wave will be given a phase depending on the time of arrival. At the output, the optical wave shown with a blue solid line exhibits a different relative phase in comparison to the input optical wave, overlayed as a red dashed line. The centre of the time lens, experiencing no phase shift, stays coherent relative to the input. The change in periodicity seen in the zoomed sections represent the actual linear instantaneous frequency shift that is being performed, but is greatly exaggerated for clarity.