Time-domain Fabry-Perot resonators formed inside a dispersive medium

We show that the temporal analog of a Fabry-Perot resonator (FPR) can be realized by using two moving temporal boundaries, formed by intense pump pulses inside a dispersive medium (such as an optical fiber). We analyze such FPRs using a transfer-matrix method, similar to that used for spatial structures containing multiple thin films. We consider a temporal slab formed using a single square-shape pump pulse and find that the resonance of such an FPR has transmission peaks whose quality (Q) factors decrease rapidly with an increasing velocity difference between the pump and probe pulses. We propose an improved design by using two pump pulses. We apply our transfer-matrix method to this design and show considerable improvement in the Q factors of various peaks. We also show that such FPRs can be realized in practice by using two short pump pulses that propagate as solitons inside a fiber. We verified the results of the transfer-matrix method by directly solving the pulse propagation equation with the split-step Fourier method. (C) 2021 Optical Society of America