Time reversal of light by linear dispersive filtering near atomic resonance

Abstract

Based on the similarity of paraxial diffraction and dispersion mathematical descriptions, the temporal imaging of optical pulses combines linear dispersive filters and quadratic phase modulations operating as time lenses. We consider programming a dispersive filter near atomic resonance in rare earth ion-doped crystals, which leads to unprecedented high values of dispersive power. This filter is used in an approximate imaging scheme, combining a single time lens and a single dispersive section and operating as a time-reversing device, with potential applications in radio-frequency signal processing. This scheme is closely related to a three-pulse photon echo with chirped pulses, but the connection with temporal imaging and dispersive filtering emphasizes new features.

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“…is the applied chirp function, where r is the chirp rate and ω 1 is the start (offset) frequency of the chirp [30].…”

“…C 1 2 is determined by the characteristic parameters of the programmed AFC such as optical depth, the finesse and the shape of the AFC peaks but independent of the compression factor. Optimizing these parameters allows in principle approaching unit efficiency in the compression (stretching) process [30]. As seen in equation (A.2), the AFC introduces a quadratic phase modulation at rate μ, i.e.…”

“…Let us finally point out that the possibility for active control of the parameter μr by adjusting the chirp rate allows one to implement compressing and stretching in a very flexible fashion. As detailed in [30], having a value of μr between 0 and 1 leads to compression (with variable compression factor) of the input pulse without changing the order of the raising and falling edge, while setting μr between 1 and 2 causes a compressed, but time-reversed output. If μr is equal to 2, time reversal of the input pulse without compression is obtained.…”

“…Here, e(t) is the waveform of the input pulse before chirping and C(t) = e iω 1 t−irt 2 /2 is the applied chirp function, where r is the chirp rate and ω 1 is the start (offset) frequency of the chirp [30].…”

“…Following the treatment carried out in [30], the first echo that is emitted from the medium of length L is expressed by…”