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.
Highlights
We use a linear dispersive filter working in the vicinity of atomic resonance
We consider the devising of the linear dispersive filters required for temporal imaging. We show that such filtering can be provided by appropriately programmed media near atomic resonances
Quite soon it was noticed that the paraxial diffraction of a spatial wavefront obeys the same mathematical description as the propagation of a time-domain waveform through a dispersive medium
Summary
With the advent of microwave and optical coherent sources, Fourier optics was actively developed in the 1960s [3]. The two-step process performs the Fourier transform of the incoming waveform in the same way as a lens takes the far field or Fraunhofer diffraction pattern of an incident wavefront into the focal plane [11]. It was pointed out that, no lens was used to bring the far-field zone to finite distance, the Fraunhofer condition could be satisfied provided the squared duration of the incoming pulse is smaller than the line dispersion coefficient μ. This procedure, known as wavelength-to-time mapping, was extended to arbitrary waveform generation [18, 19] and to approximate imaging [20, 21]
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