Abstract

The Talbot self-imaging of waves is most intuitively pictured as propagation-induced revivals of a field with transverse spatial periodicity [1]. While perhaps the spatial self-imaging is the most known variant of the Talbot effect, the effect exists also in the temporal [2] and angular [3] domains. In a given domain (space, time), the emergence of Talbot self-images is mediated by a specific quadratic phase profile in its Fourier dual domain (momentum, frequency), known as Talbot phases. This is typically achieved through propagation in a physical system where the Fourier components of the field follow a quadratic dispersion relation. In light of the Fourier duality, the Talbot effect is also equivalently seen in these Fourier domains (momentum, frequency) [2] by inducing the Talbot phases in the respective dual domains (space, time). This extended picture is known as the generalized Talbot effect, and has been recently explored and used in the time-frequency domain [2].

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