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Passive amplification of periodic images based on self-imaging

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Consider a periodic distribution of images. Is it possible, in coherent optics, to arbitrarily modify the period of the pattern without loss of energy and without changing the shape of the individual images? While the Talbot (or self-imaging) effect allows only an entire division of the period, we have demonstrated a generalization of this effect, enabling arbitrary control of the period of the images. Since the process is loss-less, it also allows the passive amplification of images.

Talbot effect is a remarkable effect in classical optics. Suppose a periodic repetition of patterns (i.e. a grating) is shined with a plane wave. Then at specific distances from the grating plane, exact images of the individual patterns reappear, but with a periodicity equal to a sub-multiple of the input grating one. Then, the density of patterns in a Talbot plane is always larger than in the input plane. Because Talbot effect is essentially a loss-less process, the intensity of the Talbot images is also a sub-multiple of the input one. Here we propose a generalized version of self-imaging, that enables to create diffraction-induced self-images of a periodic two-dimensional (2D) waveform with arbitrary control of the image spatial periods. Through the proposed scheme, the periods of the output self-image are multiples of the input ones by any desired integer or fractional factor, and they can be controlled independently across each of the two wave dimensions. The concept involves conditioning the phase profile of the input periodic wave before free-space diffraction. The wave energy is fundamentally preserved through the self-imaging process, enabling, for instance, the possibility of the passive amplification of the periodic patterns in the wave by a purely diffractive effect, without the use of any active gain.
These results have been published in Phys. Rev. Lett.