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Self-imaging in near-field diffraction is a practical application of coherentmanipulation of matter waves in Talbot interferometry. In this work, near-fielddiffraction of protons by a nanostructured metallic grating under the influenceof (a) uniform, (b) spatially modulated, and (c) temporally modulated electricfields are investigated. Time-domain simulations of two-dimensional Gaussianwave packets for protons are performed by solving the time-dependentSchr\"odinger's equation using the generalized finite difference time domain(GFDTD-Q) method for quantum systems. Effects of strength ($E_0$) andorientation ($\theta$) of the uniform electric field on the diffractionproperties, such as fringe pattern, intensity of the peaks, fringe shift, andvisibility, are investigated. The results show that the Talbot fringes shiftsignificantly in the transverse direction even for a small change in theapplied electric field ($\Delta E_0$ $=0.1$ V/m) and its orientation ($\Delta\theta$ $=0.1^o$). The potential barriers arising from a spatially modulatedelectric field are observed to cause significant distortions in the Talbotpatterns when the modulation length ($\lambda'$) is equal to the de Brogliewavelength ($\lambda_{dB}$). Sidebands are observed in the Talbot pattern dueto the efficient transfer of energy from the oscillating field to the wavepacket when the frequency of oscillation ($\omega$) is of the order of$\omega_0$ ($=2\pi/T_0$), where $T_0$ is the interaction time. This study willbe helpful in uniform electric field-controlled precision metrology, developinga highly sensitive electric field sensor based on Talbot interference, andprecisely aligning the matter wave optical setup. Furthermore, the sidebands inthe Talbot fringe can be used as a precise tool as momentum splitter in matterwave interferometry.

Near-field diffraction of protons by a nanostructured metallic grating under external electric field: Asymmetry and sidebands in Talbot self-imaging