Abstract

This work introduces a class of 1D spatial-frequency-modulated structures with transmittance $T(x)$, in which the period changes along the $x$ axis so that the corresponding spatial frequency $f(x)$ sinusoidally alternates between two values. It is shown that $T(x)$ generally is an almost-periodic function and has an impulsive spatial spectrum. However, we find the condition under which $T(x)$ is a periodic function and its spatial spectrum form a lattice of impulses. When the periodicity condition is fulfilled, we call these structures as 1D spatially chirped periodic structures. These structures are characterized by two natural numbers, named as ${n_{\rm c}}$ and ${n_{{\rm av}}}$, and a real parameter named as frequency modulation strength (FMS). As an important special case, we define a 1D spatially chirped amplitude sinusoidal grating (SCASG) based on the transmission function of a conventional amplitude sinusoidal grating, in which the phase of conventional amplitude sinusoidal grating is replaced by desired chirped phase. Then the spatial spectrum of a 1D SCASG is investigated in detail, and it is shown that the spatial spectrum can be managed by changing the value of FMS. In other words, the grating’s spectrum can be manipulated by adjusting the value of FMS. This feature might find applications in optical sharing of the incident power among different diffraction orders. Moreover, near-field diffraction from 1D SCASGs is studied by using the so-called angular (spatial) spectrum method, and Talbot distances for these gratings are determined and verified experimentally. It is shown that the intensity profiles at quartet- and octant-Talbot distances strongly depend on the values of the parameters ${n_{\rm c}}$ and ${n_{{\rm av}}}$. In comparison with the conventional gratings, we see some new and interesting aspects in the diffraction from 1D SCASGs. For instance, unlike the conventional gratings, in some propagation distances, the diffraction patterns possess sharp and smooth intensity bars at which the intensity is several times of the incident light beam’s intensity. It is shown that the maximum intensity of these bright bars over the diffraction patterns depends on the characteristic parameters of the grating, including ${n_{\rm c}}$, ${n_{{\rm av}}}$, and FMS of the grating. These intensity bars might find applications for trapping and aggregation of particles along straight lines.

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