Dynamic control of high-order diffraction grating in complex Δ∇ atomic configuration

We introduce a new model employing a four-level $\Delta \nabla$ type atomic system to diffract weak probe light into higher-order directions via the phenomenon of electromagnetically induced grating. The position-dependent atom-field interaction produces a periodic transmission spectrum, resulting in various Fraunhofer diffraction patterns generated by the all-optical grating. The key advantage of this scheme lies in the existence of M (microwave) and R (radio-frequency) fields, which enable quantum interference among different transition pathways. Our ongoing research holds substantial significance as the proposed atomic-scheme offers precise control over higher-order diffraction intensities. We present a comprehensive study of the diffraction properties of amplitude, phase, and hybrid gratings, focusing on their efficiency and tunability. Hybrid gratings, resulting from the interplay of amplitude and phase effects, achieve a peak first-order efficiency of 32.8% and exhibit sensitivity to ${\delta }_p$, $\Omega$, and L. These results provide new insights into the design and optimization of gratings for high-efficiency optical applications. Additionally, it is noteworthy that our proposed system, at resonance, has the remarkable capacity to generate a phase grating.