Inhomogeneous nonlinearity meets $\mathcal{PT}$-symmetric Bragg structures: Route to ultra-low power steering and peculiar stable states

In the context of $\mathcal{PT}$-symmetric fiber Bragg gratings, tailoring the nonlinear profile along the propagation coordinate serves to be a new direction for realizing low-power all-optical switches. The scheme is fruitful only when the nonlinearity profile will be either linearly decreasing or increasing form. If the rate of variation of the nonlinearity profile is high, the critical intensities fall below the input power of value 0.01 in the unbroken regime provided that the light launching direction is right. Nowadays, every new theoretical inception into the PTFBG has started making sense of switching in the broken $\mathcal{PT}$-symmetric regime which was once believed to be the instability regime. When the inhomogeneous nonlinearity acts together with the broken $\mathcal{PT}$-symmetry and right light incidence, it leads to two peculiar settings. First, the switch-up intensities are ultra-low. Second, the switch-down action takes place at zero critical intensities. Such OB curves are unprecedented in the context of conventional gratings and found only in plasmonic devices and anti-directional couplers. Even though the nonlinearity is inhomogeneous, the ramp-like first stable states persist in the broken $\mathcal{PT}$-symmetric regime giving an additional indication that the broken PTFBG is closely associated with the plasmonic structures. In the existing PTFBG systems, the switching intensities are relatively higher in the broken regime. However, the proposed system records the lowest switching intensities in the broken regime. The reported intensities ($< 0.005$) are also the lowest ever-switching intensities recorded in the perspective of PTFBGs to date.