In addition, fractional-order differentiator is also useful in optical encryption, which can be considered as a generalization of integer-order differentiator [
16]. A fractional-order differentiator based on a photonic MZI was proposed by Cuadrado-Laborde for the first time [
16]. Later, more effective schemes and optical devices have been demonstrated, including asymmetrical phase-shifted FBG [
17] and long period fiber grating [
18]. But in these schemes, the tunability of the differentiation order was not mentioned. Afterwards, cascaded tilted FBGs were employed to provide a tunable fractional order from 0.81 to 1.42 [
19], and a tunable fractional-order differentiator with a tuning range of 0.95−1.72 has been demonstrated by optically pumping a tilted FBG [
20]. For silicon based devices, Shahoei et al. for the first time presented a tunable fractional-order differentiator using a silicon-on-isolator (SOI) MRR with a multimode interference (MMI) coupler. The tuning range of fractional order covered from 0.37 to 1.3 [
21]. Afterward, we demonstrated tunable fractional-order differentiators based on electrically tuned MZI [
22] and MRR [
23], with tuning ranges of 0.83−1.03 and 0.58−0.97, respectively. And Jin et al. proposed a novel photonic fractional-order differentiator based on the inverse Raman scattering (IRS) in the side-coupled silicon MRR [
24]. By controlling the power of the pump lightwave, a continuously tunable differentiation order covering from 0.3 to 1.6 was achieved. As we know, the tunability of the differentiation order is one of the important figure-of-merits in fractional-order differentiator. And a large tunable range indicates more widely applications, such as immunity to cracking of encryption operation.