Tunable spatial fractional derivatives with graphene-based transmit arrays

Area of Science:

• * Physics and Applied Optics
• * Materials Science
• * Electrical Engineering

Background:

• * Optical implementation of mathematical spatial operators is key for high-speed, low-energy analog optical processors.
• * Fractional derivatives offer more accurate results in science and engineering applications.
• * Previous optical implementations focused on integer-order derivatives, with no research on fractional derivatives.

Purpose of the Study:

• * To propose a tunable optical structure for implementing fractional derivatives (orders < 2), as well as first and second orders.
• * To demonstrate a single structure capable of implementing various derivative orders, overcoming limitations of previous single-purpose designs.
• * To advance the development of versatile analog optical processors and enhance optical image processing.

Main Methods:

• * Design of a tunable structure using graphene arrays on silica.
• * Utilization of Fourier transform with two graded index lenses and three stacked periodic graphene-based transmit arrays.
• * Finite element method simulations to validate performance and analyze tunability.

Main Results:

• * Successful implementation of fractional derivative orders smaller than two, along with first and second orders.
• * Achieved tunability of the transmission coefficient within an amplitude range of [0,1] and a phase range of [-180, 180].
• * Simulation results closely match desired derivative values, confirming the structure's efficacy.

Conclusions:

• * The proposed tunable graphene structure effectively implements fractional and integer order spatial derivatives.
• * This versatile optical device is a crucial step towards practical analog optical processors.
• * The structure's capabilities extend to other spatial multi-purpose operators, promising advancements in optical computing and image processing.