The fractional Fourier transform is a generalization of the classical Fourier transform, which
is introduced from the mathematic aspect by Namias at first and has many applications in …

We introduce the concept of metamaterial analog computing, based on suitably designed
metamaterial blocks that can perform mathematical operations (such as spatial …

Various Euclidean, hyperbolic and elliptic analytic representations are introduced and
relations among them are discussed. The Bargmann analytic representation in the complex …

By adapting the concept of epitaxy to two-dimensional space, we show the growth of a
single-atomic-layer, in-plane heterostructure of a prototypical material system—graphene …

A brief introduction to the fractional Fourier transform and its properties is given. Its relation
to phase-space representations (time-or space-frequency representations) and the concept …

An algorithm for efficient and accurate computation of the fractional Fourier transform is
given. For signals with time-bandwidth product N, the presented algorithm computes the …

Fourier transforms of fractional order a are defined in a manner such that the common
Fourier transform is a special case with order a= 1. An optical interpretation is provided in …

We propose and consolidate a definition of the discrete fractional Fourier transform that
generalizes the discrete Fourier transform (DFT) in the same sense that the continuous …

A concise introduction to the concept of fractional Fourier transforms is followed by a
discussion of their relation to chirp and wavelet transforms. The notion of fractional Fourier …

A number of methods have recently been proposed in the literature for the encryption of two-
dimensional information by use of optical systems based on the fractional Fourier transform …