The linear canonical transform (LCT) is the name of a parameterized continuum of transforms that include, as particular cases, many widely used transforms in optics such as the Fourier transform, fractional Fourier transform, and Fresnel transform. It provides a generalized mathematical tool for representing the response of any first-order optical system in a simple and insightful way. In this ...

It has been shown that the fractional Fourier transform, recently very intensively investigated in mathematics, quantum mechanics, optics and signal processing, can be obtained as a special case of the earlier introduced linear coordinate transformations of the ambiguity function or Wigner distribution. Some applications of the generalized fractional transform on the time-frequency analysis are...

Two approaches resulting in two different generalizations of the space-time-fractional advection-diffusion equation are discussed. The Caputo time-fractional derivative and Riesz fractional Laplacian are used. The fundamental solutions to the corresponding Cauchy and source problems in the case of one spatial variable are studied using the Laplace transform with respect to time and the Fourier ...

In this paper, we investigate the uniqueness of the phase retrieval problem for the fractional Fourier transform (FrFT) of variable order. This problem occurs naturally in optics and quantum physics. More precisely, we show that if u and v are such that fractional Fourier transforms of order α have same modulus |Fαu| = |Fαv| for some set τ of α’s, then v is equal to u up to a constant phase fac...

In this paper, a new mathematical model of a Kelvin-Voigt type thermo-visco-elastic, infinite thermally conducting medium has been considered in the context of a new consideration of heat conduction having a non-local fractional order due to the presence of periodically varying heat sources. Three-phase-lag thermoelastic model, Green Naghdi models II and III (i.e., the models which predicts the...

In this work, a new mathematical model of thermoelasticity theory has been considered in the context of a new consideration of heat conduction with fractional order theory. A functionally graded isotropic unbounded medium is considered subjected to a periodically varying heat source in the context of space-time non-local generalization of three-phase-lag thermoelastic model and Green-Naghdi mod...

We provide a general treatment of optical two-dimensional fractional Fourier transforming systems. We not only allow the fractional Fourier transform orders to be specified independently for the two dimensions but also allow the input and output scale parameters and the residual spherical phase factors to be controlled. We further discuss systems that do not allow all these parameters to be con...

The discrete fractional Fourier transform (DFRFT) is the generalization of discrete Fourier transform. Many types of DFRFT have been derived and are useful for signal processing applications. In this paper, we will introduce a new type of DFRFT, which are unitary, reversible, and flexible; in addition, the closed-form analytic expression can be obtained. It works in performance similar to the c...

It is shown how a coherent optical signal that contains only a finite number of Hermite-Gauss modes can be reconstructed from the knowledge of its Radon-Wigner transform-associated with the intensity distribution in a fractional-Fourier-transform optical system-at only two transversal points. The proposed method can be generalized to any fractional system whose generator transform has a complet...