We propose a method to display full complex Fresnel holograms by adding the information displayed on two analogue ferroelectric liquid crystal spatial light modulators. One of them works in real-only configuration and the other in imaginary-only mode. The Fresnel holograms are computed by backpropagating an object at a selected distance with the Fresnel transform. Then, displaying the real and ...

In this study the third order nonlinear susceptibilities are theoreticallycalculated for an electron confined in an isolated PbS/ CdSe/ CdS spherical core-shellshellquantum dots. Our calculation is associated with intersubband transitions in theconduction band. We used the effective mass approximation in this study which is asimple and straightforward study of the third-order optical nonlineari...

The roots of -1 in the set of biquaternions (quaternions with complex components, or complex numbers with quaternion real and imaginary parts) are studied and it is shown that there is an infinite number of non-trivial complexified quaternion roots (and two degenerate solutions which are the complex imaginary operator and the set of unit pure real quaternions). The non-trivial roots are shown t...

We present a general approach to describe slowly driven quantum systems both in real and imaginary time. We highlight many similarities, qualitative and quantitative, between real and imaginary time evolution. We discuss how the metric tensor and the Berry curvature can be extracted from both real and imaginary time simulations as a response of physical observables. For quenches ending at or ne...

In this paper, we consider the ranks of four real matrices Gi(i = 0, 1, 2, 3) in M†, where M = M0 +M1i+M2j+M3k is an arbitrary quaternion matrix, and M† = G0 + G1i + G2j + G3k is the Moore-Penrose inverse of M . Similarly, the ranks of four real matrices in Drazin inverse of a quaternion matrix are also presented. As applications, the necessary and sufficient conditions for M† is pure real or p...