1D First-Order Optical Systems: The Huygens-Fresnel Integral

Amalia Torre

Daniel F. V. James, G. S. Agarwal

Valerian I. Tatarskii, V. V. Zavorotnyi

In the present paper a connection between the approximate Huygens-Fresnel formulae and the exact path-integral solutions is studied. We consider the approach which makes it possible to separate from the path integral the contribution that corresponds to the phase approximation of the extended Huygens-Fresnel principle. This approach is used to derive the corrections to the phase approximation.

Chuanmei Xie, Fan Hong-Yi, Shaolong Wan

Based on the displacement-squeezing related squeezed coherent state representation | z⟩ g and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator, whose matrix element in the coordinate representation leads to a generalized Collins formula (Huygens–Fresnel integration transformation describing optical diffraction). The generalized Fresnel operator is derived by a quantum mechanical mapping from z to sz - rz * in the | z⟩ g representation, while | z⟩ g in phase space is graphically denoted by an ellipse.

Moshe Nazarathy

Edouard Brainis

We show that the propagation of a N-photon field in space and time can be described by a generalized Huygens-Fresnel integral. Using two examples, we then demonstrate how familiar Fourier optics techniques applied to a N-photon wave function can be used to engineer the propagation of entanglement and to design the way the detection of one photon shapes the state of the others.