Optimal Diffractive Focusing of Quantum Waves

TL;DR

This paper derives the optimal real-valued wave functions for focusing quantum waves in 1D and 2D without phase components, compares them with traditional methods, and demonstrates their effectiveness experimentally with optical beams.

Contribution

It introduces a novel approach to wave focusing that avoids phase elements, applicable to challenging wave types like X-rays and electron beams.

Findings

Optimal focusing wave functions are real-valued and phase-free.

Experimental validation with optical beams confirms theoretical predictions.

Potential applications in wave types where phase control is difficult.

Abstract

Following the familiar analogy between the optical paraxial wave equation and the Schr\"odinger equation, we derive the optimal, real-valued wave function for focusing in one and two space dimensions without the use of any phase component. We compare and contrast the focusing parameters of the optimal waves with those of other diffractive focusing approaches, such as Fresnel zones. Moreover, we experimentally demonstrate these focusing properties on optical beams using both reflective and transmissive liquid crystal devices. Our results provide an alternative direction for focusing waves where phase elements are challenging to implement, such as for X-rays, THz radiation, and electron beams.