Particlelike scattering states in wave transport

z-shaped trajectory through a disordered cavity This web page contains information about our recent Letter "Particlelike Scattering States in Wave Transport".

Link to the Online Edition of the Article (PDF)
Link to Supporting Online Material (PDF)

See also the discussions of our paper at
Physical Review Focus
and at the following sites:
Science Daily, PhysOrg
Vienna University of Technology (also in German)
Der Standard (German), ORF (German)
Wiener Zeitung (German), APA (German)
La Recherche (French), BE Autriche (French)
Universidad de Cordoba (Spanish)
Todateoria (Portuguese)

The image on the left shows a wave scattering through a rectangular cavity with disorder (see lower panel for the disorder landscape). By suitably shaping the incoming wavefront, the wave can be made to follow the zig-zag orbit of a particle. (Image: Florian Libisch)

Additional Material (for free download, click images for Hi-Res)




The images above show scattering wave functions inside a quadratic cavity after the application of the procedure proposed in our article. This procedure allows for the generation of particlelike scattering states for which waves follow the bouncing pattern of a classical trajectory. The different states shown correspond to different initial conditions in the left lead from which the wave is injected.


Animations (click images to start)

straight-line trajectory through rectangular cavity
straight-line trajectory through rectangular cavity
The images above show a wave penetrating two different cavities along a straight line trajectory. By suitably shaping the incoming wavefront, the angle of incidence can be tuned: click on either image to see a corresponding animation.


Frequently Asked Questions


What is the most important result reported in your article?

We present a recipe for generating non-diffracting wave beams in scattering through complex systems like cavities or disordered media. Our approach relies solely on the knowledge of the system's scattering matrix.

For which types of waves does your procedure work?

The concepts which we put forward in our article are not restricted to a particular type of wave, i.e., they work for acoustic, optical or quantum waves alike. For all these cases our procedure allows to create special waves which follow the trajectory of a particle in space. One can think of these wave states as of a highly directional beam as emitted, e.g., from a laser pointer. In this very familiar case, however, the wavelength of the corresponding light wave is many orders of magnitude smaller than the typical dimensions of the space where the wave propagates after being emitted. What we demonstrate in our article is how such particle-like beams can be generated even when the wavelength is not too far away from the surrounding spatial dimensions as for sound waves propagating in a room.

Can your ideas be realized in the experiment?

Our work was strongly inspired by recent experiments in which the scattering matrix of very complex systems could be extracted (see the "Useful links" below for more information). These techniques which are now available should be the ideal tools to realize our concepts in the lab.

What kind of applications do you have in mind?

We believe that the special states which we discuss have a number of immediate advantages for applications in which a wave signal needs to be transmitted from one point to another: Due to their high directionality our beam states should not only allow to save power in the generation of the signal, but also maximize the signal reception. Also, when directing the beam directly to a receiver it would be much harder for an eavesdropper to intercept the signal transmission. Certainly also medical applications are conceivable where our concepts could be used to keep a light or ultrasound beam focused when scattering through a medium like human tissue. We have, however, not yet studied such questions explicitly.


Useful links


Two popular science articles by John Pendry as well as by Elbert van Putten and Allard Mosk on recent experiments in the field.

An entry in Wikipedia about Spatial Light Modulators which are used in the experiments to shape optical wave fronts.

In acoustics, wave focusing experiments can be carried out with electro-acoustic transducer arrays as used for "Time-reversal mirrors".