Negative phase index does not mean negative wave refraction.

Back | NIM Home | Introduction | Movies | References | LHM Publicity | CEMD | UT Austin | Next

Group vs Phase figure

NIM rips signals

Plane wave movie
The simple but subtle error in all LHM papers.
Surprisingly, the key error in all earlier LHM papers is both simple and subtle - the mistaken identification of phase propagation with energy (or signal) propagation. The negative phase refractive index of NIM implies that modulations go forward but phase goes backward. So only phase bends in negative manner but modulations bend in positive manner.

Perhaps the long success of the "slowly varying envelope approximation" for positive index media (PIM) may have lulled scientists into using strictly monochromatic waves in the new world of negative index media. This is fine in PIM where group and phase go about the same way.

But in NIM, phase and group (or signal) always go in very different directions. At normal incidence, the angle between phase and group "rays" is 180 degrees and can decrease only to 90 degrees at very oblique incidence.
So, in contrast to PIM, phase rays NEVER closely represent the energy propagation direction in NIM, and our PIM-based geometrical optics intuition can be very wrong.

Veselago's Wrong Ray Diagram

Veselago's Diagram Copied
Veselago's wrong "ray diagram" copied by all.
Note that ALL earlier LHM papers essentially copy the wrong "ray diagram" (Fig.4) from Veselago's 1968 paper that started the LHM activity.

This ray diagram is supposed to represent phase rays with arrows pointing backward inside the NIM slab. So it cannot simultaneously represent refraction of wave signals going forward all along the ray as it travels through the NIM slab.

In all LHM papers that copy this diagram from Veselago, either no arrows are shown on the "rays" or they are shown pointing forwards in the NIM slab, misleading the reader into believing that they represent something (light energy) actually going forward along those rays.

Note that "phase rays" do not have even approximate physical significance in NIM because they do not represent energy or signal transport, and MUST go backwards in NIM.
Back NIM Home Movies References LHM Publicity Back

For contact and comments, email to
© 2002 CEMD, University of Texas at Austin. All rights reserved.