# Talk:Goos-Hänchen effect

Thanks for the reviews. I am just finding the time to respond to both the reviews and will get back to you with a revised contribution and response to the suggestions within the next few weeks PRB

Here is my review for the article by Paul Berman on Goos-Hanchen effect.

The article is very nice, I think it fits well into Scholarpedia's project. It is a very good thing to have this parallel between optics and quantum mechanics. It is well written, the length is perfect. Great job already.

First point, even if I really appreciate the possibility to discuss directly with the author of the manuscript, I will tend to do a somehow "classical" review : I'll probably stay anonymous and make all my comments here. I prefer the author to modify himself the article.

Here are my suggestions/questions :

1) I consider the GH effect as the first "non specular phenomenon" that has been extensively studied. I would mention that in the introduction. Other non-specular phenomena would include lateral shift due to the excitation of resonances, the Imbert-Fedorov transverse shift, and so on. Even if a list of all these effects is beyond the scope of this particular article, maybe some of these could be mentioned.

The following article seems a valuable reference (see thereafter) : T. Tamir, 1986, "Nonspecular phenomena in beam fields reflected by multilayered media", J. Opt. Am. Soc. A, 3, 558.

Almost all the possible effects are explored.

2) k_1 is undefined. I guess $k_1 = n_1 k_0 \sin \theta$ (and then $k_0$ has to be defined too. k_1 appears in formula (1) and (2)

3) The expression for the shift is not the same if you consider the shift parallel to the surface and the shift as defined on the figure. I would underline this point. For a shift parallel to the surface the expression is more $$-\frac{1}{n_1 k_0 \sin(theta)} \frac{d\Phi}{d\theta} = -\frac{d\Phi}{dk_x}$$

4) Where, by the way, does this formula come from ?

This very formula is often refered to as "Artmann's formula", and I know two major ways to obtain it : either the way Tamir (see above) uses, or as in the following paper C.F. Li, Unified theory for Goos-Hänchen and Imbert-Fedorov effects, PHYSICAL REVIEW A 76, 013811 (2007͒).

That's for optics. Maybe it comes from quantum mechanics ?

5) If you search for "Goos-Hanchen" in Google Scholar, you can find several papers which are not about the original Goos-Hanchen effect, but use the term.

For some, that can be justified (see for instance D. Felbacq et al., "Goos–Hänchen effect in the gaps of photonic crystals", Opt. Lett., 28, 1633, 2003.).

For others, it is difficult (see for instance I.V. Shadrivov et al., "Giant Goos-Hänchen effect at the reflection from left-handed metamaterials", Appl. Phys. Lett. 83, 2713 (2003)) : very often the large lateral shift is associated with a resonance (as described in T. Tamir and L. Bertoni, "Lateral Displacement of Optical Beams at Multilayered and Periodic Structures", J. Opt. Soc. Am. A 61, 1397 (1971)) and should to my advice not called Goss-H\"anchen effect.

I would mention that in the conclusion somehow, too. I think it could be useful to the reader, especially if he's not familiar with the subject.

6) Concerning the reference to the work of Picht, I'm not so sure it is the good one (this one deals with Fourier optics, it seems). Maybe the good one is the one in which he wishes a happy birthday to von Laue : Annalen der Physik, Volume 395, Issue 4, pages 433–496, 1929.

## Reviewer B:

This is a nice article to introduce the Goos-Hänchen (GH) effect. After reading the comments by reviewer A, I add the following three comments or suggestions. At this time, I would like to remain anonymous until I find time to contribute more to this article.

Firstly, it is noticed that the group time delay is mentioned along with the introduction of the GH shift. I do not think that this is necessary. The reason is twofold. On one hand, the issue of time delay in this situation is, in my opinion, more subtle than the GH shift itself. On the other hand, there exists enough literature on the GH shift itself that makes clear the physical meaning of this effect. If the author does want to introduce the GH shift via the time delay, the citation to the literature on the time delay should be inevitable. This would make unclear the topic of this article, I think.

Secondly, as an introduction article, I think the citation of references should be as exact as possible. I found that the following references do not deal with the problems as were described in this article. So I hope the author can examine the reference one more time.

Bretenaker, F., Floch, A. L., Dutriaux, L., 1992. Phys. Rev. Lett. 68, 931

Beenakker, C. W. J., Sepkhanov, R. A., Akhmerov, A. R., Tworzydlo, J., 2009. Phys. Rev. Lett. 102, 146804

And thirdly, it seems that this article concerns only the original meaning of the GH effect that occurs in a single total reflection. For the sake of completeness, the GH shift in other configurations may be mentioned in the 4th part “Extensions to other Domains,” such as the surface plasmon resonance considered in Appl. Phys. Lett. 85, 372 (2004) by X. Yin et. al. Of course, in so doing, attention should be paid to other factors, especially the mechanism for this effect, because the reflectivity in such a case can be approximately zero.

## Diagrammatic representation

A question of clarification. Correct me if I am wrong, but I understood the effect involved a LATERAL rather than LONGITUDINAL displacement? In other words that the displacement is orthogonal to the plane containing the incident and reflected beams. If so, the diagrams in the article do not seem to represent this. Instead they show a displacement along the plane. This is a potential area of confusion, and perhaps you could consider clarifying this in the article. Thank you

## Response to Diagrammatic Representation

The displacement is lateral, but in the plane of incidence, not perpendicular to the plane of incidence.