Abstract

At total reflection, beams are not reflected ideally from their point of incidence at the reflecting boundary but shifted by a length D (Goos–Haenchen effect). Based on the model of wave bundles consisting of a composite of totally reflected partial waves with varying angles of incidence, we treat the case of matter waves for a vanishing potential step at the boundary (the critical angle of total reflection tending to π/2). It is well known from Renard’s formula that the partial wave for grazing incidence has a vanishing shift D, with an angle α0 of incidence midway between the critical angle and π/2. However, the Goos–Haenchen shift of a wave bundle goes to infinity at α0π/2. The width W of the bundle also goes to infinity because the angular interval of the partial waves goes to zero. But the quantity D/W remains constant. D/W has a value of 18% if Artmann’s formula for D is used and is 4.5% with Renard’s more refined formula for D.

© 1971 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Goos–Hänchen beam shift at total internal reflection

S. R. Seshadri
J. Opt. Soc. Am. A 5(4) 583-585 (1988)

Total Reflection: A New Evaluation of the Goos–Hänchen Shift

Rémi H. Renard
J. Opt. Soc. Am. 54(10) 1190-1197 (1964)

Reflection and Refraction of a Beam of Light at a Plane Interface

Helmut K. V. Lotsch
J. Opt. Soc. Am. 58(4) 551-561 (1968)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (5)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (37)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription