The Goos-Hanchen Shift. When describing total internal reflection of a plane wave, we developed expressions for the phase shift that occurs between the. Goos-Hänchen effect in microcavities. Microcavity modes created by non- specular reflections. This page is primarily motivated by our paper. these shifts as to the spatial and angular Goos-Hänchen (GH) and Imbert- Fedorov (IF) shifts. It turns out that all of these basic shifts can occur in a generic beam.
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Contents 1 History 2 Theory 2.
Goos-Hänchen effect – Scholarpedia
Specular reflection with phase shifts artificially removed. This is true not only for the ellipse, but even for the mundane rectangle. If we really want to understand the wave patterns in our simulations, it is important to analyze the stability of the ray on which the mode is based.
When we speak of “fictitious particles,” you should keep in mind that there is a duality between wave goos-handhen particle description of light, and the particles of light photons can manifest themselves in very real ways if we decide to measure them. The interference causes the reflected maximum to be slightly shifted from the center of the incoming beam. Two distinct cases need be considered, polarization goos-anchen the electric field perpendicular to the plane of incidence TE or transverse electric polarization and polarization parallel to the plane of incidence TM or transverse magnetic polarization.
The work to be described below and in  relies on such mirrors. The interface has to be between different dielectric materials such as glass or waterand absorption or transmission should be small enough to allow a recognizable reflected ahift to form. Currently I have known the reflection coef r, will be a complex number and its phase angle will vary with the incident angle theta.
When such a treatment is possible, it is often unnecessary to look at individual rays in the family, and instead one works with the eikonal which describes the wave fronts to which all the rays must be perpendicular. There is by definition not a lot of room in a microcavity, but one can, so to speak, make more room by shrinking the wavelength in comparison to the cavity dimensions. This means in particular that the internal dynamics of the ellipse should not display any traces of chaotic ray orbits.
The existence of a lateral shift in total internal reflection is goos-hnachen attributed to Newton, based on Proposition 94 of the Principia or Observation 1 of Book 2, Part 1 of Newton’s Optiks. So, in the lower medium, there is a field of the form:. Measuring the intensity maximum of this reflected beam, one then observes a transverse displacement.
This becomes even more important when the reflecting interface is not between a homogeneous dielectric and empty space. Most high-quality mirrors in optics are in fact of the latter type: The size of the shift can only be obtained from a wave calculation.
The simplest illustration is the plane wave, which corresponds to an infinitely extended bundle of parallel rays. Hence at angles near the critical angle, there are components in the incident beam that undergo both normal as well as total internal reflection. Outside that region, the wave can clearly be called a “beam.
One says that the Dirichlet problem in the ellipse is integrable. In such a seemingly pathological situation it’s especially interesting to snift what the relation between the ray and wave description of the system looks like.
Or by what mechanism? There’s a more formal discussion of this phenomenon at Scholarpedia. Much of this work glos-hanchen motivated by the possibility that the GHS can serve as a probe of scattering and excitations that occur at and near the interface of two bulk materials. Considering the ray limit of a dielectric cavity, the internal dynamics of the ellipse is strictly integrable when specular reflection at the interface is assumed, whereas the wave equation is not integrable.
When rays form families with well-defined caustics, one can often describe the wave solution succesfully using the WKB approximation or a generalization of it, the Einstein-Brillouin-Keller method.
We know a V-shaped ray must be self-retracingi. The reason is that the light will attempt to leak out preferentially near spots of highest curvature, and the curvature is not constant unless the ellipse degenerates to a circle.
Goos-Hänchen effect in microcavities
The moral of the story: So, shuft the lower medium, there is a field of the form: The goos-hanchfn lines forming an inverted V follow the corresponding specular-reflection path without the shift. Some paper explained this phenomenon as the light penetrates the less-dense medium a little, and re-emerge again, just like it is reflected by some virtual plane in the less-dense, but how can this be explained?
However, we did the calculations for a three-dimensional dome. Both these results reflect the fact that a beam having finite width contains a range of angles of incidence about some average angle of incidence.