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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In a fuller vector field analysis done by fully solving Maxwell’s equations, one can work out the Poynting vector and show that such fields do not bear optical power with them.

An alternative explanation of the GHS can be given in terms of the time delay associated with the scattering of a radiation pulse at the interface. Theories of a lateral shift in zhift internal reflection of electromagnetic waves were developed by Picht Picht J, and by Schaefer and Pich Schaefer and Pich, In other goos-nanchen, I end up doing a new type of billiard-ball simulation in which reflections are not specular, but to which the same methods can be applied that are known from our previous work [3].

The wave penetrates into the air and appears to travel parallel to it from left to right until the reflection forces it back into the dielectric heading toward the bottom right.

That’s what’s shown in the last image. The goos-hanche has to be between different dielectric materials such as glass or waterand absorption or transmission should be small enough to allow a recognizable reflected beam to form.

The GHS was first discussed in the context of total internal reflection of electromagnetic radiation. The importance of individual rays increases drastically in systems where the WKB method breaks down, because that corresponds to the scenario where ray chaos may appear. The shift is perpendicular to the direction of propagation, in the plane ogos-hanchen the incident and reflected beams.

Could there be a correctednon-integrable ray dynamics that describes the internal cavity fields better? Gooe-hanchen don’t quite have to solve the full Maxwell equations: The quantum GHS has the same form as syift of the optical GHS for the case of electric field polarization perpendicular to the plane of incidence.

### Goos–Hänchen effect – Wikipedia

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. If one new ray orbit creates a new mode, why doesn’t the other?

The best way to understand this phase shift is to solve and study solutions of the Helmholtz equation near the boundary between two dielectric mediums. Many standard optical setups in particular when Gaussian beams are involved can be described fully by identifying one or a few rays, and decorating them with suitable wave patterns i. Instead, they are very like inductive and capacitive energy stores; they of course have an energy density but it shuttles back and forth between neighbouring regions in the medium and so the nett power flux through any surface over a whole period is nought.

Which question are you asking? 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.

So far as I can tell by reading a couple refs, it is a coherent interference effect for an sihft beam of finite width. Cowan and Anicin Cowan and Anicin, observed the GHS shifts for both TE and TM polarizations for microwave radiation incident on a paraffin prism using a single reflection of the beam.

But what determines the “penetration depth” of the ray? shiff

## Goos-Hänchen effect in microcavities

We infer all the properties of the shift from the very presence or absence of individual resonator modes, and their properties — i.

In the eikonal, the scattering phase can be incorporated as just one of several contributions to the phase that accumulates as the wave fronts evolve. When total internal reflexion happens, the field isn’t abruptly turned around by the interface, it actually penetrates some distance beyond the interface as an evanescent field.

So if the phases of different plane waves are shifted differently upon reflection, the transverse goox-hanchen of the reflected beam will be modified.

The dome is a hemispherical shell whose height is just slightly shorter than its radius. There’s a more formal discussion of this phenomenon at Scholarpedia. Bragg mirrors are a type of dielectric mirror that can induce reflection phase shifts in a more controllable, engineered way than the simple dielectric boundary shown in the movie earlier. So there are situations where isolated ray trajectories are needed to describe the wave patterns.

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### Goos-Hänchen effect – Scholarpedia

It is a known fact that resonator shapes that would be integrable for Dirichlet boundary conditions generally do not retain that property in their wave equation when they are made of dielectric material. Sign up using Facebook. This is not related to Goos-Hanchen, which depends on coherence of the source.

So, in the lower medium, there is a field of the form:. When we speak of “fictitious particles,” you should keep in mind that there is a duality between wave and particle description of light, and the particles of light photons can manifest themselves in very real ways if we decide to measure them. An experiment has been carried out in which evidence for the GHS in neutron scattering was claimed deHaan et al. The displacement of the reflected intensity pattern due to reflection phase shifts can be re-interpreted when talking about the scattering process in the ray picture, because the resulting beam shape allows us to define a reflected ray.

One motivation came from an apparently boring test case that I originally only studied to validate my numerical computations of quasibound states: Goos-hajchen at angles near the critical angle, there are components in the incident beam that undergo both normal as well as total internal reflection. Their experimental work inspired new theoretical work by Artmann Artmann K, and v. Much of this work is 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.

The GHS continued to attract attention as new technologies became available.

My main goal here is to give a basic informal introduction to the phenomenon that forms the basis of our paper. 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.

As in the optical case, the GHS can be related to the phase of the reflection coefficient of the corresponding plane wave problem. At the time of this writing, this page certainly seems to be more explanatory than the Wikipedia entry.

The image represents exactly the same situation as shown in the grayscale movie above, only plotted differently so as to emphasize the highest intensity portions of the beam essentially, I’m plotting the time averaged energy density of the moving wave pattern on a nonlinear color scale, and this eliminates the wave trains except where they form standing-wave patterns in the region where incident and reflected waves overlap.