OAM & Surface Plasmon Resonance

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Background and Goal

The ultimate goal of the Surface Plasmon Resonance (SPR) experiment is to understand angular momentum states of surface plasmons (SPs). This wiki article assumes that the reader has general knowledge of optics and light fields.

Surface Plasmon Resonance

A surface plasmon is very similar, conceptually, to a photon confined to a 2-dimensional surface. The coupling of light to a conductor generates charge density waves that propagate based on the dielectric constant and thickness of the conductor. These two conditions generally dictate the momentum of a surface plasmon (and therefore the associated wave number, k).

When coherent light undergoes total internal reflection in at an interface in a dialectric, an evanescent field propagating parallel to the component of the incident light in the plane of the dielectric interface is generated. When a conducting film as described above, whose associated plasmon wave number matches the wave number of the evanescent field, a surface plasmon resonance is is generated. In order to tune the resonance, the incident angle of the light can be adjusted, thereby adjusting the wave number of the evanescent field. The wave number of the evanescent field can also be changed by using light of a different wavelength.

In practice, an approximately 43nm thick gold film applied to the back of a glass prism makes for an excellent plasmon setup. Gold is an excellent conductor. Better conduction increases the wave number associated with surface plasmons in a material, allowing for the plasmon resonant angle to be above the critical angle. While silver is an even better conductor, its corrosion in atmosphere makes it less practical.

When a surface plasmon encounters a defect such as a bump or a hole in the conducting surface along which it is propagating, the defect acts as a scatterer for the SP (as it is locally off-resonance for that wavelength of SP) and the SP either deflects off the defect or is re-radiated from the surface, converting back to a photon. In order to conserve linear momentum, a re-radiated SP leaves the dielectric film at the angle of incidence matching its momentum in the plane of propagation. In other words, if a plasmon generated by light of a given wavelength whose resonant angle is θ is ejected from the conductive surface, it will be ejected at the same wavelength as the generated light at the angle θ.

Since any azimuthal angle in the plane of the conductor can satisfy the above constrain on the angle of exit of a re-radiated plasmon, a hollow cone of radiation is observed when a surface plasmon resonance is generated in a film with defects sufficiently large to scatter and eject SPs.

The observation of this radiation cone is perhaps the easiest way to observe the effects of SPR, and because it is a cone whose vertex is at the dielectric/conductor interface, it is convenient to use a prism with cylindrical or spherical symmetry in the axis normal to the dielectric/conductor interface.

Angular Momentum

Diagram of wavefront helicity and associated topological charge
Light can carry both orbital and spin angular momentum. Orbital angular momentum (OAM) of light is a consequence of its spacial distribution, such as helicity, while spin angular momentum (SAM) corresponds to circular polarization states. OAM states are quantized by topological charge M which carriers any integer value, while SAM states are quantized by 1, 0, or -1 as photons are bosons.

Angular Momentum Conservation in the Generation of Surface Plasmons

This experiment seeks to understand the conversion of light carrying angular momentum into surface plasmons. That is, when an SPR is generated by light with angular momentum, the angular momentum must be conserved one way or another. It could be that surface plasmon resonance supports modes with angular momentum, or that the angular momentum is simply converted to torque at some point in the conversion of light to SPs.

Currently, this project consists of a laser system designed to generate OAM light with linear polarization and topological charge ±1, and a nearly hemispherical prism with a fairly smooth silver film in which to generate an SPR. No detection of angular momentum of plasmons has been attempted yet, but possible methods for detection are outlined below: