טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentGal Bitan
SubjectEnergy Distribution of Single and Two Photon Emitters
in Plasmonic Environments
DepartmentDepartment of Electrical Engineering
Supervisor Full Professor Orenstein Meir
Full Thesis textFull thesis text - English Version


Abstract

Plasmonic materials are commonly used to increase the rate of optical emissions. However, they absorb some of the emitted energy. These effects influence the performance of optical sources; one increases the rate while the other reduces the yield. In this work this balance is studied in a system of an emitter suspended above a plasmonic half-space.

The Green function of the system is derived and at the first stage used to classically treat the problem. The source studied is an oscillating electric dipole. The emission rate and yield are calculated. The rate was enhanced near the interface and diminished to its free-space value as the dipole is placed farther from the metal. For a parallel dipole a decrease in rate is shown near the surface as a result of interference with the reflected field.

The problem is then studied using a quantum-mechanical approach. The emitter model is a two-level system. A specialized quantization method is used for the electromagnetic field to correctly describe it near plasmonic materials. Using this quantization the same quantities are calculated as in the classical treatment.

In order to calculate the quantum yield, the Poynting vector is derived. It is shown that the Poynting vector can be divided to vacuum and a source parts. Both emitted and absorbed energies and the quantum yield are calculated. The difference between the classical and quantum results is 5%, and is lower than the 10% error of the calculation.

The problem of two-photon emission (TPE) is the core of our study and the model uses a three-level emitter. The transition rate increases close to the metal as in the single photon case. However, unlike the single photon emission, no reduction of the transition rate is found because of the broadband nature of TPE.

Using the Poynting vector formalism developed here the quantum yield of the TPE is derived. It is shown that the TPE Poynting vector is a weighted average of Poynting vectors of single photons involved in the process. The weights are determined by the process spectrum.

Finally a semi-classical approximation of the TPE Poynting vector is examined. The quantum yield of the TPE process is calculated in both exact and approximated methods. The difference between the quantum result and the approximation is 15%, and is within the 25% error of the quantum calculations. This approximation simplifies the calculation of TPE Poynting vector and paves the way to power calculations in complex systems using numerical simulations.