Optical eigenmode description of single-photon light-matter interactions
Abstract
When light scatters from an object, it can impart some physical quantity such as momentum or angular momentum. This can act as a measurement on the photon, which collapses on to an eigenstate of the measurement operator. However the corresponding operator is not the same as that describing the total linear or angular momentum in free space. Optical eigenmodes provide a powerful method to describe this interaction by expanding the field as a linear combination of some basis modes and examining the eigenvalues and eigenvectors of the quadratic measure in question. We extend this to the quantum case by writing the quantum operator corresponding to a given measurement such as energy, momentum or angular momentum as a superposition of creation and annihilation operators for each eigenmode. Upon measurement we find that the possible states of a single photon are simply the classical eigenmodes of the measurement. As an application, we examine the force and torque on a general, possibly anisotropic, material. By looking at eigenvalues of the measurement operator we show that the amount of a given quantity transferred in an interaction with matter is not in general the expected amount which a photon carries in free space, even at the single photon level. In particular the difference in linear or angular momentum from before and after is in general not equal to ∼k or ∼ which are the eigenvalues of these quantities in free space.
Citation
Ballantine , K & Mazilu , M 2019 , Optical eigenmode description of single-photon light-matter interactions . in E J Galvez , D L Andrews & J Gluckstad (eds) , Complex Light and Optical Forces XIII . , 109351B , Proceedings of SPIE , vol. 10935 , SPIE , Bellingham, WA , Complex Light and Optical Forces XIII 2019 , San Francisco , California , United States , 5/02/19 . https://doi.org/10.1117/12.2508394 conference
Publication
Complex Light and Optical Forces XIII
ISSN
0277-786XType
Conference item
Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.