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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.
Original language  English 

Title of host publication  Complex Light and Optical Forces XIII 
Editors  Enrique J. Galvez, David L. Andrews, Jesper Gluckstad 
Place of Publication  Bellingham, WA 
Publisher  SPIE 
Number of pages  7 
ISBN (Electronic)  9781510625129 
ISBN (Print)  9781510625129 
DOIs  
Publication status  Published  1 Mar 2019 
Event  Complex Light and Optical Forces XIII 2019  San Francisco, United States Duration: 5 Feb 2019 → 7 Feb 2019 Conference number: 13 
Publication series
Name  Proceedings of SPIE 

Publisher  Society of Photooptical Instutmentation Engineers 
Volume  10935 
ISSN (Print)  0277786X 
ISSN (Electronic)  1996756X 
Conference
Conference  Complex Light and Optical Forces XIII 2019 

Abbreviated title  SPIE OPTO 
Country/Territory  United States 
City  San Francisco 
Period  5/02/19 → 7/02/19 
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Dive into the research topics of 'Optical eigenmode description of singlephoton lightmatter interactions'. Together they form a unique fingerprint.Projects
 1 Finished

Shaped light at the interface: Shaped Light at the Interface
Dholakia, K., Brown, C. T. A., Di Falco, A. & Mazilu, M.
1/09/14 → 31/08/19
Project: Standard