https://doi.org/10.1140/epjp/s13360-020-00637-9
Regular Article
A quantum approach to electromagnetic wave propagation inside a dielectric
1
Atomic and Molecular Group, Faculty of Physics, Yazd University, 89195-741, Yazd, Iran
2
Science and Research Division, Bloorazma Co., Tehran, Iran
a safaei@yazd.ac.ir, abolfazl_safaei@live.com
Received:
19
April
2020
Accepted:
27
July
2020
Published online:
12
August
2020
As the quantum treatment of field propagation inside a dielectric becomes more important due to developing quantum technologies, we present a detailed study of quantum field propagation through a dielectric when up to third-order dispersion is included. Initially, a proper canonical Lagrangian is defined, leading to Maxwell’s equations and the classical energy. Then, by employing a constrained quantization approach and making use of Ostrogradski’s theorem for higher-order field derivatives in the Lagrangian, the final Hamiltonian is expanded in terms of properly defined annihilation and creation operators. These operators are applied to obtain the quantum fields describing electromagnetic waves propagation inside a dispersive and nonlinear dielectric. The number of photon–polariton pairs in the medium is defined by the number operator. The creation and the annihilation operators were used to describe the nonlinearity of the medium by adding the proper perturbation terms. The present quantum theory is applied to a single-dimensional slab when a light signal is propagating along it.
Electronic supplementary material The online version of this article (https://doi.org/10.1140/epjp/s13360-020-00637-9) contains supplementary material, which is available to authorized users.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
