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Abstract
In the recently introduced masspolariton (MP) theory of light (Partanen et al 2017 Phys. Rev. A 95 063850), the optical force of light drives in a medium forward an atomic mass density wave. In this work, we present the Lagrangian formulation of the MP theory starting directly from the principle of least action and the wellknown Lagrangian densities of the electromagnetic field and the medium within the special theory of relativity. The Lagrangian densities and the resulting EulerLagrange equations lead directly and without any further postulates to the unique expression of the optical Abraham force that dynamically couples the electromagnetic field and the medium in the MP theory of light. The fieldmedium coupling is symmetric and bidirectional and it fulfills the law of action and counteraction. The coupled dynamical equations also enable the exact description of the very small kinetic energy of the medium as a part of the total energy of the coupled state of light. Thus, the Lagrangian formulation of the present work is a complementary approach to Lorentz covariance properties of the MP theory discussed in our recent work (Partanen and Tulkki 2019 Phys. Rev. A 99 033852). We show how the coupled dynamical equations of the field and the medium can be solved analytically for a Gaussian light pulse. It is astonishing how the simple analytic results for the dynamical equations, the optical force, and the stressenergymomentum tensor of the MP theory follow ab initio from the Lagrangian densities that have been well known for almost a century.
Original language  English 

Article number  073062 
Number of pages  18 
Journal  New Journal of Physics 
Volume  21 
DOIs  
Publication status  Published  30 Jul 2019 
MoE publication type  A1 Journal articlerefereed 
Keywords
 masspolariton
 mass density wave
 Lagrangian dynamics
 optomechanics
 optical forces
 RADIATION PRESSURE
 ELECTROMAGNETIC ENERGY
 MOMENTUM
 ELECTRODYNAMICS
 WAVE

Masspolariton theory of light: from theory to simulation of experiments
Partanen, M., Tulkki, J. & Rönn, J.
01/09/2018 → 30/06/2022
Project: Academy of Finland: Other research funding

DynaLight: Lightdriven atomic dynamics in solids and liquids – from fundamentals of optics to engineering of novel photonics technologies
01/04/2019 → 31/05/2021
Project: EU: MC