Lagrangian dynamics of the coupled field-medium state of light
In the recently introduced mass-polariton (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...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2019-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/ab3069 |
| _version_ | 1797750073948372992 |
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| author | Mikko Partanen Jukka Tulkki |
| author_facet | Mikko Partanen Jukka Tulkki |
| author_sort | Mikko Partanen |
| collection | DOAJ |
| description | In the recently introduced mass-polariton (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 well-known Lagrangian densities of the electromagnetic field and the medium within the special theory of relativity. The Lagrangian densities and the resulting Euler–Lagrange 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 field-medium coupling is symmetric and bi-directional 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 stress-energy-momentum tensor of the MP theory follow ab initio from the Lagrangian densities that have been well known for almost a century. |
| first_indexed | 2024-03-12T16:27:28Z |
| format | Article |
| id | doaj.art-6a29e64ed41541d4a0e1464a3f11457a |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:27:28Z |
| publishDate | 2019-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-6a29e64ed41541d4a0e1464a3f11457a2023-08-08T15:39:29ZengIOP PublishingNew Journal of Physics1367-26302019-01-0121707306210.1088/1367-2630/ab3069Lagrangian dynamics of the coupled field-medium state of lightMikko Partanen0https://orcid.org/0000-0003-4648-340XJukka Tulkki1Engineered Nanosystems Group, School of Science, Aalto University , PO Box 12200, FI-00076 Aalto, FinlandEngineered Nanosystems Group, School of Science, Aalto University , PO Box 12200, FI-00076 Aalto, FinlandIn the recently introduced mass-polariton (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 well-known Lagrangian densities of the electromagnetic field and the medium within the special theory of relativity. The Lagrangian densities and the resulting Euler–Lagrange 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 field-medium coupling is symmetric and bi-directional 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 stress-energy-momentum tensor of the MP theory follow ab initio from the Lagrangian densities that have been well known for almost a century.https://doi.org/10.1088/1367-2630/ab3069mass-polaritonmass density waveLagrangian dynamicsoptomechanicsoptical forces |
| spellingShingle | Mikko Partanen Jukka Tulkki Lagrangian dynamics of the coupled field-medium state of light New Journal of Physics mass-polariton mass density wave Lagrangian dynamics optomechanics optical forces |
| title | Lagrangian dynamics of the coupled field-medium state of light |
| title_full | Lagrangian dynamics of the coupled field-medium state of light |
| title_fullStr | Lagrangian dynamics of the coupled field-medium state of light |
| title_full_unstemmed | Lagrangian dynamics of the coupled field-medium state of light |
| title_short | Lagrangian dynamics of the coupled field-medium state of light |
| title_sort | lagrangian dynamics of the coupled field medium state of light |
| topic | mass-polariton mass density wave Lagrangian dynamics optomechanics optical forces |
| url | https://doi.org/10.1088/1367-2630/ab3069 |
| work_keys_str_mv | AT mikkopartanen lagrangiandynamicsofthecoupledfieldmediumstateoflight AT jukkatulkki lagrangiandynamicsofthecoupledfieldmediumstateoflight |