A General Model for Linearly Polarized Optical Vector Beams
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909621823733760 |
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| author | Nichols, Jonathan Bucholtz, Frank |
| author_facet | Nichols, Jonathan Bucholtz, Frank |
| contents | We propose an approach for deriving a broad class of propagation models for inhomogeneously, linearly polarized ``vector'' beams. Our formulation leverages a complex scalar potential along with an appropriately constructed Lagrangian energy density. Importantly, we show that polarization inhomogeneities can be included by simple addition of a spatially dependent polarization angle to the complex potential phase. Thus, phase and polarization are seen to be equivalent from an energy perspective. As part of our development, we also show how the complex scalar potential arises naturally when considering polarization angle as a field symmetry during construction of the Lagrangian. We further show that the definition of linear momentum density in terms of the complex potential holds a distinct advantage over the conventional definition for inhomogeneously polarized beams. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00471 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A General Model for Linearly Polarized Optical Vector Beams Nichols, Jonathan Bucholtz, Frank Optics Mathematical Physics 35Q60, 78A60 We propose an approach for deriving a broad class of propagation models for inhomogeneously, linearly polarized ``vector'' beams. Our formulation leverages a complex scalar potential along with an appropriately constructed Lagrangian energy density. Importantly, we show that polarization inhomogeneities can be included by simple addition of a spatially dependent polarization angle to the complex potential phase. Thus, phase and polarization are seen to be equivalent from an energy perspective. As part of our development, we also show how the complex scalar potential arises naturally when considering polarization angle as a field symmetry during construction of the Lagrangian. We further show that the definition of linear momentum density in terms of the complex potential holds a distinct advantage over the conventional definition for inhomogeneously polarized beams. |
| title | A General Model for Linearly Polarized Optical Vector Beams |
| topic | Optics Mathematical Physics 35Q60, 78A60 |
| url | https://arxiv.org/abs/2505.00471 |