Tutorial of Fourier and Hankel transforms for ultrafast optics
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866908837886296064 |
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| author | Chen, Yi-Hao |
| author_facet | Chen, Yi-Hao |
| contents | This tutorial is designed to clarify a few misconceptions in the field of ultrafast optics. (1) Analytic signal that underlies the complex-conjugate decomposition of the field is discussed, as well as the misunderstanding between propagation-constant-offset and offset-frequency analytic signal and slowly-varying envelope assumption. (2) It contains complete derivations of the general formulations of several Fourier-transform relations. It shows the importance of having Fourier-transform constants as parameters, and helps clarify the arbitrary selection of Fourier-transform constants and conventions. (3) It also clarifies the correct Fourier-transform convention to be employed in ultrafast optics. (4) Moreover, multiple Fourier-transform aspects are discussed, involving convolution, aliasing, phase effect, and short-time Fourier transform. (5) In addition to the Fourier transform, a tutorial on the Hankel transform is provided. Its numerical implementation based on the fast Hankel transform with high accuracy (FHATHA) is also provided. Despite being a tutorial, I, for the first time, propose a new numerical scheme for the fast Hankel transform that outperforms both the original FHATHA and the discrete Hankel transform. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20698 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tutorial of Fourier and Hankel transforms for ultrafast optics Chen, Yi-Hao Optics This tutorial is designed to clarify a few misconceptions in the field of ultrafast optics. (1) Analytic signal that underlies the complex-conjugate decomposition of the field is discussed, as well as the misunderstanding between propagation-constant-offset and offset-frequency analytic signal and slowly-varying envelope assumption. (2) It contains complete derivations of the general formulations of several Fourier-transform relations. It shows the importance of having Fourier-transform constants as parameters, and helps clarify the arbitrary selection of Fourier-transform constants and conventions. (3) It also clarifies the correct Fourier-transform convention to be employed in ultrafast optics. (4) Moreover, multiple Fourier-transform aspects are discussed, involving convolution, aliasing, phase effect, and short-time Fourier transform. (5) In addition to the Fourier transform, a tutorial on the Hankel transform is provided. Its numerical implementation based on the fast Hankel transform with high accuracy (FHATHA) is also provided. Despite being a tutorial, I, for the first time, propose a new numerical scheme for the fast Hankel transform that outperforms both the original FHATHA and the discrete Hankel transform. |
| title | Tutorial of Fourier and Hankel transforms for ultrafast optics |
| topic | Optics |
| url | https://arxiv.org/abs/2412.20698 |