Quality factor of dielectric optical resonators
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917920453427200 |
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| author | Zambrana-Puyalto, Xavier Raza, Søren |
| author_facet | Zambrana-Puyalto, Xavier Raza, Søren |
| contents | We show analytically that the quality ($Q$) factor of magnetic and electric Mie modes in a lossless dielectric spherical resonator with high refractive index ($n \gg 1$) scales as $n^{2j+1}$ and $n^{2j+3}$ respectively, where $j$ denotes the multipolar order. We numerically validate these results and show that our high-$n$ analytical relation is accurate for the dipolar modes when $n>5$. For higher multipolar orders, the analytical relation becomes valid for increasingly lower $n$. We study the dependence of the $Q$ factor on absorption losses and determine a general functional form that describes the $Q$ factor for all Mie modes for any complex refractive index. Finally, we observe that this functional form predicts a multipolar-dependent singular value of optical gain which gives rise to a lasing condition with an infinite $Q$ factor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09360 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quality factor of dielectric optical resonators Zambrana-Puyalto, Xavier Raza, Søren Optics We show analytically that the quality ($Q$) factor of magnetic and electric Mie modes in a lossless dielectric spherical resonator with high refractive index ($n \gg 1$) scales as $n^{2j+1}$ and $n^{2j+3}$ respectively, where $j$ denotes the multipolar order. We numerically validate these results and show that our high-$n$ analytical relation is accurate for the dipolar modes when $n>5$. For higher multipolar orders, the analytical relation becomes valid for increasingly lower $n$. We study the dependence of the $Q$ factor on absorption losses and determine a general functional form that describes the $Q$ factor for all Mie modes for any complex refractive index. Finally, we observe that this functional form predicts a multipolar-dependent singular value of optical gain which gives rise to a lasing condition with an infinite $Q$ factor. |
| title | Quality factor of dielectric optical resonators |
| topic | Optics |
| url | https://arxiv.org/abs/2403.09360 |