## Abstract

We develop a method to find the quality (Q) factor of the eigenmodes of a dielectric spherical resonator as a function of its complex refractive index. First, we analytically show that the Q factor of magnetic and electric multipolar modes in a lossless spherical resonator with high refractive index (n ≫ 1) scale 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 of all multipolar modes as a function of 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.

Original language | English |
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Journal | ACS Photonics |

Volume | 11 |

Issue number | 8 |

Pages (from-to) | 3317-3322 |

ISSN | 2330-4022 |

DOIs | |

Publication status | Published - 2024 |

## Keywords

- Absorption losses
- Mie theory
- Optical cavity
- Q factor
- Refractive index