{"title":"微小的德鲁德散射体可精确模拟纳米光子学中的相干发射器","authors":"Felix Binkowski, Sven Burger, Günter Kewes","doi":"10.1515/nanoph-2024-0170","DOIUrl":null,"url":null,"abstract":"We add a missing element to the set of <jats:italic>directly</jats:italic> computable scenarios of light-matter-interaction within classical numerical Maxwell solvers, i.e., light scattering from hybrid systems of resonators and individual Fourier-limited emitters. In particular, individual emitters are incorporated as tiny polarizable and resonant spherical scatterers. This emitter model is based on well-known extremal properties of Mie modes. The spherical emitter is made from an artificial Drude metal with <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:mi>ϵ</m:mi> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mi>ω</m:mi> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mo>=</m:mo> <m:msub> <m:mrow> <m:mi>ϵ</m:mi> </m:mrow> <m:mrow> <m:mi>b</m:mi> </m:mrow> </m:msub> <m:mo>−</m:mo> <m:msubsup> <m:mrow> <m:mi>ω</m:mi> </m:mrow> <m:mrow> <m:mi>p</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msubsup> <m:mo>/</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mi>ω</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mo>+</m:mo> <m:mi>i</m:mi> <m:mi mathvariant=\"normal\">Γ</m:mi> <m:mi>ω</m:mi> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:math> <jats:tex-math>${\\epsilon}(\\omega )={{\\epsilon}}_{b}-{\\omega }_{p}^{2}/({\\omega }^{2}+i{\\Gamma }\\omega )$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_nanoph-2024-0170_ineq_001.png\"/> </jats:alternatives> </jats:inline-formula>. By tuning <jats:italic>ϵ</jats:italic> <jats:sub> <jats:italic>b</jats:italic> </jats:sub> and <jats:italic>ω</jats:italic> <jats:sub> <jats:italic>p</jats:italic> </jats:sub> we adjust the resonance frequency and the Fourier-limited linewidth and by adjusting Γ we may add non-radiative damping or dephasing. This approach automatically reproduces the ideal text book coherent scattering cross-section of Fourier-limited two level quantum systems of <jats:italic>σ</jats:italic> <jats:sub>0</jats:sub> = 3<jats:italic>λ</jats:italic> <jats:sup>2</jats:sup>/(2<jats:italic>πϵ</jats:italic> <jats:sub>out</jats:sub>) which is not possible with typically used Lorentz permittivities which only mimic optical resonances. Further, the emitter’s linewidth adopts to the surrounding optical local density of states (LDOS). To demonstrate this we successfully benchmark our approach with prominent examples from the literature.","PeriodicalId":19027,"journal":{"name":"Nanophotonics","volume":"29 1","pages":""},"PeriodicalIF":6.5000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A tiny Drude scatterer can accurately model a coherent emitter in nanophotonics\",\"authors\":\"Felix Binkowski, Sven Burger, Günter Kewes\",\"doi\":\"10.1515/nanoph-2024-0170\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We add a missing element to the set of <jats:italic>directly</jats:italic> computable scenarios of light-matter-interaction within classical numerical Maxwell solvers, i.e., light scattering from hybrid systems of resonators and individual Fourier-limited emitters. In particular, individual emitters are incorporated as tiny polarizable and resonant spherical scatterers. This emitter model is based on well-known extremal properties of Mie modes. The spherical emitter is made from an artificial Drude metal with <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\" overflow=\\\"scroll\\\"> <m:mi>ϵ</m:mi> <m:mrow> <m:mo stretchy=\\\"false\\\">(</m:mo> <m:mrow> <m:mi>ω</m:mi> </m:mrow> <m:mo stretchy=\\\"false\\\">)</m:mo> </m:mrow> <m:mo>=</m:mo> <m:msub> <m:mrow> <m:mi>ϵ</m:mi> </m:mrow> <m:mrow> <m:mi>b</m:mi> </m:mrow> </m:msub> <m:mo>−</m:mo> <m:msubsup> <m:mrow> <m:mi>ω</m:mi> </m:mrow> <m:mrow> <m:mi>p</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msubsup> <m:mo>/</m:mo> <m:mrow> <m:mo stretchy=\\\"false\\\">(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mi>ω</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mo>+</m:mo> <m:mi>i</m:mi> <m:mi mathvariant=\\\"normal\\\">Γ</m:mi> <m:mi>ω</m:mi> </m:mrow> <m:mo stretchy=\\\"false\\\">)</m:mo> </m:mrow> </m:math> <jats:tex-math>${\\\\epsilon}(\\\\omega )={{\\\\epsilon}}_{b}-{\\\\omega }_{p}^{2}/({\\\\omega }^{2}+i{\\\\Gamma }\\\\omega )$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_nanoph-2024-0170_ineq_001.png\\\"/> </jats:alternatives> </jats:inline-formula>. By tuning <jats:italic>ϵ</jats:italic> <jats:sub> <jats:italic>b</jats:italic> </jats:sub> and <jats:italic>ω</jats:italic> <jats:sub> <jats:italic>p</jats:italic> </jats:sub> we adjust the resonance frequency and the Fourier-limited linewidth and by adjusting Γ we may add non-radiative damping or dephasing. This approach automatically reproduces the ideal text book coherent scattering cross-section of Fourier-limited two level quantum systems of <jats:italic>σ</jats:italic> <jats:sub>0</jats:sub> = 3<jats:italic>λ</jats:italic> <jats:sup>2</jats:sup>/(2<jats:italic>πϵ</jats:italic> <jats:sub>out</jats:sub>) which is not possible with typically used Lorentz permittivities which only mimic optical resonances. Further, the emitter’s linewidth adopts to the surrounding optical local density of states (LDOS). To demonstrate this we successfully benchmark our approach with prominent examples from the literature.\",\"PeriodicalId\":19027,\"journal\":{\"name\":\"Nanophotonics\",\"volume\":\"29 1\",\"pages\":\"\"},\"PeriodicalIF\":6.5000,\"publicationDate\":\"2024-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nanophotonics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1515/nanoph-2024-0170\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATERIALS SCIENCE, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nanophotonics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1515/nanoph-2024-0170","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
我们为经典数值麦克斯韦求解器中可直接计算的光-物质-相互作用场景添加了一个缺失元素,即来自谐振器和单个傅立叶限制发射器混合系统的光散射。特别是,单个发射器被整合为微小的可偏振共振球形散射体。这种发射器模型基于众所周知的米氏模式极值特性。球形发射器由人造德鲁德金属制成,其 ϵ ( ω ) = ϵ b - ω p 2 / ( ω 2 + i Γ ω ) ${\epsilon}(\omega )={{\epsilon}}_{b}-{\omega }_{p}^{2}/({\omega }^{2}+i{\Gamma }\omega )$ 。通过调整 ϵ b 和 ω p,我们可以调整共振频率和傅里叶限制线宽,通过调整 Γ,我们可以增加非辐射阻尼或去相消。这种方法可以自动再现傅里叶限制的两级量子系统的理想相干散射截面 σ 0 = 3λ 2/(2πϵ out),而通常使用的洛伦兹介电常数只能模拟光学共振。此外,发射器的线宽采用了周围的光学局部态密度(LDOS)。为了证明这一点,我们成功地用文献中的著名例子对我们的方法进行了基准测试。
A tiny Drude scatterer can accurately model a coherent emitter in nanophotonics
We add a missing element to the set of directly computable scenarios of light-matter-interaction within classical numerical Maxwell solvers, i.e., light scattering from hybrid systems of resonators and individual Fourier-limited emitters. In particular, individual emitters are incorporated as tiny polarizable and resonant spherical scatterers. This emitter model is based on well-known extremal properties of Mie modes. The spherical emitter is made from an artificial Drude metal with ϵ(ω)=ϵb−ωp2/(ω2+iΓω)${\epsilon}(\omega )={{\epsilon}}_{b}-{\omega }_{p}^{2}/({\omega }^{2}+i{\Gamma }\omega )$. By tuning ϵb and ωp we adjust the resonance frequency and the Fourier-limited linewidth and by adjusting Γ we may add non-radiative damping or dephasing. This approach automatically reproduces the ideal text book coherent scattering cross-section of Fourier-limited two level quantum systems of σ0 = 3λ2/(2πϵout) which is not possible with typically used Lorentz permittivities which only mimic optical resonances. Further, the emitter’s linewidth adopts to the surrounding optical local density of states (LDOS). To demonstrate this we successfully benchmark our approach with prominent examples from the literature.
期刊介绍:
Nanophotonics, published in collaboration with Sciencewise, is a prestigious journal that showcases recent international research results, notable advancements in the field, and innovative applications. It is regarded as one of the leading publications in the realm of nanophotonics and encompasses a range of article types including research articles, selectively invited reviews, letters, and perspectives.
The journal specifically delves into the study of photon interaction with nano-structures, such as carbon nano-tubes, nano metal particles, nano crystals, semiconductor nano dots, photonic crystals, tissue, and DNA. It offers comprehensive coverage of the most up-to-date discoveries, making it an essential resource for physicists, engineers, and material scientists.