Donut-like photonic nanojet with reverse energy flow

Hao Wang; Jingjing Hao; Baifu Zhang; Cheng Han; Chunguang Zhao; Zhe Shen; Ji Xu; Jianping Ding

doi:10.3788/COL202119.102602

Journals >Chinese Optics Letters >Volume 19 >Issue 10 >Page 102602 > Article

Chinese Optics Letters
Vol. 19, Issue 10, 102602 (2021)

Donut-like photonic nanojet with reverse energy flow

Hao Wang¹, Jingjing Hao², Baifu Zhang^1、*, Cheng Han¹, Chunguang Zhao², Zhe Shen¹, Ji Xu³, and Jianping Ding^4、**

Author Affiliations

¹School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

²The 28th Research Institute of China Electronics Technology Group Corporation, Nanjing 210007, China

³College of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications, Nanjing 210023, China

⁴Collaborative Innovation Center of Advanced Microstructures and School of Physics, Nanjing University, Nanjing 210093, China

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DOI: 10.3788/COL202119.102602 Cite this Article Set citation alerts

Hao Wang, Jingjing Hao, Baifu Zhang, Cheng Han, Chunguang Zhao, Zhe Shen, Ji Xu, Jianping Ding. Donut-like photonic nanojet with reverse energy flow[J]. Chinese Optics Letters, 2021, 19(10): 102602 Copy Citation Text

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Abstract

Photonic nanojets (PNJs) are subwavelength jet-like propagating waves generated by illuminating a dielectric microstructure with an electromagnetic wave, conventionally a linearly polarized plane wave. Here, we study the donut-like PNJ produced when a circularly polarized vortex beam is used instead. This novel PNJ also has a reverse energy flow at the donut-like focal plane depending on both the optical vortex topological charge and microsphere size. Our tunable PNJ, which we investigate numerically and analytically, can find applications in optical micromanipulation and trapping.

Keywords

optical vortex photonic nanojet reverse energy flow

E \propto E_{0} (\hat{x} + i σ \hat{y}) e^{ikz} {(\frac{\sqrt{2} r}{ω_{0}})}^{| m |} e^{(- \frac{r^{2}}{ω_{0}^{2}})} e^{i m ϕ},

(1)

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E_{x} = - \frac{ikf}{2} \int_{0}^{α} \sqrt{\cos θ} \sin θ e^{ikz \cos θ} A_{m} (θ) \times [(\cos θ - 1) i^{m - 2} J_{m - 2} (k r \sin θ) e^{i (m - 2) ϕ} + (1 + \cos θ) i^{m} J_{m} (k r \sin θ) e^{i m ϕ}] d θ, E_{y} = - \frac{ikf}{2} \int_{0}^{α} \sqrt{\cos θ} \sin θ e^{ikz \cos θ} A_{m} (θ) \times [i (\cos θ - 1) i^{m - 2} J_{m - 2} (k r \sin θ) e^{i (m - 2) ϕ} - i (1 + \cos θ) i^{m} J_{m} (k r \sin θ) e^{i m ϕ}] d θ, H_{x} = - \frac{ikf}{2 c} \int_{0}^{α} \sqrt{\cos θ} \sin θ e^{ikz \cos θ} A_{m} (θ) \times [i (\cos θ - 1) i^{m - 2} J_{m - 2} (k r \sin θ) e^{i (m - 2) ϕ} + i (1 + \cos θ) i^{m} J_{m} (k r \sin θ) e^{i m ϕ}] d θ, H_{y} = - \frac{ikf}{2 c} \int_{0}^{α} \sqrt{\cos θ} \sin θ e^{ikz \cos θ} A_{m} (θ) \times [(1 - \cos θ) i^{m - 2} J_{m - 2} (k r \sin θ) e^{i (m - 2) ϕ} + (1 + \cos θ) i^{m} J_{m} (k r \sin θ) e^{i m ϕ}] d θ,

(2)

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A_{m} (θ) = {(\frac{\sqrt{2} f \sin θ}{ω})}^{| m |} \exp (- \frac{f^{2} \sin^{2} θ}{ω^{2}}),

(3)

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P_{z} = \frac{c}{8 π} R e (E_{x} H_{y}^{*} - E_{y} H_{x}^{*}),

(4)

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Hao Wang, Jingjing Hao, Baifu Zhang, Cheng Han, Chunguang Zhao, Zhe Shen, Ji Xu, Jianping Ding. Donut-like photonic nanojet with reverse energy flow[J]. Chinese Optics Letters, 2021, 19(10): 102602

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