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Minin IV, Minin OV, Cao YH, Yan B, Wang ZB et al. Photonic lenses with whispering gallery waves at Janus particles. Opto-Electron Sci 1, 210008 (2022). doi: 10.29026/oes.2022.210008
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Photonic lenses with whispering gallery waves at Janus particles
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Abstract
We show that electric field on the plane surface of truncated sphere or cylinders (so called Janus particles) have sharp resonances versus the depth of removed segment of a sphere or cylinder. These resonances are related to the excited whispering gallery waves caused by truncation. It is a new mechanism of the field localization. Optimization of this effect for cylinders permits to reach a super resolution in the line thickness, which can be used for contact optical lithography.-
Keywords:
- photonics /
- whispering gallery mode /
- whispering gallery waves /
- Janus particles
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References
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Minin IV, Minin OV, Cao YH, Yan B, Wang ZB et al. Photonic lenses with whispering gallery waves at Janus particles. Opto-Electron Sci 1, 210008 (2022). doi: 10.29026/oes.2022.210008
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Figure 1.
(a) Ray tracing for a big particle with radius R
$\gg $ -
Figure 2.
(a) Distribution of intensity calculated from the Mie theory with n = 1.5 and q = 70. Such distribution is typical for Bessoid matching solution, see e.g., Fig. 5 in ref.24. (b) Intensity distribution according to Bessoid approximation24 (solid blue line) and from the Mie theory (dotted red line).
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Figure 3.
Amplitudes
$\left| {\boldsymbol{{F}}_{{ℓ}} ^{\left( {\text{e}} \right)}} \right|$ $\left| {{F}_{{ℓ}} ^{\left( \text{m} \right)}} \right|$ ${\text{ℓ}}$ ${\text{ℓ}}$ -
Figure 4.
(a) Spherical Bessel function
${{{{\text{ψ}}}} _{{{\text{ℓ}}}} }({\text{k}}\,{\text{r}})$ ${\text{ℓ}} = $ ${\text{Π}} _{\text{ℓ}}^{\left( {\text{e}} \right)}$ ${\text{φ}} =$ ${\text{ℓ}} = $ ${\text{n}} = {\text{1.5}}$ ${\text{q}} = {\text{23.855}}$ -
Figure 5.
Distribution of electric intensity (E/E0)2 within the yz plane of the particle with refractive index n = 1.515 and size parameter q = 11.
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Figure 6.
(a) We introduce the same incidence angle φ and the refraction angle θ as in Fig. 1(a). Here h is the height of truncation normalized to particle radius R. Ray emerges from the sphere after the second refraction with the angle γ follows the Snell’s law sinγ = n sin(φ − θ). The shape of the caustic for the truncated sphere with h = 1 − 1/n and n = 1.5 is shown by dashed black line. The solid green line shows the caustic of the spherical particle with the same refractive index. (b) The same parameters and the exact solution of the Maxwell equation, corresponding to size parameter q = 2πR/λ = 100.
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Figure 7.
Distribution of electric E2 intensity (picures on the top) and magnetic H2 intensity (down pictures) within the cross section of the Janus cylinder with refractive index n = 1.5 (down), n = 1.3 (top), and size parameter q = 5π.
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Figure 8.
Maximal field enhancement around the truncated cylindrical versus the depth of truncated element.
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Figure 9.
Distribution of the field intensity for a resonant value of truncation (a) and zoom in (b) and further (c).
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Figure 10.
Internal and external electric (a) and magnetic (b) intensities versus size parameter for the cylinder with fixed truncation parameter h = 0.02. Size parameter q = 32.5 correspnds to radius of the cylinder 2R ≈ 10λ.
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Figure 11.
Schematic for a lithographic process with truncated cylinders. Here a thin protected layer between the matrix and photoresist plays an important role of anti-reflective coating, depending on the thickness of the coating.
