Partially coherent axiconic surface plasmon polariton fields

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Partially coherent axiconic surface plasmon polariton fields

Yahong Chen, Andreas Norrman, Sergey A. Ponomarenko, and Ari T. Friberg

Phys. Rev. A 97, 041801(R) – Published 13 April 2018

Abstract

We introduce a class of structured polychromatic surface electromagnetic fields, reminiscent of conventional optical axicon fields, through a judicious superposition of partially correlated surface plasmon polaritons. We show that such partially coherent axiconic surface plasmon polariton fields are structurally stable and statistically highly versatile with regard to spectral density, polarization state, energy flow, and degree of coherence. These fields can be created by plasmon coherence engineering and may prove instrumental broadly in surface physics and in various nanophotonics applications.

Received 24 October 2017

DOI:https://doi.org/10.1103/PhysRevA.97.041801

Physics Subject Headings (PhySH)

Optical coherence Plasmonics

Atomic, Molecular & OpticalPlasma Physics

Authors & Affiliations

Yahong Chen^1,2,*, Andreas Norrman³, Sergey A. Ponomarenko⁴, and Ari T. Friberg¹

¹Institute of Photonics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland
²College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215006, China
³Max Planck Institute for the Science of Light, Staudtstraße 2, D-91058 Erlangen, Germany
⁴Department of Electrical and Computer Engineering, Dalhousie University, Halifax, Nova Scotia B3J 2X4, Canada

^*hon2019@163.com

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Vol. 97, Iss. 4 — April 2018

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Images

Figure 1
Geometry and notations for the ASPP field synthesis. One of the contributing SPPs, excited on the circle of radius $a$ at the metal-air interface and propagating in the direction of ${\hat{e}}_{∥} (θ)$ , is explicitly displayed in the figure.
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Figure 2
(Left) Spectral density $S (r, ω)$ for the correlated ASPP field and (right) the degree of coherence $μ (r, ω)$ for the uncorrelated ASPP field at an Ag-air interface for the free-space wavelength $λ = 632.8 nm$ . In the left panel $I_{SPP} (ω)$ is the initial SPP intensity and $a = l_{SPP} (λ)$ , where $a$ is the circle radius and $l_{SPP} (λ)$ is the SPP propagation length. In the right panel $μ (r, ω)$ is independent of $a$ , but ${(x^{2} + y^{2})}^{1 / 2} \leq a$ . The relative permittivity of Ag is from empirical data [29].
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Figure 3
(Left) Spectral density $S (r, ω)$ for the correlated ASPP superposition as a function of the radial distance $ρ$ and free-space wavelength $λ$ for an Ag-air interface and circle radius of $a = l_{SPP} (λ)$ , where $l_{SPP} (λ)$ is the SPP propagation length. (Right) Maximum of the spectral density $S_{\max} (r, ω)$ as a function of the circle radius $a$ for the same field as in the left panel. Note that $S (r, ω)$ and $S_{\max} (r, ω)$ are normalized with respect to the initial SPP intensity $I_{SPP} (ω)$ . Empirical data [29] are used for the relative permittivity of Ag.
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Figure 4
(Left) Spectral density $S (r, ω)$ for the uncorrelated ASPP field as a function of the radial distance $ρ$ at an Ag-air interface when the circle radius $a$ is varied: $a = 0.25 l_{SPP} (λ)$ (the solid blue curve), $a = 0.50 l_{SPP} (λ)$ (the dashed green curve), $a = 0.75 l_{SPP} (λ)$ (the orange dashed-dotted curve), and $a = l_{SPP} (λ)$ (the red dotted curve). (Right) SPP propagation length $l_{SPP} (λ)$ as a function of the free-space wavelength $λ$ for the Ag-air surface according to empirical data [29]. Note that the plots of $S (r, ω)$ and $l_{SPP} (λ)$ are normalized with respect to the initial SPP intensity $I_{SPP} (ω)$ and wavelength $λ$ , respectively.
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Figure 5
(Left) Normal Poynting-vector components $S_{z} (r, ω)$ and (right) radial Poynting-vector components $S_{ρ} (r, ω)$ for the (top) correlated and (bottom) uncorrelated ASPP fields as a function of the radial distance $ρ$ and free-space wavelength $λ$ for an Ag-air surface and circle radius of $a = l_{SPP} (λ)$ , where $l_{SPP} (λ)$ is the SPP propagation length. The relative permittivity of Ag is taken from empirical data [29]. Note that the Poynting-vector components are normalized with respect to the reciprocal free-space impedance $Z_{0}^{- 1}$ and the initial SPP intensity $I_{SPP} (ω)$ .
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Figure 6
Degree of coherence $μ (r, ω)$ of the uncorrelated ASPP field as a function of the radial distance $ρ$ and free-space wavelength $λ$ at an Ag-air surface. Empirical data [29] are used for the relative permittivity of Ag, and $l_{SPP} (λ)$ is the SPP propagation length. Note the validity condition $ρ \leq a$ for $μ (r, ω)$ , where $a$ is the circle radius.
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