### Abstract

Analytic solutions to the superfocusing modes of surface plasmon polaritons in the wedge-shaped geometry are theoretically studied by solving the Helmholtz wave equation for the magnetic field using quasi-separation of variables in combination with perturbation methods. The solutions are described as a product of radial and extended angular functions and are obtained for a lossless metallic wedge and V-groove by determining the separation quantities that satisfy the boundary conditions. For the metallic wedge and V-groove, we show that the radial functions of the zeroth order are approximately described by the imaginary Bessel and modified Whittaker functions, respectively, and that the extended angular functions have odd and even symmetries, respectively, for reflection in the central plane of the wedge-shaped geometry. Importantly, we show that the wave numbers of superfocusing surface plasmon polaritons in the metallic wedge and V-groove are clearly different in their radial dependence.

Original language | English |
---|---|

Article number | 295401 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 41 |

Issue number | 29 |

DOIs | |

Publication status | Published - Jul 25 2008 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*41*(29), [295401]. https://doi.org/10.1088/1751-8113/41/29/295401

**Superfocusing modes of surface plasmon polaritons in a wedge-shaped geometry obtained by quasi-separation of variables.** / Kurihara, Kazuyoshi; Yamamoto, Kazuhiro; Takahara, Junichi; Otomo, Akira.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 41, no. 29, 295401. https://doi.org/10.1088/1751-8113/41/29/295401

}

TY - JOUR

T1 - Superfocusing modes of surface plasmon polaritons in a wedge-shaped geometry obtained by quasi-separation of variables

AU - Kurihara, Kazuyoshi

AU - Yamamoto, Kazuhiro

AU - Takahara, Junichi

AU - Otomo, Akira

PY - 2008/7/25

Y1 - 2008/7/25

N2 - Analytic solutions to the superfocusing modes of surface plasmon polaritons in the wedge-shaped geometry are theoretically studied by solving the Helmholtz wave equation for the magnetic field using quasi-separation of variables in combination with perturbation methods. The solutions are described as a product of radial and extended angular functions and are obtained for a lossless metallic wedge and V-groove by determining the separation quantities that satisfy the boundary conditions. For the metallic wedge and V-groove, we show that the radial functions of the zeroth order are approximately described by the imaginary Bessel and modified Whittaker functions, respectively, and that the extended angular functions have odd and even symmetries, respectively, for reflection in the central plane of the wedge-shaped geometry. Importantly, we show that the wave numbers of superfocusing surface plasmon polaritons in the metallic wedge and V-groove are clearly different in their radial dependence.

AB - Analytic solutions to the superfocusing modes of surface plasmon polaritons in the wedge-shaped geometry are theoretically studied by solving the Helmholtz wave equation for the magnetic field using quasi-separation of variables in combination with perturbation methods. The solutions are described as a product of radial and extended angular functions and are obtained for a lossless metallic wedge and V-groove by determining the separation quantities that satisfy the boundary conditions. For the metallic wedge and V-groove, we show that the radial functions of the zeroth order are approximately described by the imaginary Bessel and modified Whittaker functions, respectively, and that the extended angular functions have odd and even symmetries, respectively, for reflection in the central plane of the wedge-shaped geometry. Importantly, we show that the wave numbers of superfocusing surface plasmon polaritons in the metallic wedge and V-groove are clearly different in their radial dependence.

UR - http://www.scopus.com/inward/record.url?scp=52649146943&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=52649146943&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/41/29/295401

DO - 10.1088/1751-8113/41/29/295401

M3 - Article

VL - 41

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 29

M1 - 295401

ER -