## Scattering of a surface plasmon polariton by a localized dielectric surface defect |

Optics Express, Vol. 21, Issue 8, pp. 9734-9756 (2013)

http://dx.doi.org/10.1364/OE.21.009734

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### Abstract

On the basis of a rigorous, nonperturbative, purely numerical solution of the corresponding reduced Rayleigh equation for the scattering amplitudes we have studied the scattering of a surface plasmon polariton by a two dimensional dielectric defect on a planar metal surface. The profile of the defect is assumed to be an arbitrary single-valued function of the coordinates in the plane of the metal surface, and to be differentiable with respect to those coordinates. When the defect is circularly symmetric and the dependence of the scattering amplitudes on the azimuthal angle is expressed by a rotational expansion, the reduced Rayleigh equation is transformed into a pair of one-dimensional integral equations for each value of the rotational quantum number. This approach is applied to a defect in the form of an isotropic Gaussian function. The differential cross sections for the scattering of the incident surface plasmon polariton into volume electromagnetic waves in the vacuum above the surface and into other surface plasmon polaritons are calculated, as well as the intensity of the field near the surface. These results differ significantly from the corresponding results for a metallic defect on a metallic substrate.

© 2013 OSA

1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature (London) **424**, 824–830 (2003) [CrossRef] .

10. G. Brucoli and L. Martín-Moreno, “Effect of defect depth on surface plasmon scattering by subwavelength surface defects,” Phys. Rev. B **83**, 075433 (2011) [CrossRef] .

11. A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a circularly symmetric surface defect,” Phys. Rev. Lett. **78**, 4269–4272 (1997). Erratum: Phys. Rev. Lett. **79**, 2597 (1997) [CrossRef] .

13. M. Paulus and O. J. F. Martin, “Light propagation and scattering in stratified media: a Green’s tensor approach,” J. Opt. Soc. Am. A **18**, 854–861 (2001) [CrossRef] .

15. I. I. Smolyaninov, J. E. Elliott, A.V. Zayats, and C. C. Davis, “Far-field optical microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons,” Phys. Rev. Lett. **94**, 057401 (2005) [CrossRef] [PubMed] .

*ε*

_{1}) in the region

*x*

_{3}>

*ζ*(

**x**

_{‖}), where

**x**

_{‖}= (

*x*

_{1},

*x*

_{2}, 0), a dielectric medium whose dielectric constant is

*ε*

_{2}in the region 0 <

*x*

_{3}<

*ζ*(

**x**

_{‖}), and a metal whose dielectric function is

*ε*

_{3}, in the region

*x*

_{3}< 0. The surface profile function

*ζ*(

**x**

_{‖}) is a non-negative, single-valued function of

**x**

_{‖}, that is differentiable with respect to

*x*

_{1}and

*x*

_{2}, and is sensibly nonzero within a region of radius

*R*on the metal surface

*x*

_{3}= 0. It therefore defines a dielectric defect with a finite footprint on a planar metal surface. We assume that the dielectric function

*ε*

_{3}is real, because the mean free path of a surface plasmon polariton on the planar portion of the vacuum-metal interface is significantly longer than the linear dimensions of the surface defect.

*ω*is incident on the defect from the region

*x*

_{1}< −

*R*of the plane

*x*

_{3}= 0, where we have a planar interface between media 1 and 3 at

*x*

_{3}= 0. The total electric field in the region

*x*

_{3}>

*ζ*(

**x**

_{‖}) is the sum of the incident field and the scattered field,

*iωt*) has been assumed but not indicated explicitly. The two-dimensional wave vector

**k**

_{‖}is given by where is the wavenumber of the surface plasmon polariton of frequency

*ω*at the planar interface between vacuum (

*ε*

_{1}) and a metal (

*ε*

_{3}). It is the solution of the equation

*ε*

_{3}

*β*

_{1}(

*k*

_{‖}) +

*ε*

_{1}

*β*

_{3}(

*k*

_{‖}) = 0. The angle

*ϕ*

_{0}is the azimuthal angle of incidence of the surface plasmon polariton, measured counterclockwise from the positive

*x*

_{1}axis. The functions

*β*(

_{j}*q*

_{‖}) (

*j*= 1, 2, 3) are defined by A caret over a vector indicates that it is a unit vector. Finally,

*a*(

_{p,s}**q**

_{‖}) are the amplitudes of the p- and s-polarized components of the scattered field with respect to the local scattering plane defined by the vectors

**x̂**

_{3}and

**q̂**

_{‖}. The amplitudes

*a*(

_{p}**q**

_{‖}) and

*a*(

_{s}**q**

_{‖}) satisfy the pair of coupled reduced Rayleigh equations [17]:

*ζ*(

**x**

_{‖}) satisfies the assumptions about it stated above. However, they simplify significantly when

*ζ*(

**x**

_{‖}) is a function of

**x**

_{‖}only through its magnitude

*x*

_{‖}. In this case we introduce the expansions where

*ϕ*is the azimuthal angle of the vector

_{p}**p**

_{‖}, measured counterclockwise from the positive

*x*

_{1}axis. We also have the expansions where and

*J*(

_{k}*z*) is a Bessel function of the first kind and order

*k*. The equations satisfied by the amplitudes {

*k*values decouple, reducing the problem to one of solving one-dimensional integral equations.

*k*were solved by transforming them into linear matrix equations following the spirit of the method used in Ref. [18

18. A. A. Maradudin and W. M. Visscher, “Electrostatic and electromagnetic surface shape resonances,” Z. Phys. **B60**, 215–230 (1985) [CrossRef] .

*q*

_{‖}was carried out over a dimensionless variable

*y*defined by

*R*is the effective radius of the defect, and a dimensionless frequency Ω was introduced through

*y*was split into six intervals: (0, Ω), (Ω,

*y*−

_{p}*δ*), (

*y*+

_{p}*δ*, 2

*y*− Ω), (2

_{p}*y*− Ω,

_{p}*ε*

_{2}Ω), (

*ε*

_{2}Ω,

*K*Ω), (

*K*Ω, ∞), where

*K*is an integer (chosen to be 7) and

*ε*

_{2}is the dielectric constant of the defect, plus the contribution from the pole corresponding to the wavenumber of the surface plasmon polariton at

*y*=

*y*. This separation of the region of integration was based on the behavior of

_{p}*β*

_{1}(

*q*

_{‖}) and

*β*

_{3}(

*q*

_{‖}) as functions of the wave numbers

*q*

_{‖}, namely on the values of the latter variable at which they change from purely imaginary to purely real, on the location of the surface plasmon polariton pole, as well as on how the integration to infinite wave number was to be carried out. The integral over the range (

*K*Ω, ∞) was calculated by Gauss-Laguerre integration, while the integrals over the preceding five intervals were calculated by Gauss-Legendre integration. The number of discretization points in each interval was determined by evaluating the integrals over

*q*

_{‖}on the left-hand sides of Eqs. (9a) and (9b), with the expressions for

*k*= 1) appearing in the integrands given by the right-hand sides of these equations, by two different methods. In one method the integral over each interval was evaluated by an integration software package (Mathematica, that uses a method with iteration until it attains a specified accuracy). In the second method a Gaussian integration scheme was used, with the number of abscissas being increased until the same accuracy was achieved. In both of these methods the integrand is known analytically, but the discretization used by them is different. The total number of abscissas used in carrying out the

*q*

_{‖}integrations in the region (0, ∞) produced by this approach was 180. The contribution from the surface plasmon polariton pole, i.e. from the interval (

*y*−

_{p}*δ*,

*y*+

_{p}*δ*), was calculated by the use of the prescription presented in Ref. [11

11. A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a circularly symmetric surface defect,” Phys. Rev. Lett. **78**, 4269–4272 (1997). Erratum: Phys. Rev. Lett. **79**, 2597 (1997) [CrossRef] .

*P*denotes the Cauchy principal part,

*ε*(

*ω*) =

*ε*

_{3}is the dielectric function of the metal, and

*k*

_{‖}is the zero of

*f*(

_{p}*q*

_{‖}). Finally, in carrying out these calculations we set the amplitude

*E*(

_{op}**k**

_{‖}) = 1/(2

*πR*).

*a*(

_{p,s}**q**

_{‖}) have been determined we can use the results to calculate the scattered field in the vacuum region in the far zone by the use of the method described in Ref. [19

19. D. L. Mills, “Attenuation of surface polaritons by surface roughness,” Phys. Rev. B **12**, 4036–4046 (1975). Erratum: Phys. Rev. B**14**, 5539 (1976) [CrossRef] .

**ê**

*and*

_{p}**ê**

*are unit vectors defined by with where (*

_{s}*θ*,

_{x}*ϕ*) are the polar and azimuthal angles of the vector

_{x}**x̂**, while

*q*

_{‖}=

*k*

_{‖}. It is given by an outgoing cylindrical wave

*P*(

_{vac}*θ*,

_{x}*ϕ*) is the power scattered into the vacuum away from the surface in the direction

_{x}**x̂**,

*P*(

_{spp}*ϕ*) is the power scattered into other surface waves in the direction

_{x}**x̂**

_{‖}, and

*P*is the incident power per unit length in the

_{inc}*x*

_{2}direction. These powers are given by In what follows we will neglect the second term on the right-hand side of Eq. (20) due to its smallness relative to the first term.

*I*(

_{k}*z*) is a modified Bessel function of the first kind of order

*k*. The Gaussian defect is characterized by a 1/

*e*half width

*R*= 0.25

*μ*m. It is assumed to be deposited on a planar aluminum surface. It is illuminated by a surface plasmon polariton propagating in the positive

*x*

_{1}direction (

*ϕ*

_{0}= 0°). The wavelength of the incident surface plasmon polariton is

*λ*=632.8 nm, and the dielectric function of aluminum at this wavelength is

20. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B **6**, 4370–4379 (1972) [CrossRef] .

*μ*m radius of the surface defect, and justifies our treating

*ε*

_{3}as real. In these calculations the rotational quantum

*k*ranged in integer setps from −30 to +30.

*σ*(

_{vac}*θ*,

_{x}*ϕ*) for a value of the dielectric constant of the defect

_{x}*ε*

_{2}= 2.69 and (a)

*A/R*= 0.1, (b)

*A/R*= 0.2, (c)

*A/R*= 0.3. For each of these values of

*A/R*the maximum of the intensity of the field radiated into the vacuum occurs at

*θ*= 70°,

_{x}*ϕ*= 0°. More radiation into smaller values of

_{x}*θ*with increasing values of

_{x}*A/R*is seen, especially in Fig. 1(c). The total cross sections for the waves radiated into the vacuum are (a) 0.0021

*μ*m, (b) 0.0057

*μ*m, (c) 0.0099

*μ*m respectively. Thus they increase as the amplitude of the defect increases, with the values of the other parameters kept fixed.

*ε*

_{2}= 5.0, with the remaining parameters maintaining the values they have in Fig. 1 (Fig. 2), the maximum of the intensity of the field scattered into the vacuum remains at

*θ*= 70°,

_{x}*ϕ*= 0°, but the strength of the scattering is nearly doubled in comparison with the corresponding results presented in connection with Fig. 1. The total cross sections for the waves radiated into the vacuum are (a) 0.0040

_{x}*μ*m, (b) 0.0125

*μ*m, (c) 0.0290

*μ*m. Some radiation into the backward directions is seen in Fig. 2(c).

*σ*(

_{spp}*ϕ*) is presented in Fig. 3. The dielectric constant of the defect is

_{x}*ε*

_{2}= 2.69, and (a)

*A/R*= 0.1, (b)

*A/R*= 0.2, (c)

*A/R*= 0.3. We see that there is no scattering of the surface plasmon polariton into the backward direction for all three values of

*A/R*: all of the scattering is into the forward direction. These results are due presumably to the transparency of the dielectric defect. The shapes of these scattering patterns do not change with increasing values of

*A/R*, but the strength of the scattering does. The total cross sections for the scattering of the incident surface plasmon polariton into other surface plasmon polaritons are (a) 0.0019

*μ*m, (b) 0.0053

*μ*m, (c) 0.0087

*μ*m. These values are nearly the same as the values of

*σ*(

_{vac}*θ*,

_{x}*ϕ*) for the corresponding parameter values in Fig. 3.

_{x}*σ*(

_{spp}*ϕ*) is observed when

_{x}*ε*

_{2}is increased to

*ε*

_{2}= 5.0. This is seen from the results presented in Fig. 4. The values of

*A/R*for which these results are calculated are (a)

*A/R*= 0.1, (b)

*A/R*= 0.2, (c)

*A/R*= 0.3. All of the scattering is in the forward direction. The shapes of the scattering patterns do not change as the value of

*A/R*increases, while the strength of the scattering increases with increasing values of

*A/R*. The total cross sections for the scattering of the incident surface plasmon polariton into other surface plasmon polaritons are (a) 0.0035

*μ*m, (b) 0.0100

*μ*m, (c) 0.0176

*μ*m. For each value of

*A/R*increasing

*ε*

_{2}from 2.69 to 5.0 nearly doubles the total scattering cross section from the value it has for the data used in obtaining the corresponding results in connection with Fig. 3.

**E**(

**x**|

*ω*)|

^{2}as a function of

**x**

_{‖}at 5 nm above the surface profile (

*x*

_{3}=

*ζ*(

**x**

_{‖}) + 5nm), for

*ε*

_{2}= 2.69 and 5.0, respectively, while (a)

*A/R*= 0.1, (b)

*A/R*= 0.2, (c)

*A/R*= 0.3. Both figures show a weak diffractive spreading of the intensity of the field after its interaction with the defect. There is very little indication of the scattering of the surface plasmon polariton in backward directions, in agreement with the results presented in Figs. 1–2 and 3–4.

*a*(

_{p}**q**

_{‖}) and

*a*(

_{s}**q**

_{‖}) the expressions for them obtained in the small roughness limit of the first Born approximation, namely where The second of Eqs. (24) gives the expression for

*ζ̂*(

**Q**

_{‖}) corresponding to the Gaussian surface profile function (21).

*σ*(

_{vac}*θ*,

_{x}*ϕ*) in the form

_{x}*A/R*) of the defect. It is an increasing function of

*ε*

_{2}, and has a maximum at (

*θ*,

_{x}*ϕ*) = (70.75°, 0°) for the values of the parameters assumed in obtaining Fig. 1, and at (70.5, 0°) for the values assumed in obtaining Fig. 2. The insensitivity of these angles to changes of

_{x}*ε*

_{2}, and their closeness to the angular position of the maximum in these figures, namely (70°, 0°), is gratifying, given the simplicity of this approximate calculation.

*σ*(

_{spp}*ϕ*) in the form

_{x}*ε*

_{3}| +

*ε*

_{2}cos

*ϕ*)

_{x}^{2}favors scattering into the forward direction by a small amount, because of the large value of |

*ε*

_{3}|, the suppression of scattering into backward directions is due entirely to the factor

*ζ̂*(

**Q**

_{‖}), Eq. (24). The cross section (27) is proportional to the square of the defects aspect ratio, and is an increasing function of

*ε*

_{2}.

*ω*

^{5}can be understood in the following way. The cross section for the Rayleigh scattering of a volume wave from a d-dimensional object is proportional to

*ω*

^{d+1}. Since the scatterer in the present case is defined by

*x*

_{3}−

*ζ*(

**x**

_{‖}) = 0, it is a three-dimensional scatterer as far as Rayleigh scattering is concerned. The additional factor of

*ω*arises because the decay length of the surface plasmon polariton into the vacuum is proportional to its wavelength parallel to the surface, which reduces the volume within which its interaction with the defect occurs [21

21. A. A. Maradudin and D. L. Mills, “Attenuation of Rayleigh surface waves by surface roughness,” Ann. Phys. (N.Y.) **100**262–309 (1976), Ref. 9 [CrossRef] .

*θ*= 70°. This value is independent of the aspect ratios and dielectric constants of the defect assumed in our work. It is a significantly larger angle than the angle

_{x}*θ*= 28° at which the corresponding maxima occurs in the scattering of a surface plasmon polariton from a circularly symmetric Gaussian indentation (dimple) in a planar metal surface [11

_{x}11. A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a circularly symmetric surface defect,” Phys. Rev. Lett. **78**, 4269–4272 (1997). Erratum: Phys. Rev. Lett. **79**, 2597 (1997) [CrossRef] .

*θ*

_{0}= 70° [22

22. M. Kretschmann, T. A. Leskova, and A.A. Maradudin, “Excitation of surface plasmon polaritons by the scattering of a volume electromagnetic beam from a circularly symmetric defect on a planar metal surface,” Proc. SPIE **4447**, 24–33 (2001) [CrossRef] .

**78**, 4269–4272 (1997). Erratum: Phys. Rev. Lett. **79**, 2597 (1997) [CrossRef] .

*k*[14].

## APPENDIX

*x*

_{3}>

*d*+

*ζ*(

**x**

_{‖}), where

**x**

_{‖}= (

*x*

_{1},

*x*

_{2}, 0), whose dielectric constant is

*ε*

_{1}, on a dielectric film in the region 0 <

*x*

_{3}<

*d*+

*ζ*(

**x**

_{‖}) whose dielectric constant is

*ε*

_{2}, that is deposited on a semi-infinite metal whose dielectric constant is

*ε*

_{3}in the region

*x*

_{3}< 0. The electric fields in these regions are given by for

*x*

_{3}>

*d*+

*ζ*(

**x**

_{‖}), for 0 <

*x*

_{3}<

*d*+

*ζ*(

**x**

_{‖}), and for

*x*

_{3}< 0. In these equations we have introduced the wave vectors where (

*j*= 1, 2, 3) The boundary conditions on the fields at the interface

*x*

_{3}=

*d*+

*ζ*(

**x**

_{‖}) can be written where We now take the vector cross product of Eq. (A.6) with

*ε*

_{2}

**P**

^{+}(

**p**

_{‖})exp[−

*i*

**P**

^{+}(

**p**

_{‖}) ·

**x**

*]; we then take the product of Eq. (A.7) with −*

_{ζ}*iε*

_{2}exp[−

*i*

**P**

^{+}(

**p**

_{‖}) ·

**x**

*]; and we finally multiply Eq. (A.7) by −*

_{ζ}**P**

^{+}(

**p**

_{‖})exp[−

*i*

**P**

^{+}(

**p**

_{‖}) ·

**x**

*]. In these expressions we have introduced the vectors*

_{ζ}**P**

^{+}(

**p**

_{‖}) =

**p**

_{‖}+

*α*

_{2}(

*p*

_{‖})

**x̂**

_{3}, where

**p**

_{‖}is an arbitrary two-dimensional wave vector, and

**x**

*=*

_{ζ}**x**

_{‖}+

*ζ*(

**x**

_{‖})

**x̂**

_{3}. We add the three equations obtained in this manner and integrate the sum over

**x**

_{‖}. In this way we obtain the equation

*ε*

_{2}

**P**

^{−}(

**p**

_{‖})exp[−

*i*

**P**

^{−}(

**p**

_{‖}) ·

**x**

*]; we next multiply Eq. (A.7) by −*

_{ζ}*iε*

_{2}exp[−

*i*

**P**

^{−}(

**p**

_{‖}) ·

**x**

*]; and we finally multiply Eq. (A.8) by −*

_{ζ}**P**

^{−}(

**p**

_{‖})exp[−

*i*

**P**

^{−}(

**p**

_{‖}) ·

**x**

*]. Here, the vector*

_{ζ}**P**

^{−}(

**p**

_{‖}) is defined by

**P**

^{−}(

**p**

_{‖}) =

**p**

_{‖}−

*α*

_{2}(

*p*

_{‖})

**x̂**

_{3}. We add the resulting three equations and integrate the sum over

**x**

_{‖}to obtain

*x*

_{3}= 0, which can be written These three equations yield three equations for the Fourier amplitudes

**F**

^{+}(

**q**

_{‖}),

**F**

^{−}(

**q**

_{‖}),

**B**(

**q**

_{‖}), namely We eliminate

**B**(

**q**

_{‖}) from these equations and obtain the pair of equations where When we substitute the expressions for

**F**

^{+}(

**q**

_{‖}) and

**F**

^{−}(

**q**

_{‖}) obtained from Eqs. (A.10) and (A.12), respectively, into Eqs. (A.19) and (A.20) we obtain the pair of equations for

**A**(

**q**

_{‖})

**E**

_{0}(

**k**

_{‖}) and

**A**(

**q**

_{‖}) in the forms The coefficients

*E*

_{0p,s}(

**k**

_{‖}) and

*A*(

_{p,s}**q**

_{‖}) are the amplitudes of the p- and s-polarized components of the incident and scattered fields with respect to the planes of incidence and scattering, respectively. The substitution of these representations into Eqs. (A.22) and (A.23) yields a pair of equations for

*A*(

_{p}*q*

_{‖}) and

*A*(

_{s}**q**

_{‖}), which we write as

16. T. Nordam, P. A. Letnes, I. Simonsen, and A. A. Maradudin, “Satellite peaks in the scattering of light from the two-dimensional randomly rough surface of a dielectric film on a planar metal surface,” Opt. Express **20**, 11336– 11350 (2012) [CrossRef] [PubMed] .

*d*= 0 and restrict

*ζ*(

**x**

_{‖}) to be a non-negative function of

**x**

_{‖}. We also set

*E*

_{0}

*(*

_{s}**k**

_{‖}) ≡ 0 because the incident field is p polarized, and then rewrite

*I*(

*γ*|

**Q**

_{‖}) as where The relevant elements of the matrices

**M**(

**p**

_{‖}|

**q**

_{‖}) and

**N**(

**p**

_{‖}|

**k**

_{‖}) then become where

*ε*

_{3}

*β*

_{1}(

*k*

_{‖}) +

*ε*

_{1}

*β*

_{3}(

*k*

_{‖}) = 0. This is the dispersion relation for surface plasmon polaritons at a planar vacuum (

*ε*

_{1})-metal (

*ε*

_{3}) interface.

## Acknowledgments

## References and links

1. | W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature (London) |

2. | Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. |

3. | I. I. Smolyaninov, C. C. Davis, and A. V. Zayats, “Image formation in surface plasmon polariton mirrors: applications in high resolution optical microscopy,” New. J. Phys. |

4. | E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science |

5. | I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Imaging and focusing properties of plasmonic metamaterial devices,” Phys. Rev. B |

6. | H. Kim, J. Hahn, and B. Lee, “Focusing properties of surface plasmon polariton floating dielectric lenses,” Opt. Express |

7. | J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I.-C. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature |

8. | I. Chremmos, “Magnetic field integral equation analysis of surface plasmon scattering by rectangular dielectric channel discontinuities,” J. Opt. Soc. Am. A |

9. | G. Brucoli and L. Martín-Moreno, “Comparative study of surface plasmon polariton scattering by shallow ridges and grooves,” Phys. Rev. B |

10. | G. Brucoli and L. Martín-Moreno, “Effect of defect depth on surface plasmon scattering by subwavelength surface defects,” Phys. Rev. B |

11. | A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a circularly symmetric surface defect,” Phys. Rev. Lett. |

12. | E. Kretschmann and H. Raether, “Radiative decay of non radiative surface plasmons excited by light,” Z. Naturforsch |

13. | M. Paulus and O. J. F. Martin, “Light propagation and scattering in stratified media: a Green’s tensor approach,” J. Opt. Soc. Am. A |

14. | B. Baumeier, F. Huerkamp, T. A. Leskova, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a localized dielectric surface defect studied using an effective boundary condition,” Phys. Rev. |

15. | I. I. Smolyaninov, J. E. Elliott, A.V. Zayats, and C. C. Davis, “Far-field optical microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons,” Phys. Rev. Lett. |

16. | T. Nordam, P. A. Letnes, I. Simonsen, and A. A. Maradudin, “Satellite peaks in the scattering of light from the two-dimensional randomly rough surface of a dielectric film on a planar metal surface,” Opt. Express |

17. | T. A. Leskova and A. A. Maradudin (unpublished work). |

18. | A. A. Maradudin and W. M. Visscher, “Electrostatic and electromagnetic surface shape resonances,” Z. Phys. |

19. | D. L. Mills, “Attenuation of surface polaritons by surface roughness,” Phys. Rev. B |

20. | P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B |

21. | A. A. Maradudin and D. L. Mills, “Attenuation of Rayleigh surface waves by surface roughness,” Ann. Phys. (N.Y.) |

22. | M. Kretschmann, T. A. Leskova, and A.A. Maradudin, “Excitation of surface plasmon polaritons by the scattering of a volume electromagnetic beam from a circularly symmetric defect on a planar metal surface,” Proc. SPIE |

**OCIS Codes**

(240.5420) Optics at surfaces : Polaritons

(240.6680) Optics at surfaces : Surface plasmons

(250.5403) Optoelectronics : Plasmonics

(290.5825) Scattering : Scattering theory

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: February 11, 2013

Revised Manuscript: March 26, 2013

Manuscript Accepted: April 2, 2013

Published: April 12, 2013

**Citation**

Rodrigo E. Arias and Alexei A. Maradudin, "Scattering of a surface plasmon polariton by a localized dielectric surface defect," Opt. Express **21**, 9734-9756 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-8-9734

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### References

- W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature (London)424, 824–830 (2003). [CrossRef]
- Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett.5, 1726–1729 (2005). [CrossRef] [PubMed]
- I. I. Smolyaninov, C. C. Davis, and A. V. Zayats, “Image formation in surface plasmon polariton mirrors: applications in high resolution optical microscopy,” New. J. Phys.7, 175 (2005). [CrossRef]
- E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science311, 189–193 (2006). [CrossRef] [PubMed]
- I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Imaging and focusing properties of plasmonic metamaterial devices,” Phys. Rev. B76, 205424, (2007). [CrossRef]
- H. Kim, J. Hahn, and B. Lee, “Focusing properties of surface plasmon polariton floating dielectric lenses,” Opt. Express16, 3049–3057 (2008). [CrossRef] [PubMed]
- J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I.-C. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature460, 498–501 (2009). [CrossRef]
- I. Chremmos, “Magnetic field integral equation analysis of surface plasmon scattering by rectangular dielectric channel discontinuities,” J. Opt. Soc. Am. A27, 85–94 (2010). [CrossRef]
- G. Brucoli and L. Martín-Moreno, “Comparative study of surface plasmon polariton scattering by shallow ridges and grooves,” Phys. Rev. B83, 045422 (2011). [CrossRef]
- G. Brucoli and L. Martín-Moreno, “Effect of defect depth on surface plasmon scattering by subwavelength surface defects,” Phys. Rev. B83, 075433 (2011). [CrossRef]
- A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a circularly symmetric surface defect,” Phys. Rev. Lett.78, 4269–4272 (1997). Erratum: Phys. Rev. Lett. 79, 2597 (1997). [CrossRef]
- E. Kretschmann and H. Raether, “Radiative decay of non radiative surface plasmons excited by light,” Z. NaturforschA23, 2135–2136 (1963).
- M. Paulus and O. J. F. Martin, “Light propagation and scattering in stratified media: a Green’s tensor approach,” J. Opt. Soc. Am. A18, 854–861 (2001). [CrossRef]
- B. Baumeier, F. Huerkamp, T. A. Leskova, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a localized dielectric surface defect studied using an effective boundary condition,” Phys. Rev.A84, 013810 (2011).
- I. I. Smolyaninov, J. E. Elliott, A.V. Zayats, and C. C. Davis, “Far-field optical microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons,” Phys. Rev. Lett.94, 057401 (2005). [CrossRef] [PubMed]
- T. Nordam, P. A. Letnes, I. Simonsen, and A. A. Maradudin, “Satellite peaks in the scattering of light from the two-dimensional randomly rough surface of a dielectric film on a planar metal surface,” Opt. Express20, 11336– 11350 (2012). [CrossRef] [PubMed]
- T. A. Leskova and A. A. Maradudin (unpublished work).
- A. A. Maradudin and W. M. Visscher, “Electrostatic and electromagnetic surface shape resonances,” Z. Phys.B60, 215–230 (1985). [CrossRef]
- D. L. Mills, “Attenuation of surface polaritons by surface roughness,” Phys. Rev. B12, 4036–4046 (1975). Erratum: Phys. Rev. B14, 5539 (1976). [CrossRef]
- P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370–4379 (1972). [CrossRef]
- A. A. Maradudin and D. L. Mills, “Attenuation of Rayleigh surface waves by surface roughness,” Ann. Phys. (N.Y.)100262–309 (1976), Ref. 9. [CrossRef]
- M. Kretschmann, T. A. Leskova, and A.A. Maradudin, “Excitation of surface plasmon polaritons by the scattering of a volume electromagnetic beam from a circularly symmetric defect on a planar metal surface,” Proc. SPIE4447, 24–33 (2001). [CrossRef]

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