Abstract

We have investigated the focusing properties of surface plasmon polariton floating dielectric lenses. An analysis of the scattering characteristics of surface plasmon polaritons using a floating dielectric block shows that the air-gap thickness between a floating dielectric block and a metal substrate can be an effective dynamic variable for modulating the amplitude and phase of the transmission coefficient of the surface plasmon polaritons. This property can be used to realize a variable-focusing surface plasmon dielectric lens with the air-gap thickness as the dynamic variable. The focusing properties of a Fresnel lens and a parabolic lens with respect to the air-gap thickness are compared and analyzed.

© 2008 Optical Society of America

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References

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  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
    [Crossref] [PubMed]
  2. P. Berini, R. Charbonneau, and N. Lahoud, “Long-range surface plasmons on ultrathin membranes,” Nano Lett. 7, 1376–1380 (2007).
    [Crossref] [PubMed]
  3. I.-M. Lee, J. Jung, J. Park, H. Kim, and B. Lee, “Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves,” Opt. Express 15, 16596–16603 (2007).
    [Crossref] [PubMed]
  4. J. Takahara and T. Kobayashi, “Low-dimensional optical waves and nano-optical circuits,” Opt. Photon. News 15, 54–59 (2004).
    [Crossref]
  5. S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric structure surface gratings,” Appl. Phys. Lett. 90, 051113 (2007).
    [Crossref]
  6. S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
    [Crossref]
  7. I. P. Radko, S. I. Bozhevolnyi, A. B. Evlyukhin, and A. Boltasseva, “Surface plasmon polariton beam focusing with parabolic nanoparticle chains,” Opt. Express 15, 6576–6582 (2007).
    [Crossref] [PubMed]
  8. W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/bear-field conversion,” Appl. Phys. Lett. 86, 181108 (2005).
    [Crossref]
  9. R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young’s double-slit experiment,” Nature Nanotech. 2, 426–429 (2007).
    [Crossref]
  10. F. Lopez-Tejeria, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Padko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nature Phys. 3, 324–328 (2007).
    [Crossref]
  11. P. Lalanne and E. Silberstein, “Fourier-modal methods applied to waveguide computational problems,” Opt. Lett. 25, 1092–1094 (2000).
    [Crossref]
  12. H. Kim, I.-M. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” J. Opt. Soc. Am A 24, 2313–2327 (2007).
    [Crossref]
  13. J. W. Goodman, Introduction to Fourier Optics, 3rd ed., (Roberts & Company Publishers, Englewood, 2005).

2008 (1)

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[Crossref]

2007 (7)

I. P. Radko, S. I. Bozhevolnyi, A. B. Evlyukhin, and A. Boltasseva, “Surface plasmon polariton beam focusing with parabolic nanoparticle chains,” Opt. Express 15, 6576–6582 (2007).
[Crossref] [PubMed]

R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young’s double-slit experiment,” Nature Nanotech. 2, 426–429 (2007).
[Crossref]

F. Lopez-Tejeria, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Padko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nature Phys. 3, 324–328 (2007).
[Crossref]

P. Berini, R. Charbonneau, and N. Lahoud, “Long-range surface plasmons on ultrathin membranes,” Nano Lett. 7, 1376–1380 (2007).
[Crossref] [PubMed]

I.-M. Lee, J. Jung, J. Park, H. Kim, and B. Lee, “Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves,” Opt. Express 15, 16596–16603 (2007).
[Crossref] [PubMed]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric structure surface gratings,” Appl. Phys. Lett. 90, 051113 (2007).
[Crossref]

H. Kim, I.-M. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” J. Opt. Soc. Am A 24, 2313–2327 (2007).
[Crossref]

2005 (1)

W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/bear-field conversion,” Appl. Phys. Lett. 86, 181108 (2005).
[Crossref]

2004 (1)

J. Takahara and T. Kobayashi, “Low-dimensional optical waves and nano-optical circuits,” Opt. Photon. News 15, 54–59 (2004).
[Crossref]

2003 (1)

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

2000 (1)

Barnes, W. L.

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

Berini, P.

P. Berini, R. Charbonneau, and N. Lahoud, “Long-range surface plasmons on ultrathin membranes,” Nano Lett. 7, 1376–1380 (2007).
[Crossref] [PubMed]

Boltasseva, A.

Bozhevolnyi, S. I.

I. P. Radko, S. I. Bozhevolnyi, A. B. Evlyukhin, and A. Boltasseva, “Surface plasmon polariton beam focusing with parabolic nanoparticle chains,” Opt. Express 15, 6576–6582 (2007).
[Crossref] [PubMed]

F. Lopez-Tejeria, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Padko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nature Phys. 3, 324–328 (2007).
[Crossref]

Brongersma, M. L.

R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young’s double-slit experiment,” Nature Nanotech. 2, 426–429 (2007).
[Crossref]

Charbonneau, R.

P. Berini, R. Charbonneau, and N. Lahoud, “Long-range surface plasmons on ultrathin membranes,” Nano Lett. 7, 1376–1380 (2007).
[Crossref] [PubMed]

Dereux, A.

F. Lopez-Tejeria, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Padko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nature Phys. 3, 324–328 (2007).
[Crossref]

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

Devaux, E.

F. Lopez-Tejeria, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Padko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nature Phys. 3, 324–328 (2007).
[Crossref]

Ebbesen, T. W.

F. Lopez-Tejeria, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Padko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nature Phys. 3, 324–328 (2007).
[Crossref]

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

Evlyukhin, A. B.

Garcia-Vidal, F. J.

F. Lopez-Tejeria, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Padko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nature Phys. 3, 324–328 (2007).
[Crossref]

Gonzalez, M. U.

F. Lopez-Tejeria, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Padko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nature Phys. 3, 324–328 (2007).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed., (Roberts & Company Publishers, Englewood, 2005).

Jung, J.

Kim, H.

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[Crossref]

H. Kim, I.-M. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” J. Opt. Soc. Am A 24, 2313–2327 (2007).
[Crossref]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric structure surface gratings,” Appl. Phys. Lett. 90, 051113 (2007).
[Crossref]

I.-M. Lee, J. Jung, J. Park, H. Kim, and B. Lee, “Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves,” Opt. Express 15, 16596–16603 (2007).
[Crossref] [PubMed]

Kim, S.

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[Crossref]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric structure surface gratings,” Appl. Phys. Lett. 90, 051113 (2007).
[Crossref]

Kobayashi, T.

J. Takahara and T. Kobayashi, “Low-dimensional optical waves and nano-optical circuits,” Opt. Photon. News 15, 54–59 (2004).
[Crossref]

Krenn, J. R.

F. Lopez-Tejeria, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Padko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nature Phys. 3, 324–328 (2007).
[Crossref]

Lahoud, N.

P. Berini, R. Charbonneau, and N. Lahoud, “Long-range surface plasmons on ultrathin membranes,” Nano Lett. 7, 1376–1380 (2007).
[Crossref] [PubMed]

Lalanne, P.

Lee, B.

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[Crossref]

H. Kim, I.-M. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” J. Opt. Soc. Am A 24, 2313–2327 (2007).
[Crossref]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric structure surface gratings,” Appl. Phys. Lett. 90, 051113 (2007).
[Crossref]

I.-M. Lee, J. Jung, J. Park, H. Kim, and B. Lee, “Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves,” Opt. Express 15, 16596–16603 (2007).
[Crossref] [PubMed]

Lee, I.-M.

I.-M. Lee, J. Jung, J. Park, H. Kim, and B. Lee, “Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves,” Opt. Express 15, 16596–16603 (2007).
[Crossref] [PubMed]

H. Kim, I.-M. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” J. Opt. Soc. Am A 24, 2313–2327 (2007).
[Crossref]

Lim, Y.

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[Crossref]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric structure surface gratings,” Appl. Phys. Lett. 90, 051113 (2007).
[Crossref]

Lopez-Tejeria, F.

F. Lopez-Tejeria, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Padko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nature Phys. 3, 324–328 (2007).
[Crossref]

Martin-Moreno, L.

F. Lopez-Tejeria, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Padko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nature Phys. 3, 324–328 (2007).
[Crossref]

Nomura, W.

W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/bear-field conversion,” Appl. Phys. Lett. 86, 181108 (2005).
[Crossref]

Ohtsu, M.

W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/bear-field conversion,” Appl. Phys. Lett. 86, 181108 (2005).
[Crossref]

Padko, I. P.

F. Lopez-Tejeria, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Padko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nature Phys. 3, 324–328 (2007).
[Crossref]

Park, J.

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[Crossref]

I.-M. Lee, J. Jung, J. Park, H. Kim, and B. Lee, “Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves,” Opt. Express 15, 16596–16603 (2007).
[Crossref] [PubMed]

Radko, I. P.

Rodrigo, S. G.

F. Lopez-Tejeria, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Padko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nature Phys. 3, 324–328 (2007).
[Crossref]

Silberstein, E.

Takahara, J.

J. Takahara and T. Kobayashi, “Low-dimensional optical waves and nano-optical circuits,” Opt. Photon. News 15, 54–59 (2004).
[Crossref]

Weeber, J. C.

F. Lopez-Tejeria, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Padko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nature Phys. 3, 324–328 (2007).
[Crossref]

Yatsui, T.

W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/bear-field conversion,” Appl. Phys. Lett. 86, 181108 (2005).
[Crossref]

Zia, R.

R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young’s double-slit experiment,” Nature Nanotech. 2, 426–429 (2007).
[Crossref]

Appl. Phys. Lett. (3)

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric structure surface gratings,” Appl. Phys. Lett. 90, 051113 (2007).
[Crossref]

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[Crossref]

W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/bear-field conversion,” Appl. Phys. Lett. 86, 181108 (2005).
[Crossref]

J. Opt. Soc. Am A (1)

H. Kim, I.-M. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” J. Opt. Soc. Am A 24, 2313–2327 (2007).
[Crossref]

Nano Lett. (1)

P. Berini, R. Charbonneau, and N. Lahoud, “Long-range surface plasmons on ultrathin membranes,” Nano Lett. 7, 1376–1380 (2007).
[Crossref] [PubMed]

Nature (1)

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

Nature Nanotech. (1)

R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young’s double-slit experiment,” Nature Nanotech. 2, 426–429 (2007).
[Crossref]

Nature Phys. (1)

F. Lopez-Tejeria, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Padko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nature Phys. 3, 324–328 (2007).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Opt. Photon. News (1)

J. Takahara and T. Kobayashi, “Low-dimensional optical waves and nano-optical circuits,” Opt. Photon. News 15, 54–59 (2004).
[Crossref]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed., (Roberts & Company Publishers, Englewood, 2005).

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Figures (5)

Fig. 1.
Fig. 1.

Scattering of surface plasmon polariton eigenmode by a finite size dielectric block

Fig. 2.
Fig. 2.

(a) Amplitude modulation profile and (b) phase modulation profile with respect to the air-gap thickness, h, and length, t. Here, the thickness of the dielectric block is 1µm. (c) x-polarization and z-polarization electric field distributions in the case of an air-gap thickness of 0nm. (d) x-polarization and z-polarization electric field distribution in the case of an air-gap thickness of 150nm.

Fig. 3.
Fig. 3.

(a) Amplitude modulation profile, and (b) phase modulation profile with respect to air-gap thickness, h, and length, t. Here, the thickness of the dielectric block is 2µm. (c) x-polarization and z-polarization electric field distribution in the case of an air-gap thickness of 0nm. (d) x-polarization and z-polarization electric field distributions in the case of an air-gap thickness of 150nm.

Fig. 4.
Fig. 4.

Surface plasmon polariton focusing using a floating dielectric lens.

Fig. 5.
Fig. 5.

(a) Focusing using a floating parabolic lens with a focal length of 10µm, (b) focusing using a floating Fresnel lens with a focal length of 10µm, (c) focusing using a floating parabolic lens with a focal length of 5µm, and (d) focusing using a floating Fresnel lens with a focal length of 5µm.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

E R = n C n - E n - ( x , y , z ) for z < 0 ,
E T = C n spp + E n spp + ( x , y , z t ) + Σ n n spp C n + E n + ( x , y , z t ) for z > t .
C n spp + ( h , t ) = A ( h , t ) exp ( j Φ ( h , t ) ) ,
ϕ ( h , y ) = Φ ( h , t ( y ) ) k spp t ( y ) ,
Γ ( h , y ) = A spp ( l t ( y ) ) A ( h , t ( y ) ) ,
Φ ( h , t ( y ) ) Re ( k spp ) t ( y ) = Re ( k spp ) ( f c 2 + y max 2 f c 2 + y 2 ) ,
Φ ( h , t ( y ) ) Re ( k spp ) t ( y )
= Re ( k spp ) ( f c 2 + y max 2 f c 2 + y 2 ) 2 π [ Re ( k spp ) ( f c 2 + y max 2 f c 2 + y 2 ( 2 π ) ) ] ,
Π ( α ; h ) = Γ ( h , y ) exp ( j ϕ ( h , y ) ) exp ( j 2 π α y ) d y ,
E ( y , z ; h ) = Π ( α ; h ) exp ( j 2 π α y ) exp ( j ( k spp ) 2 ( 2 π α ) 2 z ) d α , for     z > 0 .
T e = 100 × Π ( α ; h ) 2 Re ( ( k spp ) 2 ( 2 π α ) 2 ) Re ( k spp ) d α ( % ) .

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