Abstract

The normal-mode-analysis method is used to model the radiative spreading of long-range surface plasmon polariton modes injected into regions where the bound surface mode is cutoff or radiative. Mode cutoff is induced by an asymmetry between the index of refraction of the top cladding layer and that of the bottom. The analysis was performed at λ0=1.55μm for infinite-width (slab) metal waveguides where the metal was Au and the bounding dielectrics were SiO2. Results show that a change in insertion loss of >20dB is possible for an appropriate waveguide geometry and dielectric asymmetry.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  32. B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44, 13556-13572 (1991).
    [CrossRef]
  33. C. Chen, P. Berini, D. Feng, S. Tanez, and V. P. Tzolov, "Efficient and accurate numerical analysis of multilayer planar optical waveguides in lossy anisotropic media," Opt. Express 7, 260-272 (2000).
    [CrossRef] [PubMed]
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    [CrossRef]
  39. G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, "The optics of surface plasmons," J. Phys. Colloq. 4, 233-241 (1984).
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2006 (1)

I. Breukelaar, R. Charbonneau, and P. Berini, "Long-range surface plasmon-polariton mode cutoff and radiation," Appl. Phys. Lett. 88, 051119 (2006).
[CrossRef]

2005 (1)

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

2003 (2)

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, "Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668-670 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature (London) 424, 824-830 (2003).
[CrossRef]

2002 (1)

I. V. Novikov and A. A. Maradudin, "Channel polaritons," Phys. Rev. B 66, 923-925 (2002).
[CrossRef]

2001 (4)

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

N. A. Janunts and Kh. V. Nerkararyan, "Modulation of light radiation during input into waveguide by resonance excitation of surface plasmons," Appl. Phys. Lett. 79, 299-301 (2001).
[CrossRef]

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures," Phys. Rev. B 63, 125417 (2001).
[CrossRef]

J. P. Kottmann and O. J. F. Martin, "Plasmon resonant coupling in metallic nanowires," Opt. Express 8, 655-663 (2001).
[CrossRef] [PubMed]

2000 (3)

1999 (1)

1998 (1)

1995 (2)

R. E. Smith and S. N. Houde-Walter, "Failure of the leaky-mode representation near the waveguide mode cutoff," Opt. Lett. 20, 1133-1135 (1995).
[CrossRef] [PubMed]

D. F. G. Gallagher and T. P. Felici, "Eigenmode expansion methods for simulation of optical propagation in photonics: pros and cons," Proc. SPIE 4987, 69-82 (1995).
[CrossRef]

1994 (1)

C. Jung, S. Yee, and K. Kuhn, "Integrated optics waveguide modulator based on surface plasmon resonance," J. Lightwave Technol. 12, 1802-1806 (1994).
[CrossRef]

1991 (3)

F. Yang, J. R. Sambles, and G. W. Bradberry, "Long-range surface modes supported by thin films," Phys. Rev. B 44, 5855-5872 (1991).
[CrossRef]

K. Welford, "Surface plasmon polaritons and their uses," Opt. Quantum Electron. 23, 1-27 (1991).
[CrossRef]

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44, 13556-13572 (1991).
[CrossRef]

1990 (2)

F. A. Burton and S. A. Cassidy, "A complete description of the dispersion relation for thin metal film plasmon-polaritons," J. Lightwave Technol. 8, 1843-1849 (1990).
[CrossRef]

J. Johnstone, G. Stewart, T. Hart, and B. Culshaw, "Surface plasmon polaritons in thin metal films and their role in fiber optic polarizing devices," J. Lightwave Technol. 8, 538-543 (1990).
[CrossRef]

1988 (1)

1987 (1)

R. A. Innes and J. R. Sambles, "Optical characterization of gold using surface plasmon polaritons," J. Phys. F: Met. Phys. 17, 277-287 (1987).
[CrossRef]

1986 (2)

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

L. Wendler and R. Haupt, "Long-range surface plasmon-polaritons in asymmetric layer structures," J. Appl. Phys. 59, 3289-3291 (1986).
[CrossRef]

1984 (1)

G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, "The optics of surface plasmons," J. Phys. Colloq. 4, 233-241 (1984).

1981 (1)

D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

1969 (1)

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

1968 (2)

A. Otto, "Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection," Z. Phys. 216, 398-410 (1968).
[CrossRef]

E. Kretschmann and H. Raether, "Radiative decay of non-radiative surface plasmons excited by light," Z. Naturforsch. A Z. Naturforsch. 23, 2135-2136 (1968).

1967 (1)

K. L. Kliewer and R. Fuchs, "Collective electronic motion in a metallic slab," Phys. Rev. 153, 498-153 (1967).
[CrossRef]

1960 (1)

E. A. Stern and R. A. Ferrell, "Surface plasma oscillations of a degenerate electron gas," Phys. Rev. 120, 130-l36 (1960).
[CrossRef]

1959 (1)

C. J. Powell and J. B. Swan, "Origin of the characteristic electron energy losses in aluminum," Phys. Rev. 115, 869-875 (1959).
[CrossRef]

1957 (1)

R. H. Ritchie, "Plasma losses by fast electrons in thin films," Phys. Rev. 106, 874-881 (1957).
[CrossRef]

1941 (1)

Atwater, H. A.

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Aussenegg, F. R.

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature (London) 424, 824-830 (2003).
[CrossRef]

Berini, P.

I. Breukelaar, R. Charbonneau, and P. Berini, "Long-range surface plasmon-polariton mode cutoff and radiation," Appl. Phys. Lett. 88, 051119 (2006).
[CrossRef]

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures," Phys. Rev. B 63, 125417 (2001).
[CrossRef]

C. Chen, P. Berini, D. Feng, S. Tanez, and V. P. Tzolov, "Efficient and accurate numerical analysis of multilayer planar optical waveguides in lossy anisotropic media," Opt. Express 7, 260-272 (2000).
[CrossRef] [PubMed]

R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka-Shrzek, "Experimental observation of plasmon-polariton waves supported by a thin metal film of finite width," Opt. Lett. 25, 844-846 (2000).
[CrossRef]

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures," Phys. Rev. B 61, 10484-10503 (2000).
[CrossRef]

P. Berini, "Plasmon-polariton modes guided by a metal film of finite width," Opt. Lett. 24, 1011-1013 (1999).
[CrossRef]

Berolo, E.

Bozhevolnyi, S. I.

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, "Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668-670 (2003).
[CrossRef]

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Bradberry, G. W.

F. Yang, J. R. Sambles, and G. W. Bradberry, "Long-range surface modes supported by thin films," Phys. Rev. B 44, 5855-5872 (1991).
[CrossRef]

Breukelaar, I.

I. Breukelaar, R. Charbonneau, and P. Berini, "Long-range surface plasmon-polariton mode cutoff and radiation," Appl. Phys. Lett. 88, 051119 (2006).
[CrossRef]

I. Breukelaar, "Surface plasmon-polaritons in thin metal strips and slabs: Waveguiding and mode cutoff," M.A.Sc. thesis (Faculty of Engineering, University of Ottawa, Ottawa, Ontario, Canada, 2004).

Burke, J. J.

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

Burton, F. A.

F. A. Burton and S. A. Cassidy, "A complete description of the dispersion relation for thin metal film plasmon-polaritons," J. Lightwave Technol. 8, 1843-1849 (1990).
[CrossRef]

Cassidy, S. A.

F. A. Burton and S. A. Cassidy, "A complete description of the dispersion relation for thin metal film plasmon-polaritons," J. Lightwave Technol. 8, 1843-1849 (1990).
[CrossRef]

Charbonneau, R.

I. Breukelaar, R. Charbonneau, and P. Berini, "Long-range surface plasmon-polariton mode cutoff and radiation," Appl. Phys. Lett. 88, 051119 (2006).
[CrossRef]

R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka-Shrzek, "Experimental observation of plasmon-polariton waves supported by a thin metal film of finite width," Opt. Lett. 25, 844-846 (2000).
[CrossRef]

Chen, C.

Culshaw, B.

J. Johnstone, G. Stewart, T. Hart, and B. Culshaw, "Surface plasmon polaritons in thin metal films and their role in fiber optic polarizing devices," J. Lightwave Technol. 8, 538-543 (1990).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature (London) 424, 824-830 (2003).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature (London) 424, 824-830 (2003).
[CrossRef]

Economou, E. N.

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Erland, J.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Fano, U.

Felici, T. P.

D. F. G. Gallagher and T. P. Felici, "Eigenmode expansion methods for simulation of optical propagation in photonics: pros and cons," Proc. SPIE 4987, 69-82 (1995).
[CrossRef]

Feng, D.

Ferrell, R. A.

E. A. Stern and R. A. Ferrell, "Surface plasma oscillations of a degenerate electron gas," Phys. Rev. 120, 130-l36 (1960).
[CrossRef]

Fuchs, R.

K. L. Kliewer and R. Fuchs, "Collective electronic motion in a metallic slab," Phys. Rev. 153, 498-153 (1967).
[CrossRef]

Gallagher, D. F. G.

D. F. G. Gallagher and T. P. Felici, "Eigenmode expansion methods for simulation of optical propagation in photonics: pros and cons," Proc. SPIE 4987, 69-82 (1995).
[CrossRef]

Hart, T.

J. Johnstone, G. Stewart, T. Hart, and B. Culshaw, "Surface plasmon polaritons in thin metal films and their role in fiber optic polarizing devices," J. Lightwave Technol. 8, 538-543 (1990).
[CrossRef]

Haupt, R.

L. Wendler and R. Haupt, "Long-range surface plasmon-polaritons in asymmetric layer structures," J. Appl. Phys. 59, 3289-3291 (1986).
[CrossRef]

Houde-Walter, S. N.

Hvam, J. M.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Innes, R. A.

R. A. Innes and J. R. Sambles, "Optical characterization of gold using surface plasmon polaritons," J. Phys. F: Met. Phys. 17, 277-287 (1987).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

Janunts, N. A.

N. A. Janunts and Kh. V. Nerkararyan, "Modulation of light radiation during input into waveguide by resonance excitation of surface plasmons," Appl. Phys. Lett. 79, 299-301 (2001).
[CrossRef]

Johnstone, J.

J. Johnstone, G. Stewart, T. Hart, and B. Culshaw, "Surface plasmon polaritons in thin metal films and their role in fiber optic polarizing devices," J. Lightwave Technol. 8, 538-543 (1990).
[CrossRef]

Jung, C.

C. Jung, S. Yee, and K. Kuhn, "Integrated optics waveguide modulator based on surface plasmon resonance," J. Lightwave Technol. 12, 1802-1806 (1994).
[CrossRef]

Kliewer, K. L.

K. L. Kliewer and R. Fuchs, "Collective electronic motion in a metallic slab," Phys. Rev. 153, 498-153 (1967).
[CrossRef]

Kottmann, J. P.

Krenn, J. R.

Kretschmann, E.

E. Kretschmann and H. Raether, "Radiative decay of non-radiative surface plasmons excited by light," Z. Naturforsch. A Z. Naturforsch. 23, 2135-2136 (1968).

Kreyszig, E.

E. Kreyszig, Advanced Engineering Mathematics, 7th ed. (Wiley, 1993).

Kuhn, K.

C. Jung, S. Yee, and K. Kuhn, "Integrated optics waveguide modulator based on surface plasmon resonance," J. Lightwave Technol. 12, 1802-1806 (1994).
[CrossRef]

Leitner, A.

Leosson, K.

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, "Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668-670 (2003).
[CrossRef]

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Lisicka-Shrzek, E.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer, 2000).

Maier, S. A.

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Maradudin, A. A.

I. V. Novikov and A. A. Maradudin, "Channel polaritons," Phys. Rev. B 66, 923-925 (2002).
[CrossRef]

G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, "The optics of surface plasmons," J. Phys. Colloq. 4, 233-241 (1984).

Martin, O. J. F.

Mysyrowicz, A.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44, 13556-13572 (1991).
[CrossRef]

Nerkararyan, Kh. V.

N. A. Janunts and Kh. V. Nerkararyan, "Modulation of light radiation during input into waveguide by resonance excitation of surface plasmons," Appl. Phys. Lett. 79, 299-301 (2001).
[CrossRef]

Nikolajsen, T.

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, "Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668-670 (2003).
[CrossRef]

Novikov, I. V.

I. V. Novikov and A. A. Maradudin, "Channel polaritons," Phys. Rev. B 66, 923-925 (2002).
[CrossRef]

Otto, A.

A. Otto, "Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection," Z. Phys. 216, 398-410 (1968).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

Powell, C. J.

C. J. Powell and J. B. Swan, "Origin of the characteristic electron energy losses in aluminum," Phys. Rev. 115, 869-875 (1959).
[CrossRef]

Prade, B.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44, 13556-13572 (1991).
[CrossRef]

Quinten, M.

Raether, H.

E. Kretschmann and H. Raether, "Radiative decay of non-radiative surface plasmons excited by light," Z. Naturforsch. A Z. Naturforsch. 23, 2135-2136 (1968).

Ritchie, R. H.

R. H. Ritchie, "Plasma losses by fast electrons in thin films," Phys. Rev. 106, 874-881 (1957).
[CrossRef]

Salakhutdinov, I.

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, "Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668-670 (2003).
[CrossRef]

Sambles, J. R.

F. Yang, J. R. Sambles, and G. W. Bradberry, "Long-range surface modes supported by thin films," Phys. Rev. B 44, 5855-5872 (1991).
[CrossRef]

R. A. Innes and J. R. Sambles, "Optical characterization of gold using surface plasmon polaritons," J. Phys. F: Met. Phys. 17, 277-287 (1987).
[CrossRef]

Sarid, D.

D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

Schildkraut, J. S.

Skovgaard, P. M. W.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Smith, R. E.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer, 2000).

Stegeman, G. I.

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, "The optics of surface plasmons," J. Phys. Colloq. 4, 233-241 (1984).

Stern, E. A.

E. A. Stern and R. A. Ferrell, "Surface plasma oscillations of a degenerate electron gas," Phys. Rev. 120, 130-l36 (1960).
[CrossRef]

Stewart, G.

J. Johnstone, G. Stewart, T. Hart, and B. Culshaw, "Surface plasmon polaritons in thin metal films and their role in fiber optic polarizing devices," J. Lightwave Technol. 8, 538-543 (1990).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Geometry for normal-mode analysis. 1, input region; 2, asymmetric region; 3, output region.

Fig. 2
Fig. 2

Propagation constant for the s b mode of a lossy Au film of labeled thickness with an SiO 2 substrate as a function of n c . n s = 1.444 and ϵ m = 131.95 + i 12.65 . The dotted curve represents the larger of n s and n c . (a) Normalized phase constant, (b) mode power attenuation.

Fig. 3
Fig. 3

H x -field profiles for a 9 nm Au film on SiO 2 for successively higher index asymmetries δ n , where n c = n s + δ n . All vertical axes are the same. Inset in fourth panel is a closeup of the metal region with the same units.

Fig. 4
Fig. 4

Radiation loss curves for SiO 2 . Curves are labeled in δ n with a factor of 10 4 suppressed. Metal thickness and s b cutoff point: (a) 4 nm , δ n CO = 4 × 10 4 ; (b) 9 nm , δ n CO = 18 × 10 4 ; (c) 13 nm , δ n CO = 34 × 10 4 ; (d) 19 nm , δ n CO = 59 × 10 4 .

Fig. 5
Fig. 5

Fractional power in each mode in the basis for cutoff in SiO 2 , with t = 4 nm and δ n = 50 × 10 4 .

Fig. 6
Fig. 6

Evolution of the H-field intensity H x 2 along z in SiO 2 , with t = 4 nm and δ n = 50 × 10 4 .

Tables (1)

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Table 1 Mode Properties for s b Modes of Au Slabs in SiO 2

Equations (15)

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H x s ( y ) = A s e k s y y < 0 , H x c ( y ) = A c e k c ( y y r + 1 ) y > y r + 1 ,
k c = β 2 n c 2 k 0 2 = ( β R + i β I ) 2 n c 2 k 0 2
= ( β R ) 2 + ( β I ) 2 n c 2 k 0 2 + i 2 β R β I ,
k c β R β I + i β R β I .
H x , 1 ( z = 0 ) = k = 1 n c k H x , 2 ( k ) ( z = 0 ) ,
c k = 1 2 E 1 × [ H 2 ( k ) ( z = 0 ) ] * z ̂ d y .
N = 1 2 E × H * z ̂ d y .
1 2 E m × ( H n ) * z ̂ d y = 1 2 E y m ( H x n ) * d y = δ m n ,
k = 1 n c k 2 = 1 .
c L = 1 2 E 3 × [ k = 1 n c k H 2 ( k ) ( z = L ) ] * z ̂ d y
= 1 2 E 3 × [ k = 1 n c k e i β k L H 2 ( k ) ( z = 0 ) ] * z ̂ d y
= k = 1 n [ ( c k e i β k L ) * 1 2 E 3 × [ H 2 ( k ) ( z = 0 ) ] * z ̂ d y ]
= k = 1 n c k 2 ( e i β k L ) * ,
IL = 20 log 10 ( c L ) .
l 1 λ 0 ( n eff , c n eff , s ) = λ 0 δ n .

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