Abstract

It is shown that the generation of surface plasmons on a metal-dielectric interface, i.e., a Au-double-slit and air interface, appreciably affects the intensity of the diffracted light. With a specific example of Au-double-slit and electro-optic devices before the slits, the spectral switching in the diffracted field with the polychromatic light is shown for the first time, to our knowledge. It is found that at the observation point due to the surface plasmon effect the intensity of the diffracted light periodically increases and decreases with the separation of the double-slit.

© 2012 Optical Society of America

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References

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  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 391, 667–669 (1998).
    [CrossRef]
  2. H. A. Bethe, “Theory of dffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
  3. U. Schroter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58, 15419–15421 (1998).
  4. H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, D. Lenstra, G. W. ’t Hooft, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
    [CrossRef]
  5. C. H. Gan, G. Gbur, and T. D. Visser, “Surface plasmons modulate the spatial coherence of light in Young’s interference experiment,” Phys. Rev. Lett. 98, 043908 (2007).
    [CrossRef]
  6. H. Rather, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).
  7. S. Ravets, J. C. Rodier, B. Ea Kim, J. P. Hugonin, L. Jacubowiez, and P. Lalanne, “Surface plasmons in the Young slit doublet experiment,” J. Opt. Soc. Am. B 26, B28–B33 (2009).
    [CrossRef]
  8. M. S. Soskin and M. V. Vasnetsov, eds. “Singular optics,” in Progress in Optics (Elsevier, 2001), pp. 219–276.
  9. J. Foley and E. Wolf, “Phenomenon of spectral switches as a new effect in singular optics with polychromatic light,” J. Opt. Soc. Am. A 19, 2510–2516 (2002).
    [CrossRef]
  10. H. C. Kandpal, “Experimental observation of the phenomenon of spectral switch,” J. Opt. A Pure Appl. Opt. 3, 296–299 (2001).
  11. P. Han, “Spectral switches for a circular aperture with a variable wedge,” J. Opt. Soc. Am. A 26, 473–479 (2009).
    [CrossRef]
  12. P. Han, Cheng-Ling Lee, Luan-Ying Chen, and San-Hao Huang, “A data transmission scheme with spectral switches of a shifting double slit in the far field,” J. Opt. 12, 035402 (2010).
  13. P. Han, “Spectral anomalies for a right triangle aperture with an adjustable hypotenuse slope,” J. Opt. A Pure Appl. Opt. 11, 015708 (2009).
  14. P. Han, “Electro-optic modulation for spectral switches and phase singularities of a double-slit in the far-field,” J. Opt. 13, 035713 (2011).
    [CrossRef]
  15. B. K. Yadav, S. Raman, and H. C. Kandpal, “Information exchange in free space using spectral switching of diffracted polychromatic light: possibilities and limitations,” J. Opt. Soc. Am. A 25, 2952–2959 (2008).
    [CrossRef]
  16. B. K. Yadav and H. C. Kandpal, “Spectral anomalies of polychromatic DHGB and its applications in FSO,” J. Lightwave Technol. 29, 960–966 (2011).
  17. P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytical model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006).
  18. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  19. J. Leng, J. Opsal, H. Chu, M. Senko, and D. E. Aspnes, “Analytic representations of the dielectric functions of materials for device and structural modeling” Thin Solid Films 313–314, 132–136 (1998).
    [CrossRef]
  20. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
  21. E. Hecht, Optics (Addison Wesley, 2002).
  22. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

2011 (2)

P. Han, “Electro-optic modulation for spectral switches and phase singularities of a double-slit in the far-field,” J. Opt. 13, 035713 (2011).
[CrossRef]

B. K. Yadav and H. C. Kandpal, “Spectral anomalies of polychromatic DHGB and its applications in FSO,” J. Lightwave Technol. 29, 960–966 (2011).

2010 (1)

P. Han, Cheng-Ling Lee, Luan-Ying Chen, and San-Hao Huang, “A data transmission scheme with spectral switches of a shifting double slit in the far field,” J. Opt. 12, 035402 (2010).

2009 (3)

2008 (1)

2007 (1)

C. H. Gan, G. Gbur, and T. D. Visser, “Surface plasmons modulate the spatial coherence of light in Young’s interference experiment,” Phys. Rev. Lett. 98, 043908 (2007).
[CrossRef]

2006 (1)

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytical model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006).

2005 (1)

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, D. Lenstra, G. W. ’t Hooft, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef]

2002 (1)

2001 (1)

H. C. Kandpal, “Experimental observation of the phenomenon of spectral switch,” J. Opt. A Pure Appl. Opt. 3, 296–299 (2001).

1998 (3)

U. Schroter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58, 15419–15421 (1998).

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 391, 667–669 (1998).
[CrossRef]

J. Leng, J. Opsal, H. Chu, M. Senko, and D. E. Aspnes, “Analytic representations of the dielectric functions of materials for device and structural modeling” Thin Solid Films 313–314, 132–136 (1998).
[CrossRef]

1972 (1)

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

1944 (1)

H. A. Bethe, “Theory of dffraction by small holes,” Phys. Rev. 66, 163–182 (1944).

’t Hooft, G. W.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, D. Lenstra, G. W. ’t Hooft, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef]

Alkemade, P. F. A.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, D. Lenstra, G. W. ’t Hooft, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef]

Aspnes, D. E.

J. Leng, J. Opsal, H. Chu, M. Senko, and D. E. Aspnes, “Analytic representations of the dielectric functions of materials for device and structural modeling” Thin Solid Films 313–314, 132–136 (1998).
[CrossRef]

Bethe, H. A.

H. A. Bethe, “Theory of dffraction by small holes,” Phys. Rev. 66, 163–182 (1944).

Blok, H.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, D. Lenstra, G. W. ’t Hooft, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Chen, Luan-Ying

P. Han, Cheng-Ling Lee, Luan-Ying Chen, and San-Hao Huang, “A data transmission scheme with spectral switches of a shifting double slit in the far field,” J. Opt. 12, 035402 (2010).

Christy, R. W.

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

Chu, H.

J. Leng, J. Opsal, H. Chu, M. Senko, and D. E. Aspnes, “Analytic representations of the dielectric functions of materials for device and structural modeling” Thin Solid Films 313–314, 132–136 (1998).
[CrossRef]

Dubois, G.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, D. Lenstra, G. W. ’t Hooft, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef]

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 391, 667–669 (1998).
[CrossRef]

Eliel, E. R.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, D. Lenstra, G. W. ’t Hooft, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef]

Etchegoin, P. G.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytical model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006).

Foley, J.

Gan, C. H.

C. H. Gan, G. Gbur, and T. D. Visser, “Surface plasmons modulate the spatial coherence of light in Young’s interference experiment,” Phys. Rev. Lett. 98, 043908 (2007).
[CrossRef]

Gbur, G.

C. H. Gan, G. Gbur, and T. D. Visser, “Surface plasmons modulate the spatial coherence of light in Young’s interference experiment,” Phys. Rev. Lett. 98, 043908 (2007).
[CrossRef]

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, D. Lenstra, G. W. ’t Hooft, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 391, 667–669 (1998).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Han, P.

P. Han, “Electro-optic modulation for spectral switches and phase singularities of a double-slit in the far-field,” J. Opt. 13, 035713 (2011).
[CrossRef]

P. Han, Cheng-Ling Lee, Luan-Ying Chen, and San-Hao Huang, “A data transmission scheme with spectral switches of a shifting double slit in the far field,” J. Opt. 12, 035402 (2010).

P. Han, “Spectral anomalies for a right triangle aperture with an adjustable hypotenuse slope,” J. Opt. A Pure Appl. Opt. 11, 015708 (2009).

P. Han, “Spectral switches for a circular aperture with a variable wedge,” J. Opt. Soc. Am. A 26, 473–479 (2009).
[CrossRef]

Hecht, E.

E. Hecht, Optics (Addison Wesley, 2002).

Heitmann, D.

U. Schroter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58, 15419–15421 (1998).

Huang, San-Hao

P. Han, Cheng-Ling Lee, Luan-Ying Chen, and San-Hao Huang, “A data transmission scheme with spectral switches of a shifting double slit in the far field,” J. Opt. 12, 035402 (2010).

Hugonin, J. P.

Jacubowiez, L.

Johnson, P. B.

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

Kandpal, H. C.

Kim, B. Ea

Kuzmin, N.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, D. Lenstra, G. W. ’t Hooft, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef]

Lalanne, P.

Le Ru, E. C.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytical model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006).

Lee, Cheng-Ling

P. Han, Cheng-Ling Lee, Luan-Ying Chen, and San-Hao Huang, “A data transmission scheme with spectral switches of a shifting double slit in the far field,” J. Opt. 12, 035402 (2010).

Leng, J.

J. Leng, J. Opsal, H. Chu, M. Senko, and D. E. Aspnes, “Analytic representations of the dielectric functions of materials for device and structural modeling” Thin Solid Films 313–314, 132–136 (1998).
[CrossRef]

Lenstra, D.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, D. Lenstra, G. W. ’t Hooft, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 391, 667–669 (1998).
[CrossRef]

Meyer, M.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytical model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006).

Opsal, J.

J. Leng, J. Opsal, H. Chu, M. Senko, and D. E. Aspnes, “Analytic representations of the dielectric functions of materials for device and structural modeling” Thin Solid Films 313–314, 132–136 (1998).
[CrossRef]

Raman, S.

Rather, H.

H. Rather, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

Ravets, S.

Rodier, J. C.

Schouten, H. F.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, D. Lenstra, G. W. ’t Hooft, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef]

Schroter, U.

U. Schroter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58, 15419–15421 (1998).

Senko, M.

J. Leng, J. Opsal, H. Chu, M. Senko, and D. E. Aspnes, “Analytic representations of the dielectric functions of materials for device and structural modeling” Thin Solid Films 313–314, 132–136 (1998).
[CrossRef]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 391, 667–669 (1998).
[CrossRef]

Visser, T. D.

C. H. Gan, G. Gbur, and T. D. Visser, “Surface plasmons modulate the spatial coherence of light in Young’s interference experiment,” Phys. Rev. Lett. 98, 043908 (2007).
[CrossRef]

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, D. Lenstra, G. W. ’t Hooft, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef]

Wolf, E.

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 391, 667–669 (1998).
[CrossRef]

Yadav, B. K.

J. Chem. Phys. (1)

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytical model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006).

J. Lightwave Technol. (1)

J. Opt. (2)

P. Han, Cheng-Ling Lee, Luan-Ying Chen, and San-Hao Huang, “A data transmission scheme with spectral switches of a shifting double slit in the far field,” J. Opt. 12, 035402 (2010).

P. Han, “Electro-optic modulation for spectral switches and phase singularities of a double-slit in the far-field,” J. Opt. 13, 035713 (2011).
[CrossRef]

J. Opt. A Pure Appl. Opt. (2)

H. C. Kandpal, “Experimental observation of the phenomenon of spectral switch,” J. Opt. A Pure Appl. Opt. 3, 296–299 (2001).

P. Han, “Spectral anomalies for a right triangle aperture with an adjustable hypotenuse slope,” J. Opt. A Pure Appl. Opt. 11, 015708 (2009).

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (1)

Nature (London) (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 391, 667–669 (1998).
[CrossRef]

Phys. Rev. (1)

H. A. Bethe, “Theory of dffraction by small holes,” Phys. Rev. 66, 163–182 (1944).

Phys. Rev. B (2)

U. Schroter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58, 15419–15421 (1998).

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

Phys. Rev. Lett. (2)

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, D. Lenstra, G. W. ’t Hooft, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef]

C. H. Gan, G. Gbur, and T. D. Visser, “Surface plasmons modulate the spatial coherence of light in Young’s interference experiment,” Phys. Rev. Lett. 98, 043908 (2007).
[CrossRef]

Thin Solid Films (1)

J. Leng, J. Opsal, H. Chu, M. Senko, and D. E. Aspnes, “Analytic representations of the dielectric functions of materials for device and structural modeling” Thin Solid Films 313–314, 132–136 (1998).
[CrossRef]

Other (5)

H. Rather, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

M. S. Soskin and M. V. Vasnetsov, eds. “Singular optics,” in Progress in Optics (Elsevier, 2001), pp. 219–276.

E. Hecht, Optics (Addison Wesley, 2002).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

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Figures (7)

Fig. 1.
Fig. 1.

Incoming TM polarized plane wave with Gaussian spectral profile is incident on the two electro-optic modulators, M1 and M2, followed by a Au-double-slit DS2. The dimensions of the slits, voltages given to the modulators, M1 and M2, are shown in the figure. The observation plane S is at a distance z in the far zone from the Au-double-slit. In all the examples the transmission coefficient of each slit, thickness of the Au-double-slit and thickness of the modulators, M1 and M2, are taken as α=0.99, tg=200nm, and tm=1μm, respectively. For slit width b=100nm, the phase shift arg(β)=205° and |β|=0.33 are taken from [5].

Fig. 2.
Fig. 2.

The plot of amplitude decay length L, given by Eq. (9c), with wavelength λ of the incident light.

Fig. 3.
Fig. 3.

(a) The comparison of normalized incident spectrum and the diffracted spectrum at the observation plane at a point x=0 are shown when voltage across the elctro-optic modulators, M1 and M2, are V1=0V and V2=0V, respectively. Here curve A represents the normalized incident spectrum, curve B represents the diffracted spectrum with the ordinary slit, and curve C represents the diffracted spectrum when the ordinary slit was replaced by a Au-double-slit. Curves B and C are normalized for the maximum value of the curve C. The parameters are the central wavelength of the incident Gaussian field λ0=600nm, the mean width σ=75nm, the slit width b=100nm, slit-separation 2d=200nm and the distance of the observation plane from the double-slit z=10μm are chosen for the study. The diffracted spectrum appears only slightly blue-shifted and the maximum normalized intensity shift ΔIs for 2d=200nm is also shown by dotted double headed arrow. (b) Shows the splitting of the incident spectrum into two peaks when the voltage V1 is increased to V1=17.663V. Curves A, B and C have the same meaning and other parameters are the same as in Fig. 3(a).

Fig. 4.
Fig. 4.

(a) Curve A shows the normalized spectrum of incident field, curves B and C represent the spectra for the diffracted spectrum with ordinary slit and with the Au-double-slit, respectively, at point x=0 on the observation plane. It can be seen that, when the voltage V1 is slightly decreased from 17.663 V to 17 V the diffracted spectrum shows a red-shift Ω shown by a double headed arrow in the figure with regards to the incident spectrum. The amplitude of the diffracted spectrum is intensified by the Au-double-slit as represented by curve B. (b) Shows that, when V1 slightly increased from 17 V to 18.3 V, the spectrum is blue-shifted with regards to the incident spectrum. Again curves A, B, and C have the same meaning. The parameters are also the same as for Fig. 3. In this case also the diffracted intensity is amplified by the plasmonic effect as shown by curve C.

Fig. 5.
Fig. 5.

Variation of the normalized intensity shift ΔIs due to the coupling of surface plasmon with slit separation 2d. The curve is normalized for the maximum value of ΔIs. The voltages V1 and V2 both are kept equal to 0 V while all other parameters are kept same as in Fig. 3 and Fig. 4.

Fig. 6.
Fig. 6.

Shows the plot of normalized spectral shift Ω=(λλ0)/λ0 with the voltage V1 given to the modulator M1 while keeping voltage V2=0. The normalization has been done for the peak wavelength λ0=600nm. All other parameters are kept the same as in the Fig. 3 and Fig. 4.

Fig. 7.
Fig. 7.

Shows the scheme of data transmission in which the red-shift is associated with a bit 0 and the blue-shift is associated with a bit 1. Here the data is assumed to be in the form of a binary string 1101.

Equations (21)

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

U(i)(λ)=exp[(λλo)22σ2]
I(i)(λ)=exp[(λλo)2σ2].
U1(i)(λ)=U(i)(λ)exp(iΔϕ1),
U2(i)(λ)=U(i)(λ)exp(iΔϕ2).
U1(λ)=αU1(i)(λ)+αβU2(i)(λ)exp(iksp2d),
U1(λ)=[αexp(iΔϕ1)+αβexp(iΔϕ2)exp(iksp2d)]U(i)(λ),U1(λ)=A×U(i)(λ).
U2(λ)=B×U(i)(λ),
A=[αexp(iΔϕ1)+αβexp(iΔϕ2)exp(iksp2d)],
B=[αexp(iΔϕ2)+αβexp(iΔϕ1)exp(iksp2d)],
εm(ω)=εωp2(ω2+iωΓ)+G1(ω)+G2(ω).
εm(λ)=ε1λp2(1λ2+iγpλ)+i=1,2Aiλi[eiϕi(1λi+1λ+iγi)+eiϕi(1λi1λiγi)],
ksp=k(εmεdεm+εd)1/2,
λsp=2πRe[ksp],
L=1Im[ksp],
g(x)=U1(λ)rect[x+db]+U2(λ)rect[xdb].
G(fx)=exp(ikz)exp(ikx2/2z)iλz[U1(λ)bsinc(bfx)e2πidfx+U2(λ)bsinc(bfx)e2πidfx].
G(fx)=exp(ikz)exp(ikx2/2z)iλzbsinc(bfx)[Ae2πidfx+Be2πidfx]U(i)(λ).
I(fx)=|G(fx)|2,
I(fx)=b2sinc2(bfx)λ2z2[|A|2+|B|2+A*Be4πidfx+AB*e4πidfx]|U(i)(λ)|2,
I(λ)=M(λ)×|U(i)(λ)|2=M(λ)×I(i)(λ),
M(λ)=I(λ)I(i)(λ)=b2sinc2(bx/λz)λ2z2[|A|2+|B|2+A*Be4πidx/λz+AB*e4πidx/λz].

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