Abstract

We report that the interference pattern of Young’s double-slit experiment changes as a function of polarization in the sub-wavelength diffraction regime. Experiments carried out with terahertz time-domain spectroscopy reveal that diffracted waves from sub-wavelength-scale slits exhibit either positive or negative phase shift with respect to Gouy phase depending on the polarization. Theoretical explanation based on the induction of electric current and magnetic dipole in the vicinity of the slits shows an excellent agreement with the experimental results.

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References

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  1. E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).
  2. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
  3. F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett.90, 213901 (2003).
    [CrossRef] [PubMed]
  4. C. Wang, C. Du, and X. Luo, “Refining the model of light diffraction from a subwavelength slit surrounded by grooves on a metallic film,” Phys. Rev. B74, 245403 (2006).
    [CrossRef]
  5. Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett.86, 5601 (2001).
    [CrossRef] [PubMed]
  6. F. Yang and J. R. Sambles, “Resonant transmission of microwaves through a narrow metallic slit,” Phys. Rev. Lett.89, 063901 (2002).
    [CrossRef] [PubMed]
  7. M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photon.3, 152–156 (2009).
    [CrossRef]
  8. J. H. Kang, D. S. Kim, and Q. Park, “Local Capacitor Model for Plasmonic Electric Field Enhancement,” Phys. Rev. Lett.102, 093906 (2009).
    [CrossRef] [PubMed]
  9. E. H. Khoo, E. P. Li, and K. B. Crozier, “Plasmonic wave plate based on subwavelength nanoslits,” Opt. Lett.36, 2498–2500 (2011).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  12. M. Yi, K. Lee, J. D. Song, and J. Ahn, “Terahertz phase microscopy in the sub-wavelength regime,” Appl. Phys. Lett.100, 161110 (2012).
    [CrossRef]
  13. K. Lee, M. Yi, S. E. Park, and J. Ahn, “Phase-shift anomaly caused by subwavelength-scale metal slit or aperture diffraction,” Opt. Lett.38, 166–168 (2013).
    [CrossRef] [PubMed]
  14. D. Grischkowsky, S. Keiding, M. van Exter, and Ch. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B7, 2006–2015 (1990).
    [CrossRef]
  15. Y.-S. Lee, Principles of Terahertz Science and Technology (Springer, 2009).
  16. P. C. M. Planken, H.-K. Nienhuys, H. J. Bakker, and T. Wenckebach, “Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe,” J. Opt. Soc. Am. B18, 313–317 (2001).
    [CrossRef]
  17. Y. Kim, M. Yi, B. G. Kim, and J. Ahn, “Investigation of THz birefringence measurement and calculation in Al2O3 and LiNbO3,” Appl. Opt.50, 2906–2910 (2011).
    [CrossRef] [PubMed]
  18. L. G. Gouy, “Sur une propriete nouvelle des ondes lumineuses,” C. R. Acad. Sci. Paris110, 1251–1253 (1890).
  19. A. Rubinowicz, “On the anomalous propagation of phase in the focus,” Phys. Rev.54, 931–936 (1938).
    [CrossRef]
  20. A. E. Siegman, Lasers (University Science Books, 1986).
  21. A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle Terahertz pulses,” Phys. Rev. Lett.83, 3410–3413 (1999).
    [CrossRef]
  22. S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett.26, 485–487 (2001).
    [CrossRef]
  23. K. Lee, “Fourier optical phenomena and applications using ultra broadband terahertz waves,” Ph. D. Thesis, KAIST (2013).

2013 (1)

2012 (1)

M. Yi, K. Lee, J. D. Song, and J. Ahn, “Terahertz phase microscopy in the sub-wavelength regime,” Appl. Phys. Lett.100, 161110 (2012).
[CrossRef]

2011 (3)

2009 (2)

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photon.3, 152–156 (2009).
[CrossRef]

J. H. Kang, D. S. Kim, and Q. Park, “Local Capacitor Model for Plasmonic Electric Field Enhancement,” Phys. Rev. Lett.102, 093906 (2009).
[CrossRef] [PubMed]

2006 (1)

C. Wang, C. Du, and X. Luo, “Refining the model of light diffraction from a subwavelength slit surrounded by grooves on a metallic film,” Phys. Rev. B74, 245403 (2006).
[CrossRef]

2003 (1)

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett.90, 213901 (2003).
[CrossRef] [PubMed]

2002 (1)

F. Yang and J. R. Sambles, “Resonant transmission of microwaves through a narrow metallic slit,” Phys. Rev. Lett.89, 063901 (2002).
[CrossRef] [PubMed]

2001 (3)

1999 (1)

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle Terahertz pulses,” Phys. Rev. Lett.83, 3410–3413 (1999).
[CrossRef]

1990 (1)

1944 (1)

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

1938 (1)

A. Rubinowicz, “On the anomalous propagation of phase in the focus,” Phys. Rev.54, 931–936 (1938).
[CrossRef]

1890 (1)

L. G. Gouy, “Sur une propriete nouvelle des ondes lumineuses,” C. R. Acad. Sci. Paris110, 1251–1253 (1890).

Ahn, J.

Alkemade, P. F. A.

Bakker, H. J.

Bethe, H. A.

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

Bosman, J.

Chimento, P. F.

Choi, S. S.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photon.3, 152–156 (2009).
[CrossRef]

Crozier, K. B.

Du, C.

C. Wang, C. Du, and X. Luo, “Refining the model of light diffraction from a subwavelength slit surrounded by grooves on a metallic film,” Phys. Rev. B74, 245403 (2006).
[CrossRef]

Ebbesen, T. W.

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett.90, 213901 (2003).
[CrossRef] [PubMed]

Eliel, E. R.

Fattinger, Ch.

Feng, S.

S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett.26, 485–487 (2001).
[CrossRef]

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle Terahertz pulses,” Phys. Rev. Lett.83, 3410–3413 (1999).
[CrossRef]

García-Vidal, F. J.

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett.90, 213901 (2003).
[CrossRef] [PubMed]

Gouy, L. G.

L. G. Gouy, “Sur une propriete nouvelle des ondes lumineuses,” C. R. Acad. Sci. Paris110, 1251–1253 (1890).

Grischkowsky, D.

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).

Hooft, G. W.’t

Jackson, J. D.

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

Kang, J. H.

J. H. Kang, D. S. Kim, and Q. Park, “Local Capacitor Model for Plasmonic Electric Field Enhancement,” Phys. Rev. Lett.102, 093906 (2009).
[CrossRef] [PubMed]

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photon.3, 152–156 (2009).
[CrossRef]

Keiding, S.

Khoo, E. H.

Kim, B. G.

Kim, D. S.

J. H. Kang, D. S. Kim, and Q. Park, “Local Capacitor Model for Plasmonic Electric Field Enhancement,” Phys. Rev. Lett.102, 093906 (2009).
[CrossRef] [PubMed]

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photon.3, 152–156 (2009).
[CrossRef]

Kim, Y.

Koo, S. M.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photon.3, 152–156 (2009).
[CrossRef]

Kuzmin, N. V.

Lee, K.

K. Lee, M. Yi, S. E. Park, and J. Ahn, “Phase-shift anomaly caused by subwavelength-scale metal slit or aperture diffraction,” Opt. Lett.38, 166–168 (2013).
[CrossRef] [PubMed]

M. Yi, K. Lee, J. D. Song, and J. Ahn, “Terahertz phase microscopy in the sub-wavelength regime,” Appl. Phys. Lett.100, 161110 (2012).
[CrossRef]

K. Lee, “Fourier optical phenomena and applications using ultra broadband terahertz waves,” Ph. D. Thesis, KAIST (2013).

Lee, Y.-S.

Y.-S. Lee, Principles of Terahertz Science and Technology (Springer, 2009).

Lezec, H. J.

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett.90, 213901 (2003).
[CrossRef] [PubMed]

Li, E. P.

Luo, X.

C. Wang, C. Du, and X. Luo, “Refining the model of light diffraction from a subwavelength slit surrounded by grooves on a metallic film,” Phys. Rev. B74, 245403 (2006).
[CrossRef]

Martín-Moreno, L.

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett.90, 213901 (2003).
[CrossRef] [PubMed]

Nienhuys, H.-K.

Park, D. J.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photon.3, 152–156 (2009).
[CrossRef]

Park, G. S.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photon.3, 152–156 (2009).
[CrossRef]

Park, H. R.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photon.3, 152–156 (2009).
[CrossRef]

Park, N. K.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photon.3, 152–156 (2009).
[CrossRef]

Park, Q.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photon.3, 152–156 (2009).
[CrossRef]

J. H. Kang, D. S. Kim, and Q. Park, “Local Capacitor Model for Plasmonic Electric Field Enhancement,” Phys. Rev. Lett.102, 093906 (2009).
[CrossRef] [PubMed]

Park, S. E.

Planken, P. C. M.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photon.3, 152–156 (2009).
[CrossRef]

P. C. M. Planken, H.-K. Nienhuys, H. J. Bakker, and T. Wenckebach, “Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe,” J. Opt. Soc. Am. B18, 313–317 (2001).
[CrossRef]

Rubinowicz, A.

A. Rubinowicz, “On the anomalous propagation of phase in the focus,” Phys. Rev.54, 931–936 (1938).
[CrossRef]

Rudd, J. V.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle Terahertz pulses,” Phys. Rev. Lett.83, 3410–3413 (1999).
[CrossRef]

Ruffin, A. B.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle Terahertz pulses,” Phys. Rev. Lett.83, 3410–3413 (1999).
[CrossRef]

Sambles, J. R.

F. Yang and J. R. Sambles, “Resonant transmission of microwaves through a narrow metallic slit,” Phys. Rev. Lett.89, 063901 (2002).
[CrossRef] [PubMed]

Seo, M. A.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photon.3, 152–156 (2009).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Song, J. D.

M. Yi, K. Lee, J. D. Song, and J. Ahn, “Terahertz phase microscopy in the sub-wavelength regime,” Appl. Phys. Lett.100, 161110 (2012).
[CrossRef]

Suwal, O. K.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photon.3, 152–156 (2009).
[CrossRef]

Takakura, Y.

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett.86, 5601 (2001).
[CrossRef] [PubMed]

van Exter, M.

Wang, C.

C. Wang, C. Du, and X. Luo, “Refining the model of light diffraction from a subwavelength slit surrounded by grooves on a metallic film,” Phys. Rev. B74, 245403 (2006).
[CrossRef]

Wenckebach, T.

Whitaker, J. F.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle Terahertz pulses,” Phys. Rev. Lett.83, 3410–3413 (1999).
[CrossRef]

Winful, H. G.

S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett.26, 485–487 (2001).
[CrossRef]

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle Terahertz pulses,” Phys. Rev. Lett.83, 3410–3413 (1999).
[CrossRef]

Yang, F.

F. Yang and J. R. Sambles, “Resonant transmission of microwaves through a narrow metallic slit,” Phys. Rev. Lett.89, 063901 (2002).
[CrossRef] [PubMed]

Yi, M.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. Yi, K. Lee, J. D. Song, and J. Ahn, “Terahertz phase microscopy in the sub-wavelength regime,” Appl. Phys. Lett.100, 161110 (2012).
[CrossRef]

C. R. Acad. Sci. Paris (1)

L. G. Gouy, “Sur une propriete nouvelle des ondes lumineuses,” C. R. Acad. Sci. Paris110, 1251–1253 (1890).

J. Opt. Soc. Am. B (2)

Nat. Photon. (1)

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photon.3, 152–156 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. (2)

A. Rubinowicz, “On the anomalous propagation of phase in the focus,” Phys. Rev.54, 931–936 (1938).
[CrossRef]

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

Phys. Rev. B (1)

C. Wang, C. Du, and X. Luo, “Refining the model of light diffraction from a subwavelength slit surrounded by grooves on a metallic film,” Phys. Rev. B74, 245403 (2006).
[CrossRef]

Phys. Rev. Lett. (5)

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett.86, 5601 (2001).
[CrossRef] [PubMed]

F. Yang and J. R. Sambles, “Resonant transmission of microwaves through a narrow metallic slit,” Phys. Rev. Lett.89, 063901 (2002).
[CrossRef] [PubMed]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett.90, 213901 (2003).
[CrossRef] [PubMed]

J. H. Kang, D. S. Kim, and Q. Park, “Local Capacitor Model for Plasmonic Electric Field Enhancement,” Phys. Rev. Lett.102, 093906 (2009).
[CrossRef] [PubMed]

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle Terahertz pulses,” Phys. Rev. Lett.83, 3410–3413 (1999).
[CrossRef]

Other (5)

K. Lee, “Fourier optical phenomena and applications using ultra broadband terahertz waves,” Ph. D. Thesis, KAIST (2013).

A. E. Siegman, Lasers (University Science Books, 1986).

Y.-S. Lee, Principles of Terahertz Science and Technology (Springer, 2009).

E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).

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

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Figures (4)

Fig. 1
Fig. 1

Experimental setup to measure sub-wavelength Young’s double-slit diffraction pattern. Inset shows double-slit geometry and electric field polarization angle.

Fig. 2
Fig. 2

(a) Experimental geometry of sub-wavelength-scale single-slit transmission. (b–g) Measured electric fields through slits of respective width of (b) d = 30, (c) 40, (d) 50, (e) 100, (f) 150, and (g) 200 μm. Red and Blue lines represent θ = 0 and π/2, respectively. Dotted lines denotes reference fields without slits. Each signal is normalized to its maximum.

Fig. 3
Fig. 3

Transmitted THz waves through sub-wavelength-scale single slits. (a) Measured time signals in θ = π/2 case and (b) their relative transmission amplitude (divided by reference signals without slits) plotted as a function of d/λ. (c) Measured time signals in θ = 0 case and (d) their relative transmission amplitude plotted as a function of d/λ. Black lines in (b) and (d) represent fitting lines based on Eqs. (3) and (5), respectively. (a) and (c) are plotted in the same scale.

Fig. 4
Fig. 4

Measured time signals and interference patterns. (a) Measured THz time signals in θ = π/2 case (normalized to the max), and (b,c) corresponding interference patterns of all THz frequencies in (b) and at 0.7 THz in (c). (d) Measured THz time signals in θ = 0 case (normalized to the max), and (e,f) corresponding interference patterns of all THz frequencies in (e) and at 0.7 THz in (f). All the time signals and patterns are normalized. Red crosses in (c) and Blue circles in (f) represent experimental data and Black dash-dot lines in (c,f) represent theoretical expectation base on scalar diffraction theory. White dash lines in (b) and (e) indicate 0.7 THz. Black dash lines represent the optical axis.

Tables (1)

Tables Icon

Table 1 Phase and amplitude behaviors of sub-wavelength-scale slit diffraction

Equations (6)

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E ( x , ω ) = ( D 1 e ϕ 1 δ ( x + a 2 ) + D 2 e ϕ 2 δ ( x a 2 ) ) e i k x x f d x ,
I ( x , ω ) = | E ( x , ω ) | 2 = 4 D 1 D 2 cos 2 ( k a 2 f x Δ ϕ 2 ) + ( D 2 D 1 ) 2 ,
E ( R ) = ( α + d i λ ) LE 0 R e i ( k R ω t ) ,
ρ ( y ) = H 0 2 π y d 2 4 y 2 ,
E | | ( R ) = k 2 d 2 LE 0 16 R e i ( k R ω t ) ,
I max I min I max + I min = 2 D 1 D 2 D 1 2 + D 2 2 ,

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