Abstract

We report on a procedure to improve the resolution of far-field imaging by using a neighboring high-index medium that is coated with a left-handed metamaterial. The resulting plot can also exhibit an enhanced transmission by considering proper conditions to retract backscattering. Based on negative refraction, geometrical aberrations are considered in detail since they may cause a great impact in this sort of diffraction-unlimited imaging by reducing its resolution power. We employ a standard aberration analysis to refine the asymmetric configuration of metamaterial superlenses. We demonstrate that low-order centrosymmetric aberrations can be fully corrected for a given object plane. For subwavelength-resolution imaging, however, high-order aberrations become of relevance, which may be balanced with defocus. Not only the point spread function but also numerical simulations based on the finite-element method support our theoretical analysis, and subwavelength resolution is verified in the image plane.

© 2012 Optical Society of America

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References

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    [CrossRef]
  2. P. Loschialpo, D. Forester, D. Smith, F. Rachford, and C. Monzon, “Optical properties of an ideal homogeneous causal left-handed material slab,” Phys. Rev. E 70, 036605 (2004).
    [CrossRef]
  3. Z. Lin and Y. Zou, “Low-order aberration corrections of multilayer flat lenses using negative-index materials,” Appl. Opt. 45, 6925–6931 (2006).
    [CrossRef]
  4. P. Valanju, R. Walser, and A. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
    [CrossRef]
  5. P. Loschialpo, D. Smith, D. Forester, F. Rachford, and J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 025602 (2003).
    [CrossRef]
  6. T. Matsumoto, S. Fujita, and T. Baba, “Wavelength demultiplexer consisting of photonic crystal superprism and superlens,” Opt. Express 13, 10768–10776 (2005).
    [CrossRef]
  7. T. Matsumoto, K.-S. Eom, and T. Baba, “Focusing of light by negative refraction in a photonic crystal slab superlens on silicon-on-insulator substrate,” Opt. Lett. 31, 2786–2788 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. J. Li and C. T. Chan, “Imaging using nano metallic films: from evanescent wave lens to resonant tunnelling lens,” arXiv:physics/0701172v1 (2007).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010 (2)

2009 (1)

2008 (2)

2007 (2)

H. Luo, Z. Ren, W. Shu, and F. Li, “Construction of a polarization insensitive lens from a quasi-isotropic metamaterial slab,” Phys. Rev. E 75, 026601 (2007).
[CrossRef]

D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express 15, 14772–14782 (2007).
[CrossRef]

2006 (5)

J. Chen, C. Radu, and A. Puri, “Aberration-free negative-refractive-index lens,” Appl. Phys. Lett. 88, 071119 (2006).
[CrossRef]

Z. Lin and Y. Zou, “Low-order aberration corrections of multilayer flat lenses using negative-index materials,” Appl. Opt. 45, 6925–6931 (2006).
[CrossRef]

T. Matsumoto, K.-S. Eom, and T. Baba, “Focusing of light by negative refraction in a photonic crystal slab superlens on silicon-on-insulator substrate,” Opt. Lett. 31, 2786–2788 (2006).
[CrossRef]

R. Marques, M. J. Freire, and J. D. Baena, “Theory of three-dimensional subdiffraction imaging,” Appl. Phys. Lett. 89, 211113 (2006).
[CrossRef]

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

2005 (4)

T. Dumelow, J. da Costa, and V. Freire, “Slab lenses from simple anisotropic media,” Phys. Rev. B 72, 235115 (2005).
[CrossRef]

T. Matsumoto, S. Fujita, and T. Baba, “Wavelength demultiplexer consisting of photonic crystal superprism and superlens,” Opt. Express 13, 10768–10776 (2005).
[CrossRef]

N. Calander, “Surface plasmon-coupled emission and Fabry-Perot resonance in the sample layer: a theoretical approach,” J. Phys. Chem. B 109, 13957–13963 (2005).
[CrossRef]

I. Bulu, H. Caglayan, and E. Ozbay, “Negative refraction and focusing of electromagnetic waves by metallodielectric photonic crystals,” Phys. Rev. B 72, 045124 (2005).
[CrossRef]

2004 (3)

D. Schurig and D. Smith, “Negative index lens aberrations,” Phys. Rev. E 70, 065601 (2004).
[CrossRef]

P. Loschialpo, D. Forester, D. Smith, F. Rachford, and C. Monzon, “Optical properties of an ideal homogeneous causal left-handed material slab,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

M. Nieto-Vesperinas, “Problem of image superresolution with a negative-refractive-index slab,” J. Opt. Soc. Am. A 21, 491–498 (2004).
[CrossRef]

2003 (1)

P. Loschialpo, D. Smith, D. Forester, F. Rachford, and J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 025602 (2003).
[CrossRef]

2002 (2)

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

P. Valanju, R. Walser, and A. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ϵ and μ,” Physics-Uspekhi 10, 509–514 (1968).
[CrossRef]

Asatsuma, T.

Baba, T.

Baena, J. D.

R. Marques, M. J. Freire, and J. D. Baena, “Theory of three-dimensional subdiffraction imaging,” Appl. Phys. Lett. 89, 211113 (2006).
[CrossRef]

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

Bulu, I.

I. Bulu, H. Caglayan, and E. Ozbay, “Negative refraction and focusing of electromagnetic waves by metallodielectric photonic crystals,” Phys. Rev. B 72, 045124 (2005).
[CrossRef]

Caglayan, H.

I. Bulu, H. Caglayan, and E. Ozbay, “Negative refraction and focusing of electromagnetic waves by metallodielectric photonic crystals,” Phys. Rev. B 72, 045124 (2005).
[CrossRef]

Calander, N.

N. Calander, “Surface plasmon-coupled emission and Fabry-Perot resonance in the sample layer: a theoretical approach,” J. Phys. Chem. B 109, 13957–13963 (2005).
[CrossRef]

Chan, C. T.

J. Li and C. T. Chan, “Imaging using nano metallic films: from evanescent wave lens to resonant tunnelling lens,” arXiv:physics/0701172v1 (2007).

Chen, J.

J. Chen, C. Radu, and A. Puri, “Aberration-free negative-refractive-index lens,” Appl. Phys. Lett. 88, 071119 (2006).
[CrossRef]

da Costa, J.

T. Dumelow, J. da Costa, and V. Freire, “Slab lenses from simple anisotropic media,” Phys. Rev. B 72, 235115 (2005).
[CrossRef]

Dumelow, T.

T. Dumelow, J. da Costa, and V. Freire, “Slab lenses from simple anisotropic media,” Phys. Rev. B 72, 235115 (2005).
[CrossRef]

Eom, K.-S.

Forester, D.

P. Loschialpo, D. Forester, D. Smith, F. Rachford, and C. Monzon, “Optical properties of an ideal homogeneous causal left-handed material slab,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

P. Loschialpo, D. Smith, D. Forester, F. Rachford, and J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 025602 (2003).
[CrossRef]

Freire, M. J.

R. Marques, M. J. Freire, and J. D. Baena, “Theory of three-dimensional subdiffraction imaging,” Appl. Phys. Lett. 89, 211113 (2006).
[CrossRef]

Freire, V.

T. Dumelow, J. da Costa, and V. Freire, “Slab lenses from simple anisotropic media,” Phys. Rev. B 72, 235115 (2005).
[CrossRef]

Friberg, A. T.

Fujita, S.

Gibbons, J. M.

Hakkarainen, T.

Kotynski, R.

Li, F.

H. Luo, Z. Ren, W. Shu, and F. Li, “Construction of a polarization insensitive lens from a quasi-isotropic metamaterial slab,” Phys. Rev. E 75, 026601 (2007).
[CrossRef]

Li, J.

J. Li and C. T. Chan, “Imaging using nano metallic films: from evanescent wave lens to resonant tunnelling lens,” arXiv:physics/0701172v1 (2007).

Lin, Z.

Loschialpo, P.

P. Loschialpo, D. Forester, D. Smith, F. Rachford, and C. Monzon, “Optical properties of an ideal homogeneous causal left-handed material slab,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

P. Loschialpo, D. Smith, D. Forester, F. Rachford, and J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 025602 (2003).
[CrossRef]

Luo, H.

H. Luo, Z. Ren, W. Shu, and F. Li, “Construction of a polarization insensitive lens from a quasi-isotropic metamaterial slab,” Phys. Rev. E 75, 026601 (2007).
[CrossRef]

Mahajan, V. N.

V. N. Mahajan, Optical Imaging and Aberrations. Part I. Ray Geometrical Optics (SPIE, 1998).

Marques, R.

R. Marques, M. J. Freire, and J. D. Baena, “Theory of three-dimensional subdiffraction imaging,” Appl. Phys. Lett. 89, 211113 (2006).
[CrossRef]

Matsumoto, T.

Miret, J. J.

Monzon, C.

P. Loschialpo, D. Forester, D. Smith, F. Rachford, and C. Monzon, “Optical properties of an ideal homogeneous causal left-handed material slab,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

Nieto-Vesperinas, M.

Ozbay, E.

I. Bulu, H. Caglayan, and E. Ozbay, “Negative refraction and focusing of electromagnetic waves by metallodielectric photonic crystals,” Phys. Rev. B 72, 045124 (2005).
[CrossRef]

Park, W.

Pastor, D.

Pendry, J. B.

D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express 15, 14772–14782 (2007).
[CrossRef]

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

Puri, A.

J. Chen, C. Radu, and A. Puri, “Aberration-free negative-refractive-index lens,” Appl. Phys. Lett. 88, 071119 (2006).
[CrossRef]

Rachford, F.

P. Loschialpo, D. Forester, D. Smith, F. Rachford, and C. Monzon, “Optical properties of an ideal homogeneous causal left-handed material slab,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

P. Loschialpo, D. Smith, D. Forester, F. Rachford, and J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 025602 (2003).
[CrossRef]

Radu, C.

J. Chen, C. Radu, and A. Puri, “Aberration-free negative-refractive-index lens,” Appl. Phys. Lett. 88, 071119 (2006).
[CrossRef]

Ramakrishna, S. A.

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

Ren, Z.

H. Luo, Z. Ren, W. Shu, and F. Li, “Construction of a polarization insensitive lens from a quasi-isotropic metamaterial slab,” Phys. Rev. E 75, 026601 (2007).
[CrossRef]

Schelleng, J.

P. Loschialpo, D. Smith, D. Forester, F. Rachford, and J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 025602 (2003).
[CrossRef]

Schultz, S.

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

Schurig, D.

D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express 15, 14772–14782 (2007).
[CrossRef]

D. Schurig and D. Smith, “Negative index lens aberrations,” Phys. Rev. E 70, 065601 (2004).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

Setälä, T.

Shu, W.

H. Luo, Z. Ren, W. Shu, and F. Li, “Construction of a polarization insensitive lens from a quasi-isotropic metamaterial slab,” Phys. Rev. E 75, 026601 (2007).
[CrossRef]

Smith, D.

P. Loschialpo, D. Forester, D. Smith, F. Rachford, and C. Monzon, “Optical properties of an ideal homogeneous causal left-handed material slab,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

D. Schurig and D. Smith, “Negative index lens aberrations,” Phys. Rev. E 70, 065601 (2004).
[CrossRef]

P. Loschialpo, D. Smith, D. Forester, F. Rachford, and J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 025602 (2003).
[CrossRef]

Smith, D. R.

D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express 15, 14772–14782 (2007).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

Stefaniuk, T.

Tsai, D. P.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

Valanju, A.

P. Valanju, R. Walser, and A. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef]

Valanju, P.

P. Valanju, R. Walser, and A. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ϵ and μ,” Physics-Uspekhi 10, 509–514 (1968).
[CrossRef]

Walser, R.

P. Valanju, R. Walser, and A. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef]

Wood, B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

Wu, Q.

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

Zapata-Rodríguez, C. J.

Zou, Y.

Appl. Opt. (2)

Appl. Phys. Lett. (2)

R. Marques, M. J. Freire, and J. D. Baena, “Theory of three-dimensional subdiffraction imaging,” Appl. Phys. Lett. 89, 211113 (2006).
[CrossRef]

J. Chen, C. Radu, and A. Puri, “Aberration-free negative-refractive-index lens,” Appl. Phys. Lett. 88, 071119 (2006).
[CrossRef]

J. Mod. Opt. (1)

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

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

J. Phys. Chem. B (1)

N. Calander, “Surface plasmon-coupled emission and Fabry-Perot resonance in the sample layer: a theoretical approach,” J. Phys. Chem. B 109, 13957–13963 (2005).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. B (3)

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

T. Dumelow, J. da Costa, and V. Freire, “Slab lenses from simple anisotropic media,” Phys. Rev. B 72, 235115 (2005).
[CrossRef]

I. Bulu, H. Caglayan, and E. Ozbay, “Negative refraction and focusing of electromagnetic waves by metallodielectric photonic crystals,” Phys. Rev. B 72, 045124 (2005).
[CrossRef]

Phys. Rev. E (4)

D. Schurig and D. Smith, “Negative index lens aberrations,” Phys. Rev. E 70, 065601 (2004).
[CrossRef]

H. Luo, Z. Ren, W. Shu, and F. Li, “Construction of a polarization insensitive lens from a quasi-isotropic metamaterial slab,” Phys. Rev. E 75, 026601 (2007).
[CrossRef]

P. Loschialpo, D. Forester, D. Smith, F. Rachford, and C. Monzon, “Optical properties of an ideal homogeneous causal left-handed material slab,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

P. Loschialpo, D. Smith, D. Forester, F. Rachford, and J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 025602 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

P. Valanju, R. Walser, and A. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef]

Physics-Uspekhi (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ϵ and μ,” Physics-Uspekhi 10, 509–514 (1968).
[CrossRef]

Other (4)

V. N. Mahajan, Optical Imaging and Aberrations. Part I. Ray Geometrical Optics (SPIE, 1998).

J. Li and C. T. Chan, “Imaging using nano metallic films: from evanescent wave lens to resonant tunnelling lens,” arXiv:physics/0701172v1 (2007).

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

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Figures (8)

Fig. 1.
Fig. 1.

Schematic representation of an asymmetric flat lens of refractive index n2 and width d.

Fig. 2.
Fig. 2.

Geometrical imaging for a flat lens of n2=2 sandwiched between dielectric media of indices of refraction n1=1 and n3=4. (a) Gaussian imaging based on Eq. (3). (b) Red line represents primary SA given by Eq. (4) and blue line represents fifth-order SA given by Eq (6).

Fig. 3.
Fig. 3.

Ray tracing for an object point located at (a) s1=0.1d, which is corrected of primary SA, (b) s1=0.4d, and (c) s1=0.5d from the front surface of a flat lens of width d. Indices of refraction are the same as in Fig. 2. Traces corresponding to paraxial (slope lower than 30°) and nonparaxial rays are drawn in different colors. Small light-colored stars represent conjugated points.

Fig. 4.
Fig. 4.

Transmission coefficient (modulus and argument) for (a)–(c) s-polarized waves and (d)–(f) p-polarized waves in a superlens of μ2=1+i0.001 and ε2=4+i0.001. Surrounding transparent media have again indices of refraction n1=1 and n3=4. We consider different widths for the LHM flat lens: (a) and (d) d=0.125λ0; (b) and (e) d=0.875λ0; (c) and (f) d=5.125λ0. Note that all the horizontal scales are not the same.

Fig. 5.
Fig. 5.

Electric line dipole composed of a continuous distribution of point dipoles that are oriented in the y direction and simulating a current I0 flowing along the y-axis.

Fig. 6.
Fig. 6.

Modulus of the electric field emitted by a line electric dipole and transmitted through a negative-index slab with μ2=1+i0.001 and ε2=4+i0.001 and different widths: (a) d=0.125λ0, (b) d=0.875λ0, and (c) d=5.125λ0. In all cases we present the field within zs3. The density plots are normalized to unity at the paraxial image point (x,z)=(0,0). The dashed line indicates points where amplitude falls off 1/2. The thin vertical line marks the Gaussian image plane. The wave fields corresponding to the Gaussian image plane for (a), (b), and (c) are plotted in (d), (e), and (f), respectively.

Fig. 7.
Fig. 7.

|H⃗| from Eq. (15) as it is evaluated in the image space of a LHM flat lens with μ2=1+i0.001 and ε2=4+i0.001 and different widths: (a) d=0.125λ0, (b) d=0.875λ0, and (c) d=5.125λ0. Again, the fields in the Gaussian image plane for (a), (b), and (c) are plotted in (d), (e), and (f), respectively.

Fig. 8.
Fig. 8.

Modulus of the 2D PSF |h2| for a LHM flat lens with μ2=1+i0.001 and ε2=4+i0.001 for different states of polarization: (a)–(c) applies for p-polarized waves and (d)–(f) for s polarization. In (g)–(i), we chart the data for the Gaussian image plane. The slab width is also varied: d=0.125λ0 for subfigures placed in the left column, d=0.875λ0 for subfigures in the central column, and d=5.125λ0 for plots on the right.

Equations (19)

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

W(h2)a200h22+a400h24+a600h26.
n1sinσ1=n2sinσ2.
s3=n3(s1n1dn2).
a400=n1n2[n13(n22n32)d+n23(n32n12)s1]8n32(n1dn2s1)4.
s1=n13(n32n22)n23(n32n12)d,
a600=n113(n12n32)(n22n32)616n22n314(n22n12)5s15.
r=r1,2+r2,3exp(2iβ2d)1+r1,2r2,3exp(2iβ2d)exp(2iβ1s1),
t=t1,2t2,3exp(iβ1s1+iβ2d+iβ3s3)1+r1,2r2,3exp(2iβ2d).
βi=σiεiμik02k⃗·k⃗,
ri,j=μjβiμiβjμjβi+μiβj,
β2d=(2m+1)π/2,
β22μ1μ3=μ22β1β3,
E⃗=ik12p4ε1H0(1)(k1R0)y^,
H0(1)(k1R0)=1πexp(ikxx+iβ1z)β1dkx,
E⃗=ik12p4πε1y^t(kx)exp(ikxx+iβ3z)β1dkx.
H⃗=ik12m4πμ1y^t(kx)exp(ikxx+iβ3z)β1dkx.
E⃗(R⃗,z)=E⃗sc(R⃗)*h(R⃗,z),
h(R⃗,z)=1(2π)2t(k⃗)exp(ik⃗R⃗+iβ3z)dk⃗,
h2(x,z)=12πt(kx)exp(ikxx+iβ3z)dkx.

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