Abstract

The characteristics of the phase retardations and the invariability against the incident angles are investigated when light enters the rectangular holes with different sizes perforated on metallic film. A kind of metallic structure with a great potential in imaging is brought forward. The finite difference time domain (FDTD) method and the Rayleigh-Sommerfeld diffraction integrals are used to testify the imaging ability at different incident angles by examining the electric field on focal plane. The calculation results indicate that a quite large view of field lens can be achieved by increasing the number of the holes per unit area with the mentioned structure. A metallic structured lens with a 280 µm aperture and 240 µm focal length is designed and the view angle range of ±15° can be achieved.

© 2008 Optical Society of America

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References

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  1. H. J. Lezec, A. Degiron., E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002).
    [CrossRef] [PubMed]
  2. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167,401 (2003).
    [CrossRef]
  3. 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. B 74, 245,403 (2006).
  4. L. Yu, D. Lin,  et al., "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041,405 (2005).
    [CrossRef]
  5. F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, "Focusing light with a single subwavelength aperture flanked by surface corrugations," Appl. Phys. Lett. 83, 4500-4502 (2003).
    [CrossRef]
  6. A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, "Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate," Appl. Phys. Lett. 81, 4661-4663 (2002).
    [CrossRef]
  7. H. Shi., C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, "Beam manipulating by metallic nano-slits with variant widths," Opt. Express 13, 6815-6820 (2005).
    [CrossRef] [PubMed]
  8. Z. Sun, and H. K. Kim, "Refractive transmission of light and beam shaping with metallic nano-optic lenses," Appl. Phys. Lett. 85, 642-644 (2004).
    [CrossRef]
  9. J. R. Krenn, "Nanoparticle waveguides: Watching energy transfer," Nat. Mater. 2, 210-211 (2003).
    [CrossRef] [PubMed]
  10. 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]
  11. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A.G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003)
    [CrossRef] [PubMed]
  12. S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990-3992 (2004).
    [CrossRef]
  13. S. A. Maier, P. G. Kik, and H. A. Atwater, "Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss," Appl. Phys. Lett. 81, 1714-1716 (2002).
    [CrossRef]
  14. J. M. Brok, and H. P. Urbach, "Extraordinary transmission through 1, 2 and 3 holes in a perfect conductor, modelled by a mode expansion technique," Opt. Express 14, 2552-2572 (2006).
    [CrossRef] [PubMed]
  15. K. Q. Zhang, and D. J. Li, Electromagnetic theory for microwaves and optoelectronics (Publishing House of Elecronics Industry, Peking, 2001).
  16. M. Born, and E. Wolf, Principles of optics, 7th ed. (Press of Cambridge University, Cambridge, 1999)

2006 (2)

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. B 74, 245,403 (2006).

J. M. Brok, and H. P. Urbach, "Extraordinary transmission through 1, 2 and 3 holes in a perfect conductor, modelled by a mode expansion technique," Opt. Express 14, 2552-2572 (2006).
[CrossRef] [PubMed]

2005 (2)

H. Shi., C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, "Beam manipulating by metallic nano-slits with variant widths," Opt. Express 13, 6815-6820 (2005).
[CrossRef] [PubMed]

L. Yu, D. Lin,  et al., "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041,405 (2005).
[CrossRef]

2004 (2)

Z. Sun, and H. K. Kim, "Refractive transmission of light and beam shaping with metallic nano-optic lenses," Appl. Phys. Lett. 85, 642-644 (2004).
[CrossRef]

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990-3992 (2004).
[CrossRef]

2003 (4)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A.G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003)
[CrossRef] [PubMed]

J. R. Krenn, "Nanoparticle waveguides: Watching energy transfer," Nat. Mater. 2, 210-211 (2003).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167,401 (2003).
[CrossRef]

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, "Focusing light with a single subwavelength aperture flanked by surface corrugations," Appl. Phys. Lett. 83, 4500-4502 (2003).
[CrossRef]

2002 (3)

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, "Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate," Appl. Phys. Lett. 81, 4661-4663 (2002).
[CrossRef]

H. J. Lezec, A. Degiron., E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

S. A. Maier, P. G. Kik, and H. A. Atwater, "Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss," Appl. Phys. Lett. 81, 1714-1716 (2002).
[CrossRef]

2001 (1)

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]

Atwater, H. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A.G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003)
[CrossRef] [PubMed]

S. A. Maier, P. G. Kik, and H. A. Atwater, "Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss," Appl. Phys. Lett. 81, 1714-1716 (2002).
[CrossRef]

Barclay, P. E.

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990-3992 (2004).
[CrossRef]

Bozhevolnyi, S. I.

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]

Brok, J. M.

Degiron, A.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167,401 (2003).
[CrossRef]

H. J. Lezec, A. Degiron., E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

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. B 74, 245,403 (2006).

Ebbesen, T. W.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167,401 (2003).
[CrossRef]

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, "Focusing light with a single subwavelength aperture flanked by surface corrugations," Appl. Phys. Lett. 83, 4500-4502 (2003).
[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]

Friedman, M. D.

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990-3992 (2004).
[CrossRef]

García-Vidal, F. J.

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, "Focusing light with a single subwavelength aperture flanked by surface corrugations," Appl. Phys. Lett. 83, 4500-4502 (2003).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167,401 (2003).
[CrossRef]

Harel, E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A.G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003)
[CrossRef] [PubMed]

Hibbins, A. P.

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, "Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate," Appl. Phys. Lett. 81, 4661-4663 (2002).
[CrossRef]

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]

Johnson, T. J.

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990-3992 (2004).
[CrossRef]

Kik, P. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A.G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003)
[CrossRef] [PubMed]

S. A. Maier, P. G. Kik, and H. A. Atwater, "Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss," Appl. Phys. Lett. 81, 1714-1716 (2002).
[CrossRef]

Kim, H. K.

Z. Sun, and H. K. Kim, "Refractive transmission of light and beam shaping with metallic nano-optic lenses," Appl. Phys. Lett. 85, 642-644 (2004).
[CrossRef]

Koel, B. E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A.G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003)
[CrossRef] [PubMed]

Krenn, J. R.

J. R. Krenn, "Nanoparticle waveguides: Watching energy transfer," Nat. Mater. 2, 210-211 (2003).
[CrossRef] [PubMed]

Lawrence, C. R.

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, "Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate," Appl. Phys. Lett. 81, 4661-4663 (2002).
[CrossRef]

Leosson, K.

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]

Lezec, H. J.

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, "Focusing light with a single subwavelength aperture flanked by surface corrugations," Appl. Phys. Lett. 83, 4500-4502 (2003).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167,401 (2003).
[CrossRef]

H. J. Lezec, A. Degiron., E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

Lin, D.

L. Yu, D. Lin,  et al., "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041,405 (2005).
[CrossRef]

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. B 74, 245,403 (2006).

Maier, S. A.

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990-3992 (2004).
[CrossRef]

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A.G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003)
[CrossRef] [PubMed]

S. A. Maier, P. G. Kik, and H. A. Atwater, "Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss," Appl. Phys. Lett. 81, 1714-1716 (2002).
[CrossRef]

Martín-Moreno, L.

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, "Focusing light with a single subwavelength aperture flanked by surface corrugations," Appl. Phys. Lett. 83, 4500-4502 (2003).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167,401 (2003).
[CrossRef]

Meltzer, S.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A.G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003)
[CrossRef] [PubMed]

Painter, O.

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990-3992 (2004).
[CrossRef]

Requicha, A. A.G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A.G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003)
[CrossRef] [PubMed]

Sambles, J. R.

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, "Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate," Appl. Phys. Lett. 81, 4661-4663 (2002).
[CrossRef]

Shi, H.

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]

Sun, Z.

Z. Sun, and H. K. Kim, "Refractive transmission of light and beam shaping with metallic nano-optic lenses," Appl. Phys. Lett. 85, 642-644 (2004).
[CrossRef]

Urbach, H. P.

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. B 74, 245,403 (2006).

Yu, L.

L. Yu, D. Lin,  et al., "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041,405 (2005).
[CrossRef]

Appl. Phys. Lett. (5)

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, "Focusing light with a single subwavelength aperture flanked by surface corrugations," Appl. Phys. Lett. 83, 4500-4502 (2003).
[CrossRef]

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, "Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate," Appl. Phys. Lett. 81, 4661-4663 (2002).
[CrossRef]

Z. Sun, and H. K. Kim, "Refractive transmission of light and beam shaping with metallic nano-optic lenses," Appl. Phys. Lett. 85, 642-644 (2004).
[CrossRef]

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990-3992 (2004).
[CrossRef]

S. A. Maier, P. G. Kik, and H. A. Atwater, "Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss," Appl. Phys. Lett. 81, 1714-1716 (2002).
[CrossRef]

Nat. Mater. (2)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A.G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003)
[CrossRef] [PubMed]

J. R. Krenn, "Nanoparticle waveguides: Watching energy transfer," Nat. Mater. 2, 210-211 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Phys. Rev. B (2)

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. B 74, 245,403 (2006).

L. Yu, D. Lin,  et al., "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041,405 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167,401 (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]

Science (1)

H. J. Lezec, A. Degiron., E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

Other (2)

K. Q. Zhang, and D. J. Li, Electromagnetic theory for microwaves and optoelectronics (Publishing House of Elecronics Industry, Peking, 2001).

M. Born, and E. Wolf, Principles of optics, 7th ed. (Press of Cambridge University, Cambridge, 1999)

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Figures (4)

Fig. 1.
Fig. 1.

Diagram of the metallic subwavelength structured lens consisting of square latticed hole array, with surface parallel to the xy plane; the optical axis is along z axis and the incident light is y-polarized plane wave with wave vector always in xz plane.

Fig. 2.
Fig. 2.

The electric fields on the focal plane (z=234 µm) of the metallic lens with hole array period equal to 1.75λo . (a) the electric field in the 600µm×600µm region on the focal plane with normal incident. (b) Electric field on the line y=0 and x from -200µm to 200 µm when the incident angle is , 10°, 15°, 20° respectively; peaks in x<0 are the secondary maximum spots and in x>0 are the focuses. The maximum electric field ratios of the focus to the secondary diffraction maximum are 1.64, 1.52, 1.10, and 0.856 for the incident angle of , 10°, 15°, 20° respectively.

Fig. 3.
Fig. 3.

The maximum electric field amplitude ratio of main focus to the secondary diffraction maximum as a function of the incident angle and array period. During our calculation, the holes’ side length a is set to be 0.8λ0,

Fig. 4.
Fig. 4.

The electric fields on the focal plane (z=234 µm) of the optimized metallic lens. (a) The electric field in the 800µm×800µm region on the focal plane with normal incident. (b) Electric field on the line y=0 and x from -300µm to 300 µm; peaks in x<0 are the secondary maximum spots and in x>0 are the focuses. The maximum electric field ratios of the focus to the secondary diffraction maximum are 6.44, 4.80, 3.10, and 2.38 when the incident angle is , 10°, 15°, 20° respectively.

Equations (7)

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

E ( x , y , z ) = [ A 1 x ̂ 0 sin ( π a y ) + A 2 y ̂ 0 sin ( π a x ) ] · exp ( i z · k 0 2 π 2 a 2 )
φ = h · k 0 2 π 2 a 2
φ ( r ) = 2 m π + 2 π λ ( r 2 + f 2 f )
E 0 ( x , y ) = n = 1 N rect [ ( x x n ) a , ( y y n ) a ] · e i k x n sin θ · e ik x 2 + y 2 2 f
E f ( x , y ) sin c ( a u , a v ) n = 1 N e i 2 π ( x n u x n sin θ λ + y n v )
u = x λ f , v = y λ f
u = 1 Δ + sin θ λ ; v = 0

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