Abstract

We show that finite-size nondiffracting beams can be generated by a subwavelength metallic hole with surrounding dielectric grating structures. An analytic field model that describes the diffractive formation of finite-size nondiffracting beams is addressed. The generation of finite-size nondiffracting beams from a subwavelength metallic hole with surrounding concentric dielectric binary gratings is numerically demonstrated by three-dimensional rigorous coupled wave analysis.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820-822(2002).
    [CrossRef] [PubMed]
  2. L. Martin-Moreno, F. J. Garcia-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, 167401 (2003).
    [CrossRef] [PubMed]
  3. F. J. Garcia-Vidal, L. Martin-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]
  4. L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y. C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71, 041405 (2005).
    [CrossRef]
  5. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
    [CrossRef] [PubMed]
  6. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39-46 (2007).
    [CrossRef] [PubMed]
  7. S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett. 90, 051113 (2007).
    [CrossRef]
  8. S. Kim, H. Kim, Y. Lim, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
    [CrossRef]
  9. J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239-245 (2001).
    [CrossRef]
  10. T. Cizmar, V. Garces-Chavez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
    [CrossRef]
  11. Q. Zhan, “Evanescent Bessel beam generation via surface plasmon resonance excitation by a radially polarized beam,” Opt. Lett. 31, 1726-1728 (2006).
    [CrossRef] [PubMed]
  12. J. Durin, “Exact solution for nondiffracting beams,” J. Opt. Soc. Am. A 4, 651-654 (1987).
    [CrossRef]
  13. H. Kim, I.-M. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” J. Opt. Soc. Am. A 24, 2313-2327(2007).
    [CrossRef]
  14. H. Kim, J. Park, and B. Lee, “Tunable directional beaming from subwavelength metal slits with metal-dielectric composite surface gratings,” Opt. Lett. 34, 2569-2571(2009).
    [CrossRef] [PubMed]

2009 (1)

2008 (1)

S. Kim, H. Kim, Y. Lim, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

2007 (3)

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39-46 (2007).
[CrossRef] [PubMed]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett. 90, 051113 (2007).
[CrossRef]

H. Kim, I.-M. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” J. Opt. Soc. Am. A 24, 2313-2327(2007).
[CrossRef]

2006 (1)

2005 (2)

T. Cizmar, V. Garces-Chavez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y. C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71, 041405 (2005).
[CrossRef]

2003 (3)

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

L. Martin-Moreno, F. J. Garcia-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, 167401 (2003).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, L. Martin-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 (1)

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

2001 (1)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239-245 (2001).
[CrossRef]

1987 (1)

Arlt, J.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Barnes, W. L.

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

Chang, Y. C.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y. C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Chen, Y.-C.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y. C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Cizmar, T.

T. Cizmar, V. Garces-Chavez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

Degiron, A.

L. Martin-Moreno, F. J. Garcia-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, 167401 (2003).
[CrossRef] [PubMed]

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

Dereux, A.

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

Devaux, E.

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

Dholakia, K.

T. Cizmar, V. Garces-Chavez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Durin, J.

Ebbesen, T. W.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39-46 (2007).
[CrossRef] [PubMed]

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

L. Martin-Moreno, F. J. Garcia-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, 167401 (2003).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, L. Martin-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]

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

Garces-Chavez, V.

T. Cizmar, V. Garces-Chavez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Garcia-Vidal, F. J.

L. Martin-Moreno, F. J. Garcia-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, 167401 (2003).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, L. Martin-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]

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

Genet, C.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39-46 (2007).
[CrossRef] [PubMed]

Huang, K.-T.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y. C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Kim, H.

H. Kim, J. Park, and B. Lee, “Tunable directional beaming from subwavelength metal slits with metal-dielectric composite surface gratings,” Opt. Lett. 34, 2569-2571(2009).
[CrossRef] [PubMed]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett. 90, 051113 (2007).
[CrossRef]

H. Kim, I.-M. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” J. Opt. Soc. Am. A 24, 2313-2327(2007).
[CrossRef]

Kim, S.

S. Kim, H. Kim, Y. Lim, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett. 90, 051113 (2007).
[CrossRef]

Lee, B.

H. Kim, J. Park, and B. Lee, “Tunable directional beaming from subwavelength metal slits with metal-dielectric composite surface gratings,” Opt. Lett. 34, 2569-2571(2009).
[CrossRef] [PubMed]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett. 90, 051113 (2007).
[CrossRef]

H. Kim, I.-M. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” J. Opt. Soc. Am. A 24, 2313-2327(2007).
[CrossRef]

Lee, C.-K.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y. C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Lee, I.-M.

Lezec, H. J.

F. J. Garcia-Vidal, L. Martin-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. Martin-Moreno, F. J. Garcia-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, 167401 (2003).
[CrossRef] [PubMed]

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

Liaw, J.-W.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y. C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Lim, Y.

S. Kim, H. Kim, Y. Lim, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett. 90, 051113 (2007).
[CrossRef]

Lin, D.-Z.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y. C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Linke, R. A.

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

Liu, J.-M.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y. C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Martin-Moreno, L.

L. Martin-Moreno, F. J. Garcia-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, 167401 (2003).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, L. Martin-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]

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

Park, J.

Sibbett, W.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Yeh, C.-S.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y. C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Yeh, J.-T.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y. C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Yu, L.-B.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y. C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Zemanek, P.

T. Cizmar, V. Garces-Chavez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

Zhan, Q.

Appl. Phys. Lett. (4)

F. J. Garcia-Vidal, L. Martin-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]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett. 90, 051113 (2007).
[CrossRef]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

T. Cizmar, V. Garces-Chavez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

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

Nature (2)

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

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39-46 (2007).
[CrossRef] [PubMed]

Opt. Commun. (1)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (1)

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y. C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

L. Martin-Moreno, F. J. Garcia-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, 167401 (2003).
[CrossRef] [PubMed]

Science (1)

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Cross-sectional x z plane ( y = 0 ) profiles of (a) field function F ( x , 0 , z ) and partial field functions of (b)  F 1 ( x , y , z ) and (c)  F 2 ( x , y , z ) , with structural parameters of A = 1.5 , R 1 = 0.6 μm , R 2 = 5 μm , χ 1 = 1 μm , χ 2 = 2 μm , and θ 2 = 25 ( deg . ) .

Fig. 2
Fig. 2

Cross-sectional x z plane ( y = 0 ) profiles of (a) field function F ( x , 0 , z ) , with a change in A ( = 3 ) and (b) field function F ( x , 0 , z ) , with a change in χ 2 ( = 16 μm ) .

Fig. 3
Fig. 3

Subwavelength metallic hole with a concentric dielectric grating: (a) finite size nondiffracting beam generation and (b) contributing partial field components F 1 and F 2 .

Fig. 4
Fig. 4

RCWA simulation results of the generation of a finite-size nondiffracting beam with a length of 10 μm from a subwavelength hole with a concentric circular binary grating structure; x-directional polarization electric field distributions | E x | at the (a)  x z plane ( y = 0 ) and (b)  y z plane ( x = 0 ) . Inset in (a) shows the field intensity profile along the z axis.

Equations (6)

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

F 1 ( x , y , 0 ) = A exp ( χ 1 x 2 + y 2 ) circ ( x 2 + y 2 / R 1 ) ,
F 2 ( x , y , 0 ) = exp ( ( χ 2 + j k θ ) x 2 + y 2 ) circ ( x 2 + y 2 / R 2 ) ,
circ ( r ) = { 1 for     | r | 1 0 for     | r | > 1 .
F ( x , y , z ) = A ( α , β ) exp ( j 2 π ( α x + β y + γ z ) ) d α d β ,
A ( α , β ) = F ( x , y , z = 0 ) exp ( j 2 π ( α x + β y ) ) d x d y ,
F ( x , y , z ) = F 1 ( x , y , z ) + F 2 ( x , y , z ) ,

Metrics