Abstract

Based on the radial finite-difference time domain method we numerically show that the illumination of a conical glass microaxicon of base radius 7μm and height 6μm (numerical aperture NA=0.6) by a radially polarized annular R-TEM01 laser mode of wavelength λ=1μm produces, 20 nm apart from the cone apex, a sharp focus of transverse diameter FWHM=0.30λ and longitudinal (axial) width FWHMz=0.08λ. The focal spot area at half-maximum intensity is HMA=0.071λ2. For comparison the focus diameter reported here is 1.7 times smaller than the diameter of the minimal diffraction spot (Airy disk, NA=1) of FWHM=0.51λ, with its area being 2.87 times smaller than that of the Airy disk HMA=0.204λ2. Also it is smaller than the diameter of a focal spot formed by a lens with NA=0.6 in an immersion medium n=1.5, FWHM=0.51λ/n  NA=0.55λ, smaller than the diffraction limit in the medium (n=1.5, NA=1) FWHM=0.51λ/n=0.33λ and smaller than the focusing limit for the Bessel beam (NA=1) FWHM=0.36λ.

© 2010 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  6. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
    [CrossRef] [PubMed]
  7. V. A. Podolskiy and E. E. Narimanov, “Near-sighted superlens,” Opt. Lett. 30, 75–77 (2005).
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  8. R. Merlin, “Analytical solution of the almost-perfect-lens problem,” Appl. Phys. Lett. 84, 1290–1292 (2004).
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    [CrossRef]
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  16. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686–1688 (2007).
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  17. R. Merlin, “Radiationless electromagnetic interference: evanescent-field lenses and perfect focusing,” Science 317, 927–929 (2007).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  33. J. Li, K. Ueda, M. Musha, A. Shirakawa, and Z. Zhang, “Converging-axicon-based radially polarized ytterbium fiber laser and evidence on the mode profile inside the gain filter,” Opt. Lett. 32, 1360–1362 (2007).
    [CrossRef] [PubMed]
  34. K. Yonezawa, Y. Kozawa, and S. Sato, “Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal,” Opt. Lett. 31, 2151–2153 (2006).
    [CrossRef] [PubMed]
  35. A. Mehta, J. D. Brown, P. Srinivasan, R. C. Rumpf, and E. G. Jhonson, “Spatially polarizing autocloned elements,” Opt. Lett. 32, 1935–1937 (2007).
    [CrossRef] [PubMed]
  36. U. Levy, C. Tsai, L. Pang, and Y. Fainman, “Engineering space-variant inhomogeneous media for polarization control,” Opt. Lett. 29, 1718–1720 (2004).
    [CrossRef] [PubMed]
  37. G. M. Lerman and U. Levy, “Generation of a radially polarized light beam using space-variant subwavelength gratings at 1064 nm,” Opt. Lett. 33, 2782–2784 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]

2010 (1)

2009 (1)

V. V. Kotlyar and S. S. Stafeev, “Sharply focusing a radially polarized laser beam using a gradient Mikaelian’s microlens,” Opt. Commun. 282, 459–464 (2009).
[CrossRef]

2008 (3)

2007 (6)

2006 (8)

J. Li, K. Ueda, M. Musha, A. Shirakawa, and L. Zhong, “Generation of radially polarized mode in Yb fiber laser by using a dual conical prism,” Opt. Lett. 31, 2969–2971 (2006).
[CrossRef] [PubMed]

K. Yonezawa, Y. Kozawa, and S. Sato, “Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal,” Opt. Lett. 31, 2151–2153 (2006).
[CrossRef] [PubMed]

S. Yang, C. Hong, and H. Yang, “Focusing concave lens using photonic crystals with magnetic materials,” J. Opt. Soc. Am. A 23, 956–959 (2006).
[CrossRef]

T. Matsumoto, K. 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] [PubMed]

H. Chien and C. Chen, “Focusing of electromagnetic waves by periodic arrays of air holes with gradually varying radii,” Opt. Express 14, 10759–10764 (2006).
[CrossRef] [PubMed]

A. A. Govyadinov and V. A. Podolskiy, “Metamaterial photonic funnels for subdiffraction light compression and propagation,” Phys. Rev. B 73, 155108 (2006).
[CrossRef]

R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, “Nonmagnetic nanocomposites for optical and infrared negative refractive index media,” J. Opt. Soc. Am. B 23, 498–505 (2006).
[CrossRef]

Z. Jacob, L. V. Alekseyev, and E. E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
[CrossRef] [PubMed]

2005 (6)

2004 (5)

2003 (3)

2001 (1)

S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78, 4071–4073 (2001).
[CrossRef]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

1998 (1)

1992 (1)

Alekseyev, L. V.

Anand, S.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelength in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Baba, T.

Bainier, C.

Berrier, A.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelength in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Beversluis, M. R.

A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, “Plasmon-coupled tip-enhanced near-field optical microscopy,” J. Microsc. 210, 220–224 (2003).
[CrossRef] [PubMed]

Blaikie, R. J.

D. O. S. Melville and R. J. Blaikie, “Super-resolution imaging through a planar silver layer,” Opt. Express 13, 2127–2134 (2005).
[CrossRef] [PubMed]

R. J. Blaikie and D. O. S. Melville, “Imaging through planar silver lenses in the optical near field,” J. Opt. A, Pure Appl. Opt. 7, S176–S183 (2005).
[CrossRef]

Bouhelier, A.

A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, “Plasmon-coupled tip-enhanced near-field optical microscopy,” J. Microsc. 210, 220–224 (2003).
[CrossRef] [PubMed]

Brown, D. L.

Brown, J. D.

Cai, W.

Chen, C.

Chettiar, U. K.

Chien, H.

Courjon, D.

Drachev, V. P.

Eberly, J. H.

Elser, J.

Eom, K.

Fainman, Y.

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[CrossRef] [PubMed]

Gibbons, J. M.

Goldberg, B. B.

S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78, 4071–4073 (2001).
[CrossRef]

Golub, I.

Govyadinov, A. A.

A. A. Govyadinov and V. A. Podolskiy, “Metamaterial photonic funnels for subdiffraction light compression and propagation,” Phys. Rev. B 73, 155108 (2006).
[CrossRef]

Grosjean, T.

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University Press, 2006).

Herrmann, J.

Hong, C.

Huang, H.

Husakou, A.

Ippolito, S. B.

S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78, 4071–4073 (2001).
[CrossRef]

Jacob, Z.

Jhonson, E. G.

Jouravlev, M. V.

Kempa, K.

Kildishev, A. V.

Kim, K. S.

Kotlyar, V. V.

V. V. Kotlyar and S. S. Stafeev, “Sharply focusing a radially polarized laser beam using a gradient Mikaelian’s microlens,” Opt. Commun. 282, 459–464 (2009).
[CrossRef]

Kozawa, Y.

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686–1688 (2007).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[CrossRef] [PubMed]

Leizer, A.

Lerman, G. M.

Levy, U.

Li, J.

Lin, Y.

Liu, H.

Liu, Z.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686–1688 (2007).
[CrossRef] [PubMed]

Mason, D. R.

Matsumoto, T.

Mehta, A.

Melville, D. O. S.

R. J. Blaikie and D. O. S. Melville, “Imaging through planar silver lenses in the optical near field,” J. Opt. A, Pure Appl. Opt. 7, S176–S183 (2005).
[CrossRef]

D. O. S. Melville and R. J. Blaikie, “Super-resolution imaging through a planar silver layer,” Opt. Express 13, 2127–2134 (2005).
[CrossRef] [PubMed]

Merlin, R.

R. Merlin, “Radiationless electromagnetic interference: evanescent-field lenses and perfect focusing,” Science 317, 927–929 (2007).
[CrossRef] [PubMed]

R. Merlin, “Analytical solution of the almost-perfect-lens problem,” Appl. Phys. Lett. 84, 1290–1292 (2004).
[CrossRef]

Mulot, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelength in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Musha, M.

Narimanov, E. E.

Novotny, L.

A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, “Plasmon-coupled tip-enhanced near-field optical microscopy,” J. Microsc. 210, 220–224 (2003).
[CrossRef] [PubMed]

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University Press, 2006).

Pang, L.

Park, W.

Pendry, J. B.

J. B. Pendry, “Perfect cylindrical lenses,” Opt. Express 11, 755–760 (2003).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

Podolskiy, V. A.

Qiu, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelength in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Ren, Z. F.

Renger, J.

A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, “Plasmon-coupled tip-enhanced near-field optical microscopy,” J. Microsc. 210, 220–224 (2003).
[CrossRef] [PubMed]

Rumpf, R. C.

Ruschin, S.

Sarychev, A. K.

Sato, S.

Seka, W.

Shalaev, V. M.

Shirakawa, A.

Shivanand,

Srinivasan, P.

Stafeev, S. S.

V. V. Kotlyar and S. S. Stafeev, “Sharply focusing a radially polarized laser beam using a gradient Mikaelian’s microlens,” Opt. Commun. 282, 459–464 (2009).
[CrossRef]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686–1688 (2007).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[CrossRef] [PubMed]

Swillo, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelength in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Talneau, A.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelength in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Thylen, L.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelength in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Tsai, C.

Ueda, K.

Unlu, M. S.

S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78, 4071–4073 (2001).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “Superlens as matching device,” arXiv:cond-mat/0501438.

Wang, X.

Wangberg, R.

Webb, K. J.

Wu, Q.

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686–1688 (2007).
[CrossRef] [PubMed]

Yang, H.

Yang, S.

Yonezawa, K.

Yuan, H.

Zhang, X.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686–1688 (2007).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[CrossRef] [PubMed]

Zhang, Z.

Zhong, L.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78, 4071–4073 (2001).
[CrossRef]

R. Merlin, “Analytical solution of the almost-perfect-lens problem,” Appl. Phys. Lett. 84, 1290–1292 (2004).
[CrossRef]

J. Microsc. (1)

A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, “Plasmon-coupled tip-enhanced near-field optical microscopy,” J. Microsc. 210, 220–224 (2003).
[CrossRef] [PubMed]

J. Opt. A, Pure Appl. Opt. (1)

R. J. Blaikie and D. O. S. Melville, “Imaging through planar silver lenses in the optical near field,” J. Opt. A, Pure Appl. Opt. 7, S176–S183 (2005).
[CrossRef]

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

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

Opt. Commun. (1)

V. V. Kotlyar and S. S. Stafeev, “Sharply focusing a radially polarized laser beam using a gradient Mikaelian’s microlens,” Opt. Commun. 282, 459–464 (2009).
[CrossRef]

Opt. Express (8)

Opt. Lett. (14)

I. Golub, “Solid immersion axicon: maximizing nondiffracting or Bessel beam resolution,” Opt. Lett. 32, 2161–2163 (2007).
[CrossRef] [PubMed]

D. R. Mason, M. V. Jouravlev, and K. S. Kim, “Enhanced resolution beyond the Abbe diffraction limit with wavelength-scale solid immersion lenses,” Opt. Lett. 35, 2007–2009 (2010).
[CrossRef] [PubMed]

T. Matsumoto, K. 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] [PubMed]

T. Grosjean, D. Courjon, and C. Bainier, “Smallest lithographic marks generated by optical focusing systems,” Opt. Lett. 32, 976–978 (2007).
[CrossRef] [PubMed]

Y. Kozawa and S. Sato, “Generation of a radially polarized laser beam by use of a conical Brewster prism,” Opt. Lett. 30, 3063–3065 (2005).
[CrossRef] [PubMed]

J. Li, K. Ueda, M. Musha, A. Shirakawa, and L. Zhong, “Generation of radially polarized mode in Yb fiber laser by using a dual conical prism,” Opt. Lett. 31, 2969–2971 (2006).
[CrossRef] [PubMed]

J. Li, K. Ueda, M. Musha, A. Shirakawa, and Z. Zhang, “Converging-axicon-based radially polarized ytterbium fiber laser and evidence on the mode profile inside the gain filter,” Opt. Lett. 32, 1360–1362 (2007).
[CrossRef] [PubMed]

K. Yonezawa, Y. Kozawa, and S. Sato, “Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal,” Opt. Lett. 31, 2151–2153 (2006).
[CrossRef] [PubMed]

A. Mehta, J. D. Brown, P. Srinivasan, R. C. Rumpf, and E. G. Jhonson, “Spatially polarizing autocloned elements,” Opt. Lett. 32, 1935–1937 (2007).
[CrossRef] [PubMed]

U. Levy, C. Tsai, L. Pang, and Y. Fainman, “Engineering space-variant inhomogeneous media for polarization control,” Opt. Lett. 29, 1718–1720 (2004).
[CrossRef] [PubMed]

G. M. Lerman and U. Levy, “Generation of a radially polarized light beam using space-variant subwavelength gratings at 1064 nm,” Opt. Lett. 33, 2782–2784 (2008).
[CrossRef] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356–3358 (2005).
[CrossRef]

V. A. Podolskiy and E. E. Narimanov, “Near-sighted superlens,” Opt. Lett. 30, 75–77 (2005).
[CrossRef] [PubMed]

H. Liu, Shivanand, and K. J. Webb, “Subwavelength imaging opportunities with planar uniaxial anisotropic lenses,” Opt. Lett. 33, 2568–2570 (2008).
[PubMed]

Phys. Rev. B (1)

A. A. Govyadinov and V. A. Podolskiy, “Metamaterial photonic funnels for subdiffraction light compression and propagation,” Phys. Rev. B 73, 155108 (2006).
[CrossRef]

Phys. Rev. Lett. (2)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelength in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Science (3)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[CrossRef] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686–1688 (2007).
[CrossRef] [PubMed]

R. Merlin, “Radiationless electromagnetic interference: evanescent-field lenses and perfect focusing,” Science 317, 927–929 (2007).
[CrossRef] [PubMed]

Other (2)

V. G. Veselago, “Superlens as matching device,” arXiv:cond-mat/0501438.

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University Press, 2006).

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Figures (9)

Fig. 1
Fig. 1

Absolute value of radial component of the electric field strength of the mode R-TEM 01 .

Fig. 2
Fig. 2

Radial section of a conical microaxicon of radius R = 7 μ m and height h = 6 μ m .

Fig. 3
Fig. 3

(a) Intensity distribution | E | 2 on the optical axis when focusing the R-TEM 01 mode (Fig. 1) with the microaxicon of Fig. 2; (b) a scaled-up fragment of the curve in (a).

Fig. 4
Fig. 4

Radial intensity distributions: | E z | 2 (curve 3), | E r | 2 (curve 2), and | E | 2 = | E r | 2 + | E z | 2 (curve 1) in the focal plane at a 20 nm distance from the axicon apex (Fig. 3).

Fig. 5
Fig. 5

FWHM (curve 2) and intensity I max in the focal spot (curve 1) as functions of the axicon height h.

Fig. 6
Fig. 6

Radial binary axicon profile and its position in the calculation window.

Fig. 7
Fig. 7

Radial amplitude distribution of the mode R-TEM 01 at z = 0 and w = 1.9 μ m .

Fig. 8
Fig. 8

(a) Intensity distribution | E | 2 on the optical axis and (b) radial intensity profiles | E z | 2 (curve 3), | E r | 2 (curve 2), and | E | 2 = | E r | 2 + | E z | 2 (curve 1) in the focal plane for a wavelength of 850 nm.

Fig. 9
Fig. 9

Instantaneous amplitude distributions of (a) E r and (b) E z resulting from the diffraction of the R-TEM 01 mode of wavelength 850 nm (Fig. 7) by the binary axicon of Fig. 6 in the region under study.

Tables (1)

Tables Icon

Table 1 The Focal Spot Diameter at FWHM and Focal Length f versus the Wavelength λ

Equations (11)

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E r ( r ) = e r ( r w ) exp { r 2 w 2 } ,
E m n ( x , y , z ) = ( σ 0 σ ( z ) ) exp { i ( m + n + 1 ) η ( z ) i k ( x 2 + y 2 ) 2 R ( z ) ( x 2 + y 2 ) σ 2 ( z ) } H m ( 2 x σ ( z ) ) H n ( 2 y σ ( z ) ) ,
E r ( x , y , z ) = ( 2 2 σ 0 σ 2 ( z ) ) exp { i 2 η ( z ) i k ( x 2 + y 2 ) 2 R ( z ) ( x 2 + y 2 ) σ 2 ( z ) } ( x e x + y e y ) ,
E r ( x , y , z ) = ( 2 2 σ 0 σ 2 ( z ) ) exp { i 2 η ( z ) i k r 2 2 R ( z ) } { r 2 σ 2 ( z ) } r e r .
NA = n h / R ( h / R ) 2 n 2 + 1 ( h / R ) 2 + 1 ,
H φ , 0 z = ε ε 0 E r , 0 t + σ E r , 0 ,
1 r ( r H φ , 0 ) r = ε ε 0 E z , 0 t + σ E z , 0 ,
E r , 0 z E z , 0 r = μ μ 0 H φ , 0 t ,
FWHM = 2 r = 0.35 R 2 + h 2 n R λ 0.31 λ .
FWHM = ln   2 4 π n   sin   θ λ 0.07 λ .
W 0 / λ 2 = ( 2 2 w λ ) 2 r 2   exp { 2 r 2 w 2 } r d r d ϕ = 2 π ( w λ ) 2 56.5.

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