Abstract

An analytical model of vector formalism is proposed to investigate the diffraction of high numerical aperture subwavelength circular binary phase Fresnel zone plate (FZP). In the proposed model, the scattering on the FZP’s surface, reflection and refraction within groove zones are considered and diffraction fields are calculated using the vector Rayleigh–Sommerfeld integral. The numerical results obtained by the proposed phase thick FZP (TFZP) model show a good agreement with those obtained by the finite-difference time-domain (FDTD) method within the effective extent of etch depth. The optimal etch depths predicted by both methods are approximately equal. The analytical TFZP model is very useful for designing a phase and hybrid amplitude-phase FZP with high-NA and short focal length.

© 2014 Optical Society of America

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References

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    [Crossref]
  2. H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2(2), 101–104 (2006).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  5. T. E. Judd, R. G. Scott, G. Sinuco, T. W. A. Montgomery, M. Martin, P. Krüger, and T. M. Fromhold, “Zone-plate focusing of Bose–Einstein condensates for atom optics and erasable high-speed lithography of quantum electronic components,” New J. Phys. 12(6), 063033 (2010).
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    [Crossref]
  8. R. G. Mote, S. F. Yu, B. K. Ng, W. Zhou, and S. P. Lau, “Near-field focusing properties of zone plates in visible regime--New insights,” Opt. Express 16(13), 9554–9564 (2008).
    [Crossref] [PubMed]
  9. R. Ashman and M. Gu, “Effect of ultrashort pulsed illumination on foci caused by a Fresnel zone plate,” Appl. Opt. 42(10), 1852–1855 (2003).
    [Crossref] [PubMed]
  10. Y. Zhang and C. Zheng, “Axial intensity distribution behind a Fresnel zone plate,” Opt. Laser Technol. 37(1), 77–80 (2005).
    [Crossref]
  11. Q. Cao and J. Jahns, “Modified Fresnel zone plates that produce sharp Gaussian focal spots,” J. Opt. Soc. Am. A 20(8), 1576–1581 (2003).
    [Crossref] [PubMed]
  12. Y. Zhang, J. Chen, and X. Ye, “Multilevel phase Fresnel zone plate lens as a near-field optical element,” Opt. Commun. 269(2), 271–273 (2007).
    [Crossref]
  13. Z. Chen and D. Zhao, “Focusing of an elliptic vortex beam by a square Fresnel zone plate,” Appl. Opt. 50(15), 2204–2210 (2011).
    [Crossref] [PubMed]
  14. M. G. Moharam and T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. A 73(9), 1105–1112 (1983).
    [Crossref]
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    [Crossref]
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    [Crossref]
  18. R. G. Mote, S. F. Yu, W. Zhou, and X. F. Li, “Subwavelength focusing behavior of high numerical-aperture phase Fresnel zone plates under various polarization states,” Appl. Phys. Lett. 95(19), 191113 (2009).
    [Crossref]
  19. Y. Zhang, C. Zheng, and Y. Zhuang, “Effect of the shadowing in high-numerical-aperture binary phase Fresnel zone plates,” Opt. Commun. 317, 88–92 (2014).
    [Crossref]
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    [Crossref]
  24. H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Lukyanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
    [Crossref]
  25. S. Wang, C. Zhou, Y. Zhang, and H. Ru, “Deep-etched high-density fused-silica transmission gratings with high efficiency at a wavelength of 1550 nm,” Appl. Opt. 45(12), 2567–2571 (2006).
    [Crossref] [PubMed]
  26. J. Jia, C. Zhou, and L. Liu, “Superresolution technology for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 228(4-6), 271–278 (2003).
    [Crossref]
  27. S. Sun, Y. Shi, D. Dai, and L. Liu, “Improvement of ICP etching process for reducing the surface roughness of SiO2 optical waveguides,” Optical Instruments 29, 71–74 (2007).

2014 (2)

Y. Zhang, C. Zheng, and Y. Zhuang, “Effect of the shadowing in high-numerical-aperture binary phase Fresnel zone plates,” Opt. Commun. 317, 88–92 (2014).
[Crossref]

Y. Zhang, C. Zheng, Y. Zhuang, and X. Ruan, “Analysis of near field subwavelength focusing of hybrid amplitude–phase Fresnel zone plates under radially polarized Illumination,” J. Opt. 16(1), 015703 (2014).
[Crossref]

2013 (1)

H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Lukyanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
[Crossref]

2011 (3)

2010 (1)

T. E. Judd, R. G. Scott, G. Sinuco, T. W. A. Montgomery, M. Martin, P. Krüger, and T. M. Fromhold, “Zone-plate focusing of Bose–Einstein condensates for atom optics and erasable high-speed lithography of quantum electronic components,” New J. Phys. 12(6), 063033 (2010).
[Crossref]

2009 (2)

H. C. Kim, H. Ko, and M. Cheng, “High efficient optical focusing of a zone plate composed of metal/dielectric multilayer,” Opt. Express 17(5), 3078–3083 (2009).
[Crossref] [PubMed]

R. G. Mote, S. F. Yu, W. Zhou, and X. F. Li, “Subwavelength focusing behavior of high numerical-aperture phase Fresnel zone plates under various polarization states,” Appl. Phys. Lett. 95(19), 191113 (2009).
[Crossref]

2008 (2)

2007 (2)

Y. Zhang, J. Chen, and X. Ye, “Multilevel phase Fresnel zone plate lens as a near-field optical element,” Opt. Commun. 269(2), 271–273 (2007).
[Crossref]

S. Sun, Y. Shi, D. Dai, and L. Liu, “Improvement of ICP etching process for reducing the surface roughness of SiO2 optical waveguides,” Optical Instruments 29, 71–74 (2007).

2006 (3)

F. Pfeiffer, C. David, J. F. Veen, and C. Bergemann, “Nanometer focusing properties of Fresnel zone plates described by dynamical diffraction theory,” Phys. Rev. B 73(24), 245331 (2006).
[Crossref]

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2(2), 101–104 (2006).
[Crossref]

S. Wang, C. Zhou, Y. Zhang, and H. Ru, “Deep-etched high-density fused-silica transmission gratings with high efficiency at a wavelength of 1550 nm,” Appl. Opt. 45(12), 2567–2571 (2006).
[Crossref] [PubMed]

2005 (2)

D. Chao, A. Patel, T. Barwicz, H. I. Smith, and R. Menon, “Immersion zone-plate-array lithography,” J. Vac. Sci. Technol. B 23(6), 2657–2661 (2005).
[Crossref]

Y. Zhang and C. Zheng, “Axial intensity distribution behind a Fresnel zone plate,” Opt. Laser Technol. 37(1), 77–80 (2005).
[Crossref]

2003 (3)

1999 (1)

E. D. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[Crossref]

1997 (1)

1983 (1)

M. G. Moharam and T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. A 73(9), 1105–1112 (1983).
[Crossref]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Acebal, P.

Ashman, R.

Barrett, R.

E. D. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[Crossref]

Barwicz, T.

D. Chao, A. Patel, T. Barwicz, H. I. Smith, and R. Menon, “Immersion zone-plate-array lithography,” J. Vac. Sci. Technol. B 23(6), 2657–2661 (2005).
[Crossref]

Bergemann, C.

F. Pfeiffer, C. David, J. F. Veen, and C. Bergemann, “Nanometer focusing properties of Fresnel zone plates described by dynamical diffraction theory,” Phys. Rev. B 73(24), 245331 (2006).
[Crossref]

Blaya, S.

Cabrini, S.

E. D. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[Crossref]

Cai, Z.

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2(2), 101–104 (2006).
[Crossref]

Cao, Q.

Cases, A. M.

Chao, D.

D. Chao, A. Patel, T. Barwicz, H. I. Smith, and R. Menon, “Immersion zone-plate-array lithography,” J. Vac. Sci. Technol. B 23(6), 2657–2661 (2005).
[Crossref]

Chen, J.

Y. Zhang, J. Chen, and X. Ye, “Multilevel phase Fresnel zone plate lens as a near-field optical element,” Opt. Commun. 269(2), 271–273 (2007).
[Crossref]

Chen, Z.

Cheng, M.

Dai, D.

S. Sun, Y. Shi, D. Dai, and L. Liu, “Improvement of ICP etching process for reducing the surface roughness of SiO2 optical waveguides,” Optical Instruments 29, 71–74 (2007).

David, C.

F. Pfeiffer, C. David, J. F. Veen, and C. Bergemann, “Nanometer focusing properties of Fresnel zone plates described by dynamical diffraction theory,” Phys. Rev. B 73(24), 245331 (2006).
[Crossref]

Escarré, S. B.

Fabrizio, E. D.

E. D. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[Crossref]

Feng, D.

Fimia, A.

Fromhold, T. M.

T. E. Judd, R. G. Scott, G. Sinuco, T. W. A. Montgomery, M. Martin, P. Krüger, and T. M. Fromhold, “Zone-plate focusing of Bose–Einstein condensates for atom optics and erasable high-speed lithography of quantum electronic components,” New J. Phys. 12(6), 063033 (2010).
[Crossref]

Fu, Y.

Gaylord, T. K.

M. G. Moharam and T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. A 73(9), 1105–1112 (1983).
[Crossref]

Gentili, M.

E. D. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[Crossref]

Gil, A. F.

González, P. A.

Gu, M.

Huang, K.

H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Lukyanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
[Crossref]

Jahns, J.

Jia, J.

J. Jia, C. Zhou, and L. Liu, “Superresolution technology for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 228(4-6), 271–278 (2003).
[Crossref]

Judd, T. E.

T. E. Judd, R. G. Scott, G. Sinuco, T. W. A. Montgomery, M. Martin, P. Krüger, and T. M. Fromhold, “Zone-plate focusing of Bose–Einstein condensates for atom optics and erasable high-speed lithography of quantum electronic components,” New J. Phys. 12(6), 063033 (2010).
[Crossref]

Kaulich, B.

E. D. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[Crossref]

Kim, H. C.

Ko, H.

Krüger, P.

T. E. Judd, R. G. Scott, G. Sinuco, T. W. A. Montgomery, M. Martin, P. Krüger, and T. M. Fromhold, “Zone-plate focusing of Bose–Einstein condensates for atom optics and erasable high-speed lithography of quantum electronic components,” New J. Phys. 12(6), 063033 (2010).
[Crossref]

Larochelle, S.

Lau, S. P.

Li, X. F.

R. G. Mote, S. F. Yu, W. Zhou, and X. F. Li, “Subwavelength focusing behavior of high numerical-aperture phase Fresnel zone plates under various polarization states,” Appl. Phys. Lett. 95(19), 191113 (2009).
[Crossref]

Lim, L. E. N.

Liu, L.

S. Sun, Y. Shi, D. Dai, and L. Liu, “Improvement of ICP etching process for reducing the surface roughness of SiO2 optical waveguides,” Optical Instruments 29, 71–74 (2007).

J. Jia, C. Zhou, and L. Liu, “Superresolution technology for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 228(4-6), 271–278 (2003).
[Crossref]

López, L. C.

Lukyanchuk, B.

H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Lukyanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
[Crossref]

Madrigal, R.

Madrigal, R. F.

Martin, M.

T. E. Judd, R. G. Scott, G. Sinuco, T. W. A. Montgomery, M. Martin, P. Krüger, and T. M. Fromhold, “Zone-plate focusing of Bose–Einstein condensates for atom optics and erasable high-speed lithography of quantum electronic components,” New J. Phys. 12(6), 063033 (2010).
[Crossref]

Menon, R.

D. Chao, A. Patel, T. Barwicz, H. I. Smith, and R. Menon, “Immersion zone-plate-array lithography,” J. Vac. Sci. Technol. B 23(6), 2657–2661 (2005).
[Crossref]

Moharam, M. G.

M. G. Moharam and T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. A 73(9), 1105–1112 (1983).
[Crossref]

Molina, M. P.

Montgomery, T. W. A.

T. E. Judd, R. G. Scott, G. Sinuco, T. W. A. Montgomery, M. Martin, P. Krüger, and T. M. Fromhold, “Zone-plate focusing of Bose–Einstein condensates for atom optics and erasable high-speed lithography of quantum electronic components,” New J. Phys. 12(6), 063033 (2010).
[Crossref]

Mote, R. G.

R. G. Mote, S. F. Yu, W. Zhou, and X. F. Li, “Subwavelength focusing behavior of high numerical-aperture phase Fresnel zone plates under various polarization states,” Appl. Phys. Lett. 95(19), 191113 (2009).
[Crossref]

R. G. Mote, S. F. Yu, B. K. Ng, W. Zhou, and S. P. Lau, “Near-field focusing properties of zone plates in visible regime--New insights,” Opt. Express 16(13), 9554–9564 (2008).
[Crossref] [PubMed]

Murciano, A.

Ng, B. K.

Nugent, K. A.

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2(2), 101–104 (2006).
[Crossref]

Patel, A.

D. Chao, A. Patel, T. Barwicz, H. I. Smith, and R. Menon, “Immersion zone-plate-array lithography,” J. Vac. Sci. Technol. B 23(6), 2657–2661 (2005).
[Crossref]

Paterson, D.

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2(2), 101–104 (2006).
[Crossref]

Peele, A. G.

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2(2), 101–104 (2006).
[Crossref]

Pfeiffer, F.

F. Pfeiffer, C. David, J. F. Veen, and C. Bergemann, “Nanometer focusing properties of Fresnel zone plates described by dynamical diffraction theory,” Phys. Rev. B 73(24), 245331 (2006).
[Crossref]

Qiu, C. W.

H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Lukyanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
[Crossref]

Quiney, H. M.

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2(2), 101–104 (2006).
[Crossref]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Romanato, F.

E. D. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[Crossref]

Ru, H.

Ruan, X.

Y. Zhang, C. Zheng, Y. Zhuang, and X. Ruan, “Analysis of near field subwavelength focusing of hybrid amplitude–phase Fresnel zone plates under radially polarized Illumination,” J. Opt. 16(1), 015703 (2014).
[Crossref]

Scott, R. G.

T. E. Judd, R. G. Scott, G. Sinuco, T. W. A. Montgomery, M. Martin, P. Krüger, and T. M. Fromhold, “Zone-plate focusing of Bose–Einstein condensates for atom optics and erasable high-speed lithography of quantum electronic components,” New J. Phys. 12(6), 063033 (2010).
[Crossref]

Sheng, Y.

Shi, Y.

S. Sun, Y. Shi, D. Dai, and L. Liu, “Improvement of ICP etching process for reducing the surface roughness of SiO2 optical waveguides,” Optical Instruments 29, 71–74 (2007).

Sinuco, G.

T. E. Judd, R. G. Scott, G. Sinuco, T. W. A. Montgomery, M. Martin, P. Krüger, and T. M. Fromhold, “Zone-plate focusing of Bose–Einstein condensates for atom optics and erasable high-speed lithography of quantum electronic components,” New J. Phys. 12(6), 063033 (2010).
[Crossref]

Smith, H. I.

D. Chao, A. Patel, T. Barwicz, H. I. Smith, and R. Menon, “Immersion zone-plate-array lithography,” J. Vac. Sci. Technol. B 23(6), 2657–2661 (2005).
[Crossref]

Sun, S.

S. Sun, Y. Shi, D. Dai, and L. Liu, “Improvement of ICP etching process for reducing the surface roughness of SiO2 optical waveguides,” Optical Instruments 29, 71–74 (2007).

Susini, J.

E. D. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[Crossref]

Teng, J.

H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Lukyanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
[Crossref]

Veen, J. F.

F. Pfeiffer, C. David, J. F. Veen, and C. Bergemann, “Nanometer focusing properties of Fresnel zone plates described by dynamical diffraction theory,” Phys. Rev. B 73(24), 245331 (2006).
[Crossref]

Wang, S.

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Ye, H.

H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Lukyanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
[Crossref]

Ye, X.

Y. Zhang, J. Chen, and X. Ye, “Multilevel phase Fresnel zone plate lens as a near-field optical element,” Opt. Commun. 269(2), 271–273 (2007).
[Crossref]

Yeo, S. P.

H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Lukyanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
[Crossref]

Yu, S. F.

R. G. Mote, S. F. Yu, W. Zhou, and X. F. Li, “Subwavelength focusing behavior of high numerical-aperture phase Fresnel zone plates under various polarization states,” Appl. Phys. Lett. 95(19), 191113 (2009).
[Crossref]

R. G. Mote, S. F. Yu, B. K. Ng, W. Zhou, and S. P. Lau, “Near-field focusing properties of zone plates in visible regime--New insights,” Opt. Express 16(13), 9554–9564 (2008).
[Crossref] [PubMed]

Zhang, Y.

Y. Zhang, C. Zheng, and Y. Zhuang, “Effect of the shadowing in high-numerical-aperture binary phase Fresnel zone plates,” Opt. Commun. 317, 88–92 (2014).
[Crossref]

Y. Zhang, C. Zheng, Y. Zhuang, and X. Ruan, “Analysis of near field subwavelength focusing of hybrid amplitude–phase Fresnel zone plates under radially polarized Illumination,” J. Opt. 16(1), 015703 (2014).
[Crossref]

Y. Zhang, J. Chen, and X. Ye, “Multilevel phase Fresnel zone plate lens as a near-field optical element,” Opt. Commun. 269(2), 271–273 (2007).
[Crossref]

S. Wang, C. Zhou, Y. Zhang, and H. Ru, “Deep-etched high-density fused-silica transmission gratings with high efficiency at a wavelength of 1550 nm,” Appl. Opt. 45(12), 2567–2571 (2006).
[Crossref] [PubMed]

Y. Zhang and C. Zheng, “Axial intensity distribution behind a Fresnel zone plate,” Opt. Laser Technol. 37(1), 77–80 (2005).
[Crossref]

Zhao, D.

Zheng, C.

Y. Zhang, C. Zheng, and Y. Zhuang, “Effect of the shadowing in high-numerical-aperture binary phase Fresnel zone plates,” Opt. Commun. 317, 88–92 (2014).
[Crossref]

Y. Zhang, C. Zheng, Y. Zhuang, and X. Ruan, “Analysis of near field subwavelength focusing of hybrid amplitude–phase Fresnel zone plates under radially polarized Illumination,” J. Opt. 16(1), 015703 (2014).
[Crossref]

Y. Zhang and C. Zheng, “Axial intensity distribution behind a Fresnel zone plate,” Opt. Laser Technol. 37(1), 77–80 (2005).
[Crossref]

Zhou, C.

S. Wang, C. Zhou, Y. Zhang, and H. Ru, “Deep-etched high-density fused-silica transmission gratings with high efficiency at a wavelength of 1550 nm,” Appl. Opt. 45(12), 2567–2571 (2006).
[Crossref] [PubMed]

J. Jia, C. Zhou, and L. Liu, “Superresolution technology for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 228(4-6), 271–278 (2003).
[Crossref]

Zhou, W.

Zhuang, Y.

Y. Zhang, C. Zheng, and Y. Zhuang, “Effect of the shadowing in high-numerical-aperture binary phase Fresnel zone plates,” Opt. Commun. 317, 88–92 (2014).
[Crossref]

Y. Zhang, C. Zheng, Y. Zhuang, and X. Ruan, “Analysis of near field subwavelength focusing of hybrid amplitude–phase Fresnel zone plates under radially polarized Illumination,” J. Opt. 16(1), 015703 (2014).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

R. G. Mote, S. F. Yu, W. Zhou, and X. F. Li, “Subwavelength focusing behavior of high numerical-aperture phase Fresnel zone plates under various polarization states,” Appl. Phys. Lett. 95(19), 191113 (2009).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. (1)

Y. Zhang, C. Zheng, Y. Zhuang, and X. Ruan, “Analysis of near field subwavelength focusing of hybrid amplitude–phase Fresnel zone plates under radially polarized Illumination,” J. Opt. 16(1), 015703 (2014).
[Crossref]

J. Opt. Soc. Am. A (4)

J. Vac. Sci. Technol. B (1)

D. Chao, A. Patel, T. Barwicz, H. I. Smith, and R. Menon, “Immersion zone-plate-array lithography,” J. Vac. Sci. Technol. B 23(6), 2657–2661 (2005).
[Crossref]

Laser Phys. Lett. (1)

H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Lukyanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
[Crossref]

Nat. Phys. (1)

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2(2), 101–104 (2006).
[Crossref]

Nature (1)

E. D. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[Crossref]

New J. Phys. (1)

T. E. Judd, R. G. Scott, G. Sinuco, T. W. A. Montgomery, M. Martin, P. Krüger, and T. M. Fromhold, “Zone-plate focusing of Bose–Einstein condensates for atom optics and erasable high-speed lithography of quantum electronic components,” New J. Phys. 12(6), 063033 (2010).
[Crossref]

Opt. Commun. (3)

Y. Zhang, J. Chen, and X. Ye, “Multilevel phase Fresnel zone plate lens as a near-field optical element,” Opt. Commun. 269(2), 271–273 (2007).
[Crossref]

J. Jia, C. Zhou, and L. Liu, “Superresolution technology for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 228(4-6), 271–278 (2003).
[Crossref]

Y. Zhang, C. Zheng, and Y. Zhuang, “Effect of the shadowing in high-numerical-aperture binary phase Fresnel zone plates,” Opt. Commun. 317, 88–92 (2014).
[Crossref]

Opt. Express (2)

Opt. Laser Technol. (1)

Y. Zhang and C. Zheng, “Axial intensity distribution behind a Fresnel zone plate,” Opt. Laser Technol. 37(1), 77–80 (2005).
[Crossref]

Optical Instruments (1)

S. Sun, Y. Shi, D. Dai, and L. Liu, “Improvement of ICP etching process for reducing the surface roughness of SiO2 optical waveguides,” Optical Instruments 29, 71–74 (2007).

Phys. Rev. B (1)

F. Pfeiffer, C. David, J. F. Veen, and C. Bergemann, “Nanometer focusing properties of Fresnel zone plates described by dynamical diffraction theory,” Phys. Rev. B 73(24), 245331 (2006).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Schematic cross section of a circular binary phase FZP.
Fig. 2
Fig. 2 The scattering of light by the piecewise interface of a binary phase FZP and geometric parameters.
Fig. 3
Fig. 3 Normalized axial intensity distribution (a) and transverse intensity distribution (b) along the x axis in the focal plane of z = 0.646 μm for a binary phase FZP with designed focal lengths fd = 0.5μm and etch depth d = 340 nm. Blue, green and red curves are the results predicted by the TFZP model, the IFZP model and the FDTD method, respectively. FZP structure of N = 8 zones is etched on glass substrate. Wavelength of incident plane wave is 633 nm.
Fig. 4
Fig. 4 Normalized peak intensity along the z axis (a) and actual focal length (b) as a function of etch depth d for the designed focal lengths of fd = 0.5 μm. Solid and dashed curves are the results predicted by the TFZP model and by the IFZP model, respectively, and the lines with the markers of filled squares are the results from the FDTD method. FZP structure of N = 8 zones is etched on glass substrate. Wavelength of incident plane wave is 633 nm.

Equations (30)

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r m = m f d λ+ (mλ/2) 2 ,m=1,2,3,,2N+1,
E x (ρ,η,z)= z 2π 0 0 2π E 0x (r,φ) ikl1 l 3 exp(ikl)rdrdφ, E y (ρ,η,z)= z 2π 0 0 2π E 0y (r,φ) ikl1 l 3 exp(ikl)rdrdφ, , E z (ρ,η,z)= 1 2π 0 0 2π [(ρcosηrcosφ) E 0x (r,φ) +(ρsinηrsinφ) E 0y (r,φ)] ikl1 l 3 exp(ikl)rdrdφ,
E i =( E ix E iy E iz )=( 1 0 0 ).
E 0x rid (r,φ)= π/2 π/2 E 0x rid (r,φ;σ)dσ , E 0y rid (r,φ)= π/2 π/2 E 0y rid (r,φ;σ)dσ ,
E 0 rid (r,φ;σ)= cos 1/2 σ R 1 (φ)Q (σ) 1 I t (w)R(φ) E i .
R(φ)=( cosφ sinφ 0 sinφ cosφ 0 0 0 1 ),Q(σ)=( cosσ 0 sinσ 0 1 0 sinσ 0 cosσ ), I t (w)=( t w p 0 0 0 t w s 0 0 0 t w p ),
t w p,s = t 12 p,s t 23 p,s exp(inkw) 1+ r 12 p,s r 23 p,s exp(2inkw) ,
t 12 p = t 12 s = 2 n+1 , r 12 p = r 12 s = n1 n+1 , r 23 p = 1ncosσ 1+ncosσ , r 23 s = ncosσ n+cosσ , t 23 p = 2n 1+ncosσ , t 23 s = 2n n+cosσ .
( E 0x rid (r,φ;σ) E 0y rid (r,φ;σ) )= 1 2 cosσ ( ( t w p cosσ+ t w s )+( t w p cosσ t w s )cos2φ ( t w p cosσ t w s )sin2φ ).
E x rid (ρ,η,z)= z 2π m=0 N r 2m r 2m+1 0 2π π/2 π/2 E 0x rid (r,φ;σ) ikl1 l 3 exp(ikl)rdrdφdσ , E y rid (ρ,η,z)= z 2π m=0 N r 2m r 2m+1 0 2π π/2 π/2 E 0y rid (r,φ;σ) ikl1 l 3 exp(ikl)rdrdφ dσ, , E z rid (ρ,η,z)= 1 2π m=0 N r 2m r 2m+1 0 2π π/2 π/2 [(ρcosηrcosφ) E 0x rid (r,φ;σ) + (ρsinηrsinφ) E 0y rid (r,φ;σ)] ikl1 l 3 exp(ikl)rdrdφdσ,
( E x gro , E y gro , E z gro )=( n=1 5 E x,n gro , n=1 5 E y,n gro , n=1 5 E z,n gro ),
E x,n gro (ρ,η,z)= z 2π m=1 N r 2m1 r 2m 0 2π σ n,1 σ n,2 E 0x,n gro ( r ,φ;σ) ik l n 1 l n 3 exp(ik l n ) r ξ n drdφdσ , E y,n gro (ρ,η,z)= z 2π m=1 N r 2m1 r 2m 0 2π σ n,1 σ n,2 E 0y,n gro ( r ,φ;σ) ik l n 1 l n 3 exp(ik l n ) r ξ n drdφ dσ, E z,n gro (ρ,η,z)= 1 2π m=1 N r 2m1 r 2m 0 2π σ n,1 σ n,2 [(ρcosη r cosφ) E 0x,n gro ( r ,φ;σ) + (ρsinη r sinφ) E 0y,n gro ( r ,φ;σ)] ik l n 1 l n 3 exp(ik l n ) r ξ n drdφdσ.
E 1 gro ( r ,φ;σ)= cosσ exp(ika) R 1 (φ)Q(σ) I r Q( π 2 σ ) I t (wd)R(φ) E i ,
I r =( r p 0 0 0 r s 0 0 0 r p ).
( E 0x,1 gro ( r ,φ;σ) E 0y,1 gro ( r ,φ;σ) )= 1 2 cosσ exp(ika)( ( t wd p r p sin2σ+ t wd s r s )( t wd p r p sin2σ+ t wd s r s )cos2φ ( t wd p r p sin2σ+ t wd s r s )sin2φ ),
σ 1,1 =arctan( r 2m r d ), σ 1,2 =arctan( 2 r 2m r 2m1 r d ),τ= r 2m r tanσ , a=d/cosσ, r = r 2m (dτ)tanσ, g 1 =π/2σ,sin g 1 =nsin g 2 , , r p = ncos g 1 cos g 2 ncos g 1 +cos g 2 , r s = cos g 1 ncos g 2 cos g 1 +ncos g 2 .
E 2 gro ( r ,φ;σ)= cosσ exp(ikb) R 1 (φ)Q (σ) 1 I t (wd)R(φ) E i .
( E 0x,2 gro ( r ,φ;σ) E 0y,z gro ( r ,φ;σ) )= 1 2 cosσ exp(ikb)( ( t wd p cosσ+ t wd s )+( t wd p cosσ t wd s )cos2φ ( t wd p cosσ t wd s )sin2φ ),
σ 2,1 =arctan( r 2m1 r d ), σ 2,2 =arctan( r 2m r d ),a= d cosσ , r =r+dtanσ.
E 3 gro ( r ,φ;σ)= cosσ exp(ikc) R 1 (φ)Q( σ ) I r Q 1 ( π 2 +σ ) I t (wd)R(φ) E i ,
( E 0x,3 gro ( r ,φ;σ) E 0y,3 gro ( r ,φ;σ) )= 1 2 cosσ exp(ikc)( ( t wd p r p sin2σ+ t wd s r s )+( t wd p r p sin2σ t wd s r s )cos2φ ( t wd p r p sin2σ t wd s r s )sin2φ ).
τ=(r r 2m1 )/tanσ,c=d/cosσ, r = r 2m1 (dτ)tanσ, g 1 =π/2+σ, sin g 1 =nsin g 2 , r p = ncos g 1 cos g 2 ncos g 1 +cos g 2 , r s = cos g 1 ncos g 2 cos g 1 +ncos g 2 , σ 3,2 =arctan( r r 2m1 d ), σ 3,1 =arctan( r 2m 2 r 2m1 +r d ).
E 4 gro ( r ,φ;σ)=ψ R 1 (φ)Q( g 4 ) I t r Q( g 3 ) I t l Q 1 ( π 2 +σ ) I t (wd)R(φ) E i ,
( E 0x,4 gro ( r ,φ;σ) E 0y,4 gro ( r ,φ;σ) )= 1 2 ψ( ( t wd p t l p t r p sinβ+ t wd s t l s t r s )+( t wd p t l p t r p sinβ t wd s t l s t r s )cos2φ ( t wd p t l p t r p sinβ t wd s t l s t r s 3 s )sin2φ ),
tan σ 4,1 = r r 2m1 τ c , g 1 =π/2+ σ 4,1 ,sin g 1 =nsin g 2 ,tan(π/2 g 2 )= r 2m1 r 2m2 d τ c .
τ=(r r 2m1 )/tanσ, g 1 =π/2+σ,sin g 1 =nsin g 2 , g 3 =π/2 g 2 , nsin g 3 =sinξ,ξ=τ/cosσ+n(dτ)/cos g 3 , r = r 2m1 (dτ)/tan g 2 t l p = 2cos g 1 ncos g 1 +cos g 2 , t l s = 2cos g 1 cos g 1 +ncos g 2 , t r p = 2ncos g 3 cos g 3 +ncos g 4 , t r s = 2ncos g 3 ncos g 3 +cos g 4 .
E 5 gro ( r ,φ;σ)= cosσ exp(ikς) R 1 (φ)Q( σ ) I t Δ Q 1 ( π 2 +σ ) I t (wd)R(φ) E i ,
( E 0x,5 gro ( r ,φ;σ) E 0y,5 gro ( r ,φ;σ) )= 1 2 cosσ exp(ikς)( ( t wd p t Δ p sin2σ+ t wd s t Δ s )( t wd p t Δ p sin2σ+ t wd s t Δ s )cos2φ ( t wd p t Δ p sin2σ+ t wd s t Δ s )sin2φ )
tan σ 5,1 = r r 2m1 τ ,sin( π 2 + σ 5,1 )=nsin g 2 ,Δτ=( r 2m1 r 2m2 )tan g 2 ,tan g 1 = dτΔτ r 2m2 r 2m3 .
g 1 = π 2 +σ,sin g 1 =nsin g 2 , g 3 = g 2 , g 4 = g 1 ,nsin g 3 =sin g 4 , τ 1 = r r 2m1 tanσ , l 1 = τ 1 /cosσ,Δτ=( r 2m1 r 2m2 )tan g 2 ,τ= τ 1 +Δτ, r = r 2m2 +(dτ)tanσ, t 1 p = 2cos g 1 ncos g 1 +cos g 2 , t 1 s = 2cos g 1 cos g 1 +ncos g 2 , r 1 p = ncos g 1 cos g 2 ncos g 1 +cos g 2 , r 1 s = cos g 1 ncos g 2 cos g 1 +ncos g 2 , t 2 p = 2ncos g 2 cos g 2 +ncos g 1 , t 2 s = 2ncos g 2 ncos g 2 +cos g 1 , r 2 p = cos g 2 ncos g 1 cos g 2 +ncos g 1 , r 2 s = ncos g 2 cos g 1 ncos g 2 +cos g 1 , t Δ p,s = t 1 p,s t 2 p,s exp[ink( r 2m1 r 2m2 )] 1+ r 1 p,s r 2 p,s exp[2ink( r 2m1 r 2m2 )] .

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