Abstract

This study explores how interference manipulation breaks through the diffraction limit and induces super-resolution nano-optical hot spots through the nonlinear Fabry–Perot cavity structure. The theoretical analytical model is established, and the numerical simulation results show that when the thickness of the nonlinear thin film inside the nonlinear Fabry–Perot cavity structure is adjusted to centain value, the constructive interference effect can be formed in the central point of the spot, which causes the nanoscale optical hot spot in the central region to be produced. The simulation results also tell us that the hot spot size is sensitive to nonlinear thin film thickness, and the accuracy is required to be up to nanometer or even subnanometer scale, which is very large challenging for thin film deposition technique, however, slightly changing the incident laser power can compensate for drawbacks of low thickness accuracy of nonlinear thin films. Taking As2S3 as the nonlinear thin film, the central hot spot with a size of 40nm is obtained at suitable nonlinear thin film thickness and incident laser power. The central hot spot size is only about λ/16, which is very useful in super-high density optical recording, nanolithography, and high-resolving optical surface imaging.

© 2014 Optical Society of America

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References

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2014 (2)

S. Cao, W. Yu, C. Wang, and Y. Fu, “Tuning the focusing spot of plasmonic nanolens by aspect ratio under linear polarization,” Chin. Opt. Lett. 12(1), 012401 (2014).
[Crossref]

R. Wang and J. Wei, “Parabolic approximation analytical model of super-resolution spot generation using nonlinear thin films: theory and simulation,” Opt. Commun. 316, 220–227 (2014).
[Crossref]

2013 (8)

S. Dastjerdi, M. Ghanaatshoar, and T. Hattori, “Design and analysis of superlens based on complex two-dimensional square lattice photonic crystal,” Chin. Opt. Lett. 11(10), 102303 (2013).
[Crossref]

Y. Zha, J. Wei, and F. Gan, “A novel design for maskless direct laser writing nanolithography: combination of diffractive optical element and nonlinear absorption inorganic resists,” Opt. Commun. 304, 49–53 (2013).
[Crossref]

X. Tsampoula, M. Mazilu, T. Vettenburg, F. Gunn-Moore, and K. Dholakia, “Enhanced cell transfection using subwavelength focused optical eigenmode beams,” Photon. Res. 1(1), 42–46 (2013).
[Crossref]

M. Khosravi, R. A. Sadeghzadeh, and M. S. Abrishamian, “Nanospheroidal particles as convenient nanoantenna elements,” Chin. Opt. Lett. 11, 112503 (2013).
[Crossref]

J. Wei, Y. Zha, and F. Gan, “Creation of super-Resolution non-diffraction beam by modulating circularly polarized light with ternary optical element,” Prog. Electromagnetics Res. 140, 589–598 (2013).

Y. Zha, J. Wei, and F. Gan, “Creation of ultra-long depth of focus super-resolution longitudinally polarized beam with ternary optical element,” J. Opt. 15(7), 075703 (2013).
[Crossref]

S. Ushiba, S. Shoji, P. Kuray, K. Masui, J. Kono, and S. Kawata, “Two photon polymerization lithography for 3D microfabrication of single wall carbon nanotube/polymer composites,” Proc. SPIE 8613, 86130Y (2013).
[Crossref]

A. Goy and D. Psaltis, “Imaging in focusing Kerr media using reverse propagation,” Photon. Res. 1(2), 96–101 (2013).
[Crossref]

2012 (2)

X. Hao, C. Kuang, Y. Li, X. Liu, Y. Ku, and Y. Jiang, “Hydrophilic microsphere based mesoscopic-lens microscope,” Opt. Commun. 285(20), 4130–4133 (2012).
[Crossref]

J. Zhao, G. Zheng, S. Li, H. Zhou, Y. Ma, R. Zhang, Y. Shi, and P. He, “A hyperlens-based device for nanoscale focusing of light,” Chin. Opt. Lett. 10(4), 042302 (2012).
[Crossref]

2011 (4)

L. Pan, Y. Park, Y. Xiong, E. Ulin-Avila, Y. Wang, L. Zeng, S. Xiong, J. Rho, C. Sun, D. B. Bogy, and X. Zhang, “Maskless plasmonic lithography at 22 nm resolution,” Sci. Rep. 1, 175 (2011).
[Crossref] [PubMed]

X. Ma and J. Wei, “Nanoscale lithography with visible light: optical nonlinear saturable absorption effect induced nanobump pattern structures,” Nanoscale 3(4), 1489–1492 (2011).
[Crossref] [PubMed]

J. Wei, S. Liu, Y. Geng, Y. Wang, X. Li, Y. Wu, and A. Dun, “Nano-optical information storage induced by the nonlinear saturable absorption effect,” Nanoscale 3(8), 3233–3237 (2011).
[Crossref] [PubMed]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering Lens Resolves Sub-100 nm Structures with Visible Light,” Phys. Rev. Lett. 106(19), 193905 (2011).
[Crossref] [PubMed]

2010 (1)

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref] [PubMed]

2008 (2)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

A. Sentenac and P. C. Chaumet, “Subdiffraction light focusing on a grating substrate,” Phys. Rev. Lett. 101(1), 013901 (2008).
[Crossref] [PubMed]

2006 (1)

J. Wei, M. Xiao, and F. Zhang, “Super-resolution with a nonlinear thin film: beam reshaping via internal multi-interference,” Appl. Phys. Lett. 89(22), 223126 (2006).
[Crossref]

2005 (3)

L. E. Helseth, “Breaking the diffraction limit in nonlinear materials,” Opt. Commun. 256(4-6), 435–438 (2005).
[Crossref]

J. W. Lichtman and J. A. Conchello, “Fluorescence microscopy,” Nat. Methods 2(12), 910–919 (2005).
[Crossref] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

2004 (3)

H. Sun and S. Kawata, “Two-photon photopolymerization and 3D lithographic micro-fabrication,” Adv. Polymer Sci. 170, 169–273 (2004).

W. C. Liu, M. Y. Ng, and D. P. Tsai, “Surface Plasmon Effects on the Far-Field Signals of AgOx-Type Super Resolution Near-Field Structure,” Jpn. J. Appl. Phys. 43(7B), 4713–4717 (2004).
[Crossref]

H. H. Lee, K. M. Chae, S. Y. Yim, and S. H. Park, “Finite-difference time-domain analysis of self-focusing in a nonlinear Kerr film,” Opt. Express 12(12), 2603–2609 (2004).
[Crossref] [PubMed]

2003 (1)

M. Xiao and N. Rakov, “Enhanced optical near-field transmission through subwavelength holes randomly distributed in a thin gold film,” J. Phys. Condens. Matter 15(4), L133–L137 (2003).
[Crossref]

2001 (1)

K. Chew, J. Osman, and D. R. Tilley, “The nonlinear Fabry–Pérot resonator: direct numerical integration,” Opt. Commun. 191(3-6), 393–404 (2001).
[Crossref]

2000 (1)

K. B. Song, J. Lee, J. H. Kim, K. Cho, and S. K. Kim, “Direct observation of self-focusing with subdiffraction limited resolution using near-field scanning optical microscope,” Phys. Rev. Lett. 85(18), 3842–3845 (2000).
[Crossref] [PubMed]

1998 (1)

J. Tominaga, T. Nakano, and N. Atoda, “An approach for recording and readout beyond the diffraction limit with an Sb thin film,” Appl. Phys. Lett. 73(15), 2078 (1998).
[Crossref]

1996 (2)

F. Michelotti, F. Caiazza, G. Liakhou, S. Paoloni, and M. Bertolotti, “Effects of nonlinear Fabry-Perot resonator response on z-scan measurements,” Opt. Commun. 124(1-2), 103–110 (1996).
[Crossref]

K. Tanaka and H. Hisakuni, “Photoinduced phenomena in As2S3 glass under sub-bandgap excitation,” J. Non-Crystalline Solids 198–200, 714–718 (1996).
[Crossref]

1994 (1)

M. Kreuzer, H. Gottschling, R. Neubecker, and T. Tschudi, “Analysis of dynamic pattern formation in nonlinear Fabry-Perot resonators,” Appl. Phys. B 59(6), 581–589 (1994).
[Crossref]

1993 (1)

M. Keller, Xiao, and S. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280(1-2), 217–230 (1993).
[Crossref]

1990 (1)

S. M. Manfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57(24), 2615–2617 (1990).
[Crossref]

1982 (1)

E. Abraham and S. D. Smith, “Nonlinear Fabry-Perot interferometers,” J. Phys. E. 15(1), 33–39 (1982).
[Crossref]

Abraham, E.

E. Abraham and S. D. Smith, “Nonlinear Fabry-Perot interferometers,” J. Phys. E. 15(1), 33–39 (1982).
[Crossref]

Abrishamian, M. S.

Akbulut, D.

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering Lens Resolves Sub-100 nm Structures with Visible Light,” Phys. Rev. Lett. 106(19), 193905 (2011).
[Crossref] [PubMed]

Atoda, N.

J. Tominaga, T. Nakano, and N. Atoda, “An approach for recording and readout beyond the diffraction limit with an Sb thin film,” Appl. Phys. Lett. 73(15), 2078 (1998).
[Crossref]

Bertolotti, J.

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering Lens Resolves Sub-100 nm Structures with Visible Light,” Phys. Rev. Lett. 106(19), 193905 (2011).
[Crossref] [PubMed]

Bertolotti, M.

F. Michelotti, F. Caiazza, G. Liakhou, S. Paoloni, and M. Bertolotti, “Effects of nonlinear Fabry-Perot resonator response on z-scan measurements,” Opt. Commun. 124(1-2), 103–110 (1996).
[Crossref]

Bogy, D. B.

L. Pan, Y. Park, Y. Xiong, E. Ulin-Avila, Y. Wang, L. Zeng, S. Xiong, J. Rho, C. Sun, D. B. Bogy, and X. Zhang, “Maskless plasmonic lithography at 22 nm resolution,” Sci. Rep. 1, 175 (2011).
[Crossref] [PubMed]

Bozhevolnyi, S.

M. Keller, Xiao, and S. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280(1-2), 217–230 (1993).
[Crossref]

Caiazza, F.

F. Michelotti, F. Caiazza, G. Liakhou, S. Paoloni, and M. Bertolotti, “Effects of nonlinear Fabry-Perot resonator response on z-scan measurements,” Opt. Commun. 124(1-2), 103–110 (1996).
[Crossref]

Cao, S.

Chae, K. M.

Chaumet, P. C.

A. Sentenac and P. C. Chaumet, “Subdiffraction light focusing on a grating substrate,” Phys. Rev. Lett. 101(1), 013901 (2008).
[Crossref] [PubMed]

Chew, K.

K. Chew, J. Osman, and D. R. Tilley, “The nonlinear Fabry–Pérot resonator: direct numerical integration,” Opt. Commun. 191(3-6), 393–404 (2001).
[Crossref]

Cho, K.

K. B. Song, J. Lee, J. H. Kim, K. Cho, and S. K. Kim, “Direct observation of self-focusing with subdiffraction limited resolution using near-field scanning optical microscope,” Phys. Rev. Lett. 85(18), 3842–3845 (2000).
[Crossref] [PubMed]

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Conchello, J. A.

J. W. Lichtman and J. A. Conchello, “Fluorescence microscopy,” Nat. Methods 2(12), 910–919 (2005).
[Crossref] [PubMed]

Dastjerdi, S.

Dholakia, K.

Dun, A.

J. Wei, S. Liu, Y. Geng, Y. Wang, X. Li, Y. Wu, and A. Dun, “Nano-optical information storage induced by the nonlinear saturable absorption effect,” Nanoscale 3(8), 3233–3237 (2011).
[Crossref] [PubMed]

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Fu, Y.

Gan, F.

Y. Zha, J. Wei, and F. Gan, “A novel design for maskless direct laser writing nanolithography: combination of diffractive optical element and nonlinear absorption inorganic resists,” Opt. Commun. 304, 49–53 (2013).
[Crossref]

J. Wei, Y. Zha, and F. Gan, “Creation of super-Resolution non-diffraction beam by modulating circularly polarized light with ternary optical element,” Prog. Electromagnetics Res. 140, 589–598 (2013).

Y. Zha, J. Wei, and F. Gan, “Creation of ultra-long depth of focus super-resolution longitudinally polarized beam with ternary optical element,” J. Opt. 15(7), 075703 (2013).
[Crossref]

Geng, Y.

J. Wei, S. Liu, Y. Geng, Y. Wang, X. Li, Y. Wu, and A. Dun, “Nano-optical information storage induced by the nonlinear saturable absorption effect,” Nanoscale 3(8), 3233–3237 (2011).
[Crossref] [PubMed]

Ghanaatshoar, M.

Gottschling, H.

M. Kreuzer, H. Gottschling, R. Neubecker, and T. Tschudi, “Analysis of dynamic pattern formation in nonlinear Fabry-Perot resonators,” Appl. Phys. B 59(6), 581–589 (1994).
[Crossref]

Goy, A.

Gunn-Moore, F.

Hao, X.

X. Hao, C. Kuang, Y. Li, X. Liu, Y. Ku, and Y. Jiang, “Hydrophilic microsphere based mesoscopic-lens microscope,” Opt. Commun. 285(20), 4130–4133 (2012).
[Crossref]

Hattori, T.

He, P.

Helseth, L. E.

L. E. Helseth, “Breaking the diffraction limit in nonlinear materials,” Opt. Commun. 256(4-6), 435–438 (2005).
[Crossref]

Hisakuni, H.

K. Tanaka and H. Hisakuni, “Photoinduced phenomena in As2S3 glass under sub-bandgap excitation,” J. Non-Crystalline Solids 198–200, 714–718 (1996).
[Crossref]

Jiang, Y.

X. Hao, C. Kuang, Y. Li, X. Liu, Y. Ku, and Y. Jiang, “Hydrophilic microsphere based mesoscopic-lens microscope,” Opt. Commun. 285(20), 4130–4133 (2012).
[Crossref]

Kawata, S.

S. Ushiba, S. Shoji, P. Kuray, K. Masui, J. Kono, and S. Kawata, “Two photon polymerization lithography for 3D microfabrication of single wall carbon nanotube/polymer composites,” Proc. SPIE 8613, 86130Y (2013).
[Crossref]

H. Sun and S. Kawata, “Two-photon photopolymerization and 3D lithographic micro-fabrication,” Adv. Polymer Sci. 170, 169–273 (2004).

Keller, M.

M. Keller, Xiao, and S. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280(1-2), 217–230 (1993).
[Crossref]

Khosravi, M.

Kim, J. H.

K. B. Song, J. Lee, J. H. Kim, K. Cho, and S. K. Kim, “Direct observation of self-focusing with subdiffraction limited resolution using near-field scanning optical microscope,” Phys. Rev. Lett. 85(18), 3842–3845 (2000).
[Crossref] [PubMed]

Kim, S. K.

K. B. Song, J. Lee, J. H. Kim, K. Cho, and S. K. Kim, “Direct observation of self-focusing with subdiffraction limited resolution using near-field scanning optical microscope,” Phys. Rev. Lett. 85(18), 3842–3845 (2000).
[Crossref] [PubMed]

Kino, G. S.

S. M. Manfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57(24), 2615–2617 (1990).
[Crossref]

Kono, J.

S. Ushiba, S. Shoji, P. Kuray, K. Masui, J. Kono, and S. Kawata, “Two photon polymerization lithography for 3D microfabrication of single wall carbon nanotube/polymer composites,” Proc. SPIE 8613, 86130Y (2013).
[Crossref]

Kreuzer, M.

M. Kreuzer, H. Gottschling, R. Neubecker, and T. Tschudi, “Analysis of dynamic pattern formation in nonlinear Fabry-Perot resonators,” Appl. Phys. B 59(6), 581–589 (1994).
[Crossref]

Ku, Y.

X. Hao, C. Kuang, Y. Li, X. Liu, Y. Ku, and Y. Jiang, “Hydrophilic microsphere based mesoscopic-lens microscope,” Opt. Commun. 285(20), 4130–4133 (2012).
[Crossref]

Kuang, C.

X. Hao, C. Kuang, Y. Li, X. Liu, Y. Ku, and Y. Jiang, “Hydrophilic microsphere based mesoscopic-lens microscope,” Opt. Commun. 285(20), 4130–4133 (2012).
[Crossref]

Kundtz, N.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref] [PubMed]

Kuray, P.

S. Ushiba, S. Shoji, P. Kuray, K. Masui, J. Kono, and S. Kawata, “Two photon polymerization lithography for 3D microfabrication of single wall carbon nanotube/polymer composites,” Proc. SPIE 8613, 86130Y (2013).
[Crossref]

Lagendijk, A.

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering Lens Resolves Sub-100 nm Structures with Visible Light,” Phys. Rev. Lett. 106(19), 193905 (2011).
[Crossref] [PubMed]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Lee, H. H.

Lee, J.

K. B. Song, J. Lee, J. H. Kim, K. Cho, and S. K. Kim, “Direct observation of self-focusing with subdiffraction limited resolution using near-field scanning optical microscope,” Phys. Rev. Lett. 85(18), 3842–3845 (2000).
[Crossref] [PubMed]

Li, S.

Li, X.

J. Wei, S. Liu, Y. Geng, Y. Wang, X. Li, Y. Wu, and A. Dun, “Nano-optical information storage induced by the nonlinear saturable absorption effect,” Nanoscale 3(8), 3233–3237 (2011).
[Crossref] [PubMed]

Li, Y.

X. Hao, C. Kuang, Y. Li, X. Liu, Y. Ku, and Y. Jiang, “Hydrophilic microsphere based mesoscopic-lens microscope,” Opt. Commun. 285(20), 4130–4133 (2012).
[Crossref]

Liakhou, G.

F. Michelotti, F. Caiazza, G. Liakhou, S. Paoloni, and M. Bertolotti, “Effects of nonlinear Fabry-Perot resonator response on z-scan measurements,” Opt. Commun. 124(1-2), 103–110 (1996).
[Crossref]

Lichtman, J. W.

J. W. Lichtman and J. A. Conchello, “Fluorescence microscopy,” Nat. Methods 2(12), 910–919 (2005).
[Crossref] [PubMed]

Liu, S.

J. Wei, S. Liu, Y. Geng, Y. Wang, X. Li, Y. Wu, and A. Dun, “Nano-optical information storage induced by the nonlinear saturable absorption effect,” Nanoscale 3(8), 3233–3237 (2011).
[Crossref] [PubMed]

Liu, W. C.

W. C. Liu, M. Y. Ng, and D. P. Tsai, “Surface Plasmon Effects on the Far-Field Signals of AgOx-Type Super Resolution Near-Field Structure,” Jpn. J. Appl. Phys. 43(7B), 4713–4717 (2004).
[Crossref]

Liu, X.

X. Hao, C. Kuang, Y. Li, X. Liu, Y. Ku, and Y. Jiang, “Hydrophilic microsphere based mesoscopic-lens microscope,” Opt. Commun. 285(20), 4130–4133 (2012).
[Crossref]

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Ma, X.

X. Ma and J. Wei, “Nanoscale lithography with visible light: optical nonlinear saturable absorption effect induced nanobump pattern structures,” Nanoscale 3(4), 1489–1492 (2011).
[Crossref] [PubMed]

Ma, Y.

Manfield, S. M.

S. M. Manfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57(24), 2615–2617 (1990).
[Crossref]

Masui, K.

S. Ushiba, S. Shoji, P. Kuray, K. Masui, J. Kono, and S. Kawata, “Two photon polymerization lithography for 3D microfabrication of single wall carbon nanotube/polymer composites,” Proc. SPIE 8613, 86130Y (2013).
[Crossref]

Mazilu, M.

Michelotti, F.

F. Michelotti, F. Caiazza, G. Liakhou, S. Paoloni, and M. Bertolotti, “Effects of nonlinear Fabry-Perot resonator response on z-scan measurements,” Opt. Commun. 124(1-2), 103–110 (1996).
[Crossref]

Mosk, A. P.

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering Lens Resolves Sub-100 nm Structures with Visible Light,” Phys. Rev. Lett. 106(19), 193905 (2011).
[Crossref] [PubMed]

Nakano, T.

J. Tominaga, T. Nakano, and N. Atoda, “An approach for recording and readout beyond the diffraction limit with an Sb thin film,” Appl. Phys. Lett. 73(15), 2078 (1998).
[Crossref]

Neubecker, R.

M. Kreuzer, H. Gottschling, R. Neubecker, and T. Tschudi, “Analysis of dynamic pattern formation in nonlinear Fabry-Perot resonators,” Appl. Phys. B 59(6), 581–589 (1994).
[Crossref]

Ng, M. Y.

W. C. Liu, M. Y. Ng, and D. P. Tsai, “Surface Plasmon Effects on the Far-Field Signals of AgOx-Type Super Resolution Near-Field Structure,” Jpn. J. Appl. Phys. 43(7B), 4713–4717 (2004).
[Crossref]

Osman, J.

K. Chew, J. Osman, and D. R. Tilley, “The nonlinear Fabry–Pérot resonator: direct numerical integration,” Opt. Commun. 191(3-6), 393–404 (2001).
[Crossref]

Pan, L.

L. Pan, Y. Park, Y. Xiong, E. Ulin-Avila, Y. Wang, L. Zeng, S. Xiong, J. Rho, C. Sun, D. B. Bogy, and X. Zhang, “Maskless plasmonic lithography at 22 nm resolution,” Sci. Rep. 1, 175 (2011).
[Crossref] [PubMed]

Paoloni, S.

F. Michelotti, F. Caiazza, G. Liakhou, S. Paoloni, and M. Bertolotti, “Effects of nonlinear Fabry-Perot resonator response on z-scan measurements,” Opt. Commun. 124(1-2), 103–110 (1996).
[Crossref]

Park, S. H.

Park, Y.

L. Pan, Y. Park, Y. Xiong, E. Ulin-Avila, Y. Wang, L. Zeng, S. Xiong, J. Rho, C. Sun, D. B. Bogy, and X. Zhang, “Maskless plasmonic lithography at 22 nm resolution,” Sci. Rep. 1, 175 (2011).
[Crossref] [PubMed]

Psaltis, D.

Rakov, N.

M. Xiao and N. Rakov, “Enhanced optical near-field transmission through subwavelength holes randomly distributed in a thin gold film,” J. Phys. Condens. Matter 15(4), L133–L137 (2003).
[Crossref]

Rho, J.

L. Pan, Y. Park, Y. Xiong, E. Ulin-Avila, Y. Wang, L. Zeng, S. Xiong, J. Rho, C. Sun, D. B. Bogy, and X. Zhang, “Maskless plasmonic lithography at 22 nm resolution,” Sci. Rep. 1, 175 (2011).
[Crossref] [PubMed]

Sadeghzadeh, R. A.

Sentenac, A.

A. Sentenac and P. C. Chaumet, “Subdiffraction light focusing on a grating substrate,” Phys. Rev. Lett. 101(1), 013901 (2008).
[Crossref] [PubMed]

Sheppard, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Shi, Y.

Shoji, S.

S. Ushiba, S. Shoji, P. Kuray, K. Masui, J. Kono, and S. Kawata, “Two photon polymerization lithography for 3D microfabrication of single wall carbon nanotube/polymer composites,” Proc. SPIE 8613, 86130Y (2013).
[Crossref]

Smith, D. R.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref] [PubMed]

Smith, S. D.

E. Abraham and S. D. Smith, “Nonlinear Fabry-Perot interferometers,” J. Phys. E. 15(1), 33–39 (1982).
[Crossref]

Song, K. B.

K. B. Song, J. Lee, J. H. Kim, K. Cho, and S. K. Kim, “Direct observation of self-focusing with subdiffraction limited resolution using near-field scanning optical microscope,” Phys. Rev. Lett. 85(18), 3842–3845 (2000).
[Crossref] [PubMed]

Sun, C.

L. Pan, Y. Park, Y. Xiong, E. Ulin-Avila, Y. Wang, L. Zeng, S. Xiong, J. Rho, C. Sun, D. B. Bogy, and X. Zhang, “Maskless plasmonic lithography at 22 nm resolution,” Sci. Rep. 1, 175 (2011).
[Crossref] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Sun, H.

H. Sun and S. Kawata, “Two-photon photopolymerization and 3D lithographic micro-fabrication,” Adv. Polymer Sci. 170, 169–273 (2004).

Tanaka, K.

K. Tanaka and H. Hisakuni, “Photoinduced phenomena in As2S3 glass under sub-bandgap excitation,” J. Non-Crystalline Solids 198–200, 714–718 (1996).
[Crossref]

Tilley, D. R.

K. Chew, J. Osman, and D. R. Tilley, “The nonlinear Fabry–Pérot resonator: direct numerical integration,” Opt. Commun. 191(3-6), 393–404 (2001).
[Crossref]

Tominaga, J.

J. Tominaga, T. Nakano, and N. Atoda, “An approach for recording and readout beyond the diffraction limit with an Sb thin film,” Appl. Phys. Lett. 73(15), 2078 (1998).
[Crossref]

Tsai, D. P.

W. C. Liu, M. Y. Ng, and D. P. Tsai, “Surface Plasmon Effects on the Far-Field Signals of AgOx-Type Super Resolution Near-Field Structure,” Jpn. J. Appl. Phys. 43(7B), 4713–4717 (2004).
[Crossref]

Tsampoula, X.

Tschudi, T.

M. Kreuzer, H. Gottschling, R. Neubecker, and T. Tschudi, “Analysis of dynamic pattern formation in nonlinear Fabry-Perot resonators,” Appl. Phys. B 59(6), 581–589 (1994).
[Crossref]

Ulin-Avila, E.

L. Pan, Y. Park, Y. Xiong, E. Ulin-Avila, Y. Wang, L. Zeng, S. Xiong, J. Rho, C. Sun, D. B. Bogy, and X. Zhang, “Maskless plasmonic lithography at 22 nm resolution,” Sci. Rep. 1, 175 (2011).
[Crossref] [PubMed]

Ushiba, S.

S. Ushiba, S. Shoji, P. Kuray, K. Masui, J. Kono, and S. Kawata, “Two photon polymerization lithography for 3D microfabrication of single wall carbon nanotube/polymer composites,” Proc. SPIE 8613, 86130Y (2013).
[Crossref]

van Putten, E. G.

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering Lens Resolves Sub-100 nm Structures with Visible Light,” Phys. Rev. Lett. 106(19), 193905 (2011).
[Crossref] [PubMed]

Vettenburg, T.

Vos, W. L.

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering Lens Resolves Sub-100 nm Structures with Visible Light,” Phys. Rev. Lett. 106(19), 193905 (2011).
[Crossref] [PubMed]

Wang, C.

Wang, H.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Wang, R.

R. Wang and J. Wei, “Parabolic approximation analytical model of super-resolution spot generation using nonlinear thin films: theory and simulation,” Opt. Commun. 316, 220–227 (2014).
[Crossref]

Wang, Y.

J. Wei, S. Liu, Y. Geng, Y. Wang, X. Li, Y. Wu, and A. Dun, “Nano-optical information storage induced by the nonlinear saturable absorption effect,” Nanoscale 3(8), 3233–3237 (2011).
[Crossref] [PubMed]

L. Pan, Y. Park, Y. Xiong, E. Ulin-Avila, Y. Wang, L. Zeng, S. Xiong, J. Rho, C. Sun, D. B. Bogy, and X. Zhang, “Maskless plasmonic lithography at 22 nm resolution,” Sci. Rep. 1, 175 (2011).
[Crossref] [PubMed]

Wei, J.

R. Wang and J. Wei, “Parabolic approximation analytical model of super-resolution spot generation using nonlinear thin films: theory and simulation,” Opt. Commun. 316, 220–227 (2014).
[Crossref]

Y. Zha, J. Wei, and F. Gan, “A novel design for maskless direct laser writing nanolithography: combination of diffractive optical element and nonlinear absorption inorganic resists,” Opt. Commun. 304, 49–53 (2013).
[Crossref]

Y. Zha, J. Wei, and F. Gan, “Creation of ultra-long depth of focus super-resolution longitudinally polarized beam with ternary optical element,” J. Opt. 15(7), 075703 (2013).
[Crossref]

J. Wei, Y. Zha, and F. Gan, “Creation of super-Resolution non-diffraction beam by modulating circularly polarized light with ternary optical element,” Prog. Electromagnetics Res. 140, 589–598 (2013).

J. Wei, S. Liu, Y. Geng, Y. Wang, X. Li, Y. Wu, and A. Dun, “Nano-optical information storage induced by the nonlinear saturable absorption effect,” Nanoscale 3(8), 3233–3237 (2011).
[Crossref] [PubMed]

X. Ma and J. Wei, “Nanoscale lithography with visible light: optical nonlinear saturable absorption effect induced nanobump pattern structures,” Nanoscale 3(4), 1489–1492 (2011).
[Crossref] [PubMed]

J. Wei, M. Xiao, and F. Zhang, “Super-resolution with a nonlinear thin film: beam reshaping via internal multi-interference,” Appl. Phys. Lett. 89(22), 223126 (2006).
[Crossref]

Wu, Y.

J. Wei, S. Liu, Y. Geng, Y. Wang, X. Li, Y. Wu, and A. Dun, “Nano-optical information storage induced by the nonlinear saturable absorption effect,” Nanoscale 3(8), 3233–3237 (2011).
[Crossref] [PubMed]

Xiao,

M. Keller, Xiao, and S. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280(1-2), 217–230 (1993).
[Crossref]

Xiao, M.

J. Wei, M. Xiao, and F. Zhang, “Super-resolution with a nonlinear thin film: beam reshaping via internal multi-interference,” Appl. Phys. Lett. 89(22), 223126 (2006).
[Crossref]

M. Xiao and N. Rakov, “Enhanced optical near-field transmission through subwavelength holes randomly distributed in a thin gold film,” J. Phys. Condens. Matter 15(4), L133–L137 (2003).
[Crossref]

Xiong, S.

L. Pan, Y. Park, Y. Xiong, E. Ulin-Avila, Y. Wang, L. Zeng, S. Xiong, J. Rho, C. Sun, D. B. Bogy, and X. Zhang, “Maskless plasmonic lithography at 22 nm resolution,” Sci. Rep. 1, 175 (2011).
[Crossref] [PubMed]

Xiong, Y.

L. Pan, Y. Park, Y. Xiong, E. Ulin-Avila, Y. Wang, L. Zeng, S. Xiong, J. Rho, C. Sun, D. B. Bogy, and X. Zhang, “Maskless plasmonic lithography at 22 nm resolution,” Sci. Rep. 1, 175 (2011).
[Crossref] [PubMed]

Yim, S. Y.

Yu, W.

Zeng, L.

L. Pan, Y. Park, Y. Xiong, E. Ulin-Avila, Y. Wang, L. Zeng, S. Xiong, J. Rho, C. Sun, D. B. Bogy, and X. Zhang, “Maskless plasmonic lithography at 22 nm resolution,” Sci. Rep. 1, 175 (2011).
[Crossref] [PubMed]

Zha, Y.

Y. Zha, J. Wei, and F. Gan, “A novel design for maskless direct laser writing nanolithography: combination of diffractive optical element and nonlinear absorption inorganic resists,” Opt. Commun. 304, 49–53 (2013).
[Crossref]

J. Wei, Y. Zha, and F. Gan, “Creation of super-Resolution non-diffraction beam by modulating circularly polarized light with ternary optical element,” Prog. Electromagnetics Res. 140, 589–598 (2013).

Y. Zha, J. Wei, and F. Gan, “Creation of ultra-long depth of focus super-resolution longitudinally polarized beam with ternary optical element,” J. Opt. 15(7), 075703 (2013).
[Crossref]

Zhang, F.

J. Wei, M. Xiao, and F. Zhang, “Super-resolution with a nonlinear thin film: beam reshaping via internal multi-interference,” Appl. Phys. Lett. 89(22), 223126 (2006).
[Crossref]

Zhang, R.

Zhang, X.

L. Pan, Y. Park, Y. Xiong, E. Ulin-Avila, Y. Wang, L. Zeng, S. Xiong, J. Rho, C. Sun, D. B. Bogy, and X. Zhang, “Maskless plasmonic lithography at 22 nm resolution,” Sci. Rep. 1, 175 (2011).
[Crossref] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Zhao, J.

Zheng, G.

Zhou, H.

Adv. Polymer Sci. (1)

H. Sun and S. Kawata, “Two-photon photopolymerization and 3D lithographic micro-fabrication,” Adv. Polymer Sci. 170, 169–273 (2004).

Appl. Phys. B (1)

M. Kreuzer, H. Gottschling, R. Neubecker, and T. Tschudi, “Analysis of dynamic pattern formation in nonlinear Fabry-Perot resonators,” Appl. Phys. B 59(6), 581–589 (1994).
[Crossref]

Appl. Phys. Lett. (3)

J. Wei, M. Xiao, and F. Zhang, “Super-resolution with a nonlinear thin film: beam reshaping via internal multi-interference,” Appl. Phys. Lett. 89(22), 223126 (2006).
[Crossref]

J. Tominaga, T. Nakano, and N. Atoda, “An approach for recording and readout beyond the diffraction limit with an Sb thin film,” Appl. Phys. Lett. 73(15), 2078 (1998).
[Crossref]

S. M. Manfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57(24), 2615–2617 (1990).
[Crossref]

Chin. Opt. Lett. (4)

J. Non-Crystalline Solids (1)

K. Tanaka and H. Hisakuni, “Photoinduced phenomena in As2S3 glass under sub-bandgap excitation,” J. Non-Crystalline Solids 198–200, 714–718 (1996).
[Crossref]

J. Opt. (1)

Y. Zha, J. Wei, and F. Gan, “Creation of ultra-long depth of focus super-resolution longitudinally polarized beam with ternary optical element,” J. Opt. 15(7), 075703 (2013).
[Crossref]

J. Phys. Condens. Matter (1)

M. Xiao and N. Rakov, “Enhanced optical near-field transmission through subwavelength holes randomly distributed in a thin gold film,” J. Phys. Condens. Matter 15(4), L133–L137 (2003).
[Crossref]

J. Phys. E. (1)

E. Abraham and S. D. Smith, “Nonlinear Fabry-Perot interferometers,” J. Phys. E. 15(1), 33–39 (1982).
[Crossref]

Jpn. J. Appl. Phys. (1)

W. C. Liu, M. Y. Ng, and D. P. Tsai, “Surface Plasmon Effects on the Far-Field Signals of AgOx-Type Super Resolution Near-Field Structure,” Jpn. J. Appl. Phys. 43(7B), 4713–4717 (2004).
[Crossref]

Nanoscale (2)

J. Wei, S. Liu, Y. Geng, Y. Wang, X. Li, Y. Wu, and A. Dun, “Nano-optical information storage induced by the nonlinear saturable absorption effect,” Nanoscale 3(8), 3233–3237 (2011).
[Crossref] [PubMed]

X. Ma and J. Wei, “Nanoscale lithography with visible light: optical nonlinear saturable absorption effect induced nanobump pattern structures,” Nanoscale 3(4), 1489–1492 (2011).
[Crossref] [PubMed]

Nat. Mater. (1)

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref] [PubMed]

Nat. Methods (1)

J. W. Lichtman and J. A. Conchello, “Fluorescence microscopy,” Nat. Methods 2(12), 910–919 (2005).
[Crossref] [PubMed]

Nat. Photonics (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Opt. Commun. (6)

X. Hao, C. Kuang, Y. Li, X. Liu, Y. Ku, and Y. Jiang, “Hydrophilic microsphere based mesoscopic-lens microscope,” Opt. Commun. 285(20), 4130–4133 (2012).
[Crossref]

Y. Zha, J. Wei, and F. Gan, “A novel design for maskless direct laser writing nanolithography: combination of diffractive optical element and nonlinear absorption inorganic resists,” Opt. Commun. 304, 49–53 (2013).
[Crossref]

L. E. Helseth, “Breaking the diffraction limit in nonlinear materials,” Opt. Commun. 256(4-6), 435–438 (2005).
[Crossref]

K. Chew, J. Osman, and D. R. Tilley, “The nonlinear Fabry–Pérot resonator: direct numerical integration,” Opt. Commun. 191(3-6), 393–404 (2001).
[Crossref]

F. Michelotti, F. Caiazza, G. Liakhou, S. Paoloni, and M. Bertolotti, “Effects of nonlinear Fabry-Perot resonator response on z-scan measurements,” Opt. Commun. 124(1-2), 103–110 (1996).
[Crossref]

R. Wang and J. Wei, “Parabolic approximation analytical model of super-resolution spot generation using nonlinear thin films: theory and simulation,” Opt. Commun. 316, 220–227 (2014).
[Crossref]

Opt. Express (1)

Photon. Res. (2)

Phys. Rev. Lett. (3)

K. B. Song, J. Lee, J. H. Kim, K. Cho, and S. K. Kim, “Direct observation of self-focusing with subdiffraction limited resolution using near-field scanning optical microscope,” Phys. Rev. Lett. 85(18), 3842–3845 (2000).
[Crossref] [PubMed]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering Lens Resolves Sub-100 nm Structures with Visible Light,” Phys. Rev. Lett. 106(19), 193905 (2011).
[Crossref] [PubMed]

A. Sentenac and P. C. Chaumet, “Subdiffraction light focusing on a grating substrate,” Phys. Rev. Lett. 101(1), 013901 (2008).
[Crossref] [PubMed]

Proc. SPIE (1)

S. Ushiba, S. Shoji, P. Kuray, K. Masui, J. Kono, and S. Kawata, “Two photon polymerization lithography for 3D microfabrication of single wall carbon nanotube/polymer composites,” Proc. SPIE 8613, 86130Y (2013).
[Crossref]

Prog. Electromagnetics Res. (1)

J. Wei, Y. Zha, and F. Gan, “Creation of super-Resolution non-diffraction beam by modulating circularly polarized light with ternary optical element,” Prog. Electromagnetics Res. 140, 589–598 (2013).

Sci. Rep. (1)

L. Pan, Y. Park, Y. Xiong, E. Ulin-Avila, Y. Wang, L. Zeng, S. Xiong, J. Rho, C. Sun, D. B. Bogy, and X. Zhang, “Maskless plasmonic lithography at 22 nm resolution,” Sci. Rep. 1, 175 (2011).
[Crossref] [PubMed]

Science (1)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Surf. Sci. (1)

M. Keller, Xiao, and S. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280(1-2), 217–230 (1993).
[Crossref]

Other (4)

B. Hyot, S. Olivier, M. F. Armand, F. Laulagnet, B. Andre, R. Truche, and X. Biquard, “High capacity Super-RENS ROM disc with InSb active layer,” E*PCOS09 European Symposium Phase Change and Ovonic Sciences, 1–8 (2009).

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

W. Robert, Boyd, Nonlinear optics, 2nd ed. (Academic, 2003).

N. Pinna and M. Knez, Atomic Layer Deposition of Nanostructured Materials (Wiley-VCH, 2011).

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Figures (10)

Fig. 1
Fig. 1

The schematic of light beam traveling through the nonlinear Fabry-Perot cavity.

Fig. 2
Fig. 2

Simplified schematic of light beam propgagtion using the effective light field.

Fig. 3
Fig. 3

The distribution of (a) cavity field intensity and (b) refractive index at incident laser power of P = 0.2mW and L = 100nm.

Fig. 4
Fig. 4

The two-dimensional intensity distribution of exiting spot through nonlinear Fabry-Perot cavity structure for P = 0.2mW (a) incident spot, (b) L = 286nm, (c) L = 386nm, (d) L = 484nm, (e) L = 586nm, and (f) L = 687nm.

Fig. 5
Fig. 5

The three-dimensional intensity distribution of exiting spot from nonlinear Fabry-Perot cavity structure for P = 0.2mW, (a) incident spot (L = 0), (b) L = 286nm, (c) L = 386nm, (d) L = 484nm, (e) L = 586nm, and (f) L = 687nm.

Fig. 6
Fig. 6

The dependence of spot characteristics on nonlinear thin film thickness, (a) normalized intensity distribution of exiting light spot from nonlinear Fabry-Perot cavity structure for different nonlinear thin film thickness, and (b) sensitivity of central spot size to nonlinear thin film thickness for L = 687~690nm and P = 0.2mW.

Fig. 7
Fig. 7

Laser power manipulation for obtaining nanoscale central optical hot spot, (a) the two-dimensional intensity distribution for L = 690nm and P = 0.2mW, (b) comparison of spot intensity among L = 890nm and P = 0.2mW, L = 690nm and P = 0.196mW, and L = 687nm and P = 0.2mW, (c) the two-dimensional intensity distribution for L = 690nm and P = 0.196mW.

Fig. 8
Fig. 8

The normalized spot intensity distribution for L = 781nm and P = 0.2mW, (a) cross-section profile along radial direction, and (b) two-dimensional spot intensity profile.

Fig. 9
Fig. 9

Super-resolution spot test schematic of nonlinear Fabry-Perot cavity structures.

Fig. 10
Fig. 10

Application schematics of the nonlinear Fabry-Perot cavity structure in nanolithography, (a)formation schematic of super-resolution spot, (b) threshold effect for lithography or optical recording .

Equations (26)

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

A 1 = E 0 exp( r 2 / w 0 2 )
I 1 = I 0 exp(2 r 2 / w 0 2 ).
ρ 12 = n 1 n ˜ n 1 + n ˜ , τ 12 = 2 n 1 n 1 + n ˜ , ρ 23 = n ˜ n 3 n ˜ + n 3 , τ 23= 2 n ˜ n ˜ + n 3 ,
n ˜ (r)=n+i λ 4π α,
R= R 12 = | ρ 12 | 2 = R 23 = | ρ 23 | 2 = | ρ | 2 T= T 12 =[ n ˜ n 1 ] | τ 12 | 2 = T 23 =[ n 3 n ˜ ] | τ 23 | 2 .
A 2 (1) = A 1 τ e ikL 1 2 αL ,
A 2 '(1) = A 1 τ e ikL 1 2 αL ρ e ikL 1 2 αL .
A 2 (2) = A 1 τ e ikL 1 2 αL R e 2ikLαL .
A 2 '(2) = A 1 τ e ikL 1 2 αL ρ e ikL 1 2 αL (R e 2ikLαL ).
A 2 (3) = A 1 τ e ikL 1 2 αL (R e 2ikLαL ) 2 .
A 2 '(3) = A 1 τ e ikL 1 2 αL ρ e ikL 1 2 αL (R e 2ikLαL ) 2 .
A 2 (i) = A 1 τ e ikL 1 2 αL (R e 2ikLαL ) (i1) .
A 2 '(i) = A 1 τ e ikL 1 2 αL ρ e ikL 1 2 αL (R e 2ikLαL ) (i1) .
A 2 (m) = A 1 τ e ikL 1 2 αL (R e 2ikLαL ) (m1) .
A 2 '(m) = A 1 τ e ikL 1 2 αL ρ e ikL 1 2 αL (R e 2ikLαL ) (m1) .
A 2 = A 2 (1) + A 2 (2) + A 2 (3) ++ A 2 (i) ++ A 2 (m) = A 1 τ e ikL 1 2 αL 1R e 2ikLαL .
A 2 ' = A 2 '( 1 ) + A 2 '( 2 ) + A 2 '( 3 ) ++ A 2 '( i ) ++ A 2 '( m ) = A 2 ρ e ikL 1 2 αL .
I 2 = | A 2 | 2 = T I 1 e αL 12R e αL cos( 4πnL/λ )+ R 2 e 2αL .
I 3 = | A 3 | 2 =T I 2 = T 2 I 1 e αL 12R e αL cos( 4πnL/λ )+ R 2 e 2αL .
I cavity = | A 2 | 2 + | A 2 ' | 2 = I 2 + I 2 ' .
I 2 ' = | A 2 ' | 2 = | A 2 ρ e ikL 1 2 αL | 2 = I 2 R e αL .
I cavity = I 2 ( 1+R e αL ).
n(r)= n 0 +γ I cavity (r) α(r)= α 0 +β I cavity (r) ,
n ˜ ( r )=[ n 0 +γ I cavity ( r ) ]+i λ 4π [ α 0 +β I cavity ( r ) ].
I 3 ( r )= | A 3 | 2 = T 2 I 0 exp( 2 r 2 w 0 2 ) 12Rcos[ 4πn( r )L λ ]+ R 2 .
L=qλ/2n,q=0,1,2.

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