Abstract

The problem of the absorption of light by a nanoscale dielectric cone is discussed. A simplified solution based on the analytical Mie theory of scattering and absorption by cylindrical objects is proposed and supported by the experimental observation of sharply localized holes in conical silicon tips after high-fluence irradiation. This study reveals that light couples with tapered objects dominantly at specific locations, where the local radius corresponds to one of the resonant radii of a cylindrical object, as predicted by Mie theory.

© 2013 OSA

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A. Vella, N. Sevelin-Radiguet, J. Houard, and B. Deconihout, “Polarization dependence of the optical absorption of a subwavelength tip,” Appl. Surf. Sci.258(23), 9202–9207 (2012).
[CrossRef]

A. R. Jones, “Some calculations on the internal electromagnetic fluxes of cylinders,” J. Opt.14(6), 065702 (2012).
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P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat Commun3, 692 (2012).
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Y. Qiu, H.-C. Hao, J. Zhou, and M. Lu, “A close to unity and all-solar-spectrum absorption by ion-sputtering induced Si nanocone arrays,” Opt. Express20(20), 22087–22094 (2012).
[CrossRef] [PubMed]

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M. I. Mishchenko, N. T. Zakharova, G. Videen, N. G. Khlebtsov, and T. Wriedt, “Comprehensive T-matrix reference database: a 2007-2009 update,” J. Quant. Spectrosc. Radiat. Transf.111(4), 650–658 (2010).
[CrossRef]

2009 (1)

J. Zhu, Z. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett.9(1), 279–282 (2009).
[CrossRef] [PubMed]

2007 (2)

A. Vella, B. Deconihout, L. Marrucci, and E. Santamato, “Femtosecond field ion emission by surface optical rectification,” Phys. Rev. Lett.99(4), 046103 (2007).
[CrossRef] [PubMed]

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett.90(19), 191104 (2007).
[CrossRef]

2006 (1)

B. Gault, F. Vurpillot, A. Vella, M. Gilbert, A. Menand, D. Blavette, and B. Deconihout, “Design of a femtosecond laser assisted tomographic atom probe,” Rev. Sci. Instrum.77(4), 043705 (2006).
[CrossRef]

2004 (2)

L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express12(6), 1025–1035 (2004).
[CrossRef] [PubMed]

M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, “T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database,” J. Quant. Spectrosc. Radiat. Transf.88, 357–406 (2004).

2003 (1)

M. Idemen, “Confluent tip singularity of the electromagnetic field at the apex of a material cone,” Wave Motion38(3), 251–277 (2003).
[CrossRef]

1997 (2)

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett.79(4), 645–648 (1997).
[CrossRef]

K. G. Ayappa, H. T. Davis, S. A. Barringer, and E. A. Davis, “Resonant microwave power absorption in slabs and cylinders,” AIChE J.43(3), 615–624 (1997).
[CrossRef]

1996 (1)

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: A review,” J. Quant. Spectrosc. Radiat. Transf.55(5), 535–575 (1996).
[CrossRef]

1994 (1)

1988 (1)

1973 (1)

1944 (1)

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev.66(7-8), 163–182 (1944).
[CrossRef]

Aspnes, D. E.

Ayappa, K. G.

K. G. Ayappa, H. T. Davis, S. A. Barringer, and E. A. Davis, “Resonant microwave power absorption in slabs and cylinders,” AIChE J.43(3), 615–624 (1997).
[CrossRef]

Babenko, V. A.

M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, “T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database,” J. Quant. Spectrosc. Radiat. Transf.88, 357–406 (2004).

Barringer, S. A.

K. G. Ayappa, H. T. Davis, S. A. Barringer, and E. A. Davis, “Resonant microwave power absorption in slabs and cylinders,” AIChE J.43(3), 615–624 (1997).
[CrossRef]

Bethe, H. A.

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev.66(7-8), 163–182 (1944).
[CrossRef]

Bian, R. X.

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett.79(4), 645–648 (1997).
[CrossRef]

Blavette, D.

B. Gault, F. Vurpillot, A. Vella, M. Gilbert, A. Menand, D. Blavette, and B. Deconihout, “Design of a femtosecond laser assisted tomographic atom probe,” Rev. Sci. Instrum.77(4), 043705 (2006).
[CrossRef]

Bohren, C. F.

Bristow, A. D.

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett.90(19), 191104 (2007).
[CrossRef]

Burkhard, G. F.

J. Zhu, Z. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett.9(1), 279–282 (2009).
[CrossRef] [PubMed]

Connor, S. T.

J. Zhu, Z. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett.9(1), 279–282 (2009).
[CrossRef] [PubMed]

Cui, Y.

J. Zhu, Z. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett.9(1), 279–282 (2009).
[CrossRef] [PubMed]

Davis, E. A.

K. G. Ayappa, H. T. Davis, S. A. Barringer, and E. A. Davis, “Resonant microwave power absorption in slabs and cylinders,” AIChE J.43(3), 615–624 (1997).
[CrossRef]

Davis, H. T.

K. G. Ayappa, H. T. Davis, S. A. Barringer, and E. A. Davis, “Resonant microwave power absorption in slabs and cylinders,” AIChE J.43(3), 615–624 (1997).
[CrossRef]

Deconihout, B.

A. Vella, N. Sevelin-Radiguet, J. Houard, and B. Deconihout, “Polarization dependence of the optical absorption of a subwavelength tip,” Appl. Surf. Sci.258(23), 9202–9207 (2012).
[CrossRef]

A. Vella, B. Deconihout, L. Marrucci, and E. Santamato, “Femtosecond field ion emission by surface optical rectification,” Phys. Rev. Lett.99(4), 046103 (2007).
[CrossRef] [PubMed]

B. Gault, F. Vurpillot, A. Vella, M. Gilbert, A. Menand, D. Blavette, and B. Deconihout, “Design of a femtosecond laser assisted tomographic atom probe,” Rev. Sci. Instrum.77(4), 043705 (2006).
[CrossRef]

Fan, S.

J. Zhu, Z. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett.9(1), 279–282 (2009).
[CrossRef] [PubMed]

Gault, B.

B. Gault, F. Vurpillot, A. Vella, M. Gilbert, A. Menand, D. Blavette, and B. Deconihout, “Design of a femtosecond laser assisted tomographic atom probe,” Rev. Sci. Instrum.77(4), 043705 (2006).
[CrossRef]

Gilbert, M.

B. Gault, F. Vurpillot, A. Vella, M. Gilbert, A. Menand, D. Blavette, and B. Deconihout, “Design of a femtosecond laser assisted tomographic atom probe,” Rev. Sci. Instrum.77(4), 043705 (2006).
[CrossRef]

Hao, H.-C.

Houard, J.

A. Vella, N. Sevelin-Radiguet, J. Houard, and B. Deconihout, “Polarization dependence of the optical absorption of a subwavelength tip,” Appl. Surf. Sci.258(23), 9202–9207 (2012).
[CrossRef]

Hsu, C. M.

J. Zhu, Z. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett.9(1), 279–282 (2009).
[CrossRef] [PubMed]

Idemen, M.

M. Idemen, “Confluent tip singularity of the electromagnetic field at the apex of a material cone,” Wave Motion38(3), 251–277 (2003).
[CrossRef]

Jones, A. R.

A. R. Jones, “Some calculations on the internal electromagnetic fluxes of cylinders,” J. Opt.14(6), 065702 (2012).
[CrossRef]

Khlebtsov, N. G.

M. I. Mishchenko, N. T. Zakharova, G. Videen, N. G. Khlebtsov, and T. Wriedt, “Comprehensive T-matrix reference database: a 2007-2009 update,” J. Quant. Spectrosc. Radiat. Transf.111(4), 650–658 (2010).
[CrossRef]

M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, “T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database,” J. Quant. Spectrosc. Radiat. Transf.88, 357–406 (2004).

Lou, J.

Lu, M.

Mackowski, D. W.

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: A review,” J. Quant. Spectrosc. Radiat. Transf.55(5), 535–575 (1996).
[CrossRef]

Marrucci, L.

A. Vella, B. Deconihout, L. Marrucci, and E. Santamato, “Femtosecond field ion emission by surface optical rectification,” Phys. Rev. Lett.99(4), 046103 (2007).
[CrossRef] [PubMed]

Mazur, E.

McGehee, M.

J. Zhu, Z. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett.9(1), 279–282 (2009).
[CrossRef] [PubMed]

Menand, A.

B. Gault, F. Vurpillot, A. Vella, M. Gilbert, A. Menand, D. Blavette, and B. Deconihout, “Design of a femtosecond laser assisted tomographic atom probe,” Rev. Sci. Instrum.77(4), 043705 (2006).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, N. T. Zakharova, G. Videen, N. G. Khlebtsov, and T. Wriedt, “Comprehensive T-matrix reference database: a 2007-2009 update,” J. Quant. Spectrosc. Radiat. Transf.111(4), 650–658 (2010).
[CrossRef]

M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, “T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database,” J. Quant. Spectrosc. Radiat. Transf.88, 357–406 (2004).

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: A review,” J. Quant. Spectrosc. Radiat. Transf.55(5), 535–575 (1996).
[CrossRef]

Mitchell, D. J.

Novotny, L.

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett.79(4), 645–648 (1997).
[CrossRef]

Pask, C.

Polman, A.

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat Commun3, 692 (2012).
[CrossRef] [PubMed]

Qiu, Y.

Rotenberg, N.

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett.90(19), 191104 (2007).
[CrossRef]

Santamato, E.

A. Vella, B. Deconihout, L. Marrucci, and E. Santamato, “Femtosecond field ion emission by surface optical rectification,” Phys. Rev. Lett.99(4), 046103 (2007).
[CrossRef] [PubMed]

Sevelin-Radiguet, N.

A. Vella, N. Sevelin-Radiguet, J. Houard, and B. Deconihout, “Polarization dependence of the optical absorption of a subwavelength tip,” Appl. Surf. Sci.258(23), 9202–9207 (2012).
[CrossRef]

Snyder, A. W.

Spinelli, P.

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat Commun3, 692 (2012).
[CrossRef] [PubMed]

Tong, L.

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: A review,” J. Quant. Spectrosc. Radiat. Transf.55(5), 535–575 (1996).
[CrossRef]

Van Driel, H. M.

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett.90(19), 191104 (2007).
[CrossRef]

Vella, A.

A. Vella, N. Sevelin-Radiguet, J. Houard, and B. Deconihout, “Polarization dependence of the optical absorption of a subwavelength tip,” Appl. Surf. Sci.258(23), 9202–9207 (2012).
[CrossRef]

A. Vella, B. Deconihout, L. Marrucci, and E. Santamato, “Femtosecond field ion emission by surface optical rectification,” Phys. Rev. Lett.99(4), 046103 (2007).
[CrossRef] [PubMed]

B. Gault, F. Vurpillot, A. Vella, M. Gilbert, A. Menand, D. Blavette, and B. Deconihout, “Design of a femtosecond laser assisted tomographic atom probe,” Rev. Sci. Instrum.77(4), 043705 (2006).
[CrossRef]

Verschuuren, M. A.

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat Commun3, 692 (2012).
[CrossRef] [PubMed]

Videen, G.

M. I. Mishchenko, N. T. Zakharova, G. Videen, N. G. Khlebtsov, and T. Wriedt, “Comprehensive T-matrix reference database: a 2007-2009 update,” J. Quant. Spectrosc. Radiat. Transf.111(4), 650–658 (2010).
[CrossRef]

M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, “T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database,” J. Quant. Spectrosc. Radiat. Transf.88, 357–406 (2004).

Vurpillot, F.

B. Gault, F. Vurpillot, A. Vella, M. Gilbert, A. Menand, D. Blavette, and B. Deconihout, “Design of a femtosecond laser assisted tomographic atom probe,” Rev. Sci. Instrum.77(4), 043705 (2006).
[CrossRef]

Wang, Q.

J. Zhu, Z. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett.9(1), 279–282 (2009).
[CrossRef] [PubMed]

Wriedt, T.

M. I. Mishchenko, N. T. Zakharova, G. Videen, N. G. Khlebtsov, and T. Wriedt, “Comprehensive T-matrix reference database: a 2007-2009 update,” J. Quant. Spectrosc. Radiat. Transf.111(4), 650–658 (2010).
[CrossRef]

M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, “T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database,” J. Quant. Spectrosc. Radiat. Transf.88, 357–406 (2004).

Xie, X. S.

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett.79(4), 645–648 (1997).
[CrossRef]

Xu, Y.

J. Zhu, Z. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett.9(1), 279–282 (2009).
[CrossRef] [PubMed]

Yasuda, T.

Yu, Z.

J. Zhu, Z. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett.9(1), 279–282 (2009).
[CrossRef] [PubMed]

Zakharova, N. T.

M. I. Mishchenko, N. T. Zakharova, G. Videen, N. G. Khlebtsov, and T. Wriedt, “Comprehensive T-matrix reference database: a 2007-2009 update,” J. Quant. Spectrosc. Radiat. Transf.111(4), 650–658 (2010).
[CrossRef]

Zhou, J.

Zhu, J.

J. Zhu, Z. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett.9(1), 279–282 (2009).
[CrossRef] [PubMed]

AIChE J. (1)

K. G. Ayappa, H. T. Davis, S. A. Barringer, and E. A. Davis, “Resonant microwave power absorption in slabs and cylinders,” AIChE J.43(3), 615–624 (1997).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett.90(19), 191104 (2007).
[CrossRef]

Appl. Surf. Sci. (1)

A. Vella, N. Sevelin-Radiguet, J. Houard, and B. Deconihout, “Polarization dependence of the optical absorption of a subwavelength tip,” Appl. Surf. Sci.258(23), 9202–9207 (2012).
[CrossRef]

J. Opt. (1)

A. R. Jones, “Some calculations on the internal electromagnetic fluxes of cylinders,” J. Opt.14(6), 065702 (2012).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Quant. Spectrosc. Radiat. Transf. (3)

M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, “T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database,” J. Quant. Spectrosc. Radiat. Transf.88, 357–406 (2004).

M. I. Mishchenko, N. T. Zakharova, G. Videen, N. G. Khlebtsov, and T. Wriedt, “Comprehensive T-matrix reference database: a 2007-2009 update,” J. Quant. Spectrosc. Radiat. Transf.111(4), 650–658 (2010).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: A review,” J. Quant. Spectrosc. Radiat. Transf.55(5), 535–575 (1996).
[CrossRef]

Nano Lett. (1)

J. Zhu, Z. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett.9(1), 279–282 (2009).
[CrossRef] [PubMed]

Nat Commun (1)

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat Commun3, 692 (2012).
[CrossRef] [PubMed]

Opt. Express (2)

Phys. Rev. (1)

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev.66(7-8), 163–182 (1944).
[CrossRef]

Phys. Rev. Lett. (2)

A. Vella, B. Deconihout, L. Marrucci, and E. Santamato, “Femtosecond field ion emission by surface optical rectification,” Phys. Rev. Lett.99(4), 046103 (2007).
[CrossRef] [PubMed]

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett.79(4), 645–648 (1997).
[CrossRef]

Rev. Sci. Instrum. (1)

B. Gault, F. Vurpillot, A. Vella, M. Gilbert, A. Menand, D. Blavette, and B. Deconihout, “Design of a femtosecond laser assisted tomographic atom probe,” Rev. Sci. Instrum.77(4), 043705 (2006).
[CrossRef]

Wave Motion (1)

M. Idemen, “Confluent tip singularity of the electromagnetic field at the apex of a material cone,” Wave Motion38(3), 251–277 (2003).
[CrossRef]

Other (7)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

P. W. Barber and S. C. Hill, Light Scattering by Particles (World Scientific, 1990).

R. Menzel, Photonics, 2nd ed. (Springer, 2007).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Courier Dover Publications, 1965)

B. R. Tull, “Femtosecond laser ablation of silicon: nanoparticles, doping and photovoltaics,” PhD thesis, Harvard University (2007)

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge, 2006).

A. W. Snyder and J. D. Love, Optical waveguide theory (Springer, 1983)

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Figures (3)

Fig. 1
Fig. 1

Resonance behavior of the electric field in a cylindrical silicon particle of radius R , illuminated with a TM wave of amplitude E 0 and wavelengths λ 0 =515 nm (full line) and λ 0 =1030 nm (dotted line), incident normally to the cylinder axis. The shown values are on the illuminated side ( r=R,ϑ=π ).

Fig. 2
Fig. 2

Variation in the right-hand side of Eq. (3) as a function of the local radius R(z) in a conical silicon particle with cone angle α=10° illuminated respectively by green (full line) and IR (dotted line) TM waves of amplitude E 0 , incident normally to the cone axis. The shown values are on the illuminated side ( r=R,ϑ=π ).

Fig. 3
Fig. 3

(left) Theoretical value of | E z,int [r=R(z),ϑ=π,z] | 4 along the illuminated side of an IR-irradiated conical silicon tip as a function of the local radius R(z) . (right) Silicon tip irradiated with a high-fluence (~100 mJ/cm2) IR pulsed laser. Resonance absorption occurs in the cross-sections with R(z) ~113, 178 and 241 nm. The tip is tilted 45° with respect to the primary beam of the SEM.

Equations (3)

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E z,int (r,ϑ)= E 0 [ d 0 ( R λ 0 ) J 0 ( 2π n ˜ λ 0 r) + k=1 2 i k d k ( R λ 0 ) J k ( 2π n ˜ λ 0 r)cos(kϑ) ] ,
R(z)=ztan(α/2),
| E z,int |>> | λ 0 tan(α/2) 2π n ˜ | 2 | 2 E z,int R 2 | .

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