Abstract

Optical absorption is usually considered deleterious, something to avoid if at all possible. We propose a broadband nanoabsorber that completely eliminates the diffracting wave, resulting in a subwavelength enhancement of the field. Broadband operation is made possible by engineering the dispersion of the complex dielectric function. The local enhancement can be significantly improved compared to the standard plane wave illumination of a metallic nanoparticle. Our numerical simulation shows that an optical pulse as short as 6 fs can be focused to a 11 nm region. Not only the local field, but also its gradient are greatly enhanced, pointing to applications in ultrafast nonlinear spectroscopy, sensing and communication with deep-subwavelength resolution.

© 2013 OSA

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References

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  1. R. Carminati, R. Pierrat, J. de Rosny, and M. Fink, “Theory of the time reversal cavity for electromagnetic fields,” Opt. Lett.32, 3107–3109 (2002).
    [CrossRef]
  2. J. de Rosny and M. Fink, “Overcoming the diffraction limit in wave physics using a time-reversal mirror and a novel acoustic sink,” Phys. Rev. Lett.89, 124301 (2002).
    [CrossRef] [PubMed]
  3. P. Kinsler, “Active drains and causality,” Phys. Rev. A13, 055804 (2011).
  4. Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, and U. Leonhardt, “Evidence for subwavelength imaging with positive refraction,” New. J. Phys.13, 033016 (2002).
    [CrossRef]
  5. Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: Time-reversed lasers,” Phys. Rev. Lett.105, 053901 (2010).
    [CrossRef] [PubMed]
  6. W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science331, 889–892 (2011).
    [CrossRef] [PubMed]
  7. H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett.108, 186805 (2012).
    [CrossRef] [PubMed]
  8. G. Montaldo, G. Lerosey, A. Derode, A. Tourin, J. de Rosny, and M. Fink, “Telecommunication in a disordered environment with iterative time reversal,” Waves in Random Media14, 287–302 (2004).
    [CrossRef]
  9. M. Pu, Q. Feng, M. Wang, C. Hu, C. Huang, X. Ma, Z. Zhao, C. Wang, and X. Luo, “Ultrathin broadband nearly perfect absorber with symmetrical coherent illumination,” Opt. Express20, 2246–2254 (2012).
    [CrossRef] [PubMed]
  10. A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Müller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun.134, 431–439 (1997).
    [CrossRef]
  11. N. Yang and A. E. Cohen, “Local geometry of electromagnetic fields and its role in molecular multipole transitions,” J. Phys. Chem. B115, 5304–5311 (2011).
    [CrossRef] [PubMed]
  12. P. A. Belov, C. R. Simovski, and S. A. Tretyakov, “Example of bianisotropic electromagnetic crystals: The spiral medium,” Phys. Rev. E67, 056622 (2003).
    [CrossRef]
  13. A. I. Rahachou and I. V. Zozoulenko, “Light propagation in nanorod arrays,” J. Opt. A: Pure and Applied Optics9, 265–270 (2007).
    [CrossRef]
  14. N. Fang, D. Xi, J. Xu, M. Ambati, W. Srituravanich, C. Sun, and X. Zhang, “Ultrasonic metamaterials with negative modulus,” Nat. Mater.5, 452–456 (2006).
    [CrossRef] [PubMed]
  15. C. Ding, L. Hao, and X. Zhao, “Two-dimensional acoustic metamaterial with negative modulus,” J. Appl. Phys.108, 074911 (2010).
    [CrossRef]

2012 (2)

2011 (3)

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science331, 889–892 (2011).
[CrossRef] [PubMed]

N. Yang and A. E. Cohen, “Local geometry of electromagnetic fields and its role in molecular multipole transitions,” J. Phys. Chem. B115, 5304–5311 (2011).
[CrossRef] [PubMed]

P. Kinsler, “Active drains and causality,” Phys. Rev. A13, 055804 (2011).

2010 (2)

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: Time-reversed lasers,” Phys. Rev. Lett.105, 053901 (2010).
[CrossRef] [PubMed]

C. Ding, L. Hao, and X. Zhao, “Two-dimensional acoustic metamaterial with negative modulus,” J. Appl. Phys.108, 074911 (2010).
[CrossRef]

2007 (1)

A. I. Rahachou and I. V. Zozoulenko, “Light propagation in nanorod arrays,” J. Opt. A: Pure and Applied Optics9, 265–270 (2007).
[CrossRef]

2006 (1)

N. Fang, D. Xi, J. Xu, M. Ambati, W. Srituravanich, C. Sun, and X. Zhang, “Ultrasonic metamaterials with negative modulus,” Nat. Mater.5, 452–456 (2006).
[CrossRef] [PubMed]

2004 (1)

G. Montaldo, G. Lerosey, A. Derode, A. Tourin, J. de Rosny, and M. Fink, “Telecommunication in a disordered environment with iterative time reversal,” Waves in Random Media14, 287–302 (2004).
[CrossRef]

2003 (1)

P. A. Belov, C. R. Simovski, and S. A. Tretyakov, “Example of bianisotropic electromagnetic crystals: The spiral medium,” Phys. Rev. E67, 056622 (2003).
[CrossRef]

2002 (3)

J. de Rosny and M. Fink, “Overcoming the diffraction limit in wave physics using a time-reversal mirror and a novel acoustic sink,” Phys. Rev. Lett.89, 124301 (2002).
[CrossRef] [PubMed]

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, and U. Leonhardt, “Evidence for subwavelength imaging with positive refraction,” New. J. Phys.13, 033016 (2002).
[CrossRef]

R. Carminati, R. Pierrat, J. de Rosny, and M. Fink, “Theory of the time reversal cavity for electromagnetic fields,” Opt. Lett.32, 3107–3109 (2002).
[CrossRef]

1997 (1)

A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Müller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun.134, 431–439 (1997).
[CrossRef]

Ambati, M.

N. Fang, D. Xi, J. Xu, M. Ambati, W. Srituravanich, C. Sun, and X. Zhang, “Ultrasonic metamaterials with negative modulus,” Nat. Mater.5, 452–456 (2006).
[CrossRef] [PubMed]

Belov, P. A.

P. A. Belov, C. R. Simovski, and S. A. Tretyakov, “Example of bianisotropic electromagnetic crystals: The spiral medium,” Phys. Rev. E67, 056622 (2003).
[CrossRef]

Cao, H.

H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett.108, 186805 (2012).
[CrossRef] [PubMed]

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science331, 889–892 (2011).
[CrossRef] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: Time-reversed lasers,” Phys. Rev. Lett.105, 053901 (2010).
[CrossRef] [PubMed]

Carminati, R.

Chong, Y.

H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett.108, 186805 (2012).
[CrossRef] [PubMed]

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science331, 889–892 (2011).
[CrossRef] [PubMed]

Chong, Y. D.

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: Time-reversed lasers,” Phys. Rev. Lett.105, 053901 (2010).
[CrossRef] [PubMed]

Cohen, A. E.

N. Yang and A. E. Cohen, “Local geometry of electromagnetic fields and its role in molecular multipole transitions,” J. Phys. Chem. B115, 5304–5311 (2011).
[CrossRef] [PubMed]

Danzmann, K.

A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Müller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun.134, 431–439 (1997).
[CrossRef]

de Rosny, J.

G. Montaldo, G. Lerosey, A. Derode, A. Tourin, J. de Rosny, and M. Fink, “Telecommunication in a disordered environment with iterative time reversal,” Waves in Random Media14, 287–302 (2004).
[CrossRef]

J. de Rosny and M. Fink, “Overcoming the diffraction limit in wave physics using a time-reversal mirror and a novel acoustic sink,” Phys. Rev. Lett.89, 124301 (2002).
[CrossRef] [PubMed]

R. Carminati, R. Pierrat, J. de Rosny, and M. Fink, “Theory of the time reversal cavity for electromagnetic fields,” Opt. Lett.32, 3107–3109 (2002).
[CrossRef]

Derode, A.

G. Montaldo, G. Lerosey, A. Derode, A. Tourin, J. de Rosny, and M. Fink, “Telecommunication in a disordered environment with iterative time reversal,” Waves in Random Media14, 287–302 (2004).
[CrossRef]

Ding, C.

C. Ding, L. Hao, and X. Zhao, “Two-dimensional acoustic metamaterial with negative modulus,” J. Appl. Phys.108, 074911 (2010).
[CrossRef]

Fang, N.

N. Fang, D. Xi, J. Xu, M. Ambati, W. Srituravanich, C. Sun, and X. Zhang, “Ultrasonic metamaterials with negative modulus,” Nat. Mater.5, 452–456 (2006).
[CrossRef] [PubMed]

Feng, Q.

Fink, M.

G. Montaldo, G. Lerosey, A. Derode, A. Tourin, J. de Rosny, and M. Fink, “Telecommunication in a disordered environment with iterative time reversal,” Waves in Random Media14, 287–302 (2004).
[CrossRef]

J. de Rosny and M. Fink, “Overcoming the diffraction limit in wave physics using a time-reversal mirror and a novel acoustic sink,” Phys. Rev. Lett.89, 124301 (2002).
[CrossRef] [PubMed]

R. Carminati, R. Pierrat, J. de Rosny, and M. Fink, “Theory of the time reversal cavity for electromagnetic fields,” Opt. Lett.32, 3107–3109 (2002).
[CrossRef]

Fleischhauer, M.

A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Müller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun.134, 431–439 (1997).
[CrossRef]

Ge, L.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science331, 889–892 (2011).
[CrossRef] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: Time-reversed lasers,” Phys. Rev. Lett.105, 053901 (2010).
[CrossRef] [PubMed]

Hao, L.

C. Ding, L. Hao, and X. Zhao, “Two-dimensional acoustic metamaterial with negative modulus,” J. Appl. Phys.108, 074911 (2010).
[CrossRef]

Hu, C.

Huang, C.

Kinsler, P.

P. Kinsler, “Active drains and causality,” Phys. Rev. A13, 055804 (2011).

Leonhardt, U.

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, and U. Leonhardt, “Evidence for subwavelength imaging with positive refraction,” New. J. Phys.13, 033016 (2002).
[CrossRef]

Lerosey, G.

G. Montaldo, G. Lerosey, A. Derode, A. Tourin, J. de Rosny, and M. Fink, “Telecommunication in a disordered environment with iterative time reversal,” Waves in Random Media14, 287–302 (2004).
[CrossRef]

Luo, X.

Ma, X.

Ma, Y. G.

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, and U. Leonhardt, “Evidence for subwavelength imaging with positive refraction,” New. J. Phys.13, 033016 (2002).
[CrossRef]

Montaldo, G.

G. Montaldo, G. Lerosey, A. Derode, A. Tourin, J. de Rosny, and M. Fink, “Telecommunication in a disordered environment with iterative time reversal,” Waves in Random Media14, 287–302 (2004).
[CrossRef]

Müller, G.

A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Müller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun.134, 431–439 (1997).
[CrossRef]

Noh, H.

H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett.108, 186805 (2012).
[CrossRef] [PubMed]

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science331, 889–892 (2011).
[CrossRef] [PubMed]

Ong, C. K.

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, and U. Leonhardt, “Evidence for subwavelength imaging with positive refraction,” New. J. Phys.13, 033016 (2002).
[CrossRef]

Pierrat, R.

Pu, M.

Rahachou, A. I.

A. I. Rahachou and I. V. Zozoulenko, “Light propagation in nanorod arrays,” J. Opt. A: Pure and Applied Optics9, 265–270 (2007).
[CrossRef]

Rinkleff, R. H.

A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Müller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun.134, 431–439 (1997).
[CrossRef]

Sahebdivan, S.

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, and U. Leonhardt, “Evidence for subwavelength imaging with positive refraction,” New. J. Phys.13, 033016 (2002).
[CrossRef]

Scully, M.

A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Müller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun.134, 431–439 (1997).
[CrossRef]

Simovski, C. R.

P. A. Belov, C. R. Simovski, and S. A. Tretyakov, “Example of bianisotropic electromagnetic crystals: The spiral medium,” Phys. Rev. E67, 056622 (2003).
[CrossRef]

Srituravanich, W.

N. Fang, D. Xi, J. Xu, M. Ambati, W. Srituravanich, C. Sun, and X. Zhang, “Ultrasonic metamaterials with negative modulus,” Nat. Mater.5, 452–456 (2006).
[CrossRef] [PubMed]

Stone, A. D.

H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett.108, 186805 (2012).
[CrossRef] [PubMed]

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science331, 889–892 (2011).
[CrossRef] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: Time-reversed lasers,” Phys. Rev. Lett.105, 053901 (2010).
[CrossRef] [PubMed]

Sun, C.

N. Fang, D. Xi, J. Xu, M. Ambati, W. Srituravanich, C. Sun, and X. Zhang, “Ultrasonic metamaterials with negative modulus,” Nat. Mater.5, 452–456 (2006).
[CrossRef] [PubMed]

Tourin, A.

G. Montaldo, G. Lerosey, A. Derode, A. Tourin, J. de Rosny, and M. Fink, “Telecommunication in a disordered environment with iterative time reversal,” Waves in Random Media14, 287–302 (2004).
[CrossRef]

Tretyakov, S. A.

P. A. Belov, C. R. Simovski, and S. A. Tretyakov, “Example of bianisotropic electromagnetic crystals: The spiral medium,” Phys. Rev. E67, 056622 (2003).
[CrossRef]

Tyc, T.

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, and U. Leonhardt, “Evidence for subwavelength imaging with positive refraction,” New. J. Phys.13, 033016 (2002).
[CrossRef]

Wan, W.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science331, 889–892 (2011).
[CrossRef] [PubMed]

Wang, C.

Wang, M.

Wicht, A.

A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Müller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun.134, 431–439 (1997).
[CrossRef]

Xi, D.

N. Fang, D. Xi, J. Xu, M. Ambati, W. Srituravanich, C. Sun, and X. Zhang, “Ultrasonic metamaterials with negative modulus,” Nat. Mater.5, 452–456 (2006).
[CrossRef] [PubMed]

Xu, J.

N. Fang, D. Xi, J. Xu, M. Ambati, W. Srituravanich, C. Sun, and X. Zhang, “Ultrasonic metamaterials with negative modulus,” Nat. Mater.5, 452–456 (2006).
[CrossRef] [PubMed]

Yang, N.

N. Yang and A. E. Cohen, “Local geometry of electromagnetic fields and its role in molecular multipole transitions,” J. Phys. Chem. B115, 5304–5311 (2011).
[CrossRef] [PubMed]

Zhang, X.

N. Fang, D. Xi, J. Xu, M. Ambati, W. Srituravanich, C. Sun, and X. Zhang, “Ultrasonic metamaterials with negative modulus,” Nat. Mater.5, 452–456 (2006).
[CrossRef] [PubMed]

Zhao, X.

C. Ding, L. Hao, and X. Zhao, “Two-dimensional acoustic metamaterial with negative modulus,” J. Appl. Phys.108, 074911 (2010).
[CrossRef]

Zhao, Z.

Zozoulenko, I. V.

A. I. Rahachou and I. V. Zozoulenko, “Light propagation in nanorod arrays,” J. Opt. A: Pure and Applied Optics9, 265–270 (2007).
[CrossRef]

J. Appl. Phys. (1)

C. Ding, L. Hao, and X. Zhao, “Two-dimensional acoustic metamaterial with negative modulus,” J. Appl. Phys.108, 074911 (2010).
[CrossRef]

J. Opt. A: Pure and Applied Optics (1)

A. I. Rahachou and I. V. Zozoulenko, “Light propagation in nanorod arrays,” J. Opt. A: Pure and Applied Optics9, 265–270 (2007).
[CrossRef]

J. Phys. Chem. B (1)

N. Yang and A. E. Cohen, “Local geometry of electromagnetic fields and its role in molecular multipole transitions,” J. Phys. Chem. B115, 5304–5311 (2011).
[CrossRef] [PubMed]

Nat. Mater. (1)

N. Fang, D. Xi, J. Xu, M. Ambati, W. Srituravanich, C. Sun, and X. Zhang, “Ultrasonic metamaterials with negative modulus,” Nat. Mater.5, 452–456 (2006).
[CrossRef] [PubMed]

New. J. Phys. (1)

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, and U. Leonhardt, “Evidence for subwavelength imaging with positive refraction,” New. J. Phys.13, 033016 (2002).
[CrossRef]

Opt. Commun. (1)

A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Müller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun.134, 431–439 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

P. Kinsler, “Active drains and causality,” Phys. Rev. A13, 055804 (2011).

Phys. Rev. E (1)

P. A. Belov, C. R. Simovski, and S. A. Tretyakov, “Example of bianisotropic electromagnetic crystals: The spiral medium,” Phys. Rev. E67, 056622 (2003).
[CrossRef]

Phys. Rev. Lett. (3)

H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett.108, 186805 (2012).
[CrossRef] [PubMed]

J. de Rosny and M. Fink, “Overcoming the diffraction limit in wave physics using a time-reversal mirror and a novel acoustic sink,” Phys. Rev. Lett.89, 124301 (2002).
[CrossRef] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: Time-reversed lasers,” Phys. Rev. Lett.105, 053901 (2010).
[CrossRef] [PubMed]

Science (1)

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science331, 889–892 (2011).
[CrossRef] [PubMed]

Waves in Random Media (1)

G. Montaldo, G. Lerosey, A. Derode, A. Tourin, J. de Rosny, and M. Fink, “Telecommunication in a disordered environment with iterative time reversal,” Waves in Random Media14, 287–302 (2004).
[CrossRef]

Supplementary Material (3)

» Media 1: AVI (4035 KB)     
» Media 2: AVI (4057 KB)     
» Media 3: AVI (3186 KB)     

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Figures (8)

Fig. 1
Fig. 1

Different configurations studied. (a) a nanoparticle illuminated by a plane wave. (b) a nanoparticle illuminated by a cylindrical wave. (c) cylindrical wave in an homogeneous medium.

Fig. 2
Fig. 2

Interference between a focusing wave (λ = 532 nm) and its diffracted wave is made constructive (s = −1) by placing a lossless metallic nanoparticle (R = 5.1 nm; ε = −1.01 for m = 1; ε = −1.001 for m = 2) at the origin (r = 0). Black solid curves (blue dashed curves) represent the radial distributions of electric field intensity with (without) the metallic scatterer for m = 1 (a,b) and m = 2 (c,d) in the linear scale (a,c) and the logarithmic scale (b,d). For comparison, the red dotted curves in (a,c) are the intensities when a plane wave is incident onto the metallic scatterer. All the intensities are normalized to the maximal values that can be obtained by focusing the same incident waves in vacuum without the particle. Maximal local field intensities are enhanced 5 orders of magnitude for m = 1 and 9 orders of magnitude for m = 2.

Fig. 3
Fig. 3

(a) Relative amplitude (black solid line) and phase (blue dashed line) of the diffracted wave s (λ = 532 nm, m = 1) as a function of the real part of the dielectric constant ε of the metallic cylinder (R = 5.1 nm). As soon as the value of Re[ε] deviates from that for s = −1, the phase of s changes dramatically, breaking the condition for constructive interference of the scattered wave and the incident wave. (b) Maximal electric field intensity Ie at the cylinder surface (r = R) as a function of the real part of ε. Ie is normalized to the maximal field intensity produced by the same incident wave in the absence of the cylinder. When s deviates from −1, Ie drops quickly.

Fig. 4
Fig. 4

(a) Relative amplitude (black solid line) and phase (blue dashed line) of the diffracted wave s (λ = 532 nm, m = 1) as a function of the imaginary part of the dielectric constant ε of the metallic cylinder (R = 5.1 nm). The real part of ε is fixed at −1.01. As the amplitude of s reaches zero, its phase experiences a π shift. (b) Maximal electric field intensity Ie at the cylinder surface (black solid line) and the focal spot size defined by the effective diameter deff (blue dashed line) as a function of the imaginary part of ε. Ie is normalized to the maximal field intensity produced by the same incident wave in the absence of the cylinder. The red dotted curve represents the fit Ie = α |1 − s|2, with α = 6.19 × 104. As the imaginary part of ε increases from 0 to 0.01, Ie decreases monotonically, while the effective spot size increases.

Fig. 5
Fig. 5

Black solid curves in (a) and (b) are the real and imaginary parts of the dielectric function ε of a nanocylinder (R = 5.1 nm) at r = 0 for perfect absorption of a cylindrical wave (m = 1) at every wavelength in the range of 456 nm – 638 nm. The blue dashed curves represents the best fitting of complex dielectric function with the Lorentz model descried by Eq. (1). The parameters are given in the text.

Fig. 6
Fig. 6

(a,b) Single-frame excerpts from movies ( Media 1, Media 2) of the spatial distribution of magnetic field Hz(r, θ) when a Gaussian pulse of width 6.7 fs impinges on a nanocylinder (R = 5.1 nm) at the origin (r = 0). The pulse has a cylindrical wavefront and an angular momentum m = 1 in (a), m = 2 in (b). The pulse spectra is centered at λ = 532 nm with a FWHM of 180 nm. The dispersive dielectric function of the nanocylinder is chosen to reach a nearly perfect absorption at all incident wavelengths. (c) Electric field intensity at the surface of the cylinder (r = R) as a function of time in the case of (a) -black solid line, and (b) - blue dashed line. The red curve represents the field intensity when the dielectric function is non-dispersive and perfect absorption is reached only at the center wavelength λ = 532 nm of the incident pulse for m = 1. The intensity is normalized by the maximal intensity of the same incident pulse without the nanocylinder. (d) Single-frame excerpts from movies showing a chirped pulse ( Media 3), whose spectrum and spatial wavefront are identical to the Gaussian pulse in (b), is nearly perfectly absorbed by the nanocylinder with the same ε(λ). The temporal profile of the pulse is described in the text.

Fig. 7
Fig. 7

Two-photon excitation rate Γ2 as a function of the radial coordinate r when a Gaussian pulse of width 6.7 fs is nearly perfectly absorbed by a nanocylinder (R = 5.1 nm) at r = 0. The incident pulse has the cylindrical wavefront of m = 1 in (a), m = 2 in (b) (black solid line). For comparison, the dashed blue curve represents the incident wave of a plane front. The pulse spectra and the dielectric function of the cylinder in (a) and (b) are identical to those in Fig. 6(a) and (b), respectively. Γ2 is normalized by the maximal two-photon excitation rate Γ0 of the same input pulse without the nanocylinder.

Fig. 8
Fig. 8

Radial gradient of the electric field component in the radial direction Er, in the case a cylindrical wave nearly perfectly absorbed by a nanocylinder (R = 5.1 nm) located at r = 0 (black solid line) and a plane wave excitation of the same cylinder (dashed blue line) at λ = 532 nm. m = 1 in (a), m = 2 in (b). |∂Er/r| is normalized by the maximal gradient without the nanocylinder.

Equations (1)

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ε ( f ) ( ω ) = ε inf ω p 2 ω 2 ω 0 2 + i ω Γ 0 ,

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