Abstract

We report on a novel micro-spectroscopic technique to quantitatively measure the extinction cross-section σext of few and single linearly polarizing nano-antennas. This technique relies on rotating the linear polarization of a monochromatic laser beam at a frequency ω1 while optically chopping the incident beam at ω2 and using lock-in detection with a switched reference frequency input to measure the amount of scattered and absorbed power. The amount of power removed from the beam corresponds to σext of the polarizing nano-structure. Furthermore, this technique is easy to integrate into existing microscopy or micro-photoluminescence setups and does not depend on the sample’s temperature.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett.105, 183901 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012

P. Berto, E. B. Ureña, P. Bon, R. Quidant, H. Rigneault, and G. Baffou, “Quantitative absorption spectroscopy of nano-objects,” Phys. Rev. B86, 165417 (2012).
[CrossRef]

M. Husnik, S. Linden, R. Diehl, J. Niegemann, K. Busch, and M. Wegener, “Quantitative experimental determination of scattering and absorption cross-section spectra of individual optical metallic nanoantennas,” Phys. Rev. Lett.109, 233902 (2012).
[CrossRef]

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75, 024402 (2012).
[CrossRef] [PubMed]

2011

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science332, 702–704 (2011).
[CrossRef] [PubMed]

2010

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9, 205–213 (2010).
[CrossRef] [PubMed]

J.-J. Greffet, M. Laroche, and F. M. C. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett.105, 117701 (2010).
[CrossRef] [PubMed]

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett.105, 183901 (2010).
[CrossRef]

A. F. Koenderink, “On the use of purcell factors for plasmon antennas,” Opt. Lett.35, 4208–4210 (2010).
[CrossRef] [PubMed]

2009

M. D. Wissert, A. W. Schell, K. S. Ilin, M. Siegel, and H.-J. Eisler, “Nanoengineering and characterization of gold dipole nanoantennas with enhanced integrated scattering properties,” Nanotechnology20, 425203 (2009).
[CrossRef] [PubMed]

T. Hanke, G. Krauss, D. Tr¨autlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett.103, 257404 (2009).
[CrossRef]

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photonics1, 438–483 (2009).
[CrossRef]

2008

J. Merlein, M. Kahl, A. Zuschlag, A. Sell, A. Halm, J. Boneberg, P. Leiderer, A. Leitenstorfer, and R. Bratschitsch, “Nanomechanical control of an optical antenna,” Nat. Photonics2, 230–233 (2008).
[CrossRef]

2006

2004

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett.93, 127401 (2004).
[CrossRef] [PubMed]

2002

M. Gluodenis and C. A. Foss, “The effect of mutual orientation on the spectra of metal nanoparticle rodrod and rodsphere pairs,” J. Phys. Chem. B106, 9484–9489 (2002).
[CrossRef]

1999

G. Ghosh, “Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals,” Opt. Commun.163, 95–102 (1999).
[CrossRef]

1986

1983

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett.50, 1903–1906 (1983).
[CrossRef]

1972

F. Kahn, “Electric-field-induced orientational deformation of nematic liquid crystals: Tunable birefringence,” Appl. Phys. Lett.20, 199–201 (1972).
[CrossRef]

1946

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev.69, 681 (1946).

1941

Arbouet, A.

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett.93, 127401 (2004).
[CrossRef] [PubMed]

Arnaud, L.

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett.93, 127401 (2004).
[CrossRef] [PubMed]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9, 205–213 (2010).
[CrossRef] [PubMed]

Baffou, G.

P. Berto, E. B. Ureña, P. Bon, R. Quidant, H. Rigneault, and G. Baffou, “Quantitative absorption spectroscopy of nano-objects,” Phys. Rev. B86, 165417 (2012).
[CrossRef]

Berto, P.

P. Berto, E. B. Ureña, P. Bon, R. Quidant, H. Rigneault, and G. Baffou, “Quantitative absorption spectroscopy of nano-objects,” Phys. Rev. B86, 165417 (2012).
[CrossRef]

Bharadwaj, P.

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photonics1, 438–483 (2009).
[CrossRef]

Biagioni, P.

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75, 024402 (2012).
[CrossRef] [PubMed]

Billaud, P.

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett.93, 127401 (2004).
[CrossRef] [PubMed]

Bon, P.

P. Berto, E. B. Ureña, P. Bon, R. Quidant, H. Rigneault, and G. Baffou, “Quantitative absorption spectroscopy of nano-objects,” Phys. Rev. B86, 165417 (2012).
[CrossRef]

Boneberg, J.

J. Merlein, M. Kahl, A. Zuschlag, A. Sell, A. Halm, J. Boneberg, P. Leiderer, A. Leitenstorfer, and R. Bratschitsch, “Nanomechanical control of an optical antenna,” Nat. Photonics2, 230–233 (2008).
[CrossRef]

Bratschitsch, R.

T. Hanke, G. Krauss, D. Tr¨autlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett.103, 257404 (2009).
[CrossRef]

J. Merlein, M. Kahl, A. Zuschlag, A. Sell, A. Halm, J. Boneberg, P. Leiderer, A. Leitenstorfer, and R. Bratschitsch, “Nanomechanical control of an optical antenna,” Nat. Photonics2, 230–233 (2008).
[CrossRef]

Broyer, M.

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett.93, 127401 (2004).
[CrossRef] [PubMed]

Busch, K.

M. Husnik, S. Linden, R. Diehl, J. Niegemann, K. Busch, and M. Wegener, “Quantitative experimental determination of scattering and absorption cross-section spectra of individual optical metallic nanoantennas,” Phys. Rev. Lett.109, 233902 (2012).
[CrossRef]

Carminati, R.

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett.105, 183901 (2010).
[CrossRef]

Castanié, E.

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett.105, 183901 (2010).
[CrossRef]

Christofilos, D.

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett.93, 127401 (2004).
[CrossRef] [PubMed]

De Wilde, Y.

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett.105, 183901 (2010).
[CrossRef]

Del Fatti, N.

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett.93, 127401 (2004).
[CrossRef] [PubMed]

Deutsch, B.

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photonics1, 438–483 (2009).
[CrossRef]

Diehl, R.

M. Husnik, S. Linden, R. Diehl, J. Niegemann, K. Busch, and M. Wegener, “Quantitative experimental determination of scattering and absorption cross-section spectra of individual optical metallic nanoantennas,” Phys. Rev. Lett.109, 233902 (2012).
[CrossRef]

Eisler, H.-J.

M. D. Wissert, A. W. Schell, K. S. Ilin, M. Siegel, and H.-J. Eisler, “Nanoengineering and characterization of gold dipole nanoantennas with enhanced integrated scattering properties,” Nanotechnology20, 425203 (2009).
[CrossRef] [PubMed]

Foss, C. A.

M. Gluodenis and C. A. Foss, “The effect of mutual orientation on the spectra of metal nanoparticle rodrod and rodsphere pairs,” J. Phys. Chem. B106, 9484–9489 (2002).
[CrossRef]

Ghosh, G.

G. Ghosh, “Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals,” Opt. Commun.163, 95–102 (1999).
[CrossRef]

Gluodenis, M.

M. Gluodenis and C. A. Foss, “The effect of mutual orientation on the spectra of metal nanoparticle rodrod and rodsphere pairs,” J. Phys. Chem. B106, 9484–9489 (2002).
[CrossRef]

Goy, P.

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett.50, 1903–1906 (1983).
[CrossRef]

Greffet, J.-J.

J.-J. Greffet, M. Laroche, and F. M. C. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett.105, 117701 (2010).
[CrossRef] [PubMed]

Gross, M.

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett.50, 1903–1906 (1983).
[CrossRef]

Halas, N. J.

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science332, 702–704 (2011).
[CrossRef] [PubMed]

Halm, A.

J. Merlein, M. Kahl, A. Zuschlag, A. Sell, A. Halm, J. Boneberg, P. Leiderer, A. Leitenstorfer, and R. Bratschitsch, “Nanomechanical control of an optical antenna,” Nat. Photonics2, 230–233 (2008).
[CrossRef]

Hanke, T.

T. Hanke, G. Krauss, D. Tr¨autlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett.103, 257404 (2009).
[CrossRef]

Haroche, S.

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett.50, 1903–1906 (1983).
[CrossRef]

Hecht, B.

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75, 024402 (2012).
[CrossRef] [PubMed]

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University, 2012).
[CrossRef]

Huang, J.-S.

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75, 024402 (2012).
[CrossRef] [PubMed]

Huntzinger, J. R.

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett.93, 127401 (2004).
[CrossRef] [PubMed]

Husnik, M.

M. Husnik, S. Linden, R. Diehl, J. Niegemann, K. Busch, and M. Wegener, “Quantitative experimental determination of scattering and absorption cross-section spectra of individual optical metallic nanoantennas,” Phys. Rev. Lett.109, 233902 (2012).
[CrossRef]

Ilin, K. S.

M. D. Wissert, A. W. Schell, K. S. Ilin, M. Siegel, and H.-J. Eisler, “Nanoengineering and characterization of gold dipole nanoantennas with enhanced integrated scattering properties,” Nanotechnology20, 425203 (2009).
[CrossRef] [PubMed]

Jacobsen, V.

Jones, R. C.

Kahl, M.

J. Merlein, M. Kahl, A. Zuschlag, A. Sell, A. Halm, J. Boneberg, P. Leiderer, A. Leitenstorfer, and R. Bratschitsch, “Nanomechanical control of an optical antenna,” Nat. Photonics2, 230–233 (2008).
[CrossRef]

Kahn, F.

F. Kahn, “Electric-field-induced orientational deformation of nematic liquid crystals: Tunable birefringence,” Appl. Phys. Lett.20, 199–201 (1972).
[CrossRef]

Kikuchi, H.

Knight, M. W.

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science332, 702–704 (2011).
[CrossRef] [PubMed]

Koenderink, A. F.

Krachmalnicoff, V.

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett.105, 183901 (2010).
[CrossRef]

Krauss, G.

T. Hanke, G. Krauss, D. Tr¨autlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett.103, 257404 (2009).
[CrossRef]

Laroche, M.

J.-J. Greffet, M. Laroche, and F. M. C. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett.105, 117701 (2010).
[CrossRef] [PubMed]

Leiderer, P.

J. Merlein, M. Kahl, A. Zuschlag, A. Sell, A. Halm, J. Boneberg, P. Leiderer, A. Leitenstorfer, and R. Bratschitsch, “Nanomechanical control of an optical antenna,” Nat. Photonics2, 230–233 (2008).
[CrossRef]

Leitenstorfer, A.

T. Hanke, G. Krauss, D. Tr¨autlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett.103, 257404 (2009).
[CrossRef]

J. Merlein, M. Kahl, A. Zuschlag, A. Sell, A. Halm, J. Boneberg, P. Leiderer, A. Leitenstorfer, and R. Bratschitsch, “Nanomechanical control of an optical antenna,” Nat. Photonics2, 230–233 (2008).
[CrossRef]

Linden, S.

M. Husnik, S. Linden, R. Diehl, J. Niegemann, K. Busch, and M. Wegener, “Quantitative experimental determination of scattering and absorption cross-section spectra of individual optical metallic nanoantennas,” Phys. Rev. Lett.109, 233902 (2012).
[CrossRef]

Marquier, F. M. C.

J.-J. Greffet, M. Laroche, and F. M. C. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett.105, 117701 (2010).
[CrossRef] [PubMed]

Merlein, J.

J. Merlein, M. Kahl, A. Zuschlag, A. Sell, A. Halm, J. Boneberg, P. Leiderer, A. Leitenstorfer, and R. Bratschitsch, “Nanomechanical control of an optical antenna,” Nat. Photonics2, 230–233 (2008).
[CrossRef]

Niegemann, J.

M. Husnik, S. Linden, R. Diehl, J. Niegemann, K. Busch, and M. Wegener, “Quantitative experimental determination of scattering and absorption cross-section spectra of individual optical metallic nanoantennas,” Phys. Rev. Lett.109, 233902 (2012).
[CrossRef]

Nordlander, P.

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science332, 702–704 (2011).
[CrossRef] [PubMed]

Novotny, L.

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photonics1, 438–483 (2009).
[CrossRef]

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University, 2012).
[CrossRef]

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9, 205–213 (2010).
[CrossRef] [PubMed]

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev.69, 681 (1946).

Quidant, R.

P. Berto, E. B. Ureña, P. Bon, R. Quidant, H. Rigneault, and G. Baffou, “Quantitative absorption spectroscopy of nano-objects,” Phys. Rev. B86, 165417 (2012).
[CrossRef]

Raimond, J. M.

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett.50, 1903–1906 (1983).
[CrossRef]

Rigneault, H.

P. Berto, E. B. Ureña, P. Bon, R. Quidant, H. Rigneault, and G. Baffou, “Quantitative absorption spectroscopy of nano-objects,” Phys. Rev. B86, 165417 (2012).
[CrossRef]

Sandoghdar, V.

Schell, A. W.

M. D. Wissert, A. W. Schell, K. S. Ilin, M. Siegel, and H.-J. Eisler, “Nanoengineering and characterization of gold dipole nanoantennas with enhanced integrated scattering properties,” Nanotechnology20, 425203 (2009).
[CrossRef] [PubMed]

Sell, A.

J. Merlein, M. Kahl, A. Zuschlag, A. Sell, A. Halm, J. Boneberg, P. Leiderer, A. Leitenstorfer, and R. Bratschitsch, “Nanomechanical control of an optical antenna,” Nat. Photonics2, 230–233 (2008).
[CrossRef]

Siegel, M.

M. D. Wissert, A. W. Schell, K. S. Ilin, M. Siegel, and H.-J. Eisler, “Nanoengineering and characterization of gold dipole nanoantennas with enhanced integrated scattering properties,” Nanotechnology20, 425203 (2009).
[CrossRef] [PubMed]

Sobhani, H.

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science332, 702–704 (2011).
[CrossRef] [PubMed]

Stoller, P.

Tr¨autlein, D.

T. Hanke, G. Krauss, D. Tr¨autlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett.103, 257404 (2009).
[CrossRef]

Uehara, K.

Ureña, E. B.

P. Berto, E. B. Ureña, P. Bon, R. Quidant, H. Rigneault, and G. Baffou, “Quantitative absorption spectroscopy of nano-objects,” Phys. Rev. B86, 165417 (2012).
[CrossRef]

Vallée, F.

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett.93, 127401 (2004).
[CrossRef] [PubMed]

Wegener, M.

M. Husnik, S. Linden, R. Diehl, J. Niegemann, K. Busch, and M. Wegener, “Quantitative experimental determination of scattering and absorption cross-section spectra of individual optical metallic nanoantennas,” Phys. Rev. Lett.109, 233902 (2012).
[CrossRef]

Wild, B.

T. Hanke, G. Krauss, D. Tr¨autlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett.103, 257404 (2009).
[CrossRef]

Wissert, M. D.

M. D. Wissert, A. W. Schell, K. S. Ilin, M. Siegel, and H.-J. Eisler, “Nanoengineering and characterization of gold dipole nanoantennas with enhanced integrated scattering properties,” Nanotechnology20, 425203 (2009).
[CrossRef] [PubMed]

Zuschlag, A.

J. Merlein, M. Kahl, A. Zuschlag, A. Sell, A. Halm, J. Boneberg, P. Leiderer, A. Leitenstorfer, and R. Bratschitsch, “Nanomechanical control of an optical antenna,” Nat. Photonics2, 230–233 (2008).
[CrossRef]

Adv. Opt. Photonics

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photonics1, 438–483 (2009).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

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Figures (4)

Fig. 1
Fig. 1

(a) shows the modulation of our Ti:Sapphire laser at frequency ω2 by an optical chopper and rotation of the polarization at frequency ω1. The λ/2 plate (HWP) is rotating at ω0 and modulates the polarization at ω1 = 4ω0. The rotating HWP also causes an intensity modulation at the frequency ω0 and at 2ω0, respectively stemming from fabrication defects of the HWP and the birefringence of the HWP. The reference frequency input of the lock-in amplifier (LIA) is switched between ω1 and ω2 by a PC which then subsequently queries the phase and amplitude. A query at ω2 returns the intensity of the beam while a query at ω1 returns the amplitude and phase of the modulation caused by a polarizing nano-particle in the beam path. (b) shows a cartoon of the electronic spectrum measured by the photodiode and demonstrates the separation of interfering signals from the signals of interest. (c) shows the design geometry of our nano-antennas and (d) a scanning electron micrograph of a single nano-antenna we fabricated by e-beam lithography.

Fig. 2
Fig. 2

Measured extinction cross-section spectra of a 4×4 dipole nano-antenna arrays. The array pitch was kept constant at 500 nm for every array. The antenna’s nominal height and width were kept at 40 nm and the nominal gap was kept at 20 nm while only the antenna’s nominal arm length L was increased from 50 nm to 200 nm in 10-nm increments. Antennas that are resonant in our Ti:Sapphire laser’s emission wavelength window have nominal arm lengths of 140 nm to 190 nm.

Fig. 3
Fig. 3

Measured extinction cross-section spectra of single dipole nano-antennas. The antenna’s nominal height and width were kept at 40 nm and the nominal gap was kept at 20 nm while only the antenna’s nominal arm length L was increased from 50 nm to 200 nm in 10-nm increments. Antennas that are resonant in our Ti:Sapphire lasers emission wavelength window have nominal arm lengths of 140 nm to 170 nm.

Fig. 4
Fig. 4

LSPR energy vs. antenna aspect ratio for 4×4 antenna arrays and single antennas. The aspect ratios were determined from scanning electron micro-graphs (SEMs) with 6 nm resolution for the arrays and 2 nm resolution for the single antennas. The error-bars represent the standard deviation of the LSPR energy and the error range of the aspect ratio.

Equations (15)

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

J out = T NP T RHWP J in
T RHWP = T ϕ 1 T λ / 2 T ϕ ,
T ϕ = ( cos ω 0 t sin ω 0 t sin ω 0 t cos ω 0 t ) ,
T λ / 2 = ( t f 0 0 t s ) ,
T NP = ( 1 σ 0 0 1 ) .
I out = A 4 ω 0 cos 4 ω 0 t + A 2 ω 0 cos 2 ω 0 t + A 0 ,
A 0 = 1 8 ( 4 3 σ ) ( t f 2 + t s 2 ) + 1 4 σ t s t f ,
A 2 ω 0 = 1 2 ( 1 σ ) ( t f 2 t s 2 ) ,
A 4 ω 0 = 1 8 σ ( t f + t s ) 2 .
I = I sig I ref = π 4 | A 4 ω 0 A 0 |
σ = 2 ( t f 2 + t s 2 ) I ( 3 2 t f 2 t s t f + 3 2 t s 2 ) I + π 8 ( t f + t s ) 2 8 I 4 I + π
σ ext = π d FWHM 2 4 log 2 ( 1 1 σ ) .
σ = i { 1 e X i 2 Y 2 m = 0 n = 0 X i 2 m + 2 n Y 2 m m ! ( m + n ) ! } ,
X i = 2 ln ( 2 ) r i d FWHM ,
Y = 2 ln ( 2 ) σ ext π d FWHM

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