Abstract

We describe and demonstrate the use of an adaptive wave front optimization scheme for enhancing the efficiency of adiabatic nanofocusing of surface plasmon polariton (SPP) waves along an ultrasharp conical gold taper. Adiabatic nanofocusing is an emerging and promising scheme for controlled focusing of far field light into nanometric volumes. It comprises three essential steps: SPP excitation by coupling far field light to an SPP waveguide, SPP propagation along the waveguide and adiabatic SPP nanofocusing towards a geometric singularity. For commonly used complex waveguide geometries, such as, e.g., conical metal tapers, a realistic modeling and efficiency optimization is challenging. Here, we use a deformable mirror to adaptively control the wave front of the incident far field light. We demonstrate an eight-fold enhancement in nanofocusing efficiency and analyze the shape of the resulting optimized wave front. The introduced wave front optimization scheme is of general interest for guiding and controlling light on the nanoscale.

© 2013 Optical Society of America

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    [CrossRef] [PubMed]

2013 (3)

M. Esmann, S. F. Becker, B. B. da Cunha, J. H. Brauer, R. Vogelgesang, P. Gross, and C. Lienau, “k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy,” Beilstein J. Nantechnol.4, 603–610 (2013).
[CrossRef]

G. R. Lemaitre, “Optical design and active optics methods in astronomy,” Opt. Rev.20(2), 103–117 (2013).
[CrossRef]

V. Kravtsov, J. M. Atkin, and M. B. Raschke, “Group delay and dispersion in adiabatic plasmonic nanofocusing,” Opt. Lett.38(8), 1322–1324 (2013).
[CrossRef] [PubMed]

2012 (4)

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature491(7423), 232–234 (2012).
[CrossRef] [PubMed]

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics6(8), 549–553 (2012).
[CrossRef]

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, “Optical control of plasmonic bloch modes on periodic nanostructures,” Nano Lett.12(2), 546–550 (2012).
[CrossRef] [PubMed]

S. Schmidt, B. Piglosiewicz, D. Sadiq, J. Shirdel, J. S. Lee, P. Vasa, N. Park, D.-S. Kim, and C. Lienau, “Adiabatic nanofocusing on ultrasmooth single-crystalline gold tapers creates a 10-nm-sized light source with few-cycle time resolution,” ACS Nano6(7), 6040–6048 (2012).
[CrossRef] [PubMed]

2011 (6)

2010 (4)

S. Verpoort and U. Wittrock, “Actuator patterns for unimorph and bimorph deformable mirrors,” Appl. Opt.49(31), G37–G46 (2010).
[CrossRef]

C. C. Neacsu, S. Berweger, R. L. Olmon, L. V. Saraf, C. Ropers, and M. B. Raschke, “Near-Field Localization in Plasmonic Superfocusing: A Nanoemitter on a Tip,” Nano Lett.10(2), 592–596 (2010).
[CrossRef] [PubMed]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Adiabatic tip-plasmon focusing for nano-raman spectroscopy,” J. Phys. Chem. Lett.1(24), 3427–3432 (2010).
[CrossRef]

2009 (1)

E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett.102(20), 203904 (2009).
[CrossRef] [PubMed]

2008 (1)

2007 (4)

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7(9), 2784–2788 (2007).
[CrossRef] [PubMed]

E. Verhagen, L. Kuipers, and A. Polman, “Enhanced nonlinear optical effects with a tapered plasmonic waveguide,” Nano Lett.7(2), 334–337 (2007).
[CrossRef] [PubMed]

M. Durach, A. Rusina, M. I. Stockman, and K. Nelson, “Toward full spatiotemporal control on the nanoscale,” Nano Lett.7(10), 3145–3149 (2007).
[CrossRef] [PubMed]

N. A. Issa and R. Guckenberger, “Optical nanofocusing on tapered metallic waveguides,” Plasmonics2(1), 31–37 (2007).
[CrossRef]

2006 (1)

G. Stibenz, C. Ropers, C. Lienau, C. Warmuth, A. S. Wyatt, I. A. Walmsley, and G. Steinmeyer, “Advanced methods for the characterization of few-cycle light pulses: a comparison,” Appl. Phys. B83(4), 511–519 (2006).
[CrossRef]

2005 (2)

K. G. Lee and Q. H. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett.95(10), 103902 (2005).
[CrossRef] [PubMed]

G. Stibenz and G. Steinmeyer, “Interferometric frequency-resolved optical gating,” Opt. Express13(7), 2617–2626 (2005).
[CrossRef] [PubMed]

2004 (2)

2003 (1)

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, “Evidence for third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,” Phys. Rev. Lett.90(21), 217404 (2003).
[CrossRef] [PubMed]

2002 (1)

S. Takahashi and A. V. Zayats, “Near-field second-harmonic generation at a metal tip apex,” Appl. Phys. Lett.80(19), 3479–3481 (2002).
[CrossRef]

2000 (1)

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys.87(8), 3785–3788 (2000).
[CrossRef]

1997 (1)

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B65(6), 779–782 (1997).
[CrossRef]

Albrecht, M.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7(9), 2784–2788 (2007).
[CrossRef] [PubMed]

Amat-Roldán, I.

Artigas, D.

Atkin, J. M.

V. Kravtsov, J. M. Atkin, and M. B. Raschke, “Group delay and dispersion in adiabatic plasmonic nanofocusing,” Opt. Lett.38(8), 1322–1324 (2013).
[CrossRef] [PubMed]

S. Berweger, J. M. Atkin, X. G. Xu, R. L. Olmon, and M. B. Raschke, “Femtosecond nanofocusing with full optical waveform control,” Nano Lett.11(10), 4309–4313 (2011).
[CrossRef] [PubMed]

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Adiabatic tip-plasmon focusing for nano-raman spectroscopy,” J. Phys. Chem. Lett.1(24), 3427–3432 (2010).
[CrossRef]

Aulbach, J.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, “Optical control of plasmonic bloch modes on periodic nanostructures,” Nano Lett.12(2), 546–550 (2012).
[CrossRef] [PubMed]

Babadjanyan, A. J.

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys.87(8), 3785–3788 (2000).
[CrossRef]

Baumert, T.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B65(6), 779–782 (1997).
[CrossRef]

Becker, S. F.

M. Esmann, S. F. Becker, B. B. da Cunha, J. H. Brauer, R. Vogelgesang, P. Gross, and C. Lienau, “k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy,” Beilstein J. Nantechnol.4, 603–610 (2013).
[CrossRef]

Bertolotti, J.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature491(7423), 232–234 (2012).
[CrossRef] [PubMed]

Berweger, S.

S. Berweger, J. M. Atkin, X. G. Xu, R. L. Olmon, and M. B. Raschke, “Femtosecond nanofocusing with full optical waveform control,” Nano Lett.11(10), 4309–4313 (2011).
[CrossRef] [PubMed]

C. C. Neacsu, S. Berweger, R. L. Olmon, L. V. Saraf, C. Ropers, and M. B. Raschke, “Near-Field Localization in Plasmonic Superfocusing: A Nanoemitter on a Tip,” Nano Lett.10(2), 592–596 (2010).
[CrossRef] [PubMed]

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Adiabatic tip-plasmon focusing for nano-raman spectroscopy,” J. Phys. Chem. Lett.1(24), 3427–3432 (2010).
[CrossRef]

Blum, C.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature491(7423), 232–234 (2012).
[CrossRef] [PubMed]

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

Brauer, J. H.

M. Esmann, S. F. Becker, B. B. da Cunha, J. H. Brauer, R. Vogelgesang, P. Gross, and C. Lienau, “k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy,” Beilstein J. Nantechnol.4, 603–610 (2013).
[CrossRef]

Brixner, T.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B65(6), 779–782 (1997).
[CrossRef]

Burns, D.

Cormack, I.

da Cunha, B. B.

M. Esmann, S. F. Becker, B. B. da Cunha, J. H. Brauer, R. Vogelgesang, P. Gross, and C. Lienau, “k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy,” Beilstein J. Nantechnol.4, 603–610 (2013).
[CrossRef]

Durach, M.

M. Durach, A. Rusina, M. I. Stockman, and K. Nelson, “Toward full spatiotemporal control on the nanoscale,” Nano Lett.7(10), 3145–3149 (2007).
[CrossRef] [PubMed]

Elsaesser, T.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7(9), 2784–2788 (2007).
[CrossRef] [PubMed]

Esmann, M.

M. Esmann, S. F. Becker, B. B. da Cunha, J. H. Brauer, R. Vogelgesang, P. Gross, and C. Lienau, “k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy,” Beilstein J. Nantechnol.4, 603–610 (2013).
[CrossRef]

Gerber, G.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B65(6), 779–782 (1997).
[CrossRef]

Gjonaj, B.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, “Optical control of plasmonic bloch modes on periodic nanostructures,” Nano Lett.12(2), 546–550 (2012).
[CrossRef] [PubMed]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

Gross, P.

M. Esmann, S. F. Becker, B. B. da Cunha, J. H. Brauer, R. Vogelgesang, P. Gross, and C. Lienau, “k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy,” Beilstein J. Nantechnol.4, 603–610 (2013).
[CrossRef]

Gualda, E.

Guckenberger, R.

N. A. Issa and R. Guckenberger, “Optical nanofocusing on tapered metallic waveguides,” Plasmonics2(1), 31–37 (2007).
[CrossRef]

Han, S.

Issa, N. A.

N. A. Issa and R. Guckenberger, “Optical nanofocusing on tapered metallic waveguides,” Plasmonics2(1), 31–37 (2007).
[CrossRef]

Johnson, P. M.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, “Optical control of plasmonic bloch modes on periodic nanostructures,” Nano Lett.12(2), 546–550 (2012).
[CrossRef] [PubMed]

Kärtner, F. X.

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, “Evidence for third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,” Phys. Rev. Lett.90(21), 217404 (2003).
[CrossRef] [PubMed]

Katz, O.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics6(8), 549–553 (2012).
[CrossRef]

Kim, D.-S.

S. Schmidt, B. Piglosiewicz, D. Sadiq, J. Shirdel, J. S. Lee, P. Vasa, N. Park, D.-S. Kim, and C. Lienau, “Adiabatic nanofocusing on ultrasmooth single-crystalline gold tapers creates a 10-nm-sized light source with few-cycle time resolution,” ACS Nano6(7), 6040–6048 (2012).
[CrossRef] [PubMed]

Koo, S.

Kravtsov, V.

Kuipers, L.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, “Optical control of plasmonic bloch modes on periodic nanostructures,” Nano Lett.12(2), 546–550 (2012).
[CrossRef] [PubMed]

E. Verhagen, L. Kuipers, and A. Polman, “Enhanced nonlinear optical effects with a tapered plasmonic waveguide,” Nano Lett.7(2), 334–337 (2007).
[CrossRef] [PubMed]

Kuipers, L. K.

E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett.102(20), 203904 (2009).
[CrossRef] [PubMed]

Lagendijk, A.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, “Optical control of plasmonic bloch modes on periodic nanostructures,” Nano Lett.12(2), 546–550 (2012).
[CrossRef] [PubMed]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature491(7423), 232–234 (2012).
[CrossRef] [PubMed]

Lee, J. S.

S. Schmidt, B. Piglosiewicz, D. Sadiq, J. Shirdel, J. S. Lee, P. Vasa, N. Park, D.-S. Kim, and C. Lienau, “Adiabatic nanofocusing on ultrasmooth single-crystalline gold tapers creates a 10-nm-sized light source with few-cycle time resolution,” ACS Nano6(7), 6040–6048 (2012).
[CrossRef] [PubMed]

D. Sadiq, J. Shirdel, J. S. Lee, E. Selishcheva, N. Park, and C. Lienau, “Adiabatic nanofocusing scattering-type optical nanoscopy of individual gold nanoparticles,” Nano Lett.11(4), 1609–1613 (2011).
[CrossRef] [PubMed]

J. S. Lee, S. Han, J. Shirdel, S. Koo, D. Sadiq, C. Lienau, and N. Park, “Superfocusing of electric or magnetic fields using conical metal tips: effect of mode symmetry on the plasmon excitation method,” Opt. Express19(13), 12342–12347 (2011).
[CrossRef] [PubMed]

Lee, K. G.

K. G. Lee and Q. H. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett.95(10), 103902 (2005).
[CrossRef] [PubMed]

Lemaitre, G. R.

G. R. Lemaitre, “Optical design and active optics methods in astronomy,” Opt. Rev.20(2), 103–117 (2013).
[CrossRef]

Li, B. M.

Liang, C.

Lienau, C.

M. Esmann, S. F. Becker, B. B. da Cunha, J. H. Brauer, R. Vogelgesang, P. Gross, and C. Lienau, “k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy,” Beilstein J. Nantechnol.4, 603–610 (2013).
[CrossRef]

S. Schmidt, B. Piglosiewicz, D. Sadiq, J. Shirdel, J. S. Lee, P. Vasa, N. Park, D.-S. Kim, and C. Lienau, “Adiabatic nanofocusing on ultrasmooth single-crystalline gold tapers creates a 10-nm-sized light source with few-cycle time resolution,” ACS Nano6(7), 6040–6048 (2012).
[CrossRef] [PubMed]

D. Sadiq, J. Shirdel, J. S. Lee, E. Selishcheva, N. Park, and C. Lienau, “Adiabatic nanofocusing scattering-type optical nanoscopy of individual gold nanoparticles,” Nano Lett.11(4), 1609–1613 (2011).
[CrossRef] [PubMed]

J. S. Lee, S. Han, J. Shirdel, S. Koo, D. Sadiq, C. Lienau, and N. Park, “Superfocusing of electric or magnetic fields using conical metal tips: effect of mode symmetry on the plasmon excitation method,” Opt. Express19(13), 12342–12347 (2011).
[CrossRef] [PubMed]

B. Piglosiewicz, D. Sadiq, M. Mascheck, S. Schmidt, M. Silies, P. Vasa, and C. Lienau, “Ultrasmall bullets of light--focusing few-cycle light pulses to the diffraction limit,” Opt. Express19(15), 14451–14463 (2011).
[CrossRef] [PubMed]

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7(9), 2784–2788 (2007).
[CrossRef] [PubMed]

G. Stibenz, C. Ropers, C. Lienau, C. Warmuth, A. S. Wyatt, I. A. Walmsley, and G. Steinmeyer, “Advanced methods for the characterization of few-cycle light pulses: a comparison,” Appl. Phys. B83(4), 511–519 (2006).
[CrossRef]

Loza-Alvarez, P.

Lubeigt, W.

Margaryan, N. L.

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys.87(8), 3785–3788 (2000).
[CrossRef]

Mascheck, M.

Morgner, U.

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, “Evidence for third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,” Phys. Rev. Lett.90(21), 217404 (2003).
[CrossRef] [PubMed]

Mosk, A. P.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature491(7423), 232–234 (2012).
[CrossRef] [PubMed]

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, “Optical control of plasmonic bloch modes on periodic nanostructures,” Nano Lett.12(2), 546–550 (2012).
[CrossRef] [PubMed]

Mücke, O. D.

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, “Evidence for third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,” Phys. Rev. Lett.90(21), 217404 (2003).
[CrossRef] [PubMed]

Neacsu, C. C.

C. C. Neacsu, S. Berweger, R. L. Olmon, L. V. Saraf, C. Ropers, and M. B. Raschke, “Near-Field Localization in Plasmonic Superfocusing: A Nanoemitter on a Tip,” Nano Lett.10(2), 592–596 (2010).
[CrossRef] [PubMed]

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7(9), 2784–2788 (2007).
[CrossRef] [PubMed]

Nelson, K.

M. Durach, A. Rusina, M. I. Stockman, and K. Nelson, “Toward full spatiotemporal control on the nanoscale,” Nano Lett.7(10), 3145–3149 (2007).
[CrossRef] [PubMed]

Nerkararyan, K. V.

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys.87(8), 3785–3788 (2000).
[CrossRef]

Niu, S. S.

Olmon, R. L.

S. Berweger, J. M. Atkin, X. G. Xu, R. L. Olmon, and M. B. Raschke, “Femtosecond nanofocusing with full optical waveform control,” Nano Lett.11(10), 4309–4313 (2011).
[CrossRef] [PubMed]

C. C. Neacsu, S. Berweger, R. L. Olmon, L. V. Saraf, C. Ropers, and M. B. Raschke, “Near-Field Localization in Plasmonic Superfocusing: A Nanoemitter on a Tip,” Nano Lett.10(2), 592–596 (2010).
[CrossRef] [PubMed]

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Adiabatic tip-plasmon focusing for nano-raman spectroscopy,” J. Phys. Chem. Lett.1(24), 3427–3432 (2010).
[CrossRef]

Park, N.

S. Schmidt, B. Piglosiewicz, D. Sadiq, J. Shirdel, J. S. Lee, P. Vasa, N. Park, D.-S. Kim, and C. Lienau, “Adiabatic nanofocusing on ultrasmooth single-crystalline gold tapers creates a 10-nm-sized light source with few-cycle time resolution,” ACS Nano6(7), 6040–6048 (2012).
[CrossRef] [PubMed]

D. Sadiq, J. Shirdel, J. S. Lee, E. Selishcheva, N. Park, and C. Lienau, “Adiabatic nanofocusing scattering-type optical nanoscopy of individual gold nanoparticles,” Nano Lett.11(4), 1609–1613 (2011).
[CrossRef] [PubMed]

J. S. Lee, S. Han, J. Shirdel, S. Koo, D. Sadiq, C. Lienau, and N. Park, “Superfocusing of electric or magnetic fields using conical metal tips: effect of mode symmetry on the plasmon excitation method,” Opt. Express19(13), 12342–12347 (2011).
[CrossRef] [PubMed]

Park, Q. H.

K. G. Lee and Q. H. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett.95(10), 103902 (2005).
[CrossRef] [PubMed]

Piglosiewicz, B.

S. Schmidt, B. Piglosiewicz, D. Sadiq, J. Shirdel, J. S. Lee, P. Vasa, N. Park, D.-S. Kim, and C. Lienau, “Adiabatic nanofocusing on ultrasmooth single-crystalline gold tapers creates a 10-nm-sized light source with few-cycle time resolution,” ACS Nano6(7), 6040–6048 (2012).
[CrossRef] [PubMed]

B. Piglosiewicz, D. Sadiq, M. Mascheck, S. Schmidt, M. Silies, P. Vasa, and C. Lienau, “Ultrasmall bullets of light--focusing few-cycle light pulses to the diffraction limit,” Opt. Express19(15), 14451–14463 (2011).
[CrossRef] [PubMed]

Polman, A.

E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett.102(20), 203904 (2009).
[CrossRef] [PubMed]

E. Verhagen, L. Kuipers, and A. Polman, “Enhanced nonlinear optical effects with a tapered plasmonic waveguide,” Nano Lett.7(2), 334–337 (2007).
[CrossRef] [PubMed]

Raschke, M. B.

V. Kravtsov, J. M. Atkin, and M. B. Raschke, “Group delay and dispersion in adiabatic plasmonic nanofocusing,” Opt. Lett.38(8), 1322–1324 (2013).
[CrossRef] [PubMed]

S. Berweger, J. M. Atkin, X. G. Xu, R. L. Olmon, and M. B. Raschke, “Femtosecond nanofocusing with full optical waveform control,” Nano Lett.11(10), 4309–4313 (2011).
[CrossRef] [PubMed]

C. C. Neacsu, S. Berweger, R. L. Olmon, L. V. Saraf, C. Ropers, and M. B. Raschke, “Near-Field Localization in Plasmonic Superfocusing: A Nanoemitter on a Tip,” Nano Lett.10(2), 592–596 (2010).
[CrossRef] [PubMed]

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Adiabatic tip-plasmon focusing for nano-raman spectroscopy,” J. Phys. Chem. Lett.1(24), 3427–3432 (2010).
[CrossRef]

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7(9), 2784–2788 (2007).
[CrossRef] [PubMed]

Ropers, C.

C. C. Neacsu, S. Berweger, R. L. Olmon, L. V. Saraf, C. Ropers, and M. B. Raschke, “Near-Field Localization in Plasmonic Superfocusing: A Nanoemitter on a Tip,” Nano Lett.10(2), 592–596 (2010).
[CrossRef] [PubMed]

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7(9), 2784–2788 (2007).
[CrossRef] [PubMed]

G. Stibenz, C. Ropers, C. Lienau, C. Warmuth, A. S. Wyatt, I. A. Walmsley, and G. Steinmeyer, “Advanced methods for the characterization of few-cycle light pulses: a comparison,” Appl. Phys. B83(4), 511–519 (2006).
[CrossRef]

Rusina, A.

M. Durach, A. Rusina, M. I. Stockman, and K. Nelson, “Toward full spatiotemporal control on the nanoscale,” Nano Lett.7(10), 3145–3149 (2007).
[CrossRef] [PubMed]

Sadiq, D.

S. Schmidt, B. Piglosiewicz, D. Sadiq, J. Shirdel, J. S. Lee, P. Vasa, N. Park, D.-S. Kim, and C. Lienau, “Adiabatic nanofocusing on ultrasmooth single-crystalline gold tapers creates a 10-nm-sized light source with few-cycle time resolution,” ACS Nano6(7), 6040–6048 (2012).
[CrossRef] [PubMed]

D. Sadiq, J. Shirdel, J. S. Lee, E. Selishcheva, N. Park, and C. Lienau, “Adiabatic nanofocusing scattering-type optical nanoscopy of individual gold nanoparticles,” Nano Lett.11(4), 1609–1613 (2011).
[CrossRef] [PubMed]

J. S. Lee, S. Han, J. Shirdel, S. Koo, D. Sadiq, C. Lienau, and N. Park, “Superfocusing of electric or magnetic fields using conical metal tips: effect of mode symmetry on the plasmon excitation method,” Opt. Express19(13), 12342–12347 (2011).
[CrossRef] [PubMed]

B. Piglosiewicz, D. Sadiq, M. Mascheck, S. Schmidt, M. Silies, P. Vasa, and C. Lienau, “Ultrasmall bullets of light--focusing few-cycle light pulses to the diffraction limit,” Opt. Express19(15), 14451–14463 (2011).
[CrossRef] [PubMed]

Saraf, L. V.

C. C. Neacsu, S. Berweger, R. L. Olmon, L. V. Saraf, C. Ropers, and M. B. Raschke, “Near-Field Localization in Plasmonic Superfocusing: A Nanoemitter on a Tip,” Nano Lett.10(2), 592–596 (2010).
[CrossRef] [PubMed]

Schmidt, S.

S. Schmidt, B. Piglosiewicz, D. Sadiq, J. Shirdel, J. S. Lee, P. Vasa, N. Park, D.-S. Kim, and C. Lienau, “Adiabatic nanofocusing on ultrasmooth single-crystalline gold tapers creates a 10-nm-sized light source with few-cycle time resolution,” ACS Nano6(7), 6040–6048 (2012).
[CrossRef] [PubMed]

B. Piglosiewicz, D. Sadiq, M. Mascheck, S. Schmidt, M. Silies, P. Vasa, and C. Lienau, “Ultrasmall bullets of light--focusing few-cycle light pulses to the diffraction limit,” Opt. Express19(15), 14451–14463 (2011).
[CrossRef] [PubMed]

Selishcheva, E.

D. Sadiq, J. Shirdel, J. S. Lee, E. Selishcheva, N. Park, and C. Lienau, “Adiabatic nanofocusing scattering-type optical nanoscopy of individual gold nanoparticles,” Nano Lett.11(4), 1609–1613 (2011).
[CrossRef] [PubMed]

Seyfried, V.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B65(6), 779–782 (1997).
[CrossRef]

Shen, J. X.

Shirdel, J.

S. Schmidt, B. Piglosiewicz, D. Sadiq, J. Shirdel, J. S. Lee, P. Vasa, N. Park, D.-S. Kim, and C. Lienau, “Adiabatic nanofocusing on ultrasmooth single-crystalline gold tapers creates a 10-nm-sized light source with few-cycle time resolution,” ACS Nano6(7), 6040–6048 (2012).
[CrossRef] [PubMed]

D. Sadiq, J. Shirdel, J. S. Lee, E. Selishcheva, N. Park, and C. Lienau, “Adiabatic nanofocusing scattering-type optical nanoscopy of individual gold nanoparticles,” Nano Lett.11(4), 1609–1613 (2011).
[CrossRef] [PubMed]

J. S. Lee, S. Han, J. Shirdel, S. Koo, D. Sadiq, C. Lienau, and N. Park, “Superfocusing of electric or magnetic fields using conical metal tips: effect of mode symmetry on the plasmon excitation method,” Opt. Express19(13), 12342–12347 (2011).
[CrossRef] [PubMed]

Silberberg, Y.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics6(8), 549–553 (2012).
[CrossRef]

Silies, M.

Small, E.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics6(8), 549–553 (2012).
[CrossRef]

Spasenovic, M.

E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett.102(20), 203904 (2009).
[CrossRef] [PubMed]

Steinmeyer, G.

G. Stibenz, C. Ropers, C. Lienau, C. Warmuth, A. S. Wyatt, I. A. Walmsley, and G. Steinmeyer, “Advanced methods for the characterization of few-cycle light pulses: a comparison,” Appl. Phys. B83(4), 511–519 (2006).
[CrossRef]

G. Stibenz and G. Steinmeyer, “Interferometric frequency-resolved optical gating,” Opt. Express13(7), 2617–2626 (2005).
[CrossRef] [PubMed]

Stibenz, G.

G. Stibenz, C. Ropers, C. Lienau, C. Warmuth, A. S. Wyatt, I. A. Walmsley, and G. Steinmeyer, “Advanced methods for the characterization of few-cycle light pulses: a comparison,” Appl. Phys. B83(4), 511–519 (2006).
[CrossRef]

G. Stibenz and G. Steinmeyer, “Interferometric frequency-resolved optical gating,” Opt. Express13(7), 2617–2626 (2005).
[CrossRef] [PubMed]

Stockman, M. I.

M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express19(22), 22029–22106 (2011).
[CrossRef] [PubMed]

M. Durach, A. Rusina, M. I. Stockman, and K. Nelson, “Toward full spatiotemporal control on the nanoscale,” Nano Lett.7(10), 3145–3149 (2007).
[CrossRef] [PubMed]

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93(13), 137404 (2004).
[CrossRef] [PubMed]

Strehle, M.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B65(6), 779–782 (1997).
[CrossRef]

Takahashi, S.

S. Takahashi and A. V. Zayats, “Near-field second-harmonic generation at a metal tip apex,” Appl. Phys. Lett.80(19), 3479–3481 (2002).
[CrossRef]

Tritschler, T.

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, “Evidence for third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,” Phys. Rev. Lett.90(21), 217404 (2003).
[CrossRef] [PubMed]

Valentine, G.

van Putten, E. G.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature491(7423), 232–234 (2012).
[CrossRef] [PubMed]

Vasa, P.

S. Schmidt, B. Piglosiewicz, D. Sadiq, J. Shirdel, J. S. Lee, P. Vasa, N. Park, D.-S. Kim, and C. Lienau, “Adiabatic nanofocusing on ultrasmooth single-crystalline gold tapers creates a 10-nm-sized light source with few-cycle time resolution,” ACS Nano6(7), 6040–6048 (2012).
[CrossRef] [PubMed]

B. Piglosiewicz, D. Sadiq, M. Mascheck, S. Schmidt, M. Silies, P. Vasa, and C. Lienau, “Ultrasmall bullets of light--focusing few-cycle light pulses to the diffraction limit,” Opt. Express19(15), 14451–14463 (2011).
[CrossRef] [PubMed]

Verhagen, E.

E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett.102(20), 203904 (2009).
[CrossRef] [PubMed]

E. Verhagen, L. Kuipers, and A. Polman, “Enhanced nonlinear optical effects with a tapered plasmonic waveguide,” Nano Lett.7(2), 334–337 (2007).
[CrossRef] [PubMed]

Verpoort, S.

Vogelgesang, R.

M. Esmann, S. F. Becker, B. B. da Cunha, J. H. Brauer, R. Vogelgesang, P. Gross, and C. Lienau, “k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy,” Beilstein J. Nantechnol.4, 603–610 (2013).
[CrossRef]

Vos, W. L.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature491(7423), 232–234 (2012).
[CrossRef] [PubMed]

Walmsley, I. A.

G. Stibenz, C. Ropers, C. Lienau, C. Warmuth, A. S. Wyatt, I. A. Walmsley, and G. Steinmeyer, “Advanced methods for the characterization of few-cycle light pulses: a comparison,” Appl. Phys. B83(4), 511–519 (2006).
[CrossRef]

Warmuth, C.

G. Stibenz, C. Ropers, C. Lienau, C. Warmuth, A. S. Wyatt, I. A. Walmsley, and G. Steinmeyer, “Advanced methods for the characterization of few-cycle light pulses: a comparison,” Appl. Phys. B83(4), 511–519 (2006).
[CrossRef]

Wegener, M.

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, “Evidence for third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,” Phys. Rev. Lett.90(21), 217404 (2003).
[CrossRef] [PubMed]

Wittrock, U.

Wyatt, A. S.

G. Stibenz, C. Ropers, C. Lienau, C. Warmuth, A. S. Wyatt, I. A. Walmsley, and G. Steinmeyer, “Advanced methods for the characterization of few-cycle light pulses: a comparison,” Appl. Phys. B83(4), 511–519 (2006).
[CrossRef]

Xu, X. G.

S. Berweger, J. M. Atkin, X. G. Xu, R. L. Olmon, and M. B. Raschke, “Femtosecond nanofocusing with full optical waveform control,” Nano Lett.11(10), 4309–4313 (2011).
[CrossRef] [PubMed]

Zayats, A. V.

S. Takahashi and A. V. Zayats, “Near-field second-harmonic generation at a metal tip apex,” Appl. Phys. Lett.80(19), 3479–3481 (2002).
[CrossRef]

Zhang, Y. H.

ACS Nano (1)

S. Schmidt, B. Piglosiewicz, D. Sadiq, J. Shirdel, J. S. Lee, P. Vasa, N. Park, D.-S. Kim, and C. Lienau, “Adiabatic nanofocusing on ultrasmooth single-crystalline gold tapers creates a 10-nm-sized light source with few-cycle time resolution,” ACS Nano6(7), 6040–6048 (2012).
[CrossRef] [PubMed]

Appl. Opt. (2)

Appl. Phys. B (2)

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B65(6), 779–782 (1997).
[CrossRef]

G. Stibenz, C. Ropers, C. Lienau, C. Warmuth, A. S. Wyatt, I. A. Walmsley, and G. Steinmeyer, “Advanced methods for the characterization of few-cycle light pulses: a comparison,” Appl. Phys. B83(4), 511–519 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

S. Takahashi and A. V. Zayats, “Near-field second-harmonic generation at a metal tip apex,” Appl. Phys. Lett.80(19), 3479–3481 (2002).
[CrossRef]

Beilstein J. Nantechnol. (1)

M. Esmann, S. F. Becker, B. B. da Cunha, J. H. Brauer, R. Vogelgesang, P. Gross, and C. Lienau, “k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy,” Beilstein J. Nantechnol.4, 603–610 (2013).
[CrossRef]

J. Appl. Phys. (1)

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys.87(8), 3785–3788 (2000).
[CrossRef]

J. Phys. Chem. Lett. (1)

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Adiabatic tip-plasmon focusing for nano-raman spectroscopy,” J. Phys. Chem. Lett.1(24), 3427–3432 (2010).
[CrossRef]

Nano Lett. (7)

S. Berweger, J. M. Atkin, X. G. Xu, R. L. Olmon, and M. B. Raschke, “Femtosecond nanofocusing with full optical waveform control,” Nano Lett.11(10), 4309–4313 (2011).
[CrossRef] [PubMed]

E. Verhagen, L. Kuipers, and A. Polman, “Enhanced nonlinear optical effects with a tapered plasmonic waveguide,” Nano Lett.7(2), 334–337 (2007).
[CrossRef] [PubMed]

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7(9), 2784–2788 (2007).
[CrossRef] [PubMed]

D. Sadiq, J. Shirdel, J. S. Lee, E. Selishcheva, N. Park, and C. Lienau, “Adiabatic nanofocusing scattering-type optical nanoscopy of individual gold nanoparticles,” Nano Lett.11(4), 1609–1613 (2011).
[CrossRef] [PubMed]

C. C. Neacsu, S. Berweger, R. L. Olmon, L. V. Saraf, C. Ropers, and M. B. Raschke, “Near-Field Localization in Plasmonic Superfocusing: A Nanoemitter on a Tip,” Nano Lett.10(2), 592–596 (2010).
[CrossRef] [PubMed]

M. Durach, A. Rusina, M. I. Stockman, and K. Nelson, “Toward full spatiotemporal control on the nanoscale,” Nano Lett.7(10), 3145–3149 (2007).
[CrossRef] [PubMed]

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, “Optical control of plasmonic bloch modes on periodic nanostructures,” Nano Lett.12(2), 546–550 (2012).
[CrossRef] [PubMed]

Nat. Photonics (2)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics6(8), 549–553 (2012).
[CrossRef]

Nature (1)

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature491(7423), 232–234 (2012).
[CrossRef] [PubMed]

Opt. Express (6)

Opt. Lett. (1)

Opt. Rev. (1)

G. R. Lemaitre, “Optical design and active optics methods in astronomy,” Opt. Rev.20(2), 103–117 (2013).
[CrossRef]

Phys. Rev. Lett. (4)

E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett.102(20), 203904 (2009).
[CrossRef] [PubMed]

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93(13), 137404 (2004).
[CrossRef] [PubMed]

K. G. Lee and Q. H. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett.95(10), 103902 (2005).
[CrossRef] [PubMed]

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, “Evidence for third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,” Phys. Rev. Lett.90(21), 217404 (2003).
[CrossRef] [PubMed]

Plasmonics (1)

N. A. Issa and R. Guckenberger, “Optical nanofocusing on tapered metallic waveguides,” Plasmonics2(1), 31–37 (2007).
[CrossRef]

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R. Davies and M. Kasper, “Adaptive Optics for Astronomy,” in Annual Review of Astronomy and Astrophysics, Vol 50, S. M. Faber and E. VanDishoeck, eds. (2012), pp. 305–351.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction Of Light, 7, (expanded) ed., reprinted with corr., 6. print. ed. (Cambridge Univ. Press, 2010), pp. XXXIII, 952 S.

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Figures (8)

Fig. 1
Fig. 1

(a) The conical taper is described in a spherical coordinate system with the apex in the center, and the surface is defined by θ=α . The laser light field is incident from the top. (b) Unwrapped tip surface with a sketch of the wave fronts of the light field incident on the tip surface (red curves).

Fig. 2
Fig. 2

Influence of the wave front distortion on the SPP electric field on the tip surface. (a) Spatial field distribution at a snap-shot in time as excited by a plane incident wave and (b) with the optimized wave front curvature. (c) Temporal electric field amplitude and (d) intensity profile of the distorted 7-fs SPP pulse from (a), integrated over angle φ (black, in the plots delayed by 30 fs) in comparison with the undistorted SPP pulse from (b) (blue, at 0 fs), showing the reduction in peak intensity.

Fig. 3
Fig. 3

Unwrapped tip surface. SPP wave fronts resulting from grating coupling a plane wave incident field via an infinitely narrow single slit are shown as red curves, and the ideal wave fronts given by SPP back propagation are shown as blue curves. The mismatch could be corrected by a curved grating as indicated by the black dashed curve.

Fig. 4
Fig. 4

Ideal wave front of the light field at the tip surface. To achieve phase matching, the wave front of the incident light should be (a) flat along the taper axis, z, and (b) curved along the y-direction. (c) Incident laser light wave front radius of curvature. From (c) and the tip radius as indicated by the broken black line results (d) the beam width at the tip surface. The resulting astigmatic focal spot with (e) a stretched beam profile along the y-direction at the taper surface and with (f) a stretched beam profile along the z-direction at the center of the taper.

Fig. 5
Fig. 5

Experimental setup. Ultrafast pulses from a 6-fs-Ti:Sapphire oscillator with chirp compensation (wedges and chirped mirrors ChM1 and ChM2) are split into two replicas by a Mach-Zehnder interferometer and the beam is expanded using a telescope (curved mirrors CM1 and CM2). After reflection off the deformable mirror (DM), the pulses are focused and grating-coupled onto the gold taper by a Cassegrain objective (CGO). The light scattered off the taper apex is collected with a microscope objective (MO) and a spectrometer. In the alternative setup (lower part, blue shaded box) the focus is scanned with a fiber probe on a three-axis piezo stage and a photomultiplier tube (PMT).

Fig. 6
Fig. 6

(a) Fitness (integrated spectral power density) of the fittest individual of each generation (red squares) in comparison to the value measured with a flat mirror profile (black squares). (b) Recorded spectra of the fittest individual of the 3rd, 10th, and 25th generation in comparison to the spectrum recorded for a flat mirror (black curve).

Fig. 7
Fig. 7

Pulse duration. (a) IFRAC traces measured with a flat mirror and (b) with the optimized shape of the DM after the optimization procedure. (c) Interferometric autocorrelation traces extracted from the IFRAC traces obtained with the flat mirror (black curves) and with the optimized curvature (red curves), and (d) retrieved spectral intensity and phase.

Fig. 8
Fig. 8

Spatial intensity profiles of the incident laser light near the focus of the CGO. The profiles are measured by scanning a near field fiber probe with an aperture diameter of ~300 nm through the focus. Shown are cross sections along the y-z plane at five different positions along the x-axis . (a)-(e) Measured intensity distribution near the focus of the CGO when the DM was set to a flat front, (f)-(j) measured intensity distribution for the DM with the optimized front curvature, and (k)-(o) calculated intensity distribution assuming spatial dispersion along the y-axis, i.e., a curved spatial phase profile.

Equations (7)

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ϕ L ( r )= k L x.
ϕ L ( r )= k L rsinαcosφ.
ϕ SPP ( r )= ϕ L ( r inc )+ r inc r k SPP ( φ ) d r
ϕ SPP ( r )= 0 r k SPP ( φ )d r = k SPP r.
Δϕ( r )= k L sinα(rcosφ r inc ) k SPP,r (r r inc ).
r gr (φ)= r inc k SPP,r k L sinα k SPP,r k L sinαcosφ .
E L ( r )= d k y d k z E ˜ ( k y , k z ) e iϕ( k y , k z ) e i k r e ^ ( k y , k z )

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