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Quantum Nanoplasmonics: Coherent Control & Nanoscale Localization

Explore the world of nanoplasmonics with a focus on coherent control and nanoscale energy localization. Discover applications of surface plasmons and efficient nanolens technology. Connect with global collaborators and delve into the underlying physics of field enhancement in nanolenses.

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Quantum Nanoplasmonics: Coherent Control & Nanoscale Localization

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  1. US Israel Binational Science Foundation Support: Picture: View from the top of the Regulator Johnson black diamond at Snowbird, Utah Coherent, Nonlinear, and Quantum NanoplasmonicsMark I. StockmanDepartment of Physics and Astronomy, Georgia State University, Atlanta, GA 30303, USAhttp://www.phy-astr.gsu.edu/stockmanDavid J. BergmanSchool of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  2. Collaborators: • Sergey V. Faleev, Sandia National Laboratories, Livermore, CA, USA • Takayoshi Kobayashi, Department of Physics, University of Tokyo, Hongo 7-3-1 Bunkyo-Ku, Tokyo 113-033, Japan • Kuiru Li, Department of Physics and Astronomy, Georgia State University, Atlanta, GA 30340, USA • Ivan Larkin, Department of Physics and Astronomy, Georgia State University, Atlanta, GA 30340, USA • Victor Klimov, Softmatter Nanotechnology and Advanced Spectroscopy Team, Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 • Joseph Zyss, Laboratoire de Photonique Quantique et Moléculaire, Ecole Normale Supérieure de Cachan, 94235 Cachan, France • Misha Ivanov, Femtosecond Science Program, SIMS National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario, K1A 0R6 Canada • Paul Corkum, Femtosecond Science Program, SIMS National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario, K1A 0R6 Canada Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  3. CONTENTS • Introduction to nanoplasmonics: surface plasmons, local fields, and examples of their applications • Efficient Nanolens • Adiabatic concentration of energy in tapered plasmonic waveguides • Coherent control of linear and nonlinear phenomena on nanoscale [PRL 88, 067402 (2002); PRB 69, 054202-1-10 (2004)]. Experimental observation by H. Petek’s group (U. Pitt.), to be published shortly. • Surface Plasmon Amplification by Stimulated Emission of Radiation (Spaser) • Conclusions Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  4. PROBLEMS IN NANOOPTICS Microscale Delivery of energy to nanoscale: Converting propagating EM wave to local fields Generation of local fields on nanoscale: SPASER Enhancement and control of the local nanoscale fields. Enhanced near-field responses Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  5. Concentration of optical (electromagnetic wave) energy … Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  6. Nanoscale: 10 nm Lattice Electrons Local (near-zone) fields and surface plasmons Enhanced Local Fields in Proximity of Metal Nanoparticle are Nanoscale-Localized Enhancement (Quality) Factor: Surface Plasmon Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  7. Efficient Self-Similar Nanolens of Nanospheres K. Li, M. I. Stockman, and D. J. Bergman, Self-Similar Chain of Metal Nanospheres as an Efficient Nanolens, Phys. Rev. Lett. 91, 227402 (2003). 5 nm 15 nm 45 nm Silver Nanospheres Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  8. Underlying physics of local field enhancement in efficient nanolens: Cascade enhancement Giant local fields in the minimum gap: Nanoscale localization of optical energy - + - + - + - + - + - + - + - Optical Electric Field Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  9. Giant Local Field Enhancement in Nanolens 5 nm 45 nm 15 nm d=0.3R Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  10. d= 0.3 R FDTD computations. C. Oubre and P. Nordlander (Private Communication). Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  11. Adiabatic Nanofocusing in Tapered Nanoplasmonic Waveguides M. I. Stockman, Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides, Phys. Rev. Lett. 93, 137404-1-4 (2004). I Propagationdirection Intensity of Local Fields at the Surface of Conic Silver Wire Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  12. Phase velocity of surface plasmon polaritons Group velocity of surface plasmon polaritons Adiabatic parameter (scaled by 10) Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  13. Local Electric Fields in Cross Section of System Transverse electric field Longitudinal electric field Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  14. This effect of adiabatic concentration may have been observed without identifying it in: H. G. Frey, F. Keilmann, A. Kriele, and R. Guckenberger, Enhancing the Resolution of Scanning near-Field Optical Microscopy by a Metal Tip Grown on an Aperture Probe, Appl. Phys. Lett. 81, 5030-5032 (2002). Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  15. COHERENT CONTROL OF THE NANOSCALE LOCALIZATION OF ULTRAFAST OPTICAL EXCITATION ENERGY • 1.  M. I. Stockman, S. V. Faleev, and D. J. Bergman, Coherent Control of Femtosecond Energy Localization in Nanosystems, Phys. Rev. Lett. 88, 067402 (2002). • M. I. Stockman, D. J. Bergman, and T. Kobayashi, Coherent Control of Nanoscale Localization of Ultrafast Optical Excitation in Nanosystems, Phys. Rev. B. 69, 054202-1-10 (2004). Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  16. Problem: The wavelength of the excitation radiation is orders of magnitude too large to control spatial distribution of local fields on nanoscale by focusing Thus, optical radiation does not have spatial degrees of freedom on the nanoscale However, it does possess spectral (phase), or temporal, degrees of freedom Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  17. RESULTS The nanosystems studied are an “engineered” V-shape and a random planar composite (RPC) , positioned in the plane. The material is silver; the spatial scale is 1-3 nm/grid unit. V-shape RPC Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  18. Exciting Pulse Local Field at Opening Local Field at Tip Best energy concentration Same spectrum Same envelope Same average period Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  19. Spatial Distribution: Local Fields in V-shape, Negative Chirp Conclusion: There is a strong localization of the excitation energy at the tip of the nanostructure during a time interval on order of the pulse length Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  20. Local Optical Fields in Random Planar Composite at the Instants of their Maxima Positive Chirp No Chirp Negative Chirp Conclusion: The phase is a controlling factor in random systems as well Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  21. Time-Averaged Responses Linear Two-Photon Same spectrum Same envelope Same average period Conclusion: For averaged linear responses, only spectrum is important. In a nonlinear case, the phase is a controlling factor. Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  22. Experimental Observation Two-Photon Interferometric Coherent Control A. Kubo, K. Onda, H. Petek, Z. Sun, Y. S. Jung, and H. K. Kim, in Attosecond Kinematic Micrography of Surface Plasmon Dynamics, Nature (2004 (submitted)). Delay Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  23. Theory: spatial distributions of two-photon excitation as a function of delay between the two excitation pulses Geometry of the system Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  24. Experiment: Distribution of the two-photon electron emission from rough silver surface. Frame are taken with 200 as periodicity in delay Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  25. Quantum Nanoplasmonics: Surface Plasmon Amplification by Stimulated Emission of Radiation (SPASER) D. J. Bergman and M. I. Stockman, Surface Plasmon Amplification by Stimulated Emission of Radiation: Quantum Generation of Coherent Surface Plasmons in Nanosystems, Phys. Rev. Lett. 90, 027402-1-4 (2003). Acknowledgement: Victor I. Klimov (LANL) and John E. Sipe (U. Toronto) Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  26. Foerster energy transfer from QD to SP’s QD SP Quantumdots Silver nanoparticle Quantumdots SPASER Schematic Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  27. RESULTS The resonant nanoparticle is an “engineered” V-shape. The material is silver; the spatial scale is 2-5 nm/grid unit. Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  28. Calculated gain for thin (three monolayers of quantum dots) active medium Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  29. Eigenmodes with highest yields for the spectral maximum at 1.2 eV Luminous eigenmode Dark eigenmode Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  30. CONCLUSIONS • Self-similar chain of silver nanospheres is an efficient nanolens enhancing local field magnitude by more than three order of magnitude. • Adiabatic concentration of energy in tapered plasmonic waveguides efficiently transfers optical fields from far zone to nanoscale without major loses of energy • Phase degrees of freedom of ultrashort pulse allow one to coherently control of the nanoscale energy localization • We have proposed the SPASER: effect and prospective quantum- nanoplasmonic device.Spaser generates intense, ultrafast, nanoscale-localized optical-frequency local fields. THE END Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  31. THEORETICAL APPROACH Because the characteristic size of a spaser is much smaller than the wavelength, the quasistatic approximation in field equations is valid. Surface plasmon field equations and boundary conditions in a material-independent form, where are eigenvalues and are eigenfunctions: Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  32. Spectral parameter: . Frequency and decay rate of surface plasmons: Quasielectrostatic Hamiltonian of an inhomogeneous dispersive nanosystem: , where is the electric field operator. Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  33. Quantized potential operator as an expansion over surface plasmons: where and are the surface plasmon creation and annihilation operators. With this, the Hamiltonian becomes The interaction Hamiltonian of the surface plasmons and two-level systems (quantum dots) of the active medium: Using the perturbation theory, kinetic equation for the population number of surface plasmons in an n-th mode is: . Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  34. The Einstein stimulated emission coefficient is Here pnis the spatial overlap factor and qnis the spectral overlap factor between the eigenmode intensity and the population inversion, Spaser gain shows how many times faster the surface plasmons are born by the stimulated emission than they decay. Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  35. The local RMS field produced by spaser: is calculated as: . Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  36. Selected Publications 1. M. I. Stockman, S. V. Faleev, and D. J. Bergman, Localization vs. Delocalization of Surface Plasmons in Nanosystems: Can One State Have Both Characteristics?, Phys. Rev. Lett. 87, 167401-1-4 (2001). 2. M. I. Stockman, S. V. Faleev, and D. J. Bergman, Coherent Control of Femtosecond Energy Localization in Nanosystems, Phys. Rev. Lett. 88, 067402 (2002); 3. M. I. Stockman, D. J. Bergman, and T. Kobayashi, Coherent Control of Nanoscale Localization of Ultrafast Optical Excitation in Nanosystems, Phys. Rev. B. 69, 054202-1-10 (2004). [Observed: Imaging of localized silver plasmon dynamics with sub-fs time and nano-meter spatial resolution, Atsushi Kubo, Ken Onda, Hrvoje Petek, Zhijun Sun, Yun S. Jung, Hong K. Kim; Univ. of Pittsburgh, USA. Conference on Ultrafast Phenomena, Talk FB1 (Invited), Niigata, Japan, July, 2004] 4. Kuiru Li, M. I. Stockman, and D. J. Bergman, Self-Similar Chain of Metal Nanospheres as an Efficient Nanolens, Phys. Rev. Lett. 91, 227402-1-4 (2003). 5. D. J. Bergman and M. I. Stockman, Surface Plasmon Amplification by Stimulated Emission of Radiation: Quantum Generation of Coherent Surface Plasmons in Nanosystems, Phys. Rev. Lett. 90, 027402-1-4 (2003). Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  37. Selected Publications (Continued) 6. A. A. Mikhailovsky, M. A. Petruska, M. I. Stockman, and V. I. Klimov, Broadband Near-Field Interference Spectroscopy of Metal Nanoparticles Using a Femtosecond White-Light Continuum, Optics Lett. 28, 1686-1688 (2003). 7. A. A. Mikhailovsky, M. A. Petruska, Kuiru Li, M. I. Stockman, and V. I. Klimov, Phase-Sensitive Spectroscopy of Surface Plasmons in Individual Metal Nanostructures, Phys. Rev. B 69, 085401-1-5 (2004). 8. M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, Enhanced Second Harmonic Generation By Metal Surfaces with Nanoscale Roughness: Nanoscale Dephasing, Depolarization, and Correlations, Phys. Rev. Lett. 92, 057402-1-4 (2004). 9. L. N. Gaier, M. Lein, M. I. Stockman, P. L. Knight, P. B. Corkum, M. Yu. Ivanov and G. L. Yudin, Ultrafast Multiphoton Forest Fires and Fractals in Clusters and Dielectrics, J. Phys. B (Letters): At. Mol. Opt. Phys. 37, L57-L67 (2004). 10.I. A. Larkin, M. I. Stockman, M. Achermann, and V. I. Klimov, Dipolar Emitters at Nanoscale Proximity of Metal Surfaces: Giant Enhancement of Relaxation, Phys. Rev. B (Rapid Communications),69, 121403(R)-1-4 (2004). 11. M. I. Stockman, Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides, Phys. Rev. Lett. 93 137404-1-4(2004). Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  38. Phase-sensitive spectroscopy with SNOM • A. A. Mikhailovsky, M. A. Petruska, Kuiru Li, M. I. Stockman, and V. I. Klimov, Phase-Sensitive Spectroscopy of Surface Plasmons in Individual Metal Nanostructures, Phys. Rev. B 69, 085401-1-5 (2004). • A. A. Mikhailovsky, M. A. Petruska, M. I. Stockman, and V. I. Klimov, Broadband Near-Field Interference Spectroscopy of Metal Nanoparticles Using a Femtosecond White-Light Continuum, Optics Lett. 28, 1686-1688 (2003). Interference of radiations emitted by metal nanoparticles and aperture allows to measure phase of surface plasmons Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  39. Local Electric Fields at Surface of Plasmonic Tapered Waveguide Transverse field Longitudinal field Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  40. Metal tip Nanoparticle Enhanced Local Optical Fields Nanoscale Scattered Light, SERS Use of Enhanced Local Fields for Nano-Microscopy • R. Hillenbrand and F. Keilmann, Optical Oscillation Modes of Plasmon Particles Observed in Direct Space by Phase-Contrast Near-Field Microscopy, Appl. Phys. B 73, 239-243 (2001). • A. Hartschuh, E. J. Sanchez, X. S. Xie, and L. Novotny, High-Resolution Near-Field Raman Microscopy of Single-Walled Carbon Nanotubes, Phys. Rev. Lett. 90, 095503 -1-4 (2003). Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  41. Nanosensors based on enhanced local fields • J. C. Riboh, A. J. Haes, A. D. McFarland, C. R. Yonzon, and R. P. Van Duyne, A Nanoscale Optical Biosensor: Real-Time Immunoassay in Physiological Buffer Enabled by Improved Nanoparticle Adhesion, J. Phys. Chem. B 107, 1772-1780 (2003). • C. R. Yonzon, C. L. Haynes, X. Y. Zhang, J. T. Walsh, and R. P. Van Duyne, A Glucose Biosensor Based on Surface-Enhanced Raman Scattering: Improved Partition Layer, Temporal Stability, Reversibility, and Resistance to Serum Protein Interference, Anal. Chem. 76, 78-85 (2004). • E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. v. Veggel, D. N. Reinhoudt, M. Moller, and D. I. Gittins, Fluorescence Quenching of Dye Molecules near Gold Nanoparticles: Radiative and Nonradiative Effects, Phys. Rev. Lett. 89, 203002 (2002). Surface plasmon frequency shifts to red upon molecules adhesion Molecule Metal Nanoparticle Raman radiation (SERS), fluorescence, quenching, … Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  42. Surface Plasmon Dephasing Time for Silver Temporal degree of freedom See also: J. Bosbach, C. Hendrich, F. Stietz, T. Vartanyan, and F. Trager, Ultrafast Dephasing of Surface Plasmon Excitation in Silver Nanoparticles: Influence of Particle Size, Shape, and Chemical Surrounding, Phys. Rev. Lett. 89, 257404 (2002). Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  43. Spatial Distribution: Local Fields in V-shape, Positive Chirp Conclusion: Excitation energy is transferred between the tip and the opening of the nanostructure. No spatial concentration of energy takes place. Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  44. Experimental Observation Two-Photon Interferometric Coherent Control A. Kubo, K. Onda, H. Petek, Z. Sun, Y. S. Jung, and H. K. Kim, in Attosecond Kinematic Micrography of Surface Plasmon Dynamics, Nature (2004 (submitted)). Phase delay Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  45. CONCLUSIONS • Phase modulation of the excitation femtosecond pulse provides a functional degree of freedom necessary to control the spatial distribution of the local optical fields in nanosystems on the femtosecond temporal and nanometer spatial scale. • Both the spectral composition and the phase modulation determine femtosecond-nanometer dynamics of local fields. • For nonlinear photoprocesses, time-integral spatial distribution is controlled by both the pulse spectrum and its phase modulation. Two-photon processes are locally enhanced at the optimum by a factor of up to 107. Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  46. Decay of Semiconductor Quantum Dot at a Proximity of Metal Surface Metal QD a I. A. Larkin, M. I. Stockman, M. Achermann, and V. I. Klimov, Dipolar Emitters at Nanoscale Proximity of Metal Surfaces: Giant Enhancement of Relaxation, Phys. Rev. B (Rapid Communications) 69, 121403(R) (2004). Proximity of metal surface causes non-radiative decay, see e.g., E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. v. Veggel, D. N. Reinhoudt, M. Moller, and D. I. Gittins, Fluorescence Quenching of Dye Molecules near Gold Nanoparticles: Radiative and Nonradiative Effects, Phys. Rev. Lett. 89, 203002 (2002). spatial dispersion (dependence on wave vector k)of metal dielectric response becomes important. In RPA: Electrons in Debye-unscreened layer at the surface give major contribution Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  47. Decay rate of QD at a distance a of metal surface Spatial-dispersion term for smaller distances Conventional Foerster term for larger distances 1/a4 1/a3 Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  48. Conclusions • At distances of ~2 nm, the spatial dispersion (including Landau damping) of the metal dielectric response becomes very important for the quenching by metal • The Debye-unscreened surface layer of electrons dominates the non-radiative damping • This leads to dependence ~1/a4, not the conventional ~1/a3 predicted by Foerster Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  49. Ivan A. Larkin and Mark I. Stockman, Imperfect Perfect Lens, Nano Lett. (2005) (In print). r Image of a washer as produced by a silver slab of 5 nm thickness in GaAs host: (a) without spatial dispersion, (b) with spatial dispersion. Photon energy: 2.2 eV. Image of a point charge produced by a 5 nm silver slab in GaAs environment, photon energy: 2.2 eV Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

  50. CONCLUSIONS • Detrimental effects of macroscopic dielectric losses can be minimized by embedding the metal slab into semiconductor (GaAs) environment, which shifts the surface plasmon resonance frequency to near-infrared • However, the spatial dispersion and Landau damping become important for small objects limiting the spatial resolution to ~5 nm, which is a principal limitation that cannot be lifted by a dielectric environment. THE END Web: http://www.phy-astr.gsu.edu/stockman E-mail: mstockman@gsu.edu

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