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Coherent control of radiation patterns of nonlinear multiphoton processes in nanoparticles.

Papoff F, McArthur D, Hourahine B - Sci Rep (2015)

Bottom Line: We propose a scheme for the coherent control of light waves and currents in metallic nanospheres which applies independently of the nonlinear multiphoton processes at the origin of waves and currents.We derive conditions on the external control field which enable us to change the radiation pattern and suppress radiative losses or to reduce absorption, enabling the particle to behave as a perfect scatterer or as a perfect absorber.The control introduces narrow features in the response of the particles that result in high sensitivity to small variations in the local environment, including subwavelength spatial shifts.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, SUPA, University of Strathclyde, 107 Rottenrow, Glasgow G4 0NG, UK.

ABSTRACT
We propose a scheme for the coherent control of light waves and currents in metallic nanospheres which applies independently of the nonlinear multiphoton processes at the origin of waves and currents. We derive conditions on the external control field which enable us to change the radiation pattern and suppress radiative losses or to reduce absorption, enabling the particle to behave as a perfect scatterer or as a perfect absorber. The control introduces narrow features in the response of the particles that result in high sensitivity to small variations in the local environment, including subwavelength spatial shifts.

No MeSH data available.


Related in: MedlinePlus

Radiation patterns with and without control.Radiation pattern along the plane θ = 90° for the same particle, frequency, and control as Fig. 2a. Inset shows an enlargement of the s22 quadrupole, the arrow indicates the direction of the control beam.
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f3: Radiation patterns with and without control.Radiation pattern along the plane θ = 90° for the same particle, frequency, and control as Fig. 2a. Inset shows an enlargement of the s22 quadrupole, the arrow indicates the direction of the control beam.

Mentions: We point out that the theory we described explains the principles of the coherent control that we propose, but no a priori theoretical knowledge is necessary to implement such control. From an operational point of view, it is only necessary to determine experimentally the multipolar fields excited by the nonlinear sources; once these are known, the control field Ec, Hc is chosen considering the multipolar terms one wants to control and the desired mode amplitudes are found by adjusting the amplitude and phase of the control field. Schematics of the proposed set-up are shown in Fig. 1. The control wave is sent along one of the directions in which the multipolar wave to be controlled is maximal, and a detector collects light coming from a solid angle centered on another direction of maximal field, without receiving light directly from the control beam. The optimal values of amplitude and phase of the control beam are determined by modulating the phase periodically and adjusting the amplitude so that the detected signal shows the largest variation. This procedure is fully self-consistent and requires only information provided by the experiment itself. To demonstrate numerically the properties discussed above, we apply this control technique to a gold nanosphere of 50 nm radius using plane waves for the pump and the control beam: we keep the pump constant, vary amplitude and phase of the control and compare local and nonlocal responses for second harmonic generation. For particles of this size, bulk nonlinearities are negligible2024 and the nonlinear polarization sheet is dominated by the radial component which excites an electric dipole with l = 1, m = 0 and electric quadrupoles with l = 2, m = 0 and l = 2, m = ±2. Both hydrodynamical and surface tensor models for nonlinear polarizations have been tested and give qualitatively similar results but with some quantitative differences. We have verified our control theory on all models. For the following calculations we assume a local response with nonlinear polarization , where the second-order susceptibility tensor component in units of 3.27 × 10−17 m/V20. The amplitudes of the multipoles generated by the nonlinear polarization and of the control beams are of the same order and scale linearly with . In Fig. 2 we control the internal and scattering modes i10 and s10 of the electric dipole. In Fig. 2a the amplitude of the control beam is chosen so that the amplitude of s10, , can vanish at the appropriate phase; we show the intensity of the field scattered in a direction orthogonal to both pump and control: other multipoles do not emit in this direction so the intensity has the same dependence of and show an extremely sharp variation. The light scattered in a solid angle centered on this direction can be monitored in an experiment to optimize the control beam; note that the phase sensitivity shown in Fig. 2a allows us to map the position of the particle with a resolution Δλ/λ = ΔΦ/2π, where λ and Φ are the wavelength and relative phase of the control beam respectively. This provides a deeply sub-wavelength spatial resolution when no other multipole radiate in the solid angle of detection and the sensitivity of the detector allows one to monitor the logarithm of the signal. The optimal solid angle can be found by considering the known radiation patterns of the multipoles27. The ratio of the amplitudes and shows that we find the condition for a perfect scatterer in Fig. 2a and for a perfect absorber in Fig. 2b, while the amplitudes of the other modes (not shown) are not affected by the control beam. By removing the dominant internal mode, we can minimize the total absorption, which is very useful to reduce heating and, as a consequence, increase stability in experiments. Figure 3 shows the radiation patterns with and without control in the equatorial plane θ = 90° of the sphere. In Fig. 4a, we control the intensity of the field scattered in a direction at π/2 with respect to the control beam and at π/4 with respect to the pump by changing the amplitudes of the modes of the electric quadrupole with l = 2, m = ±2, as shown in Fig. 4b. Even in this case we can observe a subwavelength variation of the intensity. In Fig. 5a we use an incoming multipolar wave with l = 2, m = 2 to control the scattering for the same sphere and in the same direction as in Fig. 4a. Note that in this case the variation of the intensity is smaller than in Fig. 4a because the multipolar control wave affects only the l = 2, m = 2 mode, as can be seen from Fig. 5b. We need two control beams to control independently the modes l = 2, m = 2 and l = 2, m = −2 in order to improve on the result shown in Fig. 4a, but Fig. 5a shows that using incoming multipolar waves is not necessarily more effective than using plane waves. Finally, in Fig. 6 we show how the sensitivity to phase variation can be applied to monitor small variations in the dielectric permittivity of the host medium; similar results could be achieved with variations of the magnetic permeability. With the intensity and phase of the pump and control beams optimised to suppress the s10 mode for a particular environment, εex, (corresponding to Δεex = 0 in Fig. 6) we observe a strong sensitivity to small changes in εex in the scattered intensity. As the modes of the system depend upon the local environment, the relative phase and amplitude of the control beam required to maintain suppression of the modes change with it. When we vary the optimised amplitude of the control field by ±20% we observe in Fig. 6a that the curve of the scattered intensity drifts, so that the minima no longer occurs at Δεex = 0, and the sensitivity decreases slightly. In Fig. 6b we observe that the sharpness of the feature in the scattering intensity reduces significantly when the relative phase of the control beam, Φc, is changed from the optimised value, but the position of the minima in this case does not drift. Generalizing this approach to include any number of modes and external incident waves is straightforward and explained in the Methods section.


Coherent control of radiation patterns of nonlinear multiphoton processes in nanoparticles.

Papoff F, McArthur D, Hourahine B - Sci Rep (2015)

Radiation patterns with and without control.Radiation pattern along the plane θ = 90° for the same particle, frequency, and control as Fig. 2a. Inset shows an enlargement of the s22 quadrupole, the arrow indicates the direction of the control beam.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4496782&req=5

f3: Radiation patterns with and without control.Radiation pattern along the plane θ = 90° for the same particle, frequency, and control as Fig. 2a. Inset shows an enlargement of the s22 quadrupole, the arrow indicates the direction of the control beam.
Mentions: We point out that the theory we described explains the principles of the coherent control that we propose, but no a priori theoretical knowledge is necessary to implement such control. From an operational point of view, it is only necessary to determine experimentally the multipolar fields excited by the nonlinear sources; once these are known, the control field Ec, Hc is chosen considering the multipolar terms one wants to control and the desired mode amplitudes are found by adjusting the amplitude and phase of the control field. Schematics of the proposed set-up are shown in Fig. 1. The control wave is sent along one of the directions in which the multipolar wave to be controlled is maximal, and a detector collects light coming from a solid angle centered on another direction of maximal field, without receiving light directly from the control beam. The optimal values of amplitude and phase of the control beam are determined by modulating the phase periodically and adjusting the amplitude so that the detected signal shows the largest variation. This procedure is fully self-consistent and requires only information provided by the experiment itself. To demonstrate numerically the properties discussed above, we apply this control technique to a gold nanosphere of 50 nm radius using plane waves for the pump and the control beam: we keep the pump constant, vary amplitude and phase of the control and compare local and nonlocal responses for second harmonic generation. For particles of this size, bulk nonlinearities are negligible2024 and the nonlinear polarization sheet is dominated by the radial component which excites an electric dipole with l = 1, m = 0 and electric quadrupoles with l = 2, m = 0 and l = 2, m = ±2. Both hydrodynamical and surface tensor models for nonlinear polarizations have been tested and give qualitatively similar results but with some quantitative differences. We have verified our control theory on all models. For the following calculations we assume a local response with nonlinear polarization , where the second-order susceptibility tensor component in units of 3.27 × 10−17 m/V20. The amplitudes of the multipoles generated by the nonlinear polarization and of the control beams are of the same order and scale linearly with . In Fig. 2 we control the internal and scattering modes i10 and s10 of the electric dipole. In Fig. 2a the amplitude of the control beam is chosen so that the amplitude of s10, , can vanish at the appropriate phase; we show the intensity of the field scattered in a direction orthogonal to both pump and control: other multipoles do not emit in this direction so the intensity has the same dependence of and show an extremely sharp variation. The light scattered in a solid angle centered on this direction can be monitored in an experiment to optimize the control beam; note that the phase sensitivity shown in Fig. 2a allows us to map the position of the particle with a resolution Δλ/λ = ΔΦ/2π, where λ and Φ are the wavelength and relative phase of the control beam respectively. This provides a deeply sub-wavelength spatial resolution when no other multipole radiate in the solid angle of detection and the sensitivity of the detector allows one to monitor the logarithm of the signal. The optimal solid angle can be found by considering the known radiation patterns of the multipoles27. The ratio of the amplitudes and shows that we find the condition for a perfect scatterer in Fig. 2a and for a perfect absorber in Fig. 2b, while the amplitudes of the other modes (not shown) are not affected by the control beam. By removing the dominant internal mode, we can minimize the total absorption, which is very useful to reduce heating and, as a consequence, increase stability in experiments. Figure 3 shows the radiation patterns with and without control in the equatorial plane θ = 90° of the sphere. In Fig. 4a, we control the intensity of the field scattered in a direction at π/2 with respect to the control beam and at π/4 with respect to the pump by changing the amplitudes of the modes of the electric quadrupole with l = 2, m = ±2, as shown in Fig. 4b. Even in this case we can observe a subwavelength variation of the intensity. In Fig. 5a we use an incoming multipolar wave with l = 2, m = 2 to control the scattering for the same sphere and in the same direction as in Fig. 4a. Note that in this case the variation of the intensity is smaller than in Fig. 4a because the multipolar control wave affects only the l = 2, m = 2 mode, as can be seen from Fig. 5b. We need two control beams to control independently the modes l = 2, m = 2 and l = 2, m = −2 in order to improve on the result shown in Fig. 4a, but Fig. 5a shows that using incoming multipolar waves is not necessarily more effective than using plane waves. Finally, in Fig. 6 we show how the sensitivity to phase variation can be applied to monitor small variations in the dielectric permittivity of the host medium; similar results could be achieved with variations of the magnetic permeability. With the intensity and phase of the pump and control beams optimised to suppress the s10 mode for a particular environment, εex, (corresponding to Δεex = 0 in Fig. 6) we observe a strong sensitivity to small changes in εex in the scattered intensity. As the modes of the system depend upon the local environment, the relative phase and amplitude of the control beam required to maintain suppression of the modes change with it. When we vary the optimised amplitude of the control field by ±20% we observe in Fig. 6a that the curve of the scattered intensity drifts, so that the minima no longer occurs at Δεex = 0, and the sensitivity decreases slightly. In Fig. 6b we observe that the sharpness of the feature in the scattering intensity reduces significantly when the relative phase of the control beam, Φc, is changed from the optimised value, but the position of the minima in this case does not drift. Generalizing this approach to include any number of modes and external incident waves is straightforward and explained in the Methods section.

Bottom Line: We propose a scheme for the coherent control of light waves and currents in metallic nanospheres which applies independently of the nonlinear multiphoton processes at the origin of waves and currents.We derive conditions on the external control field which enable us to change the radiation pattern and suppress radiative losses or to reduce absorption, enabling the particle to behave as a perfect scatterer or as a perfect absorber.The control introduces narrow features in the response of the particles that result in high sensitivity to small variations in the local environment, including subwavelength spatial shifts.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, SUPA, University of Strathclyde, 107 Rottenrow, Glasgow G4 0NG, UK.

ABSTRACT
We propose a scheme for the coherent control of light waves and currents in metallic nanospheres which applies independently of the nonlinear multiphoton processes at the origin of waves and currents. We derive conditions on the external control field which enable us to change the radiation pattern and suppress radiative losses or to reduce absorption, enabling the particle to behave as a perfect scatterer or as a perfect absorber. The control introduces narrow features in the response of the particles that result in high sensitivity to small variations in the local environment, including subwavelength spatial shifts.

No MeSH data available.


Related in: MedlinePlus