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TitleSubwavelength light confinement with surface plasmon polaritons
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Total Pages186
Table of Contents
General introduction
	The diffraction limit and surface plasmon polaritons
		Evanescent waves
		Surface plasmon polaritons
		Field confinement
	Surface plasmon polariton modes in planar multilayer waveguides
		Theoretical formalism
		MIM and IMI geometries
		Trade-off between confinement and loss
	Concentrating light with surface plasmon polaritons
		Localized resonances in annular apertures
	Probing the near field
	Outline of this thesis
Near-field probing of SPPs in metal-insulator-metal waveguides
		Sample fabrication
		Near-field experiments
		Polarization dependence of probe emission
	Single output slit: Interference of different SPP modes
		One-dimensional interference model
		Excitation asymmetry
		Two-dimensional interference model
	Double output slits: interference of MIM-SPPs
		MIM-SPP dispersion relation
Negative index of refraction in surface plasmon polariton waveguides
		Surface plasmon waveguide-based metamaterials
	Theoretical formalism
	Lossy dispersion and the necessary condition for negative indices
		The MIM waveguide as a negative index material
		IIM and IMI waveguides as multimode metamaterials
	Mapping plasmonic material indices and absorption
		Ag/GaP and Ag/Si3N4 MIM metamaterials
		Ag/GaP-based IIM and IMI waveguides
Enhanced upconversion of infrared light with a tapered plasmonic waveguide
		Er upconversion luminescence
		Fabrication of Ag microstructures
		Optical measurements
	Results and discussion
Nanofocusing in laterally tapered plasmonic waveguides
		Sample fabrication
		Optical measurements
	Results and discussion
		Power dependence
		Absence of cutoff
		Simulation methods
		Simulation results: Three-dimensional nanofocusing
		Comparison between excitation in substrate or in air
Nanowire plasmon excitation by adiabatic mode transformation
	Surface plasmon polariton mode transformation
		Surface plasmon polaritons on a metal cylinder
		Computation method for complex waveguiding geometries
		Stripe waveguides in a homogeneous dielectric environment
		SPP modes in stripe waveguides on a dielectric substrate
		The symmetry of the dielectric surrounding
		Phase- and polarization-sensitive near-field microscopy
	Results and discussion
		Coupling to nanowire SPPs
		Polarization nature of the nanowire mode
		Wavevector of SPPs on nanowires
		Coupling efficiency
		Calculated efficiency: comparison to conical geometry
		Exciting SPPs at the air side of the Au film
Plasmonic nanofocusing in a dielectric wedge
	SPPs on a metal surface covered with a thin dielectric film
	The geometrical optics approximation
	Comparing the geometrical optics approximation to FDTD
		Subwavelength confinement
Field enhancement in metallic subwavelength aperture arrays
	Field enhancement in hole arrays
		Quantifying field enhancement
		Dependence of enhancement on structural parameters
	The Fano model: far field transmission and near field enhancement
	Field enhancement in arrays of annular apertures
		Angle dependence of field enhancement in annular apertures
Enhanced spontaneous emission rate in annular plasmonic nanocavities
		Sample fabrication
		Optical measurements
		Tuning the localized resonance
Applications and outlook
	Integrated photonics
		Coupling light to the nanoscale
		Nanowire directional couplers
		Light absorption in plasmonic solar cells
		Adiabatic concentration of light from free-space
		Upconversion for photovoltaics
	Sensing and spectroscopy
		Localized surface plasmon resonance sensing
		Enhanced spectroscopy
	Towards a three-dimensional left-handed material
Appendix Waveguide modes in multilayer geometries: TE polarization
List of publications
About the author
Document Text Contents
Page 93

6.3 Methods

The evanescent field is collected by an Al-coated tapered fiber probe with an
aperture diameter of ∼220 nm. The probe is scanned above the sample at a height
of ∼20 nm, which is maintained by a shear-force feedback mechanism. The sample
and near-field probe are incorporated in one branch of a Mach-Zehnder interfer-
ometer (see Fig. 6.6). The light in the probe fiber interferes with a frequency-shifted
reference beam. The time-dependent interference signal is detected and analyzed
with a lock-in amplifier [165].

The polarization in the reference branch is controlled. A spatial distribution
of the measured complex signal A = |A|eiφ for any desired polarization angle θ of
the reference branch can be constructed by superimposing two images taken at
orthogonal polarizations û and v̂ in the detection fiber:

A(θ) = Au cos(θ−θu )+eiΔφ Av sin (θ−θu), (6.3)
where Δφ is a phase offset between image Au and Av , which is determined by com-
paring the image constructed with (6.3) to images measured at several polarization
angles θ.

To understand image formation in this microscope, it is important to consider
the role of the near-field probe. For a tip position rtip the field components of
the nanowire mode at position r are projected onto orthogonal fiber polarization
directions û and v̂ as

Au = Ex ∗Txu +Ey ∗Tyu +Ez ∗Tzu (6.4)
Av = Ex ∗Txv +Ey ∗Ty v +Ez ∗Tzv , (6.5)

where Txu


is the complex transfer function [168, 169] that projects the com-

ponent Ex on fiber polarization û. It is a function of position with respect to the
center of the tip. The transfer functions will obey characteristic spatial symme-
tries. The symmetry of the transfer function that maps a certain field component

Figure 6.6: Schematic of the heterodyne near-field setup.


Page 94

6 Nanowire plasmon excitation by adiabatic mode transformation

onto a particular fiber polarization is easily found by considering the reciprocal
case of illumination through the tip: it is equal to the symmetry of the component
that would be present when a fiber mode of that particular polarization is incident
through the tip. Let’s consider the particular choice of û and v̂ corresponding to
near-field polarizations x̂ and ŷ, for which Txu and Ty v are maximal. For a perfectly
cylindrically symmetric probe and fiber, this means that û = x̂ and v̂ = ŷ, but in
the actual experiment, bending of the fiber will have caused a rotation of these
directions. As we will show in section 6.4.2, it is nonetheless possible to find these
û and v̂ from near-field measurements that can be used as polarization calibration.
By considering the reciprocal case as mentioned above, we find that the functions
Txu , Ty v and Tzu should all be symmetric with respect to the xz plane. For similar
reasons Tzv , Txv and Tyu should be antisymmetric, and the latter two functions are
expected to have particularly small magnitude.

6.4 Results and discussion

6.4.1 Coupling to nanowire SPPs

Figure 6.7(a) shows a map of the measured near-field amplitude |A| obtained by
scanning the probe over the sample. In the left part of the image, the hole array with
which the SPPs are excited is visible. In the tapered section the presence of SPPs
propagating at the Au/glass interface is only evidenced by a field amplitude along
the edge of the waveguide, as for these widths almost all of the energy of the SPP
mode is located below the Au. At the end of the taper, the SPPs couple to a 150 nm
wide nanowire. Near the end of the taper a clear intensity increase is observed as
the guided wave becomes more strongly concentrated and the fraction of the modal
field in air increases at the same time. The absence of phase or wavelength changes

Figure 6.7: Near-field imaging of SPP excitation and propagation on a nanowire. (a)
Collected near-field SPP amplitude and (b) distribution of |A|cosφ. SPPs excited on
the Au/glass surface in the left are converted to a mode guided along a 150 nm wide
nanowire. The excitation wavelength is 1550 nm.


Page 185

About the author

Ewold Verhagen was born on October 28, 1980 in Leiderdorp, The Netherlands.
After obtaining his high school diploma at the Stedelijk Gymnasium Leiden in 1999,
he studied physics at Utrecht University. He performed a small research project
on two-photon fluorescence microscopy in the Molecular Biophysics group led by
prof. dr. Hans Gerritsen. He obtained his Master’s degree in 2005 with a project
performed in the Photonic Materials group at the FOM-Institute for Atomic and
Molecular Physics (AMOLF) in Amsterdam supervised by prof. dr. Albert Polman.
In September 2005 he started his PhD research at AMOLF under the supervision of
prof. dr. Albert Polman and prof. dr. Kobus Kuipers. The results of that work are
described in this thesis. In his spare time, he enjoys making music and playing with
his daughter.


Page 186

The work described in this thesis was performed at the
FOM-Institute for Atomic and Molecular Physics, Science
Park 104, 1098 XG Amsterdam, The Netherlands.


Prof. Dr. A. Polman
Center for Nanophotonics
FOM-Institute AMOLF, Amsterdam, The Netherlands

Prof. Dr. L. Kuipers
Center for Nanophotonics
FOM-Institute AMOLF, Amsterdam, The Netherlands

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