# Coupling of higher-mode-light into a single sliver nanowire

Guo-Ping Guo  Rui Yang  Xi-Feng<EMAIL_ADDRESS>Lu-Lu Wang  Key
Laboratory of Quantum Information, University of Science and Technology of
China, Hefei 230026, People’s Republic of China  Hong-Yan Shi  Bo Hu  Shu-Hong
<EMAIL_ADDRESS>University of Science and Technology of China, Hefei
230026, People’s Republic of China  Guang-Can Guo  Key Laboratory of Quantum
Information, University of Science and Technology of China, Hefei 230026,
People’s Republic of China

###### Abstract

Coupling of higher-order-mode light into a single sliver nanowire and the
degree of the coupling can be controlled by adjusting the light polarization,
showing that nanowire waveguide has no request on the spatial mode of the
input light. Photons with different orbital angular momentums (OAM) are used
to excite surface plasmons of silver nanowires. The experiment indicates the
propagating modes of surface plasmons in nanowires were not the OAM
eignenstates.

###### pacs:

78.66.Bz,73.20.MF, 71.36.+c

Today, the major problem to increase the speed of microprocessors is how to
carry digital information from one end to the other. Optical interconnectors
can carry digital data much more than that of electronic interconnectors,
while fiber optical cables can not be minimized to nanoscale due to the
optical diffraction limit. To solve this size-incompatibility problem, we may
need to integrate the optical elements on chip and fabricate them at the
nanoscale. One such proposal is surface plasmons, which are electromagnetic
waves that propagate along the surface of a conductorozbay . Plasmonics,
surface plasmon-based optics, has been demonstrated and investigated
intensively in nanoscale metallic hole arraysEbbesen98 ; Moreno ; Alt ,
metallic waveguidesPile ; Bozhevo ; Lamp , and metallic nanowiresDickson ;
Graff ; Ditlbacher ; Sanders ; Knight ; Pyayt  in recent years.

Among the various kinds of plasmonics waveguides, sliver nanowires have some
unique properties that make them particularly attractive, such as low
propagation loss due to their smooth surface and scattering of plasmons to
photons only at their sharp ends. Since the momentums of the photons and
plasmons are different, it is a challenge to couple free-space light into
plasmon waveguides efficiently. The typical methods for plasmon excitation
include grating coupling, prism coupling and focusing of light onto one end of
the nanowire with a microscope objective. Nanoparticle antenna-based approach
is also proved as an effective way for optimizing plasmon coupling into
nanowiresKnight , which realizes direct coupling into straight, continuous
nanowires by using a nanoparticle as an antenna. Recently, polymer waveguides
are used to couple light into several nanowires simultaneouslyPyayt  as well,
aiming at providing light to a number of nanoscale devices in the future
integrated photonic circuits.

Figure 1: (color online)(a) SEM image of silver nanowires. (b) TEM image taken
on the end of an individual silver nanowire. (c) HRTEM image of the singe
nanowire shown in (b). (d) SAED pattern taken from an individual nanowire.

Because the former researches about the nanowires always concentrate on using
Gaussian mode light to excite surface plasmons, here we discuss whether
surface plamons can be launched by other higher-order-mode light. We focus
laser beam with different orbital angular momentums (OAM) on one end of a
nanowire and observe scattering light from the other end. Surface plasmons are
launched not only by Gaussian mode light but also by higher-order-mode light.
The coupling strength over light polarization is also studied for higher-
order-mode light and gives the similar results with the case of Gaussian mode.
The output intensity increases linearly with the input intensity rising, and
is independent of the spatial mode of the input light.

Ag nanowires were synthesized through a polyol process in a mixture of
ethylene glycol (EG) and poly (vinyl pyrrolidone) (PVP) at a certain
temperature, which was very similar as the previous reporttao ; jiang ; korte
. Scanning electron micrograph (SEM) image in Fig.1a shows that all the
nanowires are straight and have uniform diameters that vary from 60 to 100nm
and lengths from 10 to 40$\mu m$. A typical nanowire with diameter of 60 nm is
shown in Fig. 1b. High resolution TEM image in Fig. 1c shows a lattice spacing
of 0.23 nm, corresponding to those of $(\bar{1}\bar{1}\bar{1})$ and
$(\bar{1}11)$respectively. Electron diffraction pattern taken the individual
nanowire can be indexed as two parallel zone axes, i.e. $[01\bar{1}]$ and
$[1\bar{1}\bar{1}]$(Fig. 1d). Based on the analysis, the nanowire axis is
along $[100]$.

The mode of the input light is determined by its OAM. It is known that photons
have both spin angular momentum and OAM. The light fields of photons with OAM
can be described by means of Laguerre-Gaussian ($LG_{p}^{l}$) modes with two
indices $p$ and $l$Allen92 . The $p$ index identifies the number of radial
nodes observed in the transversal plane and the $l$ index describes the number
of the $2\pi$-phase shifts along a closed path around the beam center. If the
mode function is a pure LG mode with winding number $l$ , then every photon of
this beam carries an OAM of $l\hbar$. This corresponds to an eigenstate of the
OAM operator with eigenvalue $l\hbar$Allen92 . For the sake of simplification,
here we just consider the cases for $p=0$. When $l=0$, the light is in the
general Gaussian mode, while when $l\neq 0$, the energy distribution of light
likes a doughnut due to their helical wavefronts (see inset of Fig. 2). We
usually use computer generated holograms (CGHs)ArltJMO ; VaziriJOB  to change
the winding number of LG mode light. It is a kind of transmission holograms.
Inset of Fig. 1. shows part of a typical CGH($n=+1$) with a fork in the
center. Corresponding to the diffraction order $m$, the $l$ fork hologram can
change the winding number of the input beam by $\Delta l_{m}=m*n$. In our
experiment, we use the first order diffraction light ($m=+1$) and the
efficiencies of our CGHs are all about $40\%$. The Gaussian mode light can be
identified using mono-mode fibers in connection with avalanche detectors. All
other modes light have a larger spatial extension, and therefore cannot be
coupled into the single-mode fiber efficiently.

Figure 2: (color online)Sketch illustration of the experimental setup. The OAM
of the laser (wavelength 632.8nm) was controlled by a CGH, while the
polarization was controlled by a PBS followed by a HWP. The polarized laser
beam was focused on one end of a nanowire using a 100X objective lens (Zeiss,
NA=0.75). The sample was moved by a three dimensional piezo-electric stage.
Scattering light was recorded by a CCD camera after a microscope objective.
Inset are pictures of a typical CGH ($n=1$) and the energy distribution of the
produced light.

The experimental setup was shown in Fig. 2. The wavelength of the laser beam
was 632.8 nm, which was much bigger than the diameter of the nanowires (about
100 nm). The OAM of the laser was controlled by a CGH, while the polarization
was controlled by a polarization beam splitter (PBS, working wavelength 632.8
nm) followed by a half wave plate (HWP, working wavelength 632.8 nm). Rotating
the HWP allowed us to investigate the relation between the coupling efficiency
and the polarization of light. The polarized laser beam was directed into the
microscope and focused on one end of a nanowire with the light diameter about
$5.5\mu m$ using a 100X objective lens (Zeiss, NA=0.75). The sample was moved
by a three dimensional piezo-electric stage (Physik Instrumente Co., Ltd.
NanoCube XYZ Piezo Stage). Scattering light from the nanowire was reflected by
a beam splitter (BS, 50/50) and recorded by a CCD camera.

Figure 3: (color online)Higher-order-mode light ($l=2$) was focused on one end
of a nanowire (length $9.3\mu m$) and the emission was observed from the other
end clearly, which verified that the higher-mode-light can also be transmitted
by the sliver nanowire.

The momentum of the propagating plasmon($k_{sp}$) is larger than that of the
incoming photon($k_{ph}$), there needs an additional wavevector($\Delta k$) to
sustain the momentum conservation condition. Surface plasmons in nanowires can
be excited when the symmetry were broken, for example, at the ends and sharp
bendsDickson ; Graff ; Ditlbacher ; Sanders , because an extra wavevector
($\Delta k_{scatter}$) is provided according to the scattering mechanism at
this situation. It has been proved that surface plasmons can propagated along
the length of nanowires when they were excited by Gaussian mode light, even
the diameter of nanowires were much smaller than the wavelength of light. In
our experiment, higher mode lights ($l=1$ and $2$) were focused on one end of
a nanowire (length $9.3\mu m$ ) and the emission was observed from the other
end clearly, which verified that the higher-mode-light can also be transmitted
by the sliver nanowire (Fig. 3). It is noted that the energy distribution of
the output light was not same with the input light which has a null hole in
center. This phenomenon is different from the cases of extraordinary optical
transmission through nano-hole structures, where the OAM eigenstates can be
preservedren06 ; wang . A potential explanation is that the propagation modes
of surface plasmons in nanowires are not the eigenmodes of OAM states, like
the case of multi-mode optical fiber.

Figure 4: (color online)Polarization dependence of coupling efficiency at
nanowire end. (a) The Gaussian mode light was focused on the end of nanowire.
(b) The higher-order-mode light ($l=2$) was focused on the end of nanowire.
The two cases give the similar curve.

The coupling strength was measured by changing the polarization of the input
light. For each polarization, the emission intensity was determined by
averaging the four brightest pixels at the other end of the nanowire in the
CCD images. It changed with the polarization of input light for the different
coupling efficiencies. Fig. 4 shows the relationship between the coupling
strength and the polarization of the input light. The far-field emission
curves as a function of polarization angle was approximately in accord with
the theoretical prediction (cosine or sine function)Sanders ; Knight . As a
comparison, the case of Gaussian mode light was observed and gave the similar
curve.

The end of the nanowire was also moved from one edge to the other of the laser
spot (which has a diameter about $5.5\mu m$) to give the relationship between
the input intensity of laser beam and the emission intensity from the end of
the nanowire. The results were measured for the cases of Gaussian mode light
and higher-order-mode light ($l=2$), as shown in Fig. 5, which showed that the
emission intensity increased linearly with the pump intensity and was almost
independent of the spatial mode of the input light.

Figure 5: (color online)Relationship between the input intensity of laser beam
and the emission intensity from the nanowire. The dots are experimental
results and the lines come from theoretical calculations. The Gaussian mode
light (blue round dots) and the higher-order-mode light (red square dots) were
focused on the end of a nanowire. In both cases, the emission intensity
changed linearly with the input intensity.

In conclusion, we experimentally demonstrate that higher-order-mode light can
also excite surface plasmons in sliver nanowires. The surface plasmons can
propagate along the nanowire and scatter back to photons at the other end. The
coupling strength is correlated with the polarization of input light, as the
same as the case of Gaussian mode light. The OAM eigenstates are not the
propagating modes of surface plasmons in nanowires. These results may give us
more hints to the understanding of the waveguide properties of sliver
nanowires.

This work was supported by National Fundamental Research Program (Nos.
2006CB921900, 2005CB623601), National Natural Science Foundation of China
(Nos. 10604052, 50732006, 20621061, 20671085), Chinese Academy of Sciences
International Partnership Project, the Partner Group of the CAS-MPG and
Natural Science Foundation of Anhui Province(Grants No. 090412053)..

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