Microelectronics-Photonics Graduate Program
Research Experience for Undergraduates
Summer 2007
Final Research Report
Second Harmonic Radiation and far-field Scattering Pattern from Twined ZnO Single
Nanorods in Transmission Geometry
Aaron Ricca
Dr. Shiwei Liu, Department of Physics
H. Zhou, Department of Physics
Jeevakah Weerasinghe, Department of Physics
R. Tian, Department of Chemistry and Biochemistry
Dr. Min Xiao, Department of Physics
July 27, 2007
This work was supported by National Science Foundation award EEC-0097714. Any
opinions, findings, and conclusions or recommendations expressed in this material are
those of the author(s) and do not necessarily reflect the views of the National Science
Foundation.
1
Aaron Ricca, University of Arkansas
Faculty Mentor:
Dr. Min Xiao, Physics Department
Post Doc Mentor:
Dr. Shiwei Liu, Physics Department
Second Harmonic Radiation and Far-field Scattering Pattern from Twined ZnO Single
Nanorods in Transmission Geometry
Activities: I worked with second harmonic generation (SHG) from nonlinear optical
(NLO) materials, particularly ZnO. ZnO is a very stable crystalline structure that has not
had much research conducted on its NLO properties, especially in twined nanorods. I
used a laser to generate the SH radiation from twined nanorods. I worked with setting up
optical paths of lens’ and PMT’s, using rotating polarizers and half-wave plates to alter
the beam, and computers to record the data. Matrices were created to model the
nonlinear susceptibility of SHG of the ZnO nanorods. Matlab models were created that
mirrored the visual images of the SHG from the twined nanorods.
Findings: We were able to accurately record much data on the radiation field of SHG
from a twined ZnO single nanorod. This data allowed us to use diffraction equations and
model the fields of different twined nanorods with differing sizes, using Matlab. SHG
allowed us to learn much more about the NLO properties that are present in the ZnO
crystalline structure, and even generate mathematical models that accurately depict these
properties.
Planed Publications:
Second Harmonic Radiation and far-field Scattering Pattern from Twinned ZnO Single
Nanorods in Transmission Geometry, Nature Materials, S.W. Liu, H. Zhou, J. L.
Weerasinghe, A. Ricca, R. Tian, Min Xiao
Key Illustration/Figures: Figure (a) is the numerical simulation for the z-component of
the time-average Poynting vector on the image plane, generated by Matlab. Figure (b) is
a composite of SH images and interference fringes for the single twined ZnO NRs. The
enlarged images in the insets show the weak SH signals at the center of the NRs
100
1
0.405 m
50
(b)
0
(a)
50
0
100
150
100
50
0
50
0.405 m
100
150
2
Second Harmonic Radiation and far-field Scattering Pattern from Twinned ZnO Single
Nanorods in Transmission Geometry
S. W. Liu*,†, H. Zhou‡, J. L. Weerasinghe†, A. Ricca†,§, R. Tian*,‡, Min Xiao*,†
Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701
Department of Chemistry and Biochemistry, University of Arkansas, Fayetteville,
Arkansas, 72701
Abstract
The nonlinear optical properties of ZnO nanostructures have potential applications for
nanophotonic devices but are not fully developed. The far-field scattering pattern of
second-harmonic generation (SHG) from a single nanorod is correlated with its twinning
structure. A finite dipole-wire model has been successfully employed to model the SH
scattering from the twinned or twin-free nanorod. SH measurement without the objective
in transmission geometry reduces SH back-irradiation and simplifies the analysis to a
standard four-layer system.
*
Corresponding authors. E-mail: For optical measurements: sxl03@uark.edu (S.W.L.), mxiao@uark.edu (M.X.); For
growth of ZnO samples: rtian@uark.edu (R.T.).
† Department of Physics, University of Arkansas.
‡ Department of Chemistry and Biochemistry, University of Arkansas.
§ Student via microEP REU program..
3
Zinc Oxide (ZnO) has attracted intense research interest for a long period of time because
of its multifunctional properties such as UV emission, electron field-emission, chemically
active conductivity, piezoelectric and pyroelectric effects, and ferroelectric and
ferromagnetic ordering. Based on these remarkable properties, the motivation to develop
and miniaturize novel devices has lead to the enormous efforts focused on the synthesis
and characterization of the complex ZnO nanostructures, such as nanowires and
nanorods 1,2, nanotubes 3,4, nanohelixes and nanospirals 5,6,7, nanosprings5,6, nanorings5,6,
nanobelts5,6,8 and nanoribbons 9 , nano-tetrapods 10,11 , nano-arrays1,12,13 , functional nanonetworks14, etc. Various ZnO nano-devices have been demonstrated or proposed based on
these nanostructures, such as UV nano-laser15 and photo-detector16, transistor and field
emitter 17 , 18 , gas- and bio- sensors 19 , 20 , nanogenerator 21 , and magneto-optical 22 and
spintronic23 devices, etc.
However, as a nonlinear optical material, the second-order nonlinear optical properties
(such as SHG) of ZnO nanostructures are not fully developed, and are still under
discussion. The precise measurement of the nonlinear response becomes considerably
important for their potential applications in advanced nanophotonic devices. On the other
hand, as a powerful technique, SHG has been employed to investigate the surface and
interfacial phenomena 24 , 25 , ferroelectric/ferromagnetic/anti-ferromagnetic domains and
phase transitions34,26,27,28, and the materials chirality29, due to the high sensitivity of the
SHG to the structural and magnetic symmetry. Compared to the XRD (X-ray diffraction),
SHG is sensitive to 180o domain structures that often occur in polar structures in order to
lower the system’s energy because the third-rank susceptibility tensor (  ijk ) describing
SHG changes signs after the inversion operation. As a similar structure to 180o domain,
crystal twinning often occurs in the complex ZnO nanostructures, which plays an
important role during their nucleation and growth30. In a simple case of the contact twins,
the twinned ZnO bicrystals (twinned NR) share a single composition surface appearing as
mirror images across the interface. Similarly, the mirror operation also reverses the sign
of  ijk so SHG is also a twin-sensitive tool. In this paper, we clearly observed, for the
first time, the far-field scattering pattern of the transmitted SH waves from the single
twinned and twin-free NR’s. More interesting, the distribution of the interference fringes
is associated with the twinning structures inside NR’s. A simple model based on the
radiation from a finite dipole-wire has been well developed to simulate the experimental
scattering patterns for both kinds of NR’s.
A method of near-field scanning optical microscopy (NSOM) has been used to study
SHG in single ZnO nanowires31. Also, what was essentially an epi-fluorescence second
harmonic (SH) microscopy has been used to study SHG from single GaN nanowires 32. In
both methods, the experiments were performed in the reflection geometry. The backirradiating (reflective) SH signal and the forward-irradiating (transmitted) SH signal that
is partially reflected back by the interface of the ZnO and the substrate are collected and
analyzed. Here, I want to emphasize that the coherent length of the back-irradiating SH
signal is much shorter than that of the forward-irradiating SH signal. This large difference
is ignored in Refs. 31 and 32. Considering the interferences of the back-irradiating SH
waves emitted from the different locations in ZnO along the opposite direction of the
exciting fundamental beam, the coherent length (~49 nm) for the back-irradiations is at
4
least one-order less than that (~880 nm) for transmitted SH waves at the wavelength of
810 nm in ZnO 33,34,35 . In the picture of Ref. 32 the SH signal from the real dipole
corresponds to the back-irradiation while the SH signal from the image dipole originates
from the transmitted SH signals. The exact analysis of the data is therefore very
complicated because each signal’s relative weight to the measured SH signal vary in a
large range in the reflection geometry, which depends on the different coherent lengths
between these two types of SH radiations as well as the reflection coefficient in the
interface and the diameter of the nanowire. Also, some arguments in Refs. 31 and 32
based on the theory of transmission SHG36 are debatable. For example, a) in Ref. 32 the
assumption under the quasi-static approximation that the diameter of the nanowire is
supposed to be much smaller than the coherent length does not hold for the backirradiating SH wave; b) in Ref. 31 the assumption that the coherent length is considerably
larger than the depth of field of the microscope is invalid for the back-irradiating SH
signal. In addition, as will be discussed later, ignoring of the interferences among the
distinct components of the nonlinear susceptibility tensor results in an incorrect
evaluation of the nonlinear susceptibility (especially the sign) in the method of NSOM.
Also, tightly focusing the beam spot, down to sub-micrometer, by the objective in the
epi-fluorescence microscopy, will deteriorate the plane wave approximation and cause a
significant contribution to SH signal from the scattering of the single nanowires. Finally,
Kleinman’s symmetry, which is usually assumed for analyzing the nonlinear
susceptibility tensor, only holds when the absorptions at both fundamental and SH
wavelengths are negligible. Deviation from Kleimman’s symmetry is expected for SHG
using Ti:sapphire laser around 800 nm because the SH wavelength (about 400 nm) is near
the band-edge resonance of ZnO.
The ZnO NR’s were grown on fused quartz (FQ). This involved assembling a solution
consisting of 2.4 mL of water, 0.3 mL of 0.2 molar Zn(NO3)2, 0.3 mL of 0.2 molar HMT
in a 5.0 mL vial. The solution was aged for 20 minutes. Next, the FQ was immersed in
the solution, the vial was sealed, and then heated to 60˚ C where it was held for 6 hours,
during which time the NR’s formed on both sides of the FQ. Next the FQ was removed
from solution, the backside was cleaned with an HCl solution, and the entire sample was
rinsed with water and air-dried.
In this experiment, the SH signals were measured in transmission geometry. The backirradiating SH signal is at least two-order less than the transmitted SH signal collected
under our experimental geometry37. The experimental setup for the SHG measurements is
shown in Figure 1(a). The SH radiation is generated by a mode-locked Ti:sapphire
femtolaser with a repetition rate of 82 MHz at a wavelength of 810 nm, which has a
temporal width of about 100 fs. This fundamental laser beam is then slightly focused onto
the sample (S) by a common lens (L1) to achieve a spot size of approximately 100 m.
This results in the incidence peak intensity of about 40 MW/cm2 at the sample position. A
slightly focused fundamental beam can reduce scattering and validate the plane wave
approximation. The long-pass filter (LF) is employed to block the possible SH signal in
the fundamental laser beam immediately before the sample. The band-pass filter (BF) is
employed to filter out the SH radiation immediately after the sample. A removable
objective (OB) (50, NA 0.55) was used to form the SH image and scattering pattern
5
recorded by a digital camera via the flipper mirror (FM). A half-wave plate (/2) and a
polarizer (P) are mounted on the rotating stepper motors to adjust and analyze the
polarization directions of the incidence laser beam and the generated SH radiation,
respectively. By growing ZnO NRs far separated from each other (> 100 m), we
carefully aligned the fundamental beam so that whole beam spot illuminates only one
single NR at its center. The polarization diagrams of the NR were then measured after
removing the objective. The iris diaphragm (IR) works as a zero-pass spatial filter, as will
be discussed in next paragraph. The SH signal is further dispersed in the spectrometer,
where it is then detected by a photomultiplier tube (PMT). The PMT current is finally fed
into a lock-in amplifier to achieve very clean and reliable data. About 10% of the
fundamental laser beam energy is directed through the reference arm containing a
nonlinear BBO crystal. The SH radiation from the BBO crystal passes through the same
band-pass filter and is detected by another PMT and lock-in amplifier. The SH radiation
from the BBO crystal can be used for providing a reference to remove laser intensity
fluctuations.
Figure 1(b) depicts the s- and p- polarized fundamental fields E(s , p ) illuminating a single
NR on FQ substrate with an incidence angle of  to generate the s- and p- polarized
second harmonic fields E(2s, p ) . The three beam coordinate axes are represented by s, k and
z, with the incidence plane defined as (k,z) and z as surface normal of FQ substrate. As
shown in Fig. 1(c), xo, yo and zo represent the crystallography coordinate axes of a single
ZnO NR with the diameter D. The polar direction, defined as zo, is aligned to be along the
beam coordinate axis k. Three optical rays labeled as 1, 2 and 3, indicate three typical
optical paths transmitting through the single NR. Considering the confinement of the IR
far after the ZnO NR, only directly transmitted coherent SH ray 1 is collected for the
measurement of the polarization diagrams when the objective is removed from the optical
path. More strict arguments are based on the fact that, essentially, a far-field Fraunhofer
diffraction pattern of the small NR forms on IR. The IR works as a spatial frequency
filter to pass through only the zero frequency component located at the center of this
pattern. The zero frequency corresponds to the directly transmitted ray 1 without
deviation in the theory of Fraunhofer diffraction (far-field diffraction). Therefore, we can
treat our measurement by neglecting the deviated optical rays. It simplifies the theoretical
analysis to a system of four layers, labeled in sequence as 1: vacuum; 2: FQ; 3: NR; 4:
vacuum.
The nonlinear susceptibility tensor (ijk) for SHG of ZnO (point group: 6mm) can be
written as a matrix [ d ij ] with five nonzero components and three independent
components: d 31  d 32 , d15  d 24 and d 33 . Neglecting the back-irradiating SH wave from
the nonlinear polarization37 in the NR oriented as Figs. 1(b) and (c), the transmitted sand p- polarized SH intensities I (2s, p ) as a function of the polarization angle  ( s  0 ,
p   / 2 ) can be fitted via:
I s2  (cs cos  sin  ) 2
(1a)
6
I p2  (a p cos  2  bp sin  2 ) 2
(1b)
where c s , a p and b p are the fitting parameters. Without the assumption of Kleinman’s
symmetry, we have to measure I (2s, p ) as a function of  under the incidences of two
different angles of 1  0 (normal incidence) and  2  27  to obtain all the ratios between
d ij from the fitting parameters33. The absolute values of d ij are also obtained using a
reference material of Z-cut quartz plate to calibrate the system. Note that the ratio of the
SH intensities from NR’s and quartz plate can be only determined approximately by
measuring the brightness of the SH images of the NR and the quartz plate. Therefore, the
absolute values of d ij is a rough estimate.
Figures 3(a) and (b) are the polarization diagrams describing the s- and p- polarized SH
intensities I (2s, p ) as a function of  , respectively. The measurements were performed
under the normal incidence (empty squares) and the incidence of 27o (empty triangles),
which can be well fitted via Eqs. (1a) and (1b). It indicates that the c-axis of NR is
parallel to the substrate. The ratios of d ij were calculated to be d 33/ d 31  5.4 and
d15 / d 31  1.53 . The absolute value of d 33 / d 31 is close to the value measured by NSOM
in Ref. 31 but the sign is opposite. Careful examination shows that the data’s analysis in
Ref. 31 overlooked the interferences among the distinct components of  ijk , which
resulted in the sign being omitted. If the interference effect is taken into account, our
results will be consistent. I want to mention that the negative sign of d 33 / d 31 is also
consistent with the sign for a similar material of GaN nanowire, measured at the
wavelength of 860 nm. In addition, deviation from Kleinman’s symmetry ( d15  d 31 ) was
observed with d15 / d 31  1.53 at the fundamental wavelength of 810 nm. It was expected
because the SH wavelength (405 nm) is near band-edge resonance of ZnO and certain
absorption occurs at this wavelength. The absolute value of d 33 is approximately
calibrated to be 3 pm/V, which is in the same order as 5.5 pm/V measured by NSOM.
Figure 3(a) is a typical SH image for a single NR (length: 3.8 m; diameter: about 250
nm) under the normal incidence of the p-polarized fundamental beam. The image exhibits
the strong far-field scattering fringes resulting from the inferences of the SH waves
generated from the different locations along the axis of the NR. The number of the
interference fringes decreases as the length of the NR is reduced, as shown in Fig. 3(b)
for a shorter NR (length: 1.5 m; diameter: about 120 nm). The insets are the enlarged
images of the NR with their brightness reduced to view the detailed information clearly.
It is obvious that a small dark gap with low SHG efficiency exists at the center of both
NR’s. A dark fringe, which extends out from the dark gap at a scattering angle of zero
degree, neighbors with two strongest bright fringes. This feature is much clearer for the
shorter NR where the fringes at higher scattering angles are invisible (Fig 3(b)). The
SEM image (Fig. 3(c)) reveals that the NR is bisected into halves by a special interface
structure at the center. Some authors have described this kind of structures as the
7
dumbbell-shaped bicrystals that are bisected by a central (0001) twinning plane. The
polarity is thus likely pointed away from the terminal surface, towards the central (0001)
twinning plane30. Because the third-rank susceptibility tensors (ijk) for the two twinned
crystals have an opposite sign, the SH waves generated from them will be out of phase by
180o at the scattering angle of zero degree. Their destructive interferences always lead to
a dark fringe. A rigorous treatment for this problem has to resort to the enormous
numerical analysis for the linear and second-order light scattering by a finite twinned
hexagonal rod on a substrate. However, considering that the average distribution of the
SH intensity in the image exhibits a feature of dipole radiation, we simplify the NR to a
finite bisected wire that has a uniform density of electric dipole sources but with the two
segments oscillating out of phase by 180o at the SH frequency. The effective electric
dipole sources are attributed to the nonlinear polarization PN2ω that is excited by the
fundamental field E ω ( PN2ω  χ ijk : Eω Eω ). Our assumption is similar to the quasi-static
approximation32, but takes the finite length of NRs to be considered. The presence of the
FQ substrate may be neglected due to the weak SH back-irradiating and small reflection
coefficient in the interface37. We found that many of the image’s features can be
explained by this model without losing important physics. As shown in Fig. 4(a), the two
segments of the bisected dipole wire are assumed to have an opposite polarity labeled by
two opposite blue arrows directing to  y  axes, respectively. Therefore, the z component
S z2 of the time-average Poynting vector at a point (x,y) of the image plane, which is
away from the dipole wire by an effective distance deff, can be approximately written as:
L/2
L/2
1
S z2 ( x, y, d eff )  
Re[  E z2 ( x, y, d eff , y )  dy    B y2 ( x, y, d eff , y )dy ]
L / 2
L / 2
2 
(2)
where the wire extends from y    L / 2 to y   L / 2 along y  axis; E z2 and B y2 are the
corresponding components of the SH electric and magnetic fields in the image plane,
which are generated by a unit length of electric dipole distributed along y  axis. The
fields take on the forms38,
E z2 ~ [sin 2   (3 cos 2   1)(1/ r 2  2i / c / r ) /( 2 / c) 2 ]ei 2 / cr / r
(3a)
By2 ~  sin  cos[c /( 2ir ) 1]ei 2 / cr / r
(3b)
where  signs are chosen according to the two integration spans (plus for (-L/2, 0) and
minor for (0, L/2)), which represent the positive and negative polarities of the two
segments of the bisected dipole wire, and
2 1/ 2
r  [ x 2  ( y  y) 2  d eff
]
(4a)
2
2
sin 2   ( x 2  d eff
) /[ x 2  ( y  y) 2  deff
]
(4b)
2
2
cos 2   d eff
/( x 2  d eff
)
(4c)
8
Figure 4(b) is a density plot of S z2 ( x, y, d eff ) for a bisected dipole wire with the same
length as the NR in Fig. 3(a). d eff was taken as a small parameter to optimize the
simulation, which may be caused by the finite diameter of the NR, the finite depth of
field of the objective, or the incomplete treatment due to our approximation. The
simulation exhibits a very similar distribution of the interference fringes as Fig. 3(a)
displays. Also, as expected, the dark fringe appears at the zero scattering angle in the
simulation. Figure 4(c) is another simulation for the NR in Fig. 3(b). The simulation
exhibits a smaller number of fringes and a much wider dark fringe at the scattering angle
of zero degree, which greatly agrees with the experiment. To elucidate that the dark
fringe is a unique feature of the twinned NR, we measured the far-field SH scattering
pattern (Fig. 5(a)) from a single twin-free NR with the same size as the twinned NR in
Fig. 4(b). It shows a very bright fringe at the scattering angle of zero degree. Also, no
dark gap was observed in the enlarged image as shown in the inset. The bright fringe
results from the constructive interference of the SH waves radiated by the nonlinear
polarization oscillating in phase at every point along the twin-free NR. The twin-free NR
is modeled by a finite dipole wire with polarity directing positive y  axis as shown in
Fig. 5(c). The theoretical simulation in this case is realized by omitting  signs in Eqs.
(3a) and (3b) and computing Eq. (2). As shown in Fig. 5(b), the simulation well agrees
with the measured pattern in Fig. 5(a).
In summary, we observed the SH far-field scattering patterns from single twinned or
twin-free ZnO NR’s. The distribution of the interference fringes in the pattern has been
successfully correlated with the twinning structure in ZnO NR. The fringe at the
scattering angle of zero degree is dark for twinned NR due to the destructive interference
but bright for twin-free NR due to the constructive interference. A theoretical model
based on the radiation from a finite dipole-wire has been successfully employed to
simulate the patterns for both kinds of NR’s. The SH susceptibility tensor was also
measured without the objective in transmission geometry to reduce back-irradiation and
simplify the analysis to a standard four-layer system. The measured polarization diagrams
were well explained by the nonlinear susceptibility tensor under the symmetry group
(6mm) of the ZnO lattice with its polar direction along the NR’s axis. It reveals that d33 is
the dominant component and has an opposite sign to d15 and d31, at the fundamental
wavelength of 810 nm. Kleinman’s symmetry is found to be broken due to the possible
absorption of SH waves (405 nm) near the band-edge resonance of ZnO NR.
S.W.L., J.L.W. and M.X. are partially supported by grants from the Army Research
Laboratory (DAAD19-03-2-0017) and Army Research Office (W911NF-05-1-0353);
A.R. is supported via microEP REU program at the University of Arkansas.
9
Figure 1. The experimental configuration of the transmitted SHG from a single ZnO
nanorod. (a) The schematic of the experimental setup. PMT: photo-multiplier tube; BBO:
BBO nonlinear crystal; BS: beam splitter; LF: long-pass filter; BF: band-pass filter; CH:
chopper operating at 2 KHz; /2: half-wave plate; P: Glan polarizer; L1: focusing lens;
L2: collecting lens; IR: iris diaphragm; OB: removable objective; M: mirror; FM: flipper
mirror; PC: computer; S: sample. (b)(c) Sample and beam geometry. xo, yo, and zo are the
crystallography coordinate axes of the hexagonal ZnO lattice with zo as polar direction. s,
k, and z are the beam coordinate axes with s perpendicular to and k contained in the
incidence plane.  is the incidence angle, E(s , p ) is the s- or p- polarized fundamental field,
E(2s, p ) is the s- or p- polarized SH field. 1,2,3 are three typical optical rays (dotted:
fundamental rays; solid: SH rays), D is the diameter of the nanorod. Without the
objective only directly transmitted SH ray 1 is recorded for polarization diagrams. NR:
ZnO nanorod; FQ: fused quartz; Vac: vacuum.
Spectrometer
L2
IR
P
FM
OB
BF
S
LF
L1
PMT
IR
Es
NR
E2s
Camera
(a)
k
PC

BS
Lock-in
4: Vac
z
NR
FQ
D
3: NR
k
s
z 2: FQ
Ep
Es
2 1 3
(b)
BBO BF PMT
1
yo
FQ
zo xo
Lock-in
M
3
2
s
/2
CH
Ep
E2p
1:Vac
(c)
2 KHz
82 MHz,100fs
Ti:Sapphire
Figure 2. s-polarized (a) and p-polarized (b) SH intensities as a function of the
polarization angle  of the fundamental beam under the normal incidence (empty
squares) and the incidence of 27o (empty triangles). Sin and Pin represent the s- and ppolarized fundamental beams. Sout and Pout represent the s- and p-polarized SH signals.
Solid lines correspond to the theoretical fits.
10
Sin-Sout
0.0006
90
(a)
120
60
normal incidence
o
27 incidence
theoretical fits
0.0005
0.0004
30
150
0.0003
0.0002
0.0001
0.0000
180
0
0.0000
Pin-Sout
0.0001
0.0002
0.0003
330
210
0.0004
0.0005
240
0.0006
300
270
Sin-Pout
(b)
0.0025
90
120
60
normal incidence
o
27 incidence
theoretical fits
0.0020
0.0015
30
150
0.0010
0.0005
0.0000
180
0
0.0000
Pin-Pout
0.0005
0.0010
330
210
0.0015
0.0020
0.0025
240
300
270
Figure 3. (a)(b) SH images and interference fringes for single twinned ZnO NR’s. The
enlarged images in the insets show a dark gap with the weak SH signal at the center of
the NR. (a) NR with the length 3.8 m and the diameter about 250 nm. (b) NR with the
length 1.5 m and the diameter about 120 nm. (c) SEM image showing the NR’s
morphology: dumbbell-shaped bicrystals bisected by a central (0001) twinning plane.
(a)
40 m
11
(b)
40 m
(c)
Figure 4. Theoretical analysis of the interference fringes in the SH images of twinned
NR’s. (a) calculation geometry by simplifying the twinned NR to a finite bisected dipole
wire. The dipole wire has a finite length of L and a uniform dipole density but an
opposite phase on the positive and negative y  axis. The dipole wire is away from the
image plane (xy plane) by an effective distance deff. (b)(c) numerical simulation of the zcomponent of the time-average Poynting vector on the image plane for the twinned NR’s
in Fig. 3, with (b) representing Fig. 3(a) with deff=20.25 m, and with (c) representing
Fig. 3(b) with deff=16.2 m.
y
L/2
(a)
x
y
dipole
wire
-L/2
z
image
plane
x
z
deff
12
(b)
100
1
0.405 m
50
0
50
0
100
150
100
50
0
50
0.405 m
100
150
(c)
100
1
0.405 m
50
0
50
0
100
150
100
50
0
50
0.405 m
100
150
Figure 5. SH scattering patterns for a single twin-free ZnO NR (length 1.5 m, diameter
about 120 nm). (a) SH image shows a brightest fringe at the scattering angle of zero
degree. The inset shows an enlarged image with no dark gap at the center of the NR. (b)
numerical simulation for the z-component of the time-average Poynting vector on the
image plane (xy plane). (c) calculation geometry by simplifying the single NR to a finite
dipole wire with polarity directing to positive y  axis and extending from y    L / 2 to
y   L / 2 . The dipole wire is away from the image plane by an effective distance deff.
40 m
(a)
13
100
1
0.405 m
50
0
50
0
100
(b)
150
100
50
0
50
0.405 m
100
150
y
L/2
(c)
x
y
dipole
wire
-L/2
z
image
plane
x
z
deff
14
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Under normal incidence, the coherent lengths for the back-irradiation and the forwardirradiation are calculated via o/[4(N+n)] and o/[4(N-n)], respectively. n and N represent
the refraction indices at the fundamental (o) and SH wavelengths.
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Before the partial reflection of the back-irradiating SH signal in the interface between
the ZnO and fused quartz, the back-irradiating SH intensity may be comparable with the
forward-irradiating SH signal for the small NR (tens of nanometers), but is two-order less
for the large NR (hundreds of nanometers). In both cases, considering the low reflection
(~4%) of the back-irradiation in the interface afterward, the back-irradiating SH intensity
that was collected under our transmission geometry is at least two-order less than the
collected transmitted SH intensity.
38
Jackson, J. D. Classical Electrodynamics; John Wiley & Sons, Inc.; New York, 1999.
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Intellectual Property – Commercialization Value
There is no immediate commercialization value for the research that I helped conduct
over this summer. There is future value in that we provided very useful information that
can be used one day in the commercialization of ZnO. ZnO NR’s are a nano-sized
nonlinear optical material that contains many other useful properties, such as UV
emission, electron field-emission, chemically active conductivity, piezoelectric and
pyroelectric effects, and ferroelectric and ferromagnetic ordering, as was discussed earlier
in the paper. All of these properties, coupled with the fact that ZnO is a very stable,
easily fabricated material, almost guarantees that there will be much use for ZnO in
industry. It can be used to create lasers that operate at frequencies and energies that were
not always feasible. They could be used anywhere from the medical field to the
entertainment industry. Our findings this summer don’t immediately make this possible,
but they do provide further information on the topic.
Impact of REU on Personal Goals and Plans
Being in this REU program this summer has greatly increased my knowledge on what
goes on in a laboratory to further scientific understanding. I have always been intrigued
with the progression of science, and now I have learned how it comes about, with lots of
dedicated people who work very hard to make that happen. I have a new appreciation for
the persevering people who can sit in a lab all day and run experiments to gather data,
then have the fortitude to stay and analyze their findings. I have really been exposed to
how progress in science is conducted, and have come to learn that it might not be for me.
I still plan to go to graduate school, but for what future I am not sure. I might pursue a
career at a company that conducts a lot of research. I really realized that I could work
with people who do the research and try and make it applicable to the industrial world,
but I couldn’t be the one to continually be in the lab for the rest of my life.
Acknoledgements I would first like to express my gratitude to Dr. Liu for mentoring me
so much this summer. I have learned a great deal about how to properly conduct
research, and the time and dedication it takes to create useful findings. I am also leaving
this lab with a much more extensive knowledge on nonlinear optics. From the program, I
feel that I have learned a lot about how to handle my future with respect to graduate
school, and my career, from Ken and this program. I was much more successful this
summer because I learned how to deal with adversity and problems. I also grew a bit
more confident when faced with mild confrontation, and I even learned a little bit about
ethics. I look forward to continue to grow and develop, while taking a hands-on
approach to preparing myself for my future career.
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