Near-resonant second-order nonlinear susceptibility in c-axis oriented ZnO nanorodsWeiwei Liu, Kai Wang, Hua Long, Sheng Chu, Bing Wang, and Peixiang Lu

Citation: Applied Physics Letters 105, 071906 (2014); doi: 10.1063/1.4893599 View online: http://dx.doi.org/10.1063/1.4893599 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/105/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Effect of Lorentz local field for optical second order nonlinear susceptibility in ZnO nanorod J. Appl. Phys. 111, 103112 (2012); 10.1063/1.4721379 Second-order susceptibilities of ZnO nanorods from forward second-harmonic scattering J. Appl. Phys. 105, 063531 (2009); 10.1063/1.3093903 Second and third order nonlinear optical properties of microrod ZnO films deposited on sapphire substrates bythermal oxidation of metallic zinc J. Appl. Phys. 102, 113113 (2007); 10.1063/1.2822461 Second-harmonic performance of a -axis-oriented ZnO nanolayers on sapphire substrates Appl. Phys. Lett. 87, 171108 (2005); 10.1063/1.2112199 Third-order optical nonlinearity in ZnO microcrystallite thin films Appl. Phys. Lett. 75, 3321 (1999); 10.1063/1.125338

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Near-resonant second-order nonlinear susceptibility in c-axis orientedZnO nanorods

Weiwei Liu,1 Kai Wang,1 Hua Long,1 Sheng Chu,2 Bing Wang,1,a) and Peixiang Lu1,b)

1Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Scienceand Technology, Wuhan 430074, China2School of Physics and Engineering, Sun Yat-Sen University, Guangzhou 510275, China

(Received 5 July 2014; accepted 8 August 2014; published online 19 August 2014)

Near-resonant second-harmonic generation (SHG) in c-axis oriented ZnO nanorods is studied under

the femtosecond laser with wavelength from 780 nm to 810 nm. A highly efficient SHG is obtained,

which is attributed to the d131 component of the second-order nonlinear susceptibility. The largest

d131 value is estimated to be 10.2 pm/V at the pumping wavelength of 800 nm, which indicates a

large SHG response of the c-axis oriented ZnO nanorods in the near-resonant region. Theoretical

calculation based on finite-difference time-domain simulation suggests a four-fold local-field

enhancement of the SHG. VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4893599]

Recently, the second-harmonic generation (SHG) of

nanostructures has attracted a wide range of interests due to

the potential applications in nanodevices such as nanosour-

ces,1,2 nonlinear converters,3 optical correlator,4 and other

nanophotonic devices.5–7 ZnO, a direct wide bandgap

(3.37 eV) semiconductor, has shown great promise in optical

applications.8–10 ZnO has a wurtzite crystal structure and

belongs to the 6 mm point group, which leads to three com-

ponents of the second-order nonlinear susceptibility, d131,

d311, and d333.11 The large second-order nonlinear coeffi-

cients and wide transparency range make ZnO a good candi-

date for SHG from the infrared to the near-ultraviolet

region.12 There have been a variety of studies on the SHG in

ZnO nanostructures such as nanolayer,13 nanowire,9 and

nanorods.11,14 Most of the previous works focused on the

off-resonant SHG in which d131 is equal to d311 according to

the Kleinman’s symmetry condition. As a result, only the

values of d311 and d333 were measured.9,12,14,15 However,

Kleinman’s symmetry would be destroyed when the SHG

wavelength is close to the bandgap of ZnO, which results in

an enhancement of the d131 component.16,17 Thus, the deter-

mination of the d131 near resonances would be important for

the researchers to character and optimize the SHG efficien-

cies. Among ZnO nanostructures, the d131 value of the c-axis

oriented ZnO nanorods can be conveniently determined just

with the normal incident pumping laser, which makes it

more suitable for SHG study and applications in the near-

resonant region.

In this work, near-resonant SHG in c-axis oriented ZnO

nanorods is studied under the femtosecond laser of wave-

lengths from 780 nm to 810 nm. A highly efficient SHG is

obtained in the experiment, which is attributed to the d131

component of the second-order nonlinear susceptibility. The

value of near-resonant d131 in the c-axis oriented ZnO nano-

rods is determined. The largest d131 value is estimated to be

10.2 pm/V at the pumping wavelength of 800 nm, which is

calibrated with a ZnO [0001] single crystal. The calculated

electric-field distribution by finite-difference time-domain

(FDTD) simulation suggests a four-fold local-field enhance-

ment of the SHG.

High quality ZnO nanorod arrays were synthesized on

Si substrates by chemical vapor deposition (CVD) method.

The detailed growth procedure can be found elsewhere.18,19

Top viewed scanning electron microscopy (SEM) images of

the samples were taken to show the diameters and distribu-

tions, while lateral images were taken to illustrate the height

of the nanorods. Linear absorption and reflection properties

of the nanorod arrays were measured in the range of

250–900 nm by a standard UV-VIS-NIR spectrophotometer

(UV-2550, Shimadzu).

In the SHG experiment, an inverted microscope configu-

ration was used for optical measurements at room tempera-

ture, as schematically illustrated in Figure 1. A mode-locked

Ti/Sapphire oscillator (Tsunami, Spectra-Physics, 50 fs,

80 MHz) acted as the pumping source. The wavelength of the

femtosecond laser is tuned from 780 nm to 810 nm to study

the near-resonance property of the SHG. A 40� objective

FIG. 1. The experimental setup scheme of the SHG measurement.

a)Electronic mail: wangbing@hust.edu.cnb)Electronic mail: lupeixiang@hust.edu.cn

0003-6951/2014/105(7)/071906/4/$30.00 VC 2014 AIP Publishing LLC105, 071906-1

APPLIED PHYSICS LETTERS 105, 071906 (2014)

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222.20.93.187 On: Wed, 20 Aug 2014 01:16:26

(Olympus, NA¼ 0.6) focused the laser beam to the sample

with a spot diameter of 4 lm. The reflected signal was col-

lected with the same objective and then focused by a lens

(f¼ 20 cm) to the spectrometer (Princeton Instruments Acton

2500i with Pixis camera) for spectra measurement or to a

CCD camera for dark-field imaging, which is selected by a

folding mirror after the lens. A 720 nm short-pass filter was

placed in front of the lens to filter out the pumping laser. A

ZnO [0001] single crystal (10 mm� 5 mm� 0.5 mm,

d131¼ d311¼ 2 pm/V (Ref. 15)) is used for SHG calibration.

Figures 2(a) and 2(b) show the top and lateral viewed

SEM images of the ZnO nanorods, respectively. As seen

from Figure 2(a), the ZnO nanorods distribute randomly with

the c-axis orientated normal to the substrate. The diameters

of the nanorods range from 100 nm to 500 nm. The inset

presents a single nanorod with diameter of about 300 nm.

The regular hexagonal cross-section and well-faceted surface

imply the high quality of the nanocrystal. Figure 2(b) reveals

that the nanorods have an average height of 1 lm. Figures

2(c) and 2(d) show the measured linear absorption and

reflection spectra of the ZnO nanorods on Si substrate. From

the absorption spectrum, one can see that the absorption

edge is around 378 nm (3.28 eV), which is very close to the

bandgap of bulk ZnO (3.37 eV). No other obvious peaks can

be observed from the absorption spectrum, which indicates

the high crystal quality and low defect concentrations of the

ZnO nanorods. The reflection spectrum shows a high reflec-

tivity of the structure from 378 nm to 900 nm.

When pumped by the femtosecond laser, a variety of

optical signals could be obtained from the ZnO nanorods.

Figure 3(a) shows a bright blue pattern observed from the

CCD camera under an average power of 21 mW. Since no

signal can be obtained in a pure Si substrate, the signal can

only be ascribed to the ZnO nanorods. The round blue pat-

tern (�20 lm) is much larger than the focus spot of the

pumping laser, which results from the transmission and scat-

tering of the generated signal. The far-field spectra of the

blue signal are shown in Figure 3(b). The spectra present a

strong peak at about 410 nm. It is exactly the frequency

doubling signal of the pumping laser (820 nm), indicating

the SHG process. A small peak located at about 389 nm sug-

gests a much weaker multi-photon absorption (MPA)

induced photoluminescence (PL). This emission is 180 meV

below the band gap (3.37 eV) and is generally ascribed to the

recombination of excitons.8 The spectrum of the pumping

laser was measured by placing an attenuator of 4.2� 10�7 in

front of the spectrometer.

For further study, peak intensities of the SHG, PL, and

pumping laser as functions of the incident power are meas-

ured, respectively. Figure 3(c) presents the experimental

results (dots) and the theoretical fittings. The SHG intensity

has a quadratic dependence on the incident power (blue

line), which agrees with the theory well.20 The measured PL

intensity as a function of the pumping power can be well fit-

ted with y¼Ax3 (green line). The cubic dependence suggests

a three-photon absorption (TPA) induced PL process. Since

MPA is not effective under weak excitations, SHG process is

dominant in the experiment.21 Figure 3(d) shows the SHG

efficiency, g, as a function of the pumping power. The effi-

ciency is estimated with g ¼ PSHG=ðR � PpumpÞ, where PSHG

and Ppump are the measured peak intensities of the SHG and

pumping laser. R is the measured reflectivity of the sample at

410 nm, which is about 20% from Figure 2(d). The results

indicate that the SHG conversion efficiency is proportional

to the pumping power. Particularly, the SHG efficiency is

about 1.4� 10�5 under the pumping power of 21 mW

(�167.1 kW/cm2).

The SHG efficiency is directly relevant to the second-

order nonlinear susceptibilities of the materials. For the

c-axis oriented ZnO nanorods with coaxial pumping, the

second-order polarization components can be expressed as

FIG. 2. (a) and (b) Top-viewed and lateral-viewed SEM images of the ZnO

nanorods for experiment. The inset in (a) shows the SEM image of a single

nanorod (scale bar 200 nm). (c) and (d) Plots of the measured absorption and

reflectivity spectra of the ZnO nanorods on Si substrate, respectively.

FIG. 3. (a) The dark-field image of the signal under a pumping power of 21

mW. (b) Plot of the spectra for the PL, SHG, and pumping laser, respec-

tively. (c) Plots of the measured peak intensities of the SHG (PSHG), PL

(PPL), and pumping laser (PPump) as functions of the pumping power, respec-

tively. The pumping laser was measured with an attenuator of 4.2� 10�7. (d)

Plot of the estimated SHG efficiency, g, as a function of the pumping power.

071906-2 Liu et al. Appl. Phys. Lett. 105, 071906 (2014)

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222.20.93.187 On: Wed, 20 Aug 2014 01:16:26

Px

Py

Pz

264

375 ¼ ½ dij � �

E2x

E2y

E2z

EyEz

EzEy

EzEx

ExEz

ExEy

EyEx

2666666666666666664

3777777777777777775

: (1)

[dij], the matrix form of the second-order nonlinear suscepti-

bility tensor for ZnO, can be written as

½ dij � ¼0 0 0 0 0 d131 d113 0 0

0 0 0 d113 d131 0 0 0 0

d311 d311 d333 0 0 0 0 0 0

264

375:(2)

As d131¼ d113,16 Eq. (1) can be simplified as

Px

Py

Pz

264

375 ¼

2d131ExEz

2d131EyEz

d311E2x þ d311E2

y þ d333E2z

2664

3775: (3)

It should be noted that the Pz component is polarized along

the z axis. Thus, the related SHG signal propagates in the xy

plane, which can not be collected by the objective in our

experiment. As a result, the SHG signal detected is domi-

nantly caused by Px and Py, the intensity of which can be

expressed as

I / P2x þ P2

y ¼ 8d2131ðE2

xE2z þ E2

yE2z Þ: (4)

From Eq. (4), one can see that the intensity of the SHG

measured is isotropic because the ZnO nanorods distribute

randomly on the Si substrate. More importantly, it demon-

strates that only the d131 component of the second-order non-

linear susceptibility makes contribution to the collected SHG

signal that propagates along z axis.

In the experiment, the near-resonant property of the d131

component is studied by tuning the pumping wavelength

from 780 nm to 810 nm. Figure 4(a) shows the normalized

SHG intensity as a function of the wavelength. One can see

that the strongest SHG is obtained at the pumping wave-

length of 800 nm, corresponding to the largest resonant

enhancement of the d131 component. The SHG wavelength is

a little deviated from the bandgap of the ZnO nanorods,

which should be due to the strong absorption of the SHG

close to the bandgap. The inset of Figure 4(a) presents the

polarization property of the collected SHG signal at 400 nm.

The isotropy of the signal is in good agreement with the the-

oretical analysis, which further confirms that only the d131

component has contributed to the collected SHG.

The value of d131 at the pumping wavelength of 800 nm

for the c-axis oriented ZnO nanorods is determined by refer-

ring to a ZnO [0001] single crystal (500 lm thickness,

d131R¼ 2 pm/V). The SHG for the ZnO nanorods and the

single crystal are measured in the same experimental condi-

tions. Figure 4(b) shows that the SHG intensity of the nano-

rods is much stronger than that of the single crystal. Since

the thickness is much larger than the coherent length of ZnO,

the serious phase-mismatch in the ZnO single crystal results

in a much weaker SHG.16 The SHG signal intensity from the

ZnO samples can be expressed as13

I2x ¼C

n2xn2x

d2131I2

xL2 sinc2 jDk � Lj=2ð Þ; (5)

where x and 2x denote the fundamental and SHG beam,

respectively, n the refractive indices, L the path length, and

Dk¼ 2kx� k2x the wave vector mismatch between funda-

mental and SHG beam. According to Eq. (5), the value of

d131 can be calculated as

d131 ¼sin DkLR

2

sin DkL2

ffiffiffiffiI

IR

rd131R � 5:1d131R ¼ 10:2 pm=V; (6)

where I and IR are the SHG intensities for the ZnO nanorods

and single crystal, respectively. L and LR are the thickness of

the two samples. The refractive indices of ZnO are calcu-

lated with Sellmeier dispersion relationship.22 Compared

with the most commonly used second-order nonlinear mate-

rials such as beta-barium borate (BBO) and potassium dihy-

drogen phosphate (KDP), the d131 value is much larger than

the nonlinear coefficients of them in the near-infrared region

(�2 pm/V for BBO14 and �0.39 pm/V for KDP23), which

indicates a large SHG response of the c-axis oriented ZnO

nanorods in the near-resonant region.

FIG. 4. (a) Normalized SHG intensity as a function of the pumping wave-

length (SHG wavelength). Inset: Measured polarization property of the SHG

signal at 400 nm. (b) Measured SHG spectra for the ZnO nanorods (red) and

ZnO single crystal (black), respectively.

071906-3 Liu et al. Appl. Phys. Lett. 105, 071906 (2014)

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222.20.93.187 On: Wed, 20 Aug 2014 01:16:26

The measured d131 value is much larger than that

reported by Neumann et al. in the ZnO nanolayer near

resonances (2.6 pm/V).13 Different from the nanolayer, light-

matter interaction in the ZnO nanorods can be enhanced due

to local-field effect.24 The electric field distribution at the

pumping wavelength of 800 nm is calculated with FDTD

simulations. The distribution and sizes of the nanorods are

retrieved from the SEM image in Figure 1(a). Figure 5 shows

the calculated distribution of jEj2 in the transverse cross-

section at half height of the nanorods. The strongest electric

field intensity is achieved in the multiple nanorods with a

large number of hot spots, which results from the local-field

enhancement effect obviously. Moreover, the averaged elec-

tric field intensity inside the nanorods can be written as

IAve ¼Ð

Idv=V, where I is the electric field intensity in each

small domain and V is the total volume of the nanorods. IAve

is calculated to be 2 times of the incident intensity, corre-

sponding to a four-fold enhancement of the SHG intensity by

the local-field effect.

In conclusion, the near-resonant SHG in c-axis oriented

ZnO nanorods is studied under the femtosecond laser of

wavelength from 780 nm to 810 nm. Theoretical analysis and

experiment results indicate that the SHG signal is domi-

nantly contributed by the d131 component of the second-

order nonlinear susceptibility. The largest value of d131 is

measured to be 10.2 pm/V at the pumping wavelength of

800 nm, which indicates a large second-order nonlinear

optical response of the c-axis oriented ZnO nanorods in the

near-resonant region. FDTD simulation suggests a four-fold

enhancement of the SHG by the local-field effect. The result

is important for the application of ZnO nanostructures as

nonlinear integrated optical devices in a wide wavelength

range from the infrared to the near-ultraviolet region.

This work was supported by National Natural Science

Foundation of China (11104095, 11204097, and 51002059),

the Doctoral fund of Ministry of Education of China under

Grant No. 20130142110078, and the 973 Programs under

Grants 2014CB921301 and 2011CB933300.

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FIG. 5. The calculated electric field distribution ðjEj2Þ at pumping wave-

length (800 nm) for the ZnO nanorods.

071906-4 Liu et al. Appl. Phys. Lett. 105, 071906 (2014)

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