## Abstract

Au triangular nanoprisms with strong dipole plasmon absorption peak at 1240 nm were prepared by wet chemical methods. Both numerical calculations and experiments were carried out to investigate the optical properties of the samples. Finite difference time domain (FDTD) and Local Density of States (LDOS) calculations demonstrate that strong electric field enhancement and large LDOS can be obtained at tip areas of the Au triangular nanoprisms. Z scan techniques were used to characterize the nonlinear absorption, nonlinear refraction, as well as one- and two-photon figures of merit (*W* and *T*, respectively) of the sample. The results show that maximum nonlinear refractive index can be obtained around the resonance absorption wavelength of 1240 nm, detuning the wavelength from the absorption peak will lead to the decrease of the nonlinear refractive index *n*_{2}, while the nonlinear absorption coefficient *β* doesn’t change much with the wavelength. This large wavelength dependence of *n*_{2} and small change of *β* enable the sample to satisfy the all-optical switching demand of *W*> 1 and *T*< 1 easily in a large wavelength range of 1200-1300 nm. These significant nonlinear properties of the sample imply that Au triangular nanoprism is a good candidate for future optical switches in infrared optical communication wavelength region.

©2013 Optical Society of America

## 1. Introduction

Over the past decade, considerable research interests have been apportioned to noble metallic materials for its ability to support surface plasmon modes, which are collective oscillations of electron gas in metal that couple with electromagnetic fields [1–5]. With the ability to concentrate and enhance near electric field, plasmonic nanostructures have found numerous promising applications in quantum devices [6–8], plasmon lasers [9–11], and biochemical sensing substrates [12–14]. In addition, the growing demand in design and fabrication of photonics and plasmonic devices makes plasmonic material become critical import [15–17].

Among the various investigated plasmonic materials, triangular nanoprism is distinctive since large surface plasmon local field enhancement can be obtained at its sharp corner due to the large electric field confinements [18–21]. Many works on triangular nanostructures have been reported, such as optical waveguides [22,23], nanoantennas, biochemical sensors and surface enhanced Raman scattering (SERs) structures [24,25]. Besides the above mentioned applications of triangular nanostructures, noble metal nanostructures with strong local field enhancement also possess large third-order optical nonlinearities which can be used in optical limiting [26], all optical switching [27,28], and energy transferring [29–31]. Despite many distinguish works related to plasmonics of triangular prisms have been reported previously, seldom work has been done to investigate its third-order optical nonlinearities.

In this paper, third-order optical nonlinearities including nonlinear absorption coefficient *β* and refractive index *n*_{2} have been investigated, the one- and two-photon figures of merit (FOM) were also evaluated. Furthermore, electric field distribution and local density of state (LDOS) of the Au nanoprism were also simulated. All these remarkable optical properties make the Au triangular nanoprisms have great potential applications in infrared communications and optical switches [32–35].

## 2. Experiment

The Au triangular nanoprism is synthesized by seeded growth method [30]. Au nanoparticle seeds were prepared by the reduction reaction with the presence of sodium citrate (0.275mM, 36.33mL), HAuCl_{4} aqueous solution (15mM, 0.67mL), and NaBH_{4} (100mM, 1mL). In order to the complete hydrolysis of unreacted NaBH_{4} adequately, the mixed solution needed to react for a whole night.

Three groups of growth solutions were prepared for the seed-mediated growth steps. Solution A and B were identical which contained NaOH (0.1M, 0.05mL), ascorbic acid (0.1M, 0.05mL), KI (0.1M, 0.075mL), CTAB (0.05M, 9mL) and HAuCl_{4} (10mM, 0.25mL). While solution C contained NaOH (0.1M, 0.50mL), ascorbic acid (0.1M, 0.50mL), KI (0.1M, 0.075mL), CTAB (0.05M, 90mL) and HAuCl_{4} (10mM, 2.5mL). All these three groups of solutions were prepared by adding chemicals in the sequence listed above.

Au particle formation started by adding 1mL of seed solution to growth solution A. The mixture was gently shaken, then 1mL of this mixture was added to growth solution B. After a while of gently shaking, the whole mixture was added into solution C. The color of the final mixed solution was changed from clear colorless to purple red in about 20 minutes. The water used in the experiments was purified to 18.2 MΩ cm by using a Millipore Mili-Q water system.

The scanning electron microscopy (SEM) was performed by using a Zeiss Auriga-39-34 electron microscope operated at an accelerating voltage of 20.0 kV. The absorption spectra were recorded by a UV-VIS-NIR spectrophotometer (PerkinElmer Lambda950). The nonlinear optical measurements were performed using a Z-scan setup. For Z-scan measurements, a Ti:Sapphire femtosecond laser (Coherent, Mira 900) pump optical parametric oscillator (OPO, Coherent, APE OPO) was used as a laser sources to obtain the infrared laser emission, the pulse duration of the output laser beam from OPO is about 200 fs and the repetition rate is 76 MHz. Both open- and closed-aperture Z-scan measurements were done to get the third-order optical nonlinear absorption coefficient and refraction index.

## 3. Results and discussion

Figure 1 is the SEM image and absorption spectra of Au nanoprisms. From Fig. 1(a), one can see that the edge-length of Au nanoprisms is about 170 ± 30 nm with a thickness of ~7 nm, and the yield of Au triangular nanoprisms is estimated to be about 55-70%. The inset of Fig. 1(b) is the SEM image of Au nanoprisms with an inclined angle of 45°. As the measured thickness is 5.2 nm, the real thickness of Au nanoprism is about 7.4 nm, which is close to those previous reports [36].

Figure 1(b) is the absorption spectra of Au nanoprisms in water solution. Two absorption bands can be easily observed, and the one locates at around 530 nm is due to the dipole plasmon resonance of spherical Au nanoparticle with diameter of about 50 nm [36]. The stronger absorption peak locates at about 1240 nm is dipole plasmon resonance of Au triangular nanoprisms, and the broad absorption peak is caused by the contribution of the irregular shape prisms. It should note that the absorption intensity at 1240 nm is stronger than that of Au nanoparticles, which implies that the yield of Au nanoprisms is high. Also, there is a small absorption band located at about 800 nm, which is the quadrupole plasmon mode of Au triangular nanoprisms first discovered by J. E. Millstone *et al.*.

To confirm the plasmon resonance property of Au nanoprims, simulations have been done using finite difference time domain (FDTD) method (commercial software FDTD Solutions 8.0). During the simulation, perfectly matched layer (PML) boundary condition was performed, and the cell size was set as 1 × 1 × 0.5 nm^{3}, the edge-length and thickness of Au triangular nanoprism were set as 170 nm and 7 nm, respectively, where the complex dielectric constants of gold were taken from the literature reported by Johnson and Christy [37] according to previous reports [38–40], and the refractive index of water is 1.33. Fig. 2(a) is the simulated absorption spectra of Au triangular nanoprism (red curve) and spherical Au nanoparticle (blue curve). It is clear that the absorption intensity of spherical Au nanoparticle (blue curve) is three orders of magnitude smaller around 1240 nm, and does not support plasmon resonance. The field distribution of Au nanoprism and spherical Au nanoparticle at 1240 nm are shown in Fig. 2(b) and Fig. 2(c) respectively, the excitation light perpendicularly incidents (along *z* axis) with the electric field parallel to Au nanoprism (along *y* axis). From Fig. 2(b), one can see the maximum points of the field locate at the three tips of the Au nanoprism while the minimum points appear at the centre of the side-edge. This field distribution demonstrates the existence of dipole plasmon resonance. From Fig. 2(c) with the same scale bar, the electric field enhancement can hardly be found, and the maximum electric field intensity enhancement of Au nanoprism is 55.9 times larger than that of spherical Au nanoparticle according to the simulation results (the calculated field enhancement of spherical Au nanoparticle is only 2.9).

To further investigate the near field enhancement property of Au triangular nanoprism, the local density of states (LDOS) along the side-edge of Au nanoprism was calculated. As the LDOS enhancement is proportional to the emission rate of nano-emitters around Au nanoprisms, the LDOS results can directly demonstrate the plasmon-photon interaction property of Au triangular nanoprisms, which is critical for its applications.

The LDOS calculation was performed by using the Green function method with the help of the COMSOL software (version 4.2a). The dielectric constant of the gold was taken from the literature [37]. An electric point dipole is set 10 nm above the center of side edge of the Au triangular prism [Fig. 3(a)], with side-edge length and thickness being 170 nm and 7 nm. To get a good mesh, a sphere with radius 4 nm is set to surround the dipole, furthermore, two blocks with sizes of 272 × 272 × 30 nm^{3} and 500 × 500 × 100 nm^{3} are set to separate the nanoprism and the Perfectly Matched Layers (PML). The PML is set to general type with size 1000 × 1000 × 500 nm^{3}. The mesh is predefined as finer. The scattering boundary is set to the outside of the PML.

With the help of the Green function, the LDOS is given as [41]

Where Im stands for the imaginary part and *tr* denotes the trace of the Green tensor matrix in brackets.

From the Maxwell equations, one can get$\overrightarrow{E}(\overrightarrow{r},\omega )=i\omega {\mu}_{0}{\displaystyle \int d\overrightarrow{r}\text{'}\overleftrightarrow{G}(\overrightarrow{r},\overrightarrow{r}\text{'},\omega )}\cdot \overrightarrow{j}(\overrightarrow{r},\omega )$. By setting a dipole source $\overrightarrow{j}(\overrightarrow{r}\text{'},\omega )=\overrightarrow{j}(\omega )\delta (\overrightarrow{r}\text{'}-{\overrightarrow{r}}_{0})$, the Green function can be calculated by the electric field at the position of the dipole as $\overrightarrow{E}({\overrightarrow{r}}_{0},\omega )=i\omega {\mu}_{0}\overleftrightarrow{G}({\overrightarrow{r}}_{0},{\overrightarrow{r}}_{0},\omega )\cdot \overrightarrow{j}(\omega )$.

Also the matrix form of $\overrightarrow{E}({\overrightarrow{r}}_{0},\omega )$ can be written as:

After choosing three $\overrightarrow{j}$ of different directions, all the elements of the Green matrix can be obtained, so as to get the LDOS.

In Fig. 3(b), the dipole source is placed at the centre of the Au nanoprism with 10 nm above the surface (*z* = 10 nm), and the zero point is set at the centre of edge-side as shown in Fig. 3(a). Define the LDOS enhancement as the ratio between the LDOS of dipole source above Au nanoprism and in vacuum. As shown in Fig. 3(b), the LDOS enhancement increases dramatically as the calculation point moving from the centre to the tip. An LDOS enhancement of 1000 times has been found at the triangular tip, which suggests strong near field enhanced photon-electron interaction [42].

As strong near electric field can induce large optical nonlinearities [43], third-order nonlinear absorption and refraction properties as well as one-photon- and two-photon- figures of merit in Au triangular nanoprisms were investigated using z-scan measurements. Figure 4(a) is the schematic of Z-scan setup, a laser source generated from an OPO pumped by a Ti:Sappire femtosecond was used to generate the laser emissions from 1100 nm to 1300 nm. After the attenuation by a neutral density filter, the laser emission with appropriate power was focused onto the sample by a lens with focal length of 100 mm. To minimize the possible heat effect by laser irradiance, the peak irradiance intensity of the laser beam at the focus position *I*_{0} was fixed at 0.43GW/cm^{2}_{.} The sample held by a 1 mm thick quartz cell was put onto a moving stage which can sweep along the laser beam directions ( ± Z direction), two power detectors (D1 and D2) were used to monitor the laser powers. The transmission *T* was extracted from the ratio between power value obtained by detector D2 and the that at the front of the sample calculated from detector D1.

Figure 4(b) presents the normalized open aperture transmittance *T* as functions of sample position *z*. The hollow dots are experimental data, and the solid lines are fitting curves using the theoretical expression of *T* = Σ(-q_{0})^{m}/(1 + *z ^{2}*/

*z*)

_{0}^{2}^{m}(1 + m)

^{3/2}(m = 0,1,2,…) [44], where

*z*is Rayleigh range and equals to nπω

_{0}_{0}

^{2}/λ, ω

_{0}is Gaussian beam spot radius at focus (z = 0), q

_{0}=

*βI*

_{0}L

_{eff}, L

_{eff}is effective thickness of the sample. The nonlinear absorptions between 1100 and 1300 were measured, all the curves are valley types which imply that the third-order nonlinear absorption of the gold triangular prisms here are two-photon induced absorption. Figure 4(b) is the normalized results of the closed-aperture z scan measurements, the hollow dots are experimental data, and the solid lines are fittings. The theoretical relation between

*T*and

*z*is expressed as

*T*= 1 + 4ΔΦ

_{0}(

*z*/

*z*)/{[(

_{0}*z*/

*z*)

_{0}^{2}+ 9]·[(

*z*/

*z*)

_{0}^{2}+ 1]}, where ΔΦ

_{0}=

*n*

_{2}

*kI*0

*L*eff,

*n*is the nonlinear refraction index, and

_{2}*k*is the wave number. All the curves are peak-valley types, which mean that the third-order nonlinear refractive indexes of the sample are negative.

From the data and the fittings in Fig. 4(b) and (c), the third-order optical nonlinear absorption coefficient *β* and nonlinear refractive index *n*_{2} can be extracted. As shown in Fig. 4(d), the wavelength dependent *β* and *n _{2}* values are demonstrated.

*β*doesn’t change much with the change of the wavelength and

*β*is about 0.189 cm/GW at 1240 nm, while

*n*increases as the wavelength goes close to the resonance absorption wavelength, and the maxima is 1.87 × 10

_{2}^{−4}cm

^{2}/GW. The corresponding χ

^{(3)}susceptibility of the sample can be calculated using χ

^{(3)}= Im{χ

^{(3)}} + Re{χ

^{(3)}}, where Im{χ

^{(3)}} comes from nonlinear absorption of the sample and can be calculated from

*β*(Im{χ

^{(3)}} =

*n*), Re{χ

_{0}^{2}ε_{0}c^{2}β/ω^{(3)}} is contributed by the nonlinear refraction

*n*(Re{χ

_{2}^{(3)}} =

*2n*), the imaginary and real part of χ

_{0}^{2}ε_{0}cn_{2}^{(3)}at 1240 nm are calculated to be 1.03 × 10

^{−13}esu and 1.25 × 10

^{−11}esu, respectively. From these calculated results of χ

^{(3)}, it is clear that third-order nonlinear refraction is dominant effect in the sample. Due to the limiting of our laser sources, the measurements under the wavelength shorter than 1100 nm and longer than 1300 nm can’t be obtained. However, the value of χ

^{(3)}at 1240 nm is 20 times larger that obtained at 800 nm (6.48 × 10

^{−13}esu), which means that the large nonlinearities around 1240 nm are due to the local field enhanced plasmon resonance effects. It is important to notice that there are some Au nanoparticles existing in the solution of Au triangular prisms, since the absorption peak of the nanoparticles locates at around 530 nm, which is far away from the measurement wavelength that we used at 1100-1300 nm region, the nonlinear effects attributed from spherical Au nanoparticles can be ignored [45].

One-photon-FOM (*W*) and two-photon-FOM (*T*) are two parameters defined for evaluating the properties of the device, *W*> 1 and *T*<1 are essential for the application in all-optical switching. Where *W = n _{2}I/αλ* and

*T = βλ/n*,

_{2}*W*is proportional to the ratio between

*n*and the linear absorption coefficient

_{2}*α*,

*T*is related to

*β*and

*n*Fig. 4(e) presents the values of

_{2}.*W*and

*T*as functions of wavelength. All the

*T*values across the range of 1100nm-1300nm satisfy the demand

*T*<1, which benefit from the small NLA coefficient β, while

*W*increases from 0.31 at 1100nm to 1.15 at 1240nm and W satisfies the demand of

*W*>1 in the wavelength range of 1200nm-1300nm with I

_{0}= 0.43GW/cm

^{−2}. Since

*W*is also linearly proportional to I

_{0,}further increase of I

_{0}will make

*W*>1 available for a much larger wavelength region. Therefore, Au triangular prisms are proved to be a good candidate for future optical switches in this communication wavelength region.

## 4. Conclusion

We have experimentally and theoretically investigated the nonlinear property of Au triangular nanoprisms synthesized by seeded growth method. The UV-VIS-NIR analysis and FDTD simulation indentify the existence of dipole plasmon resonance at 1240nm. The LDOS calculation shows an enhancement of 1000 times at the triangular tip, which suggests strong near field enhanced photon-electron interaction. The results of Z-scan measurement indicate that third-order susceptibility is 1.25 × 10^{−11} esu at 1240nm which is about 20 times larger than that obtained at 800nm, and this result confirms the inference of theoretical simulations and calculations. The significant third-order nonlinearity across the range of 1200nm-1300nm satisfy the demands that *W*>1 and *T*<1 which suggest Au triangular prisms are good candidate for future of all-optical switching in the 1300 nm telecommunication wavelength band.

## Acknowledgment

We greatly thank Prof. Huanjun Chen for helpful discussions. This work was supported in part by NSFC (11204385), National Basic Research Program of China (2010CB923200, 2011TS105), the Fundamental Research Funds for the Central Universities (Grant 12lgpy45), and Fund of Education department of Guangdong Province (2012LYM_0011).

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