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# 白金ナノ粒子のFDTD法による光学特性シミュレーション

## Abstract

The optical charactaristic of a layer of platinum nanoparticles were analyzed by using the electromagnetic wave analysis software KeyFDTD. The dielectric properties of platinum were approximated by a dispersion model, and a Gaussian pulse was incident into a layer of 80 nm platinum nanoparticles. And the transmission and reflection spectra in the visible to UV region were calculated. The platinum nanoparticle layer shows little reflection across all wavelengths, but the Local surface plasmon resonance reduces the transmission below wavelength 570 [nm] and shows the minimum transmission at wavelength 430 [nm].

The optical charactaristic of a layer of platinum nanoparticles were analyzed by using the electromagnetic wave analysis software KeyFDTD. The dielectric properties of platinum were approximated by a dispersion model, and a Gaussian pulse was incident into a layer of 80 nm platinum nanoparticles. And the transmission and reflection spectra in the visible to UV region were calculated. The platinum nanoparticle layer shows little reflection across all wavelengths, but the Local surface plasmon resonance reduces the transmission below wavelength 570 [nm] and shows the minimum transmission at wavelength 430 [nm].

## 2. 解析条件

Fig.1 Simulation model

$$\varepsilon(\omega) = \varepsilon_\infty+\frac{\omega_{p1}^2}{\omega(\omega+j\nu_c)}+\Delta\varepsilon_1\frac{\omega_{p2}^2}{\omega_{p2}^2+j\omega\delta_{p1}-\omega^2}$$

$$+\Delta\varepsilon_2\frac{\omega_{p3}^2}{\omega_{p3}^2+j\omega\delta_{p2}-\omega^2} +\Delta\varepsilon_3\frac{\omega_{p4}^2}{\omega_{p4}^2+j\omega\delta_{p3}-\omega^2}・・・(Eq.1)$$

Table.1 Dispersion paramters

 Model1 $\varepsilon_\infty$ $\omega_p [rad/sec]$ $\nu_c [rad/sec]$ $2.00$ $2.05\times10^{16}$ $3.08\times10^{14}$

Table.2 Dispersion paramters

 Model2 Model3 Model4 $\Delta\varepsilon$ $\omega_p [rad/sec]$ $\delta_p [rad/sec]$ $2.00$ $5.40\times10^{15}$ $1.62\times10^{15}$ $0.500$ $6.90\times10^{15}$ $1.24\times10^{15}$ $4.00$ $1.40\times10^{16}$ $1.26\times10^{16}$

Fig.3 Relative permittivity of platinum

この条件で中心周波数800[THz]のガウシアンパルスを入射し、入射波形と白金ナノ粒子層を透過・反射した波形のフーリエ変換後のエネルギー比から透過・反射スペクトルを算出した。

## 3. 解析結果

Fig.3に透過・反射スペクトルを示す。透過率は波長570[nm]より短波長側で低下し430[nm]で最小値を示した。反射率は小さく、透過率低下の要因は吸収である。Fig.4に波長430、700[nm]の正弦波を入射した時の粒子近傍電界分布を示す。430[nm]で粒子表面に電界集中が見られ、局在表面プラズモン共鳴(LSPR)による吸収が捉えられている。

Fig.3 Reflectance and transmittance spectra

λ=430[nm]

λ=700[nm]

Fig.4 Electric field distribution(Diameter=80nm)

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