[2013] [paper notes] terahertz band nano particle surface enhanced Raman——

Preface

type
$Terahertz+scattering$
Periodical
$Spectroscopy\; and\; spectral\; analysis$
author
$Wu\; Yudeng,Ren\; Guangjun,Hao\; Yun,Yaojianquan$
Time
$2013$

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Surface enhanced Raman scattering SERS

When material molecules are adsorbed on some specific metal surfaces , The Raman scattering intensity of molecules will be greatly enhanced
（ The enhancement factor can reach $10^3\sim 10^7$）

For nano scale rough surfaces , The enhancement of the signal can reach a million billion times

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Raman scattering

The frequency of light wave changes after being scattered

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Electromagnetic enhancement

Surface plasmon resonance SPR Local electromagnetic field enhancement caused
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Chemical enhancement

There is charge transfer between the substrate and the adsorbed material
Mainly due to The polarizability of molecules adsorbed on rough surfaces changes The enhancement of Raman signal caused by .
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research objective

1 Terahertz + Combination of low frequency Raman spectra

Intermolecular and intramolecular low-frequency stretching of some macromolecules 、 Bending vibration , Lattice phonon vibration , Hydrogen bond stretching 、 Torsional vibration
—— The corresponding absorption frequencies are distributed in THz Band

• Terahertz has great application prospects in the detection of macromolecules

But macromolecules THz Research Absorption frequency

Low frequency Raman spectroscopy can reflect the vibration characteristics of macromolecules

SERS Surface enhanced Raman scattering can make THz Combined with low-frequency Raman spectroscopy

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2 explain SERS

Is there anything else （2013） A complete theoretical explanation SERS（ Surface enhanced Raman scattering ） Enhancement mechanism of

Recognized mechanism ：
Based on surface plasmon theory Electromagnetic enhancement Mechanism + Based on charge transfer theory Chemical enhancement Mechanism

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Research methods

Electromagnetic enhancement ： Including the surface plasma model 、 Antenna resonator model 、 Mirror field model

Based on the above model, we can use FDTD Finite difference time domain , The simple results are simulated accurately

FDTD There are different expressions in different media

This paper discusses the surface strengthening effect of metal nanoparticles

Mesh scale ：$0.5nm\times 0.5nm$
The number of grids ：$200\times 200$
Nanoparticles ： gold Au Nanoparticles
Model ： Plane model
Particle size ：$20nm$
Incident wave ： Plane linearly polarized wave

For different sizes of two particles 、 Simulate with different spacing

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Research models

Metal nanoparticles are dispersive , use Drude The function represents its relative dielectric constant ：
$$\epsilon (\omega )=1+\frac{{\omega }_p^2}{\omega (i{\nu }_c-\omega )}=1+\chi (\omega )$$
among ${\omega }_p$ Is the plasma frequency of dispersive medium ,${\nu }_c$ Is the plasma collision frequency of dispersive medium

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Dispersive medium , Time domain
$$D(t)={\epsilon }_{\infty }{\epsilon }_{0}E(t)+{\epsilon }_0{\int }_0^{t}E(t-\tau )\cdot \chi (\tau )d\tau$$
among $\chi (\tau )$ Is the inverse Fourier transform of the polarization rate ,${\epsilon }_{\infty }$ yes $\omega \to \infty$ The relative permittivity of

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Yee Coriolis grid
Use Yee The time is discretized by T-grid ,$t=n\Delta t$, be
$$\begin{gathered} D(t)\approx D(n\Delta t)=D^n={\epsilon }_{\infty }{\epsilon }_0{E}^n+ \\ {\epsilon }_0{\int }_0^{n\Delta t}E(n\Delta t-\tau )\cdot \chi (\tau )d\tau \end{gathered}$$
When $t<0$ when ,$D(t)=E(t)=0$
Take the field value of each step as a constant , Yes
$$D^n={\epsilon }_{\infty }{\epsilon }_0{E}^n+{\epsilon }_0\sum _{m=0}^{n-1}{E}^{n-m}\cdot {\int }_{m\Delta t}^{(m+1)\Delta t}\chi (\tau )d\tau$$
$$D^{n+1}={\epsilon }_{\infty }{\epsilon }_0{E}^{n+1}+{\epsilon }_0\sum _{m=0}^n{E}^{n-m+1}\cdot {\int }_{m\Delta t}^{(m+1)\Delta t}\chi (\tau )d\tau$$

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Isotropic metal medium
For isotropic metallic media , Yes
$$\begin{gathered} \nabla \times H=\partial D/\partial t \\ \nabla \times E=\partial B/\partial t \\ B=\mu H \\ D=\epsilon H \end{gathered}$$
among $\mu and\epsilon$ They are the permeability and dielectric constant of dispersive medium

according to Yee Grid definition $x=i\Delta x,y=i\Delta y,t=n\Delta t$, take $D^{n}And{D}^{n+1}$ Substituting into dispersive medium maxwell Fang Chengzhong , The electric field difference equation of dispersive medium is obtained ：

$$\begin{gathered} E_x^{n,s}(i,j)=\frac{{\epsilon }_{\infty }{\epsilon }_0}{{\epsilon }_{\infty }{\epsilon }_0+\sigma \Delta t+{\epsilon }_0{\chi }^0}{E}_x^{n-1,s}(i,j)- \\ \frac{\sigma \Delta t}{{\epsilon }_{\infty }{\epsilon }_0+\sigma \Delta t+{\epsilon }_0{\chi }^0}{E}_x^{n,i}(i,j)+ \\ \frac{{\epsilon }_0}{{\epsilon }_{\infty }{\epsilon }_0+\sigma \Delta t+{\epsilon }_0{\chi }^0}{\Psi }_x^n(i,j)- \\ \frac{({\epsilon }_{\infty }-1){\epsilon }_0\Delta t}{{\epsilon }_{\infty }{\epsilon }_0+\sigma \Delta t+{\epsilon }_0{\chi }^0}\frac{\partial E_x^{n,i}(i+1/2,j)}{\partial t}- \\ \frac{{\epsilon }_0\Delta t}{{\epsilon }_{\infty }{\epsilon }_0+\sigma \Delta t+{\epsilon }_0{\chi }^0}\frac{\partial }{\partial t}{\int }_0^n{E}_x^i(t-\tau )\chi (\tau )d\tau + \\ \frac{\Delta t}{{\epsilon }_{\infty }{\epsilon }_0+\sigma \Delta t+{\epsilon }_0{\chi }^0}[\frac{H_z^{n-1/2,s}(i,j)-H_z^{n-1/2,s}(i,j-1)}{\Delta y}] \end{gathered}$$

among
$${\Psi }_x^n(i,j)=E_s^n(i,j)\Delta {\chi }^0+{\Psi }_x^{n-1}(i,j)e^{-{\nu }_c\Delta t}$$

$${\chi }^0=\frac{{\omega }_p^2}{{\nu }_c}\Delta t-(\frac{{\omega }_p}{{\nu }_c}{)}^2[1-e^{-{\nu }_c\Delta t}]$$

$$\Delta {\chi }^m=-(\frac{{\omega }_p}{{\nu }_c}{)}^2{e}^{-m{\nu }_c\Delta t}[1-e^{-{\nu }_c\Delta t}{]}^2$$

$$\chi (\tau )=\frac{{\omega }_p^2}{{\nu }_c}[1-e^{-{\nu }_c\tau }]U(\tau )$$

Through the above analysis, free space 、 Perfect matching layer 、 The surface electromagnetic enhancement of nanoparticles is simulated by setting dispersive media respectively

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Analysis of simulation results

Sure ？ See the plane wave incident spectral enhancement factor （$|\frac{E}{E_0}{|}^2$） Concentrated at the junction and edge of the two nanoparticles , The enhancement of the junction reflects Interaction of nanoparticles under light wave irradiation Influence on the spectrum

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Conclusion

By changing the different parameters of metal nanoparticles , Under the irradiation of terahertz wave , Different electromagnetic enhancement effects are obtained

• It is proved that terahertz wave also has electromagnetic enhancement effect on the surface of metal nanoparticles

bring Surface enhanced Raman scattering SERS, From visible light + The infrared band is extended to THz Band

bring SERS Combined with terahertz wave Make it possible （2013）

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problem

2022 Year now ,SERS And THz How is the combination ？ What are the results ？

Right now SERS Has the reason for the mechanism been modified ？

Chemical enhancement and THz What are the combined results ？

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