Tissue Engineering And Nanotheranostics

“9.61x6.69” b2815 Tissue Engineering and Nanotheranostics

Plasmonic Nanoparticles Application in Biosensor and Bioimaging 157

We may therefore recast Equations (1) and (2) in the form:

() ()()

() ()()

1

1

/

,

/

n nn

n

nn

n

D mx m x x

x

a

n

D mx m x x

x

ψψ

ξξ

−

−

+−



=



+−



(13)

() ()()

() ()()

1

1

,

n nn

n

nn

n

mD mx x x

x

b

n

mD mx x x

x

ψψ

ξξ

−

−

+−



=



+−



(14)

where we have used the recurrence relations:

11 () ()()

21

n nn,

n

x xx

x

ψψψ+−

+

=−

ξψχnn n=−i , (15)

1

1

n.

n

n

D

n

ρ D

ρ

− =−

+

These relations are evaluated beginning with:

ψψ−^10 ()()()()x x xx==cos , sin ,

χχ−^10 ()()()()xx x x==sin , cos , (16)

where DiNmax=+0.0 0.0,

1

Nmax=+++Maxx 4 x^3 2,mx 15.



2.4. Nanoparticle Coupled Models

Nobel nanoparticles interact with induced light to produce the LSPR

phenomenon. When two or more nanoparticles move close to each