1 Introduction to Laser Micro-to-Nano Manufacturing
19
Fig. 1.12 Mode field distributions of dielectric optical nanofibers with thicknesses of a 400 nm
and b 200 nm, respectively.
in which
U = a(k
2
0 n
2
1 − β
2
)
1/2
W = a(β
2
− k
2
0 n
2
2 )
1/2
V = k 0 a
n
2
1 − n
2
2
J v and K v is the Bessel function of the first kind and the modified Bessel function
of the second kind.
Figure 1.12 demonstrates the field distributions of nanofibers with diameters of
400 and 200 nm. A thinner nanofiber leads to a larger fractional evanescent fields
which intrigue new opportunities for nanoscale light manipulation [80].
Surface Plasmon Polaritons (SPPs) are the coherent longitudinal charge oscillations of the conduction electrons coupled to the electromagnetic field at the interface
of a metal and a dielectric, and are able to propagate along the interface [24]. Electromagnetic waves can be tightly confined around the interface in evanesce waves
form with exponential distributions outwards from the dielectric-metal interfaces to
both sides of metal and dielectric. [70] For plasmonic nanofibers, the fields decay
exponentially in both the metal core and surrounding medium. The optical properties of SPPs can be deduced from Maxwell’s equations of macroscopic electromagnetism and solve Helmholtz equation. The electromagnetic waves propagation along
z directions matches the equations
β
2
+ k
2
x + k
2
y = ε m μ 0 ω
2
(1.2.18)
β
2
− κ
2
x − κ
2
y = ε d μ 0 ω
2
(1.2.19)