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176 5 Near Field
480 nm

(a) d = 34 nm
(b) d = 68 nm
280 nm (c) d = 136 nm

d
640 nm
Clad
Core
320
nm Clad

Plane wave
Fig. 5.9. 2-D Cartesian computational domain of 480 nm × 640 nm for calculation
of E x around tapered fiber end with silica core and perfect conductor clad. Here,
the refractive index and electrical permittivity of silica are 1.46 and 2.25ε r,(ε r:
free-space permittivity), respectively

Example 5.4. Compute the scattered light field from an optically trapped gold
particle in the evanescent light, which is produced by a total reflection on a
prism–air interface.

Solution. First, we produce an evanescent light by the incident s-polarized
plane wave expressed by the followingequations at an angle of θ =45 with
◦
a wavelength of λ = 488 nm:
√

ε r
E z (i, j)=sin 2πf n∆t − (i − 1)∆x sin θ ,
c
√
1 ε r ∆y

H y (i, j)= − sin 2πf n − ∆t − (i − 1)∆x sin θ + cos θ
2 c 2
√
ε r
× cos θ,
Z
√ √

1 ε r ε r
H x (i, j)=sin 2πf n − ∆t − (i − 1)∆x sin θ × sin θ.
2 c Z
Here, f = c/λ, c is the speed of light in vacuum, ε r is the free-space permit-
tivity and Z is the intrinsic impedance.
Next, a 100-nm-diameter perfect conductor sphere is located 10 nm above
the surface of the prism and the electromagnetic field near the surface is