Biomedical Engineering Reference
In-Depth Information
1500
1400
1300
1200
1100
1000
900
800
700
600
0
5
10
15
aspect ratio
Figure 12.2
Fabry-Perot resonance wavelengths of an 85 nm wide gold
nanorod as compared with experimentally measured resonances. Adapted
from Ref. (Gordon, 2009)with permission.
where
β
is given by Eq. 12.2 above,
φ
is the phase of reflection.
Of course, this equation requires a way to solve for the phase of
reflection.
Simplesinglemodematchingcanbeusedtoderivethereflection
amplitude and phase for a narrow wire, where it is assumed
that there is only a single mode along the wire and that this is
matchedtoacontinuumoffree-spacemodeswiththesameuniform
azimuthal symmetry (Gordon, 2009). Figure 12.2 shows the Fabry-
Perot resonances calculated for a 85 nm wide gold wire with
aspect ratios, and compared with the measured resonances from
experiment (Payneet al., 2006).
For rounded ends, an approximate expression for the phase of
reflection has been assumed (Novotny,2007):
φ
=
2
β
a
(12.5)
to give an effective wavelength scaling in designing resonant
nanoantennas.
