Page 210 - Principles and Applications of NanoMEMS Physics

5. NANOMEMS APPLICATIONS: PHOTONICS 199

that is, when an incidence angle θ exists at which the sum or difference of
0
the component of the light wave vector and a multiple of the grating
reciprocal lattice vector equal an SP wave vector. Reduction of an SP vector
by k∆ transforms it into light, whereas addition of k∆ to the light’s
x x
wave vector transforms it into an SP.
In the ATR method, , see Fig. 5-4, the wave vector of light impinging
upon a hemispherical prism of dielectric constant ε and the metal interface
0
at an angle θ resolves its wave vector into components that are
0
perpendicular and parallel to the prism-metal interface. In this case, coupling
between light and SPs occurs when the component of the light’s wave vector
along the interface, k = ε ω sin θ c , equals the SP wave vector,
x 0 0
k = ω ε ε c ε + ε . If the metal thickness is finite, e.g., of extent d,
SP 1 2 1 2
there exists the possibility that for a certain value of d, the evanescent field at
the ε / ε interface may couple to the lower ε / ε interface, where it
0 1 1 2
could also excite SPs [215], see Fig. 5-14.

ω ω Norm
Norm al al
c c
ω ω
0 ε 0 ε
c c
θ θ
ε ε 0 0
k’
k’ x x
d d ε ε 1 1

ε ε 2 2

Figure 5-4. Concept of ATR coupler. A metal layer of thickness d and dielectric constant ε
1
is sandwiched between a prism of dielectric constantε and a dielectric ε . (After [215].)
0
2

5.3.2 One-Dimensional Surface Plasmon Propagation

Once light has been converted into SPs, the next question is how to
provide efficient energy guidance. To elucidate the issues involved, a
number of studies on surface plasmon propagation, utilizing various forms of
waveguide, have been undertaken.