Nanotechnology-Enabled Sensors

3.3 Optical Waveguide based Transducers 67
gation of optical waves and transducers based on surface plasmon (SP)
waves. Prior to presenting them, information regarding light propagation
and the sensitivity of such waveguides is first provided.
3.3.1 Propagation in Optical Waveguides
The propagation of optical waves is generally evanescent, meaning that
they decay exponentially with distance from the point at which they are
sourced. However, we usually refer to waves as propagating waves, if they
can propagate for relatively long distances before losing their intensity.
The optical waves are transverse, as they oscillate perpendicularly to the
direction of propagation, as in Fig. 3.4. An optical waveguide is a path
which confines optical waves within one or two dimensions. Depending on
the waveguide, only certain propagating waves, or guided modes, are possible.
All optical modes may consist solely of the electrical or magnetic
wave components, or they may be a combination of both.
y
z
Oscillation perpendicular to propagation direction
H
x
Fig. 3.4 Propagation of a transverse optical waves.
E
The guided waves in a planar optical waveguide, confined in two dimensions,
are either TMm (transverse magnetic or p-polarized) or TEm
(transverse electric or s-polarized), where m is an integer called the mode
number. 2 At any time, t, a single frequency (monochromatic) propagating
mode in the x direction may be represented by the function 3 :
i x
( k x−ωt
)
Propagation direction
f ( x,
t)
= e , (3.5)
where ω = 2πf is the angular frequency and kx is the propagation constant
in x direction.
One of the most important parameters in sensing applications is the effective
refractive index, N, as the device’s sensitivity directly depends on