WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

4.4 Ridge waveguides 39
w
ε =1
?
ε
a) b) c)
Figure 4.7 a) Design problem for a 2D model of a photonic ridge waveguide splitter.
The objective is to distribute 50% of the input energy into the top and bottom output
ports and thus avoid reflection and radiation at the T-junction, b) optimized design for
E-polarized waves, c) optimized design for H-polarized waves. Black: dielectric material,
light gray: air. From paper [17].
4.4 Ridge waveguides
The examples of optimized waveguide components are all based on waveguides
carved out in photonic crystal structures. This provides a basis for confinement
of the light which is very useful for waveguiding purposes. However, another type
of waveguides, denoted strip or ridge waveguides, are applicable to photonic circuits
as well. These consist of dielectric strips with a rectangular cross section placed on
a substrate and surrounded by air. Such strips may provide perfect waveguiding for
straight guides. However, the problems at bends and junctions are even more severe
than for photonic crystal waveguides in that the waves are no longer confined to the
guide and thus additional in-plane scattering losses may be induced.
Nevertheless, the same design procedure can be applied as for the photonic crystal
waveguide components. Fig. 4.7a shows an optimization problem for the design
of a T-junction in a 2D model of a ridge waveguide. The optimized junctions in
Fig. 4.7b,c correspond to the case of E- and H-polarized waves, respectively. In both
cases the optimization is performed for waves with a wavelength close to 1550nm
which is relevant for telecommunication purposes 4 .
For both optimized junctions the obtained efficiency is close to 100% near the
wavelength 1550nm, yet, the required junction area is larger (relative to the strip
width w) for the case of the E-polarized waves (Fig. 4.7b). This is due to the
wavelength/strip width ratio being larger for this polarization. If a smaller design
domain is used, the efficiency is reduced accordingly. Fig. 4.7c illustrates also that
4 It should be noted that the two different polarizations correspond to two different values of
the strip width w and dielectric constant ε.