Guided Modes in Channel Waveguides

Guided Modes in Channel Waveguides

In general, the integrated photonic devices presented in Chapter 1 are based on channel
(or 2D) waveguides, in which the light is confined in two directions, allowing the
propagation in only one direction, in contrast with the planar waveguides studied in
the previous sections, where light is confined only in the direction perpendicular to
the interfaces. In this way, radiation travelling in channel waveguides can propagate
without suffering diffraction, that will otherwise give rise to power loss. Therefore, for
performing functions such as modulation, switching, amplification, etc., the channel
waveguide is the right choice for the fabrication of integrated optical devices.
The most common geometries used for the definition of channel waveguides in
integrated photonic devices are the stripe and the buried waveguides (Figure 3.32).
The rib waveguide can be considered to be special case of stripe waveguide, as was
explained in Section 3.1. Stripe optical waveguides are widely used for semiconductorbased
photonic chips, such as GaAs or InP, and also in polymeric-based integrated
photonic devices. Channel waveguide fabrication involves a selective etching of a
high index film previously deposited onto a low index substrate. The etching can be

performed by means of physical methods (ion milling) or chemical methods (solvents,
acids, etc.), or even by a combination of both, such as in reactive ion etching (RIE)
[13]. In general, stripe and rib waveguides tend to have relatively high propagation
losses (∼1 dB/cm) due to the roughness of the top and lateral walls which define
the optical channels. One way of reducing losses in these waveguides is to deposit a
cladding material covering the channels, which also serves as a protection layer against
environmental chemical agents.
Buried waveguides are fabricated by the refractive index increase of a substrate, in
regions previously defined by appropriate photolithographic masks. The index increase
is usually carried out by diffusion processes, and because of that, the channel waveguides
fabricated following this method give rise to graded-index profiles [14]. The
main advantage of this type of channel waveguides, typical in glasses and ferro-electric
materials, is the low propagation losses that can be achieved (less than 0.1 dB/cm).
Also, buried channel waveguide geometry allows easy placing of the metallic control
electrodes, such as in the case of electro-optic modulators and switches.
When dealing with planar waveguides, whether step-index or graded index structures,
light propagation can be described in terms of two mutually orthogonal polarisations,
namely, the TE and TM propagating modes. In contrast, in channel optical waveguides
there are no pure TE or TM modes, but instead there are two families of hybrid
transversal electromagnetic modes (TEM). Fortunately, the TEM modes that propagate
in channel waveguides are strongly polarised along the x or y direction (z being the
direction of propagation of light), and therefore a classification can be made according
to the major component of the electric field associated with the electromagnetic
radiation. Optical modes having the main electric field component along the x axis are
called Ex
pq modes, and behave very similarly to the TM modes in a planar waveguide.
For this reason, they are known as quasi-TM modes. The subscripts p and q denote
the number of nodes of the electric field Ex in the x and y direction, respectively.
Accordingly, the Ey
pq modes have Ey as the major component of the electric field, and
are closely related to the TE modes in a planar waveguide, and can be considered as
quasi-TE modes.
An exact treatment of the modal characterisation in 2D waveguides is not possible,
even in the simplest case of a symmetric rectangular channel waveguide. Therefore,
in order to solve this problem, some approximation should be made, and there are
several numerical methods which yield good results in general. Here we will explain
two widely used methods: Marcatili’s method and the effective index method. While
the first one allows us to calculate the electromagnetic field in a rectangular channel
waveguide (with a homogeneous central core), with the latter we can obtain the optical

modes supported by a channel waveguide with arbitrary geometry, even with graded
index regions (whether the core or the surroundings).