Accurate Modeling of Optical Multiplexer/Demultiplexer Concatenation
in Transparent Multiwavelength Optical Networks

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I. INTRODUCTION
IN TRANSPARENT multiwavelength optical networks,
each lightwave signal may be optically multiplexed/demultiplexed
several times during propagation from its source
to its destination [1]. Optical multiplexers/demultiplexers
(MUXs/DMUXs) exhibit nonideal amplitude and phase
transfer functions within the optical signal band. That is, their
amplitude transfer functions might present passband curvature,
tilt, and ripple. In addition, their phase transfer functions
might not vary linearly with frequency. These impairments are
enhanced when a large number of these devices are cascaded
together.



II. THEORETICAL MODEL
This section is divided into five parts. The first topic that is
treated is the representation of an optical network topology by
two separate equivalent channels for the signal and the ASE
noise, respectively. For illustrative purposes and without loss of
generality, a chain of optical network elements is studied, since
it is the elementary building block of more complex network
topologies. In addition, a reference network is defined and is
used for comparison with the actual network.


Signal and Noise Representation
For mathematical convenience, a low-pass equivalent representation
[49] of the optical signals and components is used in
the following. To distinguish vectors from scalars, we identify
vector quantities with boldface type. Matrices are also denoted
by boldface type. The distinction should be clear from the context.