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Channel Multiplexing Techniques 395

White light
1 + 2 + ... + N
1
2

N * 1

N

Figure 9.5 Wavelength separation using a prism.

(or combines) the different colors of white light, as shown in Fig. 9.5. But the angular separations provided by
the prism are not large enough to separate the wavelengths of a WDM signal. The multiplexers can be divided
into two categories: (i) interference-based multiplexers use Mach–Zehnder or other types of interferometer;
(ii) diffraction-based multiplexers make use of diffraction to spatially separate the wavelengths. Examples
include prisms and gratings.

9.3.1.1 Mach–Zehnder Interferometer-Based Demultiplexer

Mach–Zehnder interferometers can be cascaded to form a 1 × N demultiplexer [2–5]. Let us first consider the
theory of the 1 × 2 demultiplexer that separates two wavelengths. Fig. 9.6 shows a schematic of the demulti-
plexer. The 3-dB coupler is described by a matrix,
[ ]
1 1 i
M coupler = √ . (9.28)
2 i 1
The outputs of the 3-dB coupler 1 are
A co1 = M coupler A , (9.29)
out
in
where [ ]
A 0
A = 0 , (9.30)
in
A is the input field envelope. Substituting Eqs. (9.28) and (9.30) in Eq. (9.29), we find
0
√
A co1 = A ∕ 2, (9.31)
out,1 0
√
A co1 = iA ∕ 2 (9.32)
out,2 0
L + ΔL/2
Port 1
3-dB 3-dB
Coupler 1 Coupler 2
A 0 Port 2
L * ΔL/2

Figure 9.6 1 × 2 wavelength demultiplexer.