Chapter 10
WDM concepts and components
10.1 Operational principle of WDM
10.2 Passive Components
- The 2x2 Fiber Coupler
- Scattering Matrix Representation
- The 2x2 Waveguide Coupler
- Mach-Zehnder Interferometer Multiplexers
- Fiber Grating Filters
10.3 Tunable Sources
10.4 Tunable Filters
- System considerations
- Tunable filter types
- Outline
10.1 Operational Principle of WDM
¾ What is WDM : The technology of combining a number of wavelengths
onto the same fiber is known as wavelength-division-multiplexing or WDM
¾ DWDM : dense wavelength-division-multiplexing (channel spacing is
dense)
10.1 Operational Principle of WDM
¾ ITU (International Telecommunication Union) specify channel spacing in
terms of frequency
-
C band (conventional band) : 1524 – 1560 nm
L band (longer wavelength band) : 1570 – 1610 nm
frequency reference 193.10 THz (1552.524 nm)
Channel spacing: 200 GHz, 100 GHz, 50 GHz, 25 GHz
ITU GRID TABLE (part of it)
Channel
#
Frequency
(GHz)
Wavelength
(nm)
557
192700
1555.75
553
192750
1555.34
549
192800
1554.94
545
192850
1554.54
541
192900
1554.13
537
192950
1553.73
533
193000
1553.33
529
193050
1552.93
10.1 Operational Principle of WDM
¾ Frequency spacing, wavelength spacing:
⎛ c ⎞
Δν = ⎜ 2 ⎟ Δλ ,
⎝λ ⎠
(10 − 1)
Example 10-1
If one takes a spectral band of 0.8 nm (or, equivalently, a mean
frequency spacing of 100 GHz) within which narrow-linewidth lasers are
transmitting, ask how many channels can be sent in the 1525-to-1565nm band on a single fiber.
¾ Advantages:
-
Capacity upgrade
Transparency: each optical channel can carry any transmission format
(asynchronous and synchronous digital data; analog information)
Wavelength routing
Wavelength switching
10.1 Operational Principle of WDM
¾ Key feature of WDM is that the discrete wavelengths form an orthogonal set of
carriers that can be separated, routed and switched without interfering each other
¾ The implementation of WDM networks requires a variety of passive and active
devices to combine, distribute, isolate, and amplify optical power at different
wavelength.
¾ Active devices: Tunable optical filters, tunable sources, optical amplifier, etc.
¾ Passive devices: Multiplexer / Demultiplexer, Add/drop filters Æ couplers, grating, etc
10.2 Passive Components
¾ Passive devices operate completely in the optical domain to split or
combine light stream
¾ Three fundamental technologies for making passive components are
based on optical fibers, integrated optical waveguides, and bulk microoptics.
10.2.1 The 2x2 Fiber Coupler
2x2 coupler:
Input P0
Throughout power P1, P2
Crosstalk: P3 , P4
10.2 Passive Components
10.2.1 The 2x2 Fiber Coupler
¾ For ideal coupler :
P2 = P0 sin 2 (κz ), (10 − 2)
P1 = P0 cos 2 (κz ), (10 − 3)
z : coupler drawing length
κ : coupling coefficient describing the
interaction between the fields in the two fibers
¾ Fused coupler can be used as a
WDM (see next slide)
10.2.1 The 2x2 Fiber Coupler
¾ Principle : Multiplexer / Demultiplexer (MUX/DEMUX) using fused coupler :
¾ Also called WDM :
such as, WDM (980/1550 nm)
WDM (1480/1550 nm)
P2 = P0 sin 2 (κz ), (10 − 2)
P1 = P0 cos 2 (κz ), (10 − 3)
z : coupler drawing length
κ : coupling coefficient describing the
interaction between the fields in the two fibers
Question 10-3
consider the coupling ratios as a function of pull lengths as shown in fig p103 for a fused biconical tapered coupler. The performance are given for 1310
nm and 1540 nm operation. Discuss the behavior of the coupler for each
wavelength if it pull length is stopped at the following points: A, B, C, D, E,
and each F.
10.2 Passive Components
10.2.1 The 2x2 Fiber Coupler
¾ Parameters :
-
Coupling ratio (splitting ratio)
Excess loss
Insertion loss
Crosstalk
⎛ P2
Coupling ratio = ⎜
⎝ P1 + P2
⎞
⎟ × 100%, (10 − 4)
⎠
⎛ P0
Excess loss=10log ⎜
⎝ P1 + P2
⎛P
Insertion loss=10log ⎜ i
⎜ Pj
⎝
i: input; j: output
⎛P
Crosstalk loss=10log ⎜ 3
⎝ P0
⎞
⎟ , (10 − 5)
⎠
⎞
⎟⎟ , (10 − 6)
⎠
⎞
⎟ , (10 − 7)
⎠
Example 10-2
A 2x2 biconical tapered fiber coupler has an input optical power level of
P0=200μW. The output powers at the other three ports are P1=90μW P2=85μW
and P3=6.3nW. Find coupler ratio, excess loss, insertion loss, and crosstalk.
10.2 Passive Components
10.2.2 Scattering Matrix Representation
¾ One can analyze a 2x2 guided-wave coupler as a four terminal device that has
2 inputs and 2 outputs by using matrix method
Scattering Matrix
⎡ a1 ⎤
⎥
⎣ 2⎦
Input field: a = ⎢ a
⎡ b1 ⎤
⎥
⎣ 2⎦
Output field:b = ⎢ b
Coupler :
Assume coupler is lossless :
I0 =b1*b1 + b2*b2 = a1*a1 + a2* a2
j ε ⎤
⎥
1 − ε ⎦⎥
s12 ⎤
s 22 ⎥⎦
b = S ⋅a
and
One can find the matrix for coupler :
⎡ 1− ε
S=⎢
⎣⎢ j ε
⎡s
S = ⎢ 11
⎣ s 21
ε : coupling ratio from port a1 to port b2
⎡ b1 ⎤ ⎡ s11
⎢b ⎥ = ⎢s
⎣ 2 ⎦ ⎣ 21
s12 ⎤ ⎡ a1 ⎤ ⎡ a1s11 + a 2 s12 ⎤
⋅⎢ ⎥ = ⎢
⎥
s22 ⎦ ⎣ a 2 ⎦ ⎣ a1s21 + a 2 s22 ⎥⎦
Example 10-3
Assume we have a 3-dB coupler,
so that half of the input power
gets coupled to the second fiber.
Find coupling ratio of the coupler
and coupler matrix.
10.2 Passive Components
10.2.3 The 2x2 waveguide coupler
¾ Wavewguide devices have an intrinsic wavelength dependence in the
coupling region (guide width w, gap s, and refractive index)
¾ Loss in semiconductor waveguide devices:
0.05 < α < 0.3 cm-1
P2 = P0 sin 2 (κz )e −α z , (10 − 18)
α ; optical loss coefficient
z : coupler drawing length
κ : coupling coefficient describing the
interaction between the fields in the two fibers
10.2 Passive Components
10.2.3 The 2x2 waveguide coupler
P2 = P0 sin 2 (κz )e −α z , (10 − 18)
α ; optical loss coefficient
z : coupler drawing length
κ : coupling coefficient describing the interaction
between the fields in the two fibers
¾ Complete power transfer to the 2nd guide occurs when the guide length L is :
L=
π
(2m + 1),
2κ
with m = 0,1, 2... (10 − 21)
Example 10-4
A symmetric waveguide coupler has a coupling coefficient κ = 0.6 mm-1.
Find the coupling length for m=1
10.2 Passive Components
10.2.5 Mach-Zehnder Interferometer Multiplexers
¾ Wavelength-dependent multiplexer/demultiplexer (WDM) can be made using
Mach-Zehnder (MZ) interferometers.
¾ 2x2 MZ interferometer consists of 3 stages: 3-dB splitter, phase shift, 3-dB
combiner.
¾ Due to the phase shift between the two arms, the recombined signals will
interference constructively at one output and destructively at the other :
Demultiplexer (Demux) : Ein,1 will separate at Eout,1, Eout,2
Multiplexer (Mux) : Both outputs Eout,1 and Eout,2 combine at Ein,1
λ1, λ2
λ1
λ2
10.2.5 Mach-Zehnder Interferometer Multiplexers
How to find output P1 and P2 by using matrix method ?
¾ Write matrix for each stage:
- phase shift : MΔφ
- 3-dB splitting coupler : Mcoupler
- 3-dB combining coupler : Mcoupler
¾ Obtain the total matrix for MZ interferometer :
M=M coupler ⋅ M Δφ ⋅ M coupler
¾ Find output E-field Eout,1 and Eout,2 :
⎡ E out,1 ⎤
⎡ E in,1 ⎤ ⎡ M 11
=
⋅
M
⎢E ⎥
⎢E ⎥ = ⎢
⎣ out,2 ⎦
⎣ in,2 ⎦ ⎣ M 21
M 12 ⎤ ⎡ E in,1 ⎤
⋅⎢
⎥
⎥
M 22 ⎦ ⎣ E in,2 ⎦
¾ Find output power (or intensity) Pout,1 and Pout,2 :
2
Pout,1 = E out,1 =E out,1 ⋅ E
*
out,1
;
2
Pout,2 = E out,2 =E out,2 ⋅ E *out,2
10.2.5 Mach-Zehnder Interferometer Multiplexers
¾ Details for matrix of each component :
3-dB splitting coupler : Mcoupler
⎡ s11
M
=
Coupler matrix : coupler ⎢
⎣ s21
s12 ⎤ ⎡ cos κd
=⎢
⎥
s22 ⎦ ⎣ jsinκd
3-dB coupler matrix (no loss) : M 3-dB coupler =
j sin κd ⎤
, (10 − 29)
⎥
cos κd ⎦
1
2
⎡1 j ⎤
⎢ j 1 ⎥ , (10 − 30)
⎣
⎦
2π n1
2π n2
phase shift : MΔφ
L−
( L + ΔL ), (10 − 31)
Δφ =
λ
λ
Assuming same sources for the two arms,
phase shift due to the arm length difference: Assume: n1=n2=neff ; k =2πneff/λ ,
Δφ = k ΔL ,
(10 − 32)
Matrix of the phase shift :
M Δφ
⎡ e jk ΔL / 2
=⎢
⎣ 0
⎤
, (10 − 33)
− jk ΔL / 2 ⎥
e
⎦
0
Total matrix : M
⎡M
M=M coupler ⋅ M Δφ ⋅ M coupler = ⎢ 11
⎣ M 21
M 12 ⎤
=
⎥
M 22 ⎦
⎡ sin( k ΔL / 2) cos( k ΔL / 2) ⎤
j⎢
⎥
⎣ cos( k ΔL / 2) − sin( k ΔL / 2) ⎦
(10 − 35)
10.2.5 Mach-Zehnder Interferometer Multiplexers
¾ Find output E-field Eout,1 and Eout,2 :
⎡ E out,1 ⎤
⎡ E in,1 ⎤ ⎡ M 11
M
=
⋅
⎢E ⎥
⎢E ⎥ = ⎢
⎣ out,2 ⎦
⎣ in,2 ⎦ ⎣ M 21
M=M coupler ⋅ M Δφ ⋅ M coupler
⎡ M 11
=⎢
⎣ M 21
M 12 ⎤ ⎡ E in,1 ⎤
⋅⎢
⎥
⎥
M 22 ⎦ ⎣ E in,2 ⎦
M 12 ⎤
=
M 22 ⎥⎦
⎡ sin( k ΔL / 2) cos( k ΔL / 2) ⎤
j⎢
⎥
⎣ cos( k ΔL / 2) − sin( k ΔL / 2) ⎦
E out,1 =j ⎡⎣ Ein ,1 sin( k ΔL / 2) + Ein ,2 cos( k ΔL / 2) ⎤⎦
(10 − 36)
E out,2 =j ⎡⎣ Ein ,1 cos( k ΔL / 2) + Ein ,2 sin( k ΔL / 2) ⎤⎦
(10 − 37)
Assume that Ein,2 = 0,
E out,1 =j ⎡⎣ Ein ,1 sin( k ΔL / 2) ⎤⎦
E out,2 =j ⎡⎣ Ein ,1 cos( k ΔL / 2) ⎤⎦
¾ Find output power (or intensity) Pout,1 and Pout,2 :
*
Pout,1 =Eout,1 Eout,1
=Pin ,1 sin 2 ( k ΔL / 2)
*
Pout,2 =Eout,2 Eout,2
=Pin ,1 cos 2 ( k ΔL / 2)
(10 − 35)
10.2.5 Mach-Zehnder Interferometer Multiplexers
¾ Spectrum or magnitude response of Pout,1 and Pout,2:
Ref: “optical filter design and analysis”p167
*
Pout,1 =Eout,1 Eout,1
=Pin ,1 sin 2 ( k ΔL / 2)
*
Pout,2 =Eout,2 Eout,2
=Pin ,1 cos 2 ( k ΔL / 2)
¾ Maximum and minimum of Pout,1 and Pout,2:
When: k ΔL / 2 = mπ
k ΔL / 2 = mπ
Δf =
Pout,1= 0; Pout,2= 1
Frequency spacing for bar or cross:
c
neff ΔL
neff: effective refractive
index of a waveguide
¾ This gives rise to the frequency spacing for the two Mux/Demux frequency is
c
Δf / 2, i.e.,
,
(10 − 41) (different approach with our books)
Δf =
2neff ΔL
10.2 Passive Components
10.2.5 Mach-Zehnder Interferometer Multiplexers
Example 10-6
Assume that the input wavelengths of 2x2 silicon MZI are separated by 10
GHz (i.e., Δλ =0.08 nm at 1550 nm). With neff =1.5 in a silicon waveguide, find
the waveguide length difference ΔL.
¾ Example of 4x4 MZI:
c
2 neff (2Δν)
(10-42)
c
= 2ΔL1
2neff ( Δν)
(10-43)
ΔL1 = ΔL2 =
ΔL3 =