Download Lecture Optical Communications Optical Filters Prof. Dr.-Ing. Dipl.-Wirt.-Ing. Stephan Pachnicke

Lecture
Optical Communications
Optical Filters
Prof. Dr.-Ing. Dipl.-Wirt.-Ing. Stephan Pachnicke
Optical Filters
Applications:
• Noise reduction (ASE noise of optical amplifiers)
• De-multiplexer in WDM-systems  Bandpass filter bank for selection of (wavelength-)
channels, bandwidth ≈ channel spacing
1
2
3
4
1 2 3 4
1 2 3 4
MUX
DMUX
1
2
3
4
• Mux and Demux in network elements (add-drop multiplexer, wavelength routers)
08 – Filters
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Applications
• Dispersion compensation (delay filter with linear group delay)
g(f)|Filter
fT
f
g(f)|SSMF
ok_6_filteranwend.dsf
• Equalization of frequency response of EDFA (power gain spectrum is not flat!) .
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Technology & Properties
Technologies:
• Integrated optical wave-guides based on Si, InGaAs, polymer  planar light-wave
circuits (PLC) = photonic integrated circuits (PIC)
• Free space optical filters
• Filters based on optical fibre
Properties:
• Optical filters can be described by transfer functions H(f) (magnitude |H(f)| and phase
b(f) = -arg{H(f)} response) for the optical field  power transfer function |H(f)|2
• Filter function in bandpass domain at optical fc. May be transformed to equivalent LP
domain by BP-LP transformation
• We may want to tune the center frequency (tuneable filters) or the filter bandwidth
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Filter Parameters

Attenuation

Bandwidth (1dB, 3dB)

Crosstalk (Isolation)
CW
1dB
 To adjacent channels
 To non-adjacent channels
Außerband:
Pumpwellenlängen und
ASE-Unterdrückung
I ADJ
 Phase response
I ASE
I 980
I 1480
I NADJ
 Dispersion
 Ripples

Polarization dependence
 Polarization mode dispersion (PMD)
 Polarization dependent loss (PDL)


Passive / active
Ci

Ci+1
 Ci+2
 Is temperature control required?
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Fabry-Perot Filter (Dielectric Filter)
Also called “etalon” (e.g. used as laser resonator)
Cavity (Resonanzraum)
n
E0 t1e- z
t1
r1
E0t1t2e- L
r 2 t2
E0t1t2r1r2e- L
L
Facet
(Spiegel)
oc_6_filter.dsf
z
t1,t2: transmission- r1,r2 reflection coefficients of facets
2 n
2 n f
 /2 j
Propagation constant:    / 2  j    / 2  j

c
E-field at right output of mirror (facet):
Et  E0t1t2e L 1  r1r2e 2 L  (r1r2e 2 L ) 2 

6
 L
  t1t2e
E
 1  r r e2 L 0
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Calculation of Transfer Function
GFP 
| Et |2
| t1t2e  L |2

| E0 |2 |1  r1r2e 2 L |2
With power reflection coefficient:
R1  r12 , R2  r22
and no loss at facets:
GFP 
finally for
t12  r12  1
t1  1  r12 , t2  1  r22
 L
(1  R1 )(1  R2 )e
(1  R1R2 e L )2  4 R1R2 e L sin 2 (  L)
R1  R2  R,   0
1
GFP ( f ) 
1
LM 2 R sin( 2 n L f )OP2
c
N1  R
Q
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Power Transfer Function
In f periodic transfer function
GFP(f) = max if:
f k
c
, k  0,1,2,...
2nL
i.e. choose n and L such that waves add constructively at filter output
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Calculation of Free Spectral Range
Free Spectral Range (FSR) = distance between peaks
f 
c
2nL
Full Width at Half Maximum (FWHM) bandwidth:
BFWHM 
c
nL
FG 1  R IJ
H2 RK
arcsin
Finesse:
F
f
 R

BFWHM 1  R
for large
R 1
Typical values: insertion loss 1…2dB, Finesse > 150
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08 – Filters
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Filter Tuning
Change Cavity-length L or refractive index n by
• Mechanical displacement of mirrors (facets)
• Piezo-electrical material  Cavity length is reduced by ext. appl. voltage
Multistage Filters
Cascade of F-P filters with various values of FSR
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Bragg Gratings
A Bragg Reflector is a periodic array of reflective “mirrors” (made from any boundary surface
like refractive index step changes). Maximum reflectivity occurs, if distance between mirrors
is such that reflected waves from all mirrors superimpose constructively. I.e. if the distance of
mirrors is related to half wavelength, resulting in full wavelength optical path difference of all
reflected waves.
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Fiber Bragg Gratings
Piece of single mode fiber, where “mirrors” are implemented by
refractive index variations of fiber core along z.
Interaction between forward and backward travelling waves
described by a pair of coupled mode equations
Solution for reflected optical field (for uniform grating)
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08 – Filters
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Fiber Bragg Grating Properties
Frequency response for the reflected optical field:
r ( L,  ) 
| A2 ( z  0) |
 j B sinh (L)

| A1( z  0) | j  cosh (L)   k sinh (L)
with:
B 
 (n3  n2 )


k 
1

1
   B2  (k ) 2
 /(2neff ) 
where  fraction of
wave intensity in core (e.g. 0,6)
n  n3  n2
typically 10-5 …10-3
Maximum power reflectivity R=|r|2 at
Bragg wavelenght:
Bandwidth:
 
Rmax  R (k  0)  tanh 2 ( B L)
B2
 2  ( B L)2
 neff L
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Spectra
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08 – Filters
Applications
Band pass filters: a circulator drops the reflected (backwards) wave (4) at port 3
Band stop filter: transmitted wave
Add-Drop-Multiplexer in WDM-Networks BP und Band stop filter for channel selection
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08 – Filters
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Fiber Gratings for Dispersion Compensation
Dispersion in anomalous regime (e.g. D=+17ps/(nm  km)):
Increasing wavelength  increasing group delay, linearly increasing group delay over 
therefore we need: a filter, with linearly decreasing group delay
and constant magnitude in a wide frequency range  flat top BP filter
 Chirped Fibre-Bragg-Grating
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Working Principle
ok_6_FBG_dispersionskomp.dsf
L
large 
small 
max
min
large (red) are reflected at beginning of
FBG  short delay
small (blue) are reflected at end of FBG
 large delay
 delay compensation = Dispersion
compensation
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Optical Delay-Line Filters
Basics
IIR-filter (Infinite Impulse Response), recursive filter, filter degree n
(=ARMA-filter (Auto-Regressive Moving Average))
x(t)
bn
+
-cn
ok_64_dig_filter.dsf
bn-1
T
+
T
-c n-1
b1
+
b0
T
y(t)
-c1
y (t )  bn x(t  nT )  bn 1x(t  (n  1)T )  ...  b1x(t  T )  b0 x(t )
 cn y (t  nT )  cn 1 y (t  (n  1)T )  ...  c1 y (t  T )
n
H ( z) 
 b z 
Y ( z)
  0
n
X ( z)
1   c z  
 1
Filter with poles and zeroes in complex z-plane
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FIR Filter
FIR-filter (Finite Impulse Response), non-recursive filter, filter degree n (MA-filter)
x(t)
T
b0
T
b1
T
ok_64_dig_filter.dsf
bn
+
n
y (t ) 
 b x(t  T )
+
H ( z) 
 0
n
 b z
y(t)
v
 0
Filter with zeroes in z-plane, all poles at z=0
H( f ) 
n
 b e j 2 Tf
 0
h0 (t ) 
n
 b  0 (t  T )
coeff. = impulse response
 0
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Phase and Frequency Response
FIR-filter has linear phase, if all coefficients are symmetrical:
m1 = multiplicity of zero at e jT  z  1
b  (1)m1 bn 
FIR and IIR: frequency response periodic with   2 / T
H ( )  H (  m
2
)
T
m integer m  0,  1,  2,...
Normalisation:
e j 2 fT  e jT  e j  z 1  esT
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Digital vs. Optical Filters
Digital filters: T=sampling interval (delay by 1 sampling interval), frequency response
is periodic with f s  1/ T . We are interested (in most cases) in the spectral range
0  f  f s  1/ T
Optical filters: T=time delay of a delay line (e.g) (we assume time delays are integer
multiples of an elementary delay T in order to be able to apply z-transform).
Periodicity = free spectral range (FSR). We are interested in the frequency range (i.e.
the period) close to optical carrier frequency (e.g. 193 THz)
dig. LP-filter
ok_64_dig_filter.dsf
0
0
1/T
1
0
0
1/T
1
2/T
2
f

opt. BP-filter(=LP in equiv. baseband
for compl. envelope)
fT
ok_64_dig_filter.dsf
21
(m-1)/T
m-1
m/T
(m+1)/T
m
m+1
optical
carrier frequency
f

08 – Filters
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Optical Delay-Line Filters
Basic building blocks: Signal splitting, delay, coefficients, adders
by choosing appropriate
Requirements:
Adaptive, reconfigurable
parameters (coefficients,
flexible frequency resp. designs
degree, etc.)
Delay lines: wave-guides of appropriate length L :
speed of wave: v 
c
m L
 2 108 
n
s
T
L
T
FSR
2cm
100ps
10GHz
0,2cm
10ps
100GHz
for n  1.46 (fibre)
Signal splitting and combining: directional couplers
Coefficients:

coupling ratio of splitting couplers

attenuator / opt. amplifier (EDFA)

phase shifter (negative and complex coefficients are possible!)

modulators (EAM,MZM) fast reconfigurable  adaptive optical filter
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Mach-Zehnder-Filters
Single stage optical FIR filter
Schematic
coupler 1
coupler 2
Input 1
Output 1
Length
difference L
ok_63_bilder.dsf
Input 2
Output 2
Two couplers connected via two paths of different lengths.
c
S1   1
 js1
coupler 1:
c1,2  cos(1,2 L1,2 )
js1 

c1 
c
S2   2
 js2
coupler 2:
js2 

c2 
where L= coupling length,
s1,2  sin(1,2 L1,2 )
= coupling coefficient
08 – Filters
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Mathematical Model
length difference L
2 n
 Phase shift:
L    L
 delay:

n
T 
 L
2 f
c

 L
2 n
f  
c
delay in frequency domain:
e j T   e j 2T  f  z 1  e j
(  T  )
Model MZ-filter:
Ei1
c1
+
c1
+
1
 Eo1    s1s2  c1c2 z


 Eo 2   j ( s1c2  c1s2 z 1 )
24
c2
+
Eo1
c2
+
Eo2
js2
js1
Ei2
z-1
js2
js1
ok_63_bilder.dsf
j ( s1c2  c1s2 z 1 )   Ei1   H11 ( z ) H12 ( z )   Ei1 




c1c2  s1s2 z 1   Ei 2   H 21 ( z ) H 22 ( z )   Ei 2 
= non-recursive filter functions of 1 st order
Filter coefficients: coupling ratio in coupler 1 and 2.
Complex filter coefficients are possible!
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Example
Example: coupler 1 = coupler 2 = 3dB-coupler:
c1  c2  1/ 2 ,

Ei 2  0
s1  s2  1/ 2
Transfer functions at out 1 and out 2
1 1
1

 
1
1 
Eo1 ( z )  H11 ( z ) Ei1 ( z )  ( 1  z 1) Ei1( z )   z 2  z 2  z 2  Ei1( z )


2
2



Eo 2 ( z )  H 21 ( z ) Ei1 ( z ) 
1 1
1

 
j
j 
(1  z 1) Ei1( z )  z 2  z 2  z 2  Ei1( z )


2
2


08 – Filters
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Example: coupler 1 = coupler 2 = 3dB-coupler:

c1  c2  1/ 2 ,
s1  s2  1/ 2
Ei 2  0
Transfer functions at out 1 and out 2

Eo 2 ( z )  H 21 ( z ) Ei1 ( z ) 
Magnitude of frequency response:

| H11 |
| Eo1 |
| H 21 |
| Eo 2 |
| Ei1 |
~ sin
1 1
1

 
1
1 
Eo1 ( z )  H11 ( z ) Ei1 ( z )  ( 1  z 1) Ei1( z )   z 2  z 2  z 2  Ei1( z )


2
2



1
 sin T 
2
2


| Ei1 |
1 1
1

 
j
j 
(1  z 1) Ei1( z )  z 2  z 2  z 2  Ei1( z )


2
2


~ cos

1
 cos T 
2
2



f FSR 
Periodic frequency response with free spectral range:
1
T
Interleaving transfer functions at out 1 and out 2.
08 – Filters
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Mutli Stage Filters
(2) Filter cascade for narrowband bandpass filtering:
MZI
(L)
MZI
(2L)
MZI
(3L)
4 stages Mach-Zehnder filter
27
MZI
(4L)
ok_63_bilder.dsf
08 – Filters
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Optical FIR-Filter for Equalization of Signal Distortion
6-1

cascaded Mach-Zehnder Filter
coupler 1
coupler 3
coupler 2
coupler N
coupler N+1
Input 1
Output 1
L
***
L
L
Input 2
Output 2

single-input single-output device

the output 1 can be reached from input 1 by following N+1 different paths
characterized by delay times from 0 to N T

therefore the time domain output response y(t) for an input signal x(t) is:
N
y (t )   cn x(t  nT )
n 0
which is the response of a FIR-Filter!

equalization of all single channel distortions: chromatic dispersion, SelfPhase Modulation, Polarization mode Dispersion, Group Delay Ripple
08 – Filters
28
Arrayed Waveguide Grating
•
•
•
The incoming WDM signal (1) is coupled into an array of planar
waveguides after passing through a free-propagation region (2) in the form
of a lens.
In each waveguide (3), the WDM signal experiences a different phase shift
because of different lengths of waveguides. Moreover, the phase shifts are
wavelength dependent because of the frequency dependence of the
mode-propagation constant.
As a result, different channels focus (4) to different output waveguides (5)
when the light exiting from the array diffracts in another free-propagation
region. The net result is that the WDM signal is demultiplexed into
individual channels.
08 – Filters
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Application Example in WDM-System
Channel 1
C-Band
C-Band
even
odd
160 Channels
50 GHz
Basic technologies :
Dielectric filters
Fiber gratings
30
even
odd
80 Channels
50 GHz
Interleaver
186 187 188 189 190 191 192 193 194 195 196THz
C-/L-Band Filter
192 193 194 195 196THz
Basic technologies :
MZI (fiber, integrated optical)
40 Channels
even,100 GHz
...
even
C-Band
L-Band
100 GHz
DEMUX
195 196THz
192 193 194 195 196THz
40 Channels
odd,100 GHz
Basic technologies:
Dielectric filters
Arrayed Waveguide Grating
Gratings
Fiber gratings
08 – Filters
10
Wrap Up
What you should recall from this chapter:
• Give the requirements for an optical filter to be used as EDFA gain equalizer
• Give the Bragg condition for reflection by (i) a formula and (ii) by your own words
• An optical filter has center wavelength 1555 nm and spectral width (FWHM) of 0.1 nm.
Calculate the center frequency and the 3-dB-bandwidth in Hz.
• Explain how FBG filters can be fabricated
• Explain how an Add-drop Multiplexer with circulator and FBG works
• Explain the working principle of an FBG, which is used for dispersion compensation
• Explain the pros and cons, if an FBG instead of a DCF is used as dispersion compensator
• Which types of optical filters do you know?
• Which components are required for designing an optical FIR filter?
• Explain how an interleaver based on a single stage Mach-Zehnder filter works.
• Calculate the FSR and L of an interleaver based WDM demultiplexer for 100 GHz channel
spacing
• Explain the working principle of an AWG
31
08 – Filters
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