In a subscriber WDM system, filters separate the bands of 1.31 and 1.55um are needed, and these filters are often called WDM filters. The passband of filters should be broad enough to cover all the using channels in C and L bands, that is, ranges from 1.53 to 1.62um. Due to such a broad bandwidth needed in operation, the adiabatic filters are one of the candidates. The principles of directional coupler filter can be found in many text books so here we will just explain it conceptually. We all know only the phase match of two guides the power can flow completely to another port. If we tune the refractive index and structure of one of the guides to match at some designed wavelength, we will find that it will leave the matching condition when the operational wavelength shifts.
Excepting the designed wavelength, we see the two phase constant lines in Fig.
4-7 separate further when leaving away from the designed wavelength. Such a machenism can clearly be used as a filter. For now we still provide three basic structures for comparison, which are all designed matched at wavelength of 1.55um in Fig. 4-8.
The thinner guide is simulated using another polymer material, CN120-S80, of which the refractive index is 1.5547. The other guide and the cladding are both the same as the switch
All three structures in Fig. 4-8 are of two different guides designed matched at
functions of tapered coupling and tapered widths. Case A contains two guides of uniform coupling and widths. Case B (which had been proposed in [17], and the advantage of tapering of a filter is studied in [21]) adopt the tapered coupling but constant widths. Case C, which based on adiabatic coupler, surely has tapered structures of both coupling and widths. We should note the device lengths are slightly different due to tuning to its optimum filter function.
Input
1.29um ~1.7um Output
1.31um band
Output 1.55um band
≈
1=1 P
P
1P
2As the above indicated, we pumped all power of wavelength distributed from 1.29 to 1.7um into guide 1 and observed the outputs.
It’s clear from Fig. 4-9 that the case A oscillates seriously outside the narrow stop band of guide 1 and lengthen the transition band making it ineffective in operation.
Using the tapered coupling in case B, it apparently eliminates the sidelobes of case A.
This behavior is like the case B in preceding section, which is in the temperature domain. The reason that the tapered coupling can eliminate the sidelobes is almost the same as the case of grating. When weakly coupling between two modes, the power can be written as the formula below [22]
( )
L ≈−j∫
LC( ) (
z − j z)
dzA2 0 exp 2 δ
It is assumed that A2
( )
0 =0. So outside the strong coupling region, the behavior of power in guide 2 is proportional to the Fourier transform of the coupling coefficient.The case A in switch or filter holds coupling cons tant mapping to a sinc alike function
which has significant sidelobes, and the tapered coupling used for migrating the problems can be imaged now. The same method is often used in a grating, too.
Besides tapering the waveguide separation, tapering the widths can also provide additional advantage of broad bandwidth. If we need a crosstalk less than 10dB near the 1.55um band, then only the adiabatic can sustain over the range of 1.5 to 1.64um.
The only price is the deterioration of crosstalk at exact 1.55um compared to case B.
Fig. 4-10 shows the adiabatic filter in different lengths. We can see when the device becomes longer, the filter exhibits more bandwidth and abbreviate the transition band between the bands of 1.3 and 1.55m.
We defined the bandwidth as the band of crosstalk lower than -20dB near the communication band of 1.55um.
Device
Length(cm) Range(um) Bandwidth(nm) Crosstalk at 1.31um(P2 in dB)
0.7 1.544~1.566 22 -24.35
1.2 1.514~1.596 82 -30.96
2.0 1.504~1.610 106 -35.58
Table 4-1 Bandwidths and crosstalk comparisons of adiabatic filters
For the three different lengths we found that longer device can exhibit broader bandwidth and lower crosstalk.
Summary
We had demonstrated two adiabatic devices of switch and filter, and compared with the conventional ones to point out the advantages of tapering in separation and widths. The tapered coupling can help mitigate the significant sidelobes and the tapered widths can enhance its working bandwidth. And we proposed filters that exhibit bandwidth of 106nm near 1.55um and low crosstalk less than -20dB whether in 1.31or 1.55 bands.
In both adiabatic devices, longer one can always reduce transition band obviously, but more space and cost are paid. There exists a trade off between the
device.
β
k β
2β
1 'β
22 /
= 1 k
Fig. 4-1 Phase constants of different states
(A)
W1 W1
G1
Heater
(B)
α =
0.41W1 W1
G1
G2
Heater
(C)
α = 1
W2 W 3
G1
G2
Heater
Fig. 4-2 The switch layouts
6 . 10 2
6 . 7 1
48 . 6 3
58 . 5 2
03 . 6 1
:
=
=
=
=
=
G G W W W
um
Units
-15 -10 -5 0 5 10 15 0.0
0.2 0.4 0.6 0.8 1.0 Output Power
∆T
(A) (B) (C)
P
1P
2Fig. 4-3 Output powers of two switch states
1.3 1.4 1.5 1.6 1.7
-35 -30 -25 -20 -15 -10 -5 0
(A) (B) (C) Output Power
( )
umλ
( )
dBP1
Fig. 4-4(a) Crosstalk in guide 1 of switched state
1.3 1.4 1.5 1.6 1.7 -36
-34 -32 -30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6
(A) (B) (C)
( )
umλ
Output Power
( ) dB
P
2Fig. 4-4(b) Crosstalk in guide 2 of unswitched state
-15 -10 -5 0 5 10 15
0.0 0.2 0.4 0.6 0.8 1.0
∆T
Output Power
2D 3.5D 6D
P
1P2
Fig. 4-5 Output power of different states with different lengths
1.3 1.4 1.5 1.6 1.7 -60
-50 -40 -30 -20 -10
D = 2 D = 3.5 D =6
( ) um
λ
Output Power
( ) dB
P
1Fig. 4-6(a) Crosstalk of adiabatic filter in guide 1 of switched state
1.3 1.4 1.5 1.6 1.7
-36 -34 -32 -30 -28 -26 -24 -22 -20 -18
D = 2 D = 3.5 D = 6
( ) um
λ
Output Power
( ) dB
P
2Fig. 4-6(b) Crosstalk of adiabatic filter in guide 2 of unswitched state
Width Refractive
Index n
n
0n
1n
2W
1W
2Fig. 4-7(a) Matched waveguides with different dimensions
β
Phase velocity
β
2β
1Wavelength
λ
Designed match point
Fig. 4-7(b) Variation of phase constant versus wavelength
(A)
W2=5.12 W1=1.69
G1=6.2
L=6900
(B)
W1=1.69 W2=5.12
G1=6.2
G2=9.34
L=6900
41 .
= 0 α
(C)
W2=4.8 W1=1.75
W3=1.68 W4=5.44
G1=6.2
G2=9.34
L=7000
= 1 α
Fig. 4-8 Filter layouts. Unit:micro
1.3 1.4 1.5 1.6 1.7 -45
-40 -35 -30 -25 -20 -15 -10 -5 0
(A) (B) (C)
( ) um
λ
Output Power
( )
dBP1
Fig. 4-9 Output power of the conventional and adiabatic filters
( )
umλ Output Power(dB)
1.3 1.4 1.5 1.6 1.7
-55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5
L = 0.7cm L = 1.2cm L = 2.0cm
-20dB
P
1P
2Fig. 4-10 Output power of the adiabatic filters with different lengths
Chapter 5 Conclusion
In this thesis we had done that:
1. We provided three additional profiles originally from DSP application to the adiabatic couplers and their analytic form of crosstalk are derived.
2. We predicted the performance of the dimension linearized coupler more accurately with phase considered and proved tha t the optimum length ratio in this case should depend on the length of the device.
3. We had shown two examples of applications in switches and filters and derived the filter of length of 2cm which had bandwidth of 106um.
Better performance can always be observed as long as we lengthen the device. We had not found the optimal profile of the adiabatic coupler since the complexity of mathematical form of crosstalk. Even if the optimum profile exists, that will be a complex function and require much critical parameters in fabrication. Another way of shorten the length instead of searching the optimum profile is to enlarge the evanescent wave and reduce the beat length and overall length can be shorten. This will be more practical compared to model computing. .
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