Chapter 3 Design approach
3.4 Multimode taper design
3.4.3 Effect of taper length on the effective beat length
We notice that Leff are varied with the taper length in Figure 3.4-2. The variations of the effective beat length Leff with the taper length Lt is displayed in Figure 3.4-5. Without inserting a taper (i.e., Lt=0 nm), the effective beat length is equal to the beat length. As the taper length Lt increases, the effective beat length Leff decreases and is smaller than the beat length.
0 500 1000 1500
1600
E ffe cti v e b ea t l en g th (n m )
Taper length (nm)
Figure 3.4-5 Effective beat length Leff as a function of the taper length Lt.
When the field propagates through this multimode taper, a phase difference between TE00 and TE02 modes is induced at the junction of the multimode taper and the MMI
waveguide because the modes interfere along this multimode taper. The self-image with phase difference of 2π is observed as the field propagates an effective beat length along the MMI
waveguide. The effective beat length, therefore, can be calculated by
1)
where initial phase difference is the phase difference of the TE00 and TE02 modes at the output
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of the multimode taper.
As the taper length increases, the length for mode interference increases. As a result, the initial phase difference increases and the effective beat length decreases with the increase of the taper length. As the taper length is 560 nm, the corresponding effective beat length is 1889.3 nm and the length of MMI waveguide is chosen to be twice of the effective beat length to implement a MMI waveguide crossing.
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3.5 Performances of MMI based crossings with linear tapers
Figure 3.5-1 shows the FDTD simulation results of these taper-integrated MMI based waveguide crossings with the taper length Lt of 0 nm, 560 nm, 1000 nm and 2000 nm, respectively. Here, the length of the MMI section in each design is chosen to be twice of the effective beat length obtained in the aforementioned section. In the case of Lt = 0 nm, field is diffracted dramatically at the crossing region and significant scattering field radiates into the orthogonal MMI waveguide. In the case of Lt = 560 nm, we see a narrowing field at the center of the crossing and the wave fronts at the front and back of the crossing are almost the same with reversal sign of phases. In the cases of the larger Lt, as shown in Figure 3.5-1 (c) and (d), the field scatters through the crossing region without significant crosstalk because the dominant component of the field is the TE00 mode with a narrow angular spectrum.
However, we can see wave front expands more widely at the back of the crossing region, and this results in more insertion loss.
Table 1 lists the parameters and performance of these four taper-integrated MMI crossing structures with taper lengths of 0, 560, 1000 and 2000 nm, respectively. As η decreases, dimension of the crossing increases but the crosstalk decreases. The lowest insertion loss of these taper-integrated MMI based crossings is obtained as the taper length is 560 nm.
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In the case of Lt = 0 nm, the diffraction loss is roughly equal to 0.58 dB and the insertion
loss (~0.78 dB) is roughly equal to the sum of the transition loss (0.226 dB) and diffraction loss, meaning 16.44% of the input power is lost after the filed propagates through the MMI based waveguide crossing without inserting a taper. In the case of Lt=560 nm (for η = 0.27), the diffraction loss is about 0.12 dB and its insertion loss is 0.24 dB.
In the cases of Lt = 1000 nm and 2000 nm, the field diverges at the crossing region such that the guided modes of the MMI waveguide and the diverged field at the back of the crossing are mismatch, resulting in substantial insertion loss. Compared with the MMI based crossing without inserting tapers (i.e. the case of Lt = 0), the taper-integrated MMI based crossings perform smaller insertion loss and less crosstalk.
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Figure 3.5-1 FDTD simulations of the input guided mode propagation through MMI based waveguide crossings sandwiched by four identical linear tapers
with (a) Lt=0 and Lm=4543.4 nm, (b) Lt=560 nm and Lm=3778.5 nm, (c) Lt=1000 nm and Lm=3600 nm and (d) Lt=2000 nm and Lm=3450.4 nm.
Table 1 Properties of MMI based waveguide crossings integrated with linear tapers at the wavelength of 1550 nm
Lt (nm) η L
eff (nm) L m+2L
t (nm)
Insertion loss (dB)
Crosstalk (dB) 0 0.52 2271.7 4543.4 0.78 -23.19 560 0.27 1889.3 4898.5 0.24 -45.39 1000 0.18 1800.0 5600.0 0.25 -48.12 2000 0.07 1725.2 7450.4 0.43 -50.63
(a) (b)
(c) (d)
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3.6 Effect of the Taper Profiles
In the previous section, we realized the smallest insertion loss as the amplitude ratio η = 0.27. In order to achieve this value, the corresponding linear taper length Lt is 560 nm, and, as a consequence, the transition loss of this taper is 0.08dB and the effective beat length is 1889.3 nm.
Here, we investigate the effect of the taper profiles on the transition loss and the effective beat length. The studied taper profiles expand in width with an initial value of 500 nm to the final value of 1200 nm and are given by
( ) ( )
(eq.3.6-1)
n
t g m g
t L
w z w w z
w
×
− +
=
where wt(z) is the taper width and n is the profile index .
Here, we chose the taper profiles with n = 0.25, 0.5, 1 and 2 and the corresponding Lt are 750, 530, 560 and 1000 nm in order to realize η=0.27.
The field distributions along these four taper and MMI sections are shown in Figure 3.6-1. In the case of n=0.25 and n=0.5, the width varies steeply, and, as a result, the effective beat length for each design decreases to be 1400 nm and 1735 nm, respectively.
However, the transition loss is larger than the case of the linear taper. In the case of n=2, the transition loss is 0.02 dB with longer effective beat length (1900 nm).
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Figure 3.6-1 Evolution of the input guided mode propagation through different taper profiles with n= (a) 0.25, (b) 0.5, (c) 1 and (d) 2 and the MMI waveguide
(a) Lt = 750 nm, n=0.25
(b) Lt = 530 nm, n=0.5
(c) Lt = 560 nm, n=1
(d) Lt = 1000 nm, n=2
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Figure 3.6-2 FDTD simulations of the input guided mode propagation through MMI based waveguide crossings sandwiched by four different tapers with (a) Lt=750nm and n=0.25, (b) Lt=530 nm and n=0.5, (c) Lt=560 nm and n=1 and (d) Lt=1000 nm and n=2.
Table 2 Performance of waveguide crossings with different taper profiles at the wavelength of 1550 nm
n
Lt (nm)
Leff (nm)
Total length of the crossing Lm+2Lt (nm)
Transition loss (dB)
Insertion loss (dB)
Crosstalk (dB)
0.25 750 1400.0 4300.0 0.17 0.37 -39.83
0.5 530 1735.0 4530.0 0.12 0.33 -42.85
1 560 1889.3 4898.5 0.08 0.24 -45.39
2 1000 1900.0 5800.0 0.02 0.15 -42.34
(a) (b)
(c) (d)
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Figure 3.6-2 exhibits the simulated fields of the input wave propagating through these taper-integrated MMI based crossings with (a) n=0.25, (b) n=0.5, (c) n=1 and (d) n=2. The transverse fields at the junction of the taper and the input waveguide are different but the
self-images formed at Leff of the MMI waveguide in these cases have the same beam waist at due to the fixed value of η.
Table 2 summarizes the parameters and performances of simulated taper-integrated MMI based crossings at the wavelength of 1550 nm for the cases of n = 0.25, 0.5, 1 and 2. The lengths of the MMI crossings in the cases of n = 0.25 and n=0.5 are less than twice of the beat length and their insertion loss are lower than that without inserting a taper. Although the dimension of the MMI crossing increases as n increases, the transition loss of the taper decreases and better performance of the waveguide crossing is obtained. In the case of n = 2, the MMI waveguide crossing has the insertion loss of 0.15 dB and the dimension of 5800×
5800 nm2. In addition, the crosstalk in these designs are imperceptible, roughly -40dB.
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3.7 Wavelength dependence on insertion loss and crosstalk
Insertion losses and crosstalks of these designed MMI based waveguide crossings with different taper profiles as a function of wavelength are shown in Figure 3.7 (a) and (b). The insertion loss decreases as n increases because the transition losses of the tapers reduce. In each case, the variations of insertion loss is less than 0.1 dB at the wavelength ranging from 1500 to 1600 nm. All the crosstalks of these MMI based crossings are lower than -30 dB at the wavelength ranging from 1500 to 1600 nm. These results indicate these crossings exhibit broad transmission spectra around the wavelength of 1550 nm. In the case of n = 2, the insertion loss is averagely 0.18 dB and the crosstalk is less than -40 dB.
Figure 3.7 (a) Simulated insertion loss spectra and (b) calculated crosstalk spectra of the designed MMI-based waveguide crossings for n=0.25 (black
curves), 0.5 (red curves), 1 (blue curves) and 2 (green curves)
(a) (b)
1500 1520 1540 1560 1580 1600
-50 -45 -40 -35 -30
Crosstalk (dB)
Wavelength (nm)
n=0.25 n=0.5 n=1 n=2
1500 1520 1540 1560 1580 1600
0.0 0.1 0.2 0.3 0.4 0.5
Insertion loss (dB)
Wavelength (nm)
n=0.25 n=0.5 n=1 n=2
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Chapter 4 Conclusion
In this thesis, we present a novel compact MMI based crossing by using multimode tapers. As a short multimode taper is inserted in between the input/output and MMI waveguides, the transition loss reduces and the length of the required multimode waveguide
reduces to be less than twice of the beat length. Besides, the diffraction loss is determined by the profile of the self-image, and its minimum is obtained as η is 0.27.
In the case of using the quadratic taper, the size of the MMI based waveguide crossing is 5800×5800 nm2, the insertion loss is around 0.15 dB and the crosstalk is lower than -40 dB. In addition, these devices can be fabricated by using standard CMOS fabrication process.
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