Design a 2x2 compact mode switching using multimode interference based on silicon material

division multiplexing switching device on optical 
chip that has been demonstrated experimentally using a Y junction structure and a MMI coupler 
[17]. The switching between the ports is achieved by a lateral PN junction. The device can perform 
switches for 2 modes TE0 and TE1, simulated insertion loss is less than 0.3dB for both TE0 and TE1 
inputs over the wavelength range from 1530nm to 1570nm but a disadvantage of this device is 
quite large in size, approximately 400μm in length. Next, another research used 2 MMI couplers 
and a thermo-optic phase shifter to design a switching device [18], but the device’s insertion loss 
is quite high up to 1dB at the central wavelength. However, the general characteristics of those 
devices has not evaluated performance on the system. 
In this paper, we study to combine the advantages of these two MMI structures to create a 
2x2 mode switching device using silicon on insulator with switching the modes TE0 between two 
inputs and two outputs. The high optical conversion efficiency over 97% and compact size of 
4.2𝜇𝑚 x 0.22𝜇𝑚 x 110.4𝜇𝑚 are advantages of the proposed device. In addition, we evaluate the 
fabrication tolerance of the device, the results demonstrate that the device can work well with a 
large manufacturing errors. Moreover, we also evaluate the effectiveness of devices on complex 
communication systems, the simulation results show that the device can operate effectively with 
performance more than 70% in a wide bandwidth up to 100nm. Furthermore, the proposed device 
can work with an extremely high bit rate of up to 35Gbps while bit error rate is always remained 
smaller than 10-10. 
2 Device structure and design principle. 
2.1 MMI theory 
The self-imaging phenomenon is the basic properties in waveguides as stated by Soldano [19]. 
The beat length Lπ is an important parameter to determine the appropriate length in order to 
create the desired periodic images in the waveguide as shown in Figure 1, this beat length is 
defined by two lowest-order modes in the MMI and it is given by formula 
Lπ =
4neffWeff
2
3λ
 (1) 
Weff = WMMI +
λ0
π
(
nc
nr
)
2σ
(nr
2 − nc
2)−(1 2)⁄ (2) 
For σ = 0 (TE mode), σ = 1 (TM mode) and where Weff, λ, neff, nr and nc are the effective 
width of MMI, wavelength, effective refractive index, core (effective) refractive index and 
cladding (effective) refractive index, respectively. 
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Fig. 1. The self-imaging theory in 2×2 MMI coupler 
The self-imaging in waveguide is created by one of two interference mechanisms: general 
interference and restricted interference mechanisms. 
For general interference mechanism is shown by formula 
LMMI = 
p
N
(3Lπ) (3) 
And restricted interference mechanism 
LMMI = 
p
N
(Lπ) (4) 
Where N is the number of input and output ports of the MMI, p denotes the periodic 
properties of image along the MMI. We usually choose p = 1 to shorten the size of the device as 
much as possible. Comparing between two interference mechanisms above, notice that the length 
of devices using the restricted interference mechanism is three times shorter than that using the 
general interference mechanism. 
2.2 Phase shifter 
The phase shifter plays an important role in this article with the aim of controlling the 
signal path in waveguides. We choose the fixed length Lps of 16.8μm as described in Figure 3. By 
varying the center width of the phase shifter as shown in Figure 2, the phase difference between 
input and output port also will vary. From the simulation result is indicated in Figure 2, if the 
center width of the phase shifter Wps = 0.35μm then the phase difference at output port is 180 
degrees. This phase difference will be 90 degrees when Wps = 0.38μm. 
2.3 Structure design 
Structure of the mode switch is shown in Figure 3. The proposed switch consists of two 
2x2 MMI couplers that are linked together by access waveguides. The width of these access 
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waveguides is selected Win = 0.3μm to support one TE0 fundamental modes. They are posited in 
±WMMI/6 position compared to center position of the MMI region. In this design, we choose width 
of the MMI region as WMMI = 4.8μm, and its length is chosen as LMMI = Lπ/2 = 22.8μm. To improve 
transmission efficiency between the access waveguides and MMI device, a taper will be used with 
the length Ltp and width Wtp of 7μm and 0.85μm, respectively. The height of device is H = 
0.22μm. 
The device is based on SOI (Silicon on Insulator) material platform with channel structure. 
The core layer is made of silicon with refractive index nr = 3.47 while cladding layer is made of 
silica with refractive index nc = 1.44. 
Fig. 2. Surveying the phase difference at output of the phase shifter by varying the center width 
(a) (b) 
Fig. 3. The general schematic and parameters of the proposed switch, (a) 3D, (b) 2D 
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Fig. 4. Electric field patterns of proposed switching device 
From these electric field patterns (Figure 4), we can observe a very small amount of light 
radiated out of guided-wave regions, which can be shown that the optical conversion efficiency 
is also very high. Figure 4 shows the field distribution of the optical mode switch at wavelength 
of 1.55μm when fundamental mode is launched to the device. To better understand this issue, we 
will explain the principle of operation as follows: 
1. When there is no phase shifter: if a signal is launched at input I1, the output O2 will 
receive the signal. Otherwise, the output O1 will obtain the signal if a signal is 
transmitted at input I2. 
2. When the phase shifter is added to the device: if a signal is launched at input I1, the 
output O1 will receive the signal. If a signal is transmitted at input I2, the output O2 
will surely obtain the signal from input I2. 
Besides, we also evaluate the optical performances of the proposed device by using 3D-
BPM numerical simulation method. The important parameters taken into account are insertion 
loss (I.L) and crosstalk (CT) which are defined by 
IL (dB) = 10 log10
Pout−desirable
Pin
 (5) 
CT (dB) = 10 log10
Pout−unwanted
Pout−desirable
 (6) 
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Where Pin is the input power of the device, Pout-desirable is the received power at the desired 
output and Pout-unwanted is the leakage power at the another ouput. 
Fig. 5. Insertion loss and crosstalk of the proposed optical mode switching as a function of the wavelength 
Figure 5 shows the graph of insertion loss and crosstalk. At the central wavelength λ = 
1.55μm, insertion loss and crosstalk are less than 0.5dB and -35dB, respectively. Furthermore, if 
we expand the wide bandwidth range to 100nm, the insertion loss is also less than 1.5dB and 
crosstalk is always less than -30dB. 
Fig. 6. Tolerance of the proposed switching device on variation of the MMI length 
Next, we examine the tolerance of the device which is very important to etch and 
manufacture it in practice. We evaluate two important parameters of the devices, the length and 
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width of MMI region corresponding to its tolerance is ΔLMMI and ΔWMMI. From figures 6 and 7, if 
the length of MMI region of LMMI = 23.2 ± 0.9μm and the width of MMI region of WMMI = 4.8 ± 
0.05μm, insertion loss always less than 1.5dB and 1dB, respectively. Notice that the tolerance of 
MMI region length is larger than tolerance of width. Therefore, etching the width of the device 
should ensure high accuracy for the device to operate with the best performance. 
Fig. 7. Tolerance of the proposed switching device on variation of the MMI width 
3 Evaluation on system 
After evaluating the optical conversion efficiency of the device at the physical level, we 
continue to evaluate this proposed device at the system level. Note that the simulation parameters 
of optical mode switch in this system are exactly the same as the structure’s parameters described 
above. The switching system is presented in Figure 8. It includes three parts: transmitter, 
transmission channel and receiver. In the transmitter consists of bit sequence generator, NRZ-
pulse generator, laser and Mach-Zehnder modulator. The transmission channel is the switch 
device. The receiver consists of APD photodiode and BER analyzer. 
First, the electric bit strings are generated by the bit sequence generators. These bit strings 
will be encoded by NRZ encoder before being inserted to the Mach-Zehnder modulator. Next, 
the Mach-Zehnder modulator combines with laser to produce the light bit strings and launching 
into the device. After that, the optical signal at the outputs of the device will be taken to the APD 
photodiode with the aim of converting the optical signal to the electric signal. Finally, BER 
analyzers will evaluate the system quality through the bit error rate parameter. 
We proceed to investigate BER by parameters: wavelength, transmit power and data bit rate. 
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In the figure 9, two fixed parameters are the bit rate of 30Gbps and the transmitter power 
of 0dBm. We scan the wavelength from 1.5μm to 1.6μm, the bit error rate is always less than 10-
9. This bit error rate is also standard when manufacturing device. 
Fig. 8. Switching system model 
Fig. 9. Bit error rate of the system on variation of the wavelength 
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Fig. 10. Bit error rate of the system on variation of the transmitting power 
Similarly, figure 10 shows the bit error rate as function of transmitter power with the 
wavelength and the bit rate are fixed of 1.55μm and 30Gbps, respectively. To achieve the 
minimum bit error rate of 10-9, the transmitter power must be greater than -1.4dBm. 
Fig. 11. Bit error rate of the system on variation of the bit rate 
Finally, we evaluate quality of the system at the central wavelength of 1.55μm and the 
transmitter power of 0dBm. From figure 11, the system can operate well bit rate up to 35Gbps 
with log of BER below -10. The result also shows that the BER ratio gradually decreases as the bit 
rate increases. 
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4 Conclusion 
We have presented a design of an optical mode switching device with the compact size based on 
SOI material. The device is constructed by two MMIs and a phase shifter which is capable of 
flexible switching fundamental optical modes from input ports to output ports by changing the 
phase shifter. This switching device can route TE0 modes to the arbitrary desired output with a 
small insertion loss and crosstalk. With these advantages are compact size and large efficiency, 
we hope that the proposed optical chip is expected to replace electrical chips in the future. 
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