An 8-Channel Wavelength MMI Demultiplexer in Slot Waveguide Structures

We propose a novel 8-channel wavelength multimode interference (MMI) demultiplexer in slot waveguide structures that operate at 1530 nm, 1535 nm, 1540 nm, 1545 nm, 1550 nm, 1555 nm, 1560 nm, and 1565 nm. Gallium nitride (GaN) surrounded by silicon (Si) was found to be a suitable material for the slot-waveguide structures. The proposed device was designed by seven 1 × 2 MMI couplers, fourteen S-bands, and one input taper. Numerical investigations were carried out on the geometrical parameters using a full vectorial-beam propagation method (FV-BPM). Simulation results show that the proposed device can transmit 8-channel that works in the whole C-band (1530–1565 nm) with low crosstalk (−19.97–−13.77 dB) and bandwidth (1.8–3.6 nm). Thus, the device can be very useful in optical networking systems that work on dense wavelength division multiplexing (DWDM) technology.


Introduction
Dense wavelength division multiplexing (DWDM) is an optical multiplexing technology used to increase the bandwidth over existing fiber networks [1]. DWDM works by combining and transmitting multiple signals simultaneously at different wavelengths on the same fiber [2].
A slot-waveguide is a unique structure that enables light to be strongly confined and guided inside a narrow nanometer-scale region of low index material that is surrounded by two layers with high index material [8].
Using this unique structure leads to a variety of advantages such as a small beat length of the guided light and a strong confinement in the slot region that results in extremely low losses. Another benefit is that CMOS compatible materials and technology can be used in slot-waveguide fabrication [9].
A major improvement in the fabrication of semiconductor circuits is the introduction of silicon on insulator (SOI) technology. This technology is characterized by low power consumption, improved heat dissipation, and low-voltage activity. As a result, the performance of semiconductor circuits has improved significantly [10,11].
The principle work of the MMI coupler is that an input field is duplicated in single or multiple images at periodic intervals along the light propagation in the MMI waveguide coupler. This effect is called self-imaging [12,13]. Figure 1a,b shows a schematic sketch of the 1 × 8 wavelength MMI demultiplexer x-z cross sectional view at y = 0 and 3D view of the MMI coupler. In this figure, the green areas denote pure silicon (Si), purple areas denote GaN, and the white areas denote silica (SiO 2 ). The Si layer height is H Si , and the GaN layer height is H slot as shown in Figure 1b. It can be seen in Figure 1a that the device is based on seven 1 × 2 MMI couplers, fourteen S-bands, and one input taper. Table 1 shows the refractive index values of Si, GaN, and SiO 2 at the operated wavelengths.

The 1 × 8 MMI Demultiplexer Structure and Theoretical Aspect
The width of the input taper varies from 0.4 µm to 0.6 µm with a length of 60 µm. The width of the output S-band is 0.4 µm and varies from 0.35 µm to 0.4 µm for the left and right outputs in the MMI coupler. The gap distance between the two S-bands at the output MMI coupler is 0.73 µm.  The MMI coupler is based on the self-imaging effect of multimode interference [24,25]. The beat length Lπ is given by [24]     2 eff m e,m π,m m 4n λ W L ; m 1,2,3,..., 8. 3λ (1) λm are the operating wavelengths (   The MMI coupler is based on the self-imaging effect of multimode interference [24,25]. The beat length L π is given by [24]  1525 + 5m (nm)). The n eff (λ m ) is the effective refractive index of the core (GaN and Si) and is solved by the FV-BPM mode solver. The W e,m is the effective width of the MMI couplers; for the transverse magnetic (TM) mode, the W e,m is approximated by [24] W e,m = W MMI + λ m π n SiO2 (λ m ) n eff (λ m ) where W MMI is the width of the MMI coupler as shown in Figure 1b. Its size was optimized in order to minimize the size of the beat length inside the MMI coupler. In order to obtain the directed or the mirrored image of the entered field at the output coupler, the MMI coupler length needs to be equal to a natural number duplicated with the beat length (L mmi = pLπ).
The conditions for dividing two different wavelengths in MMI coupler are given by where p is a natural number, and q is an odd number. The conditions for dividing four different wavelengths in MMI coupler are given by The conditions for dividing eight different wavelengths in MMI coupler are given by In order to obtain a compact device, the location of the input taper was shifted ± 1 6 We from the center of W mmi . This shift can lead to a cancellation of the third mode inside the MMI coupler. In addition, many optimizations were carried to find the optimal values of the seven MMI coupler lengths that satisfied the conditions in Equations (3)-(5).
The crosstalk is given by where P n is the power transmission for the suitable port, and P m is the interference power transmission from the other port. The insertion losses are given by where P out is the power at the output port, and P in is the power in the input taper.

Results
The simulations were done using a FV-BPM-based RSoft Photonics CAD Suite software. The optimal values of the slot-waveguide structure were calculated by FV-BPM simulations combined with Matlab software. The optimal values are H Si = 300 nm, H Slot = 100 nm, and W mmi = 1.8 µm. Figure 2 shows the normalized intensity in the slot area as function of H Slot . The optimal tolerance values of H Slot were set between 70%-100% of the normalized intensity (black line in Figure 2). From Figure 2, it can be noticed that the tolerance values of HSlot are around 6-7 nm. Figure 3a,b show the field patterns of the quasi-TM fundamental mode at 1.55 µm. It can be seen in Figure 3a that there are no confinement losses due to the strong confinement of the electric field (Ey) inside the slot area (red color). A similar mode profile field was obtained for the other operated wavelengths.
(a) (b) The values of neff (λm) were found by solving the field mode profile. By solving Equations (1) and (2), the values of the beat length for the operated wavelengths (see Table 2) can be found. It can be seen in Table 2 that the variation of the beat length value is only 170 nm in the C-band range. From Figure 2, it can be noticed that the tolerance values of H Slot are around 6-7 nm. Figure 3a,b show the field patterns of the quasi-TM fundamental mode at 1.55 µm. It can be seen in Figure 3a that there are no confinement losses due to the strong confinement of the electric field (Ey) inside the slot area (red color). A similar mode profile field was obtained for the other operated wavelengths. From Figure 2, it can be noticed that the tolerance values of HSlot are around 6-7 nm. Figure 3a,b show the field patterns of the quasi-TM fundamental mode at 1.55 µm. It can be seen in Figure 3a that there are no confinement losses due to the strong confinement of the electric field (Ey) inside the slot area (red color). A similar mode profile field was obtained for the other operated wavelengths.  The values of neff (λm) were found by solving the field mode profile. By solving Equations (1) and (2), the values of the beat length for the operated wavelengths (see Table 2) can be found.  It can be seen in Table 2 that the variation of the beat length value is only 170 nm in the C-band range. The values of neff (λm) were found by solving the field mode profile. By solving Equations (1) and (2), the values of the beat length for the operated wavelengths (see Table 2) can be found. It can be seen in Table 2 that the variation of the beat length value is only 170 nm in the C-band range. Figure 4 shows the lengths of the seven MMI couplers that satisfy the conditions in Equations (3)-(5). The wavelength pairs (around the C-band) values are 1.53 µm, 1.535-1.57 µm (blue triangles); 1.535 µm, 1.54-1.57 µm (red circles); 1.54 µm, 1.545-1.57 µm (yellow rectangles); 1.545 µm, 1.55-1.57 µm (purple circles); 1.55 µm, 1.555-1.57 µm (green rectangles); 1.555 µm, 1.56-1.57 µm (light blue circles); 1.56 µm, 1.565-1.57 µm (brown triangles).
It can be seen in Figure 5a-h that the coupling length along the z-axis is 6.6 mm. This value indicates that this device has a compact size compared with the MMI demultiplexer device based on conventional Si waveguides [23]. and Lmmi,7 = 3.451 mm. We chose these wavelengths because they have the best approximation for Lmmi,7, which is suitable for four wavelength pairs that belong to the C-band range. Lmmi,7 (green arrows in Figure 4) is suitable for λ1, λ2 (blue triangle), λ3, λ4 (yellow rectangle), λ5, λ6 (green rectangle), and λ7, λ8 (brown triangle); Lmmi,6 (blue arrows in Figure 4) is suitable for λ2, λ4 (red circle), and λ6, λ8 (light blue circle); Lmmi,5 (red arrows in Figure 4) is suitable for λ1, λ3 (blue triangle) and λ5, λ7 (green rectangle); Lmmi,4 (orange arrow in Figure 4) is suitable for λ2, λ6 (red circle); Lmmi,3 (purple arrow in Figure 4) is suitable for λ4, λ8 (purple circle); Lmmi,2 (gray arrow in Figure 4) is suitable for λ3, λ7 (yellow rectangle); Lmmi,1 (pink arrow in Figure 4) is suitable for λ1, λ5 (blue triangle). Figure 5a-h show the intensity profile of the optical signals at the x-z plane. The first MMI coupler divides eight wavelengths (λ2, λ4, λ6, λ8 and λ1, λ3, λ5, λ7) at z = 3.5 mm; the second MMI coupler divides four wavelengths (λ2, λ4) and (λ4, λ8) as shown in Figure 5b,d,f,h at z = 5.5 mm; the third MMI coupler divides four wavelengths (λ1, λ3 and λ5, λ7) as shown in Figure 5a,c,e,g at z = 5.4 mm; the fourth MMI coupler divides two wavelengths (λ2 and λ6) as shown in Figure 5b,f at z = 6.6 mm; the fifth MMI coupler divides two wavelengths (λ4 and λ8) as shown in Figure 5d,h at z = 6.6 mm; the sixth MMI coupler divides two wavelengths (λ3 and λ7) as shown in Figure 5c,g at z = 6.6 mm; the seventh MMI coupler divides two wavelengths (λ1 and λ5) as shown in Figure 5a,e at z = 6.6 mm.  It can be seen in Figure 5a-h that the coupling length along the z-axis is 6.6 mm. This value indicates that this device has a compact size compared with the MMI demultiplexer device based on conventional Si waveguides [23].
FV-BPM simulations combined with Matlab code was performed to determine the 1 × 8 wavelength MMI demultiplexer properties. Figure 6 shows the spectral transmission results for the wavelengths around the C-band range (1530-1565 nm). FV-BPM simulations combined with Matlab code was performed to determine the 1 × 8 wavelength MMI demultiplexer properties. Figure 6 shows the spectral transmission results for the wavelengths around the C-band range (1530-1565 nm). By solving Equations (6) and (7), combined with the results of Figure 6, the values of the crosstalk, full width maximum (fwhm), and insertion losses can be found. Table 3 shows the values of the crosstalk, bandwidth (fwhm), and loss for each port.

Conclusions
To summarize, in this paper, we have shown that a 1 × 8 wavelength MMI demultiplexer can be implemented in slot Si-GaN waveguide structures.
Simulation results show that eight wavelengths-1530, 1535, 1540, 1545, 1550, 1555, 1560, and 1565 mm-that belong to the C-band range can be divided after a propagation length of 6.6 mm with insertion losses in the range of 0.9-2.12 dB.
We managed to shorten the coupling distance along the z-axis from 18 mm [23] to 6.6 mm. The device has low crosstalk (−19.97-−13.77 dB), with a bandwidth range of 1.8-3.6 nm. Therefore, this device can be very useful in optical networking systems that work on DWDM technology.
Although only the demultiplexer configuration is considered in this manuscript, the demultiplexer can also operate as a multiplexer in a reversed direction of the guided light.
Due to the use of the slot Si-GaN waveguide structure, the device has great potential for integration with CMOS technology for the design of a photonic-chip. By solving Equations (6) and (7), combined with the results of Figure 6, the values of the crosstalk, full width maximum (fwhm), and insertion losses can be found. Table 3 shows the values of the crosstalk, bandwidth (fwhm), and loss for each port.

Conclusions
To summarize, in this paper, we have shown that a 1 × 8 wavelength MMI demultiplexer can be implemented in slot Si-GaN waveguide structures.
Simulation results show that eight wavelengths-1530, 1535, 1540, 1545, 1550, 1555, 1560, and 1565 mm-that belong to the C-band range can be divided after a propagation length of 6.6 mm with insertion losses in the range of 0.9-2.12 dB.
We managed to shorten the coupling distance along the z-axis from 18 mm [23] to 6.6 mm.
The device has low crosstalk (−19.97-−13.77 dB), with a bandwidth range of 1.8-3.6 nm. Therefore, this device can be very useful in optical networking systems that work on DWDM technology.
Although only the demultiplexer configuration is considered in this manuscript, the demultiplexer can also operate as a multiplexer in a reversed direction of the guided light.
Due to the use of the slot Si-GaN waveguide structure, the device has great potential for integration with CMOS technology for the design of a photonic-chip.