# Polarization Effect on the Performance of On-Chip Wireless Optical Point-to-Point Links

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{3}N

_{4}technology has been chosen in this paper as a case of study, but the Vivaldi antenna design criteria and the multilayer propagation analysis can be virtually extended to any technology. Silicon nitride (SiN) is one of the platforms, together with silicon-on-insulator (SOI), that enable the on-chip integration of the optical networks thanks to the compatibility with Complementary Metal-Oxide Semiconductor (CMOS) technology. The proposed dielectric antenna can be regarded as a building block for optical wireless NoCs (OWiNoCs). Moreover, thanks to its compatibility with standard optical integrated technology, this antenna building block can be combined with standard waveguide components, thus widening the possibility of network design exploration.

## 2. Design of the Dielectric Vivaldi Antenna

_{1}, y

_{1}and x

_{2}, y

_{2}are the edge coordinates of the Vivaldi profile in the xy plane.

_{SiO2}= 1.445 at the wavelength λ = 1.55 μm. This assumption eases the calculation of the far-field radiation diagrams because a homogeneous medium is required when the near-to-far-field transformations are performed.

_{a}. The initial total width of the slot waveguide, which opens according to the Vivaldi profile, is geometrically constrained by the width w of the input strip waveguide. Specifically, these geometrical parameters are linked according to the equation w = g + 2s, where w is the strip width, g is the initial gap of the slot Vivaldi antenna, and s is the width of the slot rails. The antenna gain can be optimized by changing the cross-section geometrical parameters (i.e., w, g, and s). For a given value of the strip width w, the gap g can be suitably chosen to maximize the gain. Moreover, once the antenna cross section has been optimized, the antenna gain can be further improved by changing the length L

_{a}of the Vivaldi radiator.

#### 2.1. Direct-Mode Coupling Analysis

**E**

_{1}and

**E**

_{2}are the electric field components in the strip and in the slot waveguides, respectively, and ${H}_{1}^{*}$ and ${H}_{2}^{*}$ are the complex conjugates of the corresponding magnetic field components.

_{1}and A

_{2}by the Discrete Fourier Transform (DFT) of the time domain fields obtained via 3D-FDTD simulation of the whole structure. Sections A

_{1}and A

_{2}in Figure 1 correspond, respectively, to the strip and to the slot waveguides. The overlap integral of Equation (3) was calculated, either for the TE or for the TM fundamental modes, considering the electric and magnetic field distributions at these two sections.

#### 2.2. Vivaldi Antenna Radiation Analysis

_{SiO2}= 1.445) as required by near-to-far field projection calculation. The antenna gain G(θ,ϕ) is defined as:

_{in}is the input power launched into the strip waveguide [49].

_{a}= 25 μm. Moreover, Figure 3c,d report the electric field pattern of the Vivaldi antenna, which is calculated via 3D-FDTD in the xy plane for z = 0 μm (i.e., in the middle of the antennas) for the TE and TM polarizations. The geometry of the Vivaldi antenna is also evidenced by the black lines in Figure 3c,d. The color bar represents the normalized amplitude of the electric field in logarithmic scale. It is worth pointing out that the field patterns of Figure 3c,d are calculated in the antenna region at the wavelength λ = 1.55 µm via DFT of the time domain fields. Therefore, they are not far-fields, but they can help to qualitatively explain the far-field radiation diagrams.

_{Φ}and H

_{θ}are the dominant components for the TE polarization, whereas E

_{θ}and H

_{Φ}are the dominant ones for the TM polarization. As will be shown in the following, although the gain is the same, the difference in the dominant components will lead to a different behavior of the wireless propagation in the multilayer on-chip structure.

_{a}. Figure 5a,b show the maximum gain for the TE (solid curves) and the TM (dashed curves) modes, respectively, in the case of the three configurations A (w = 600 nm—blue curve), B (w = 900 nm—red curve), and C (w = 1100 nm—yellow curve). The results reported in Figure 5 were calculated by arbitrarily choosing the antenna length value L

_{a}= 25 μm. In each case, the radiation diagrams are similar to those shown in Figure 3a,b.

_{11}|

^{2}at the input strip waveguide. The Vivaldi antenna is a single port device with negligible dielectric losses. Therefore, if the back reflection at the input port is low, most of the input power is coupled from the strip waveguide to the Vivaldi antenna, and then, it is radiated in the surrounding space. Figure 6 shows the power reflection coefficient |S

_{11}|

^{2}calculated at the input port for the TE (solid curve) and TM (dashed curves) modes as a function of the initial slot gap value g. The blue, red, and yellow curves correspond to the configurations A (w = 600 nm), B (w = 900 nm), and C (w = 1100 nm), respectively.

_{11}|

^{2}coefficient is less than −21 dB for all the considered cases, the power is efficiently coupled from the strip waveguide to the Vivaldi antenna coherently with the mode overlap integral in Figure 2.

_{a}of the Vivaldi radiator. As an example, Figure 7 shows the maximum gain as a function of the antenna length L

_{a}for the TE (solid curve) and the TM (dashed curve) modes, in the case of configuration B (w = 900 nm) with slot gap g = 300 nm and slot rail width s = 300 nm. The results of the other configurations are not reported to avoid redundancies.

_{2}medium, are useful for defining the design criteria of the antenna and for identifying those configurations that show similar radiation characteristics, which are expressed in terms of gain, for both the TE and the TM polarizations. This makes it possible to study the TE and TM propagation in on-chip point-to-point wireless links with the same antenna gain. According to the well-known Friis transmission equation, when the wireless communication takes place in homogeneous medium, the received power is related to the antenna gain of the transmitter and of the receiver. Therefore, the same received power is estimated, in homogeneous medium, for both the TE and TM polarizations in point-to-point links between two integrated Vivaldi antennas.

## 3. Wireless Propagation in On-Chip Multilayer Structure with TE and TM Polarizations

_{2}of height ${\mathrm{h}}_{\mathrm{S}}=2\mathsf{\mu}\mathrm{m}$, and a further layer of SiN of thickness $\mathrm{t}=300\mathrm{nm}$, housing the standard waveguides and the Vivaldi antennas. The antenna layer is then covered with a polymer-based cladding layer. The topmost layer, i.e., air, and the bottom one, i.e., bulk Si, were modeled as infinite in the simulations through Perfectly Matched Layer (PML) boundary conditions. The PML conditions were also applied on all the edges of the computational domain.

_{p}= 1.4925) very near to that of SiO

_{2}(n

_{SiO2}= 1.445).

_{link}for different values d of the cladding layer thickness. The transmittances, which were obtained through a mode expansion monitor [45], are expressed in dB, and they represent the fraction of power coupled to the mode of the receiving waveguide by the corresponding antenna.

_{SiO2}= 1.445) was also calculated by the well-known Friis transmission equation [49]:

_{Tx}is the power in input to the transmitter waveguide, P

_{Rx}is the power coupled to the receiver waveguide, G

_{Tx}and G

_{Rx}are the gains of the transmitting and of the receiving antenna (calculated, as before, when the antennas are immersed in a homogeneous SiO

_{2}medium), λ

_{SiO2}is the wavelength in the propagation medium, and d

_{link}is the link distance, i.e., the distance between the Rx and the Tx antennas. Friis-formula transmittance is also reported in Figure 9 for the TE and for the TM polarizations (black curves). Because the gain of the Vivaldi antenna is the same for the two polarizations, the curves calculated by the Friis transmission equation are equal for the TE and the TM propagations.

_{link}= 150 µm and d = 3 µm, the transmittances are T = −16.8 dB and T = −6.2 dB for the TE and the TM polarizations, respectively.

_{Φ}and H

_{θ}are the dominant components for the TE polarization, whereas E

_{θ}and H

_{Φ}are the dominant ones for the TM polarization. Therefore, when the fundamental TE mode is given in input to the transmitting antenna, the radiated electromagnetic field can be considered to be s-polarized with respect to the multilayer interfaces, being the electric field E

_{Φ}parallel to the interfaces. Similarly, the TM mode gives a p-polarized electromagnetic field. The different behavior of the TE- and the TM-polarized waves is, therefore, associated to the different boundary conditions at the interfaces and to the different Fresnel coefficients.

_{link}= 100 μm, and different values of the thickness d are considered, namely: (a) d = 0.5 μm, (b) d = 0.9 μm, (c) d = 3 μm, and (d) d = 4 μm. The antennas and the multilayer interfaces are denoted by the black lines.

_{2}) layer, and it experiences a decay while propagating from the Tx to the Rx antenna because it is partly transmitted in the Si bulk substrate and in the air overlayer. Therefore, the Rx antenna can collect only a small part of the overall electromagnetic field. When d = 0.9 μm (Figure 10b), the field tends to concentrate more in the cladding layer (PMMA), and it is received more efficiently by the Rx antenna. This guiding effect in the PMMA layer becomes more apparent in the case of d = 3 μm (Figure 10c). In the case of d = 4 μm (Figure 10d), we can still consider the field to be mainly confined in the PMMA cladding, but an interference pattern is clearly visible, which explains the oscillations of the transmittance (green curve in Figure 9a) as a function of the link distance.

_{link}= 100 μm. Furthermore, in this case, different values of the thickness d are considered, namely: (a) d = 0.5 μm, (b) d = 0.9 μm, (c) d = 3 μm, and (d) d = 4 μm.

_{link}= 100 μm. Different values of the thickness d are considered, namely: (a) d = 0.5 μm, (b) d = 0.9 μm, (c) d = 3 μm, and (d) d = 4 μm. The solid lines denote the geometry of the antennas, and the color bar represents the normalized amplitude of the electric field in logarithmic scale.

_{Φ}and H

_{θ}are the dominant components for the TE polarization, whereas E

_{θ}and H

_{Φ}are the dominant ones for the TM polarization.

_{clad}= 1.492 and for n

_{clad}= 1.592, whereas it is lower when the cladding refractive index is equal to that of the SiO

_{2}substrate (red dashed curve of Figure 14b).

_{link}= 100 µm, and the PMMA is considered to be a cladding polymer (thickness d = 3 µm) in the multilayer structure. As Figure 15 shows, the transmittance is almost constant with the wavelength (variation in less than 0.6 dB for both the polarizations), covering the entire C-band. Given the broadband behavior, the proposed antenna is suitable for the implementation of WDM schemes in on-chip communication.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Scheme of the dielectric Vivaldi antenna directly coupled to a strip waveguide. The antenna is composed of silicon nitride and, to investigate its radiation properties, it is embedded into a homogenous medium with refractive index n

_{SiO2}= 1.445.

**Figure 2.**Overlap integral calculated according to Equation (3) as a function of the initial slot gap value g. The blue, red, and yellow curves correspond to configurations A (w = 600 nm), B (w = 900 nm), and C (w = 1100 nm), respectively. For each value of the slot gap g, the slot rail width s can be calculated from the formula s = (w − g)/2. The wavelength is λ = 1.55 µm.

**Figure 3.**(

**a**,

**b**) Gain as a function of (

**a**) the angle θ (with Φ = 0) and (

**b**) the angle Φ (with θ = π/2), for the TE (solid curves) and TM (dashed curves) modes in the case of the Vivaldi antenna with strip width w = 900 nm, slot gap g = 300 nm, slot rail width s = 300 nm, and antenna length L

_{a}= 25 μm. (

**c**,

**d**) Electric field pattern calculated via 3D-FDTD in the xy plane for z = 0 μm (i.e., in the middle of the antennas) for the TE (

**c**) and TM (

**d**) polarizations. The color bar represents the normalized amplitude of the electric field in logarithmic scale. The wavelength is λ = 1.55 µm.

**Figure 4.**(

**a**,

**b**) Gain as a function of (

**a**) the angle θ (with Φ = 0) and (

**b**) the angle Φ (with θ = π/2), for the TE (solid curves) and TM (dashed curves) modes in the case of the truncated waveguide. (

**c**,

**d**) Electric field pattern calculated via 3D-FDTD in the xy plane for z = 0 μm (i.e., in the middle of the antennas) for the TE (

**c**) and TM (

**d**) polarizations. The color bar represents the normalized amplitude of the electric field in logarithmic scale. The wavelength is λ = 1.55 µm.

**Figure 5.**Maximum gain for (

**a**) the TE (solid curves) and (

**b**) the TM (dashed curves) in the case of the three configurations A (w = 600 nm), B (w = 900 nm), and C (w = 1100 nm). In all the considered cases, the gain maximum occurs at Φ = 0 and θ = π/2. The antenna length is L

_{a}= 25 μm, and the wavelength is λ = 1.55 µm.

**Figure 6.**Power reflection coefficient |S

_{11}|

^{2}calculated at the input port for the TE (solid curve) and TM modes (dashed curves) as a function of the initial slot gap value g. The blue, red, and yellow curves correspond to configurations A (w = 600 nm), B (w = 900 nm), and C (w = 1100 nm), respectively. For each value of the slot gap g, the slot rail width s can be calculated from the formula s = (w −g)/2. The wavelength is λ = 1.55 µm.

**Figure 7.**Maximum gain as a function of the antenna length L

_{a}for the TE (solid curve) and the TM (dashed curve) modes, in the case of configuration B (w = 900 nm) with slot gap g = 300 nm and slot rail width s = 300 nm. The wavelength is λ = 1.55 µm.

**Figure 8.**Scheme of the on-chip multilayered structure: (

**a**) yz cross-section, and (

**b**) xz cross-section.

**Figure 9.**Transmittance in dB, which is calculated at the receiver waveguide as a function of the link distance for different values of the PMMA top-layer thickness: (

**a**) TE and (

**b**) TM polarizations. The black curves denote the transmittance calculated by the Friis transmission equation for a point-to-point link in a homogeneous medium (with refractive index n

_{SiO2}= 1.445). The wavelength is λ = 1.55 µm.

**Figure 10.**Normalized electric field (in logarithmic scale) calculated in the xz-vertical plane for y = 0 μm (i.e., in the middle of the antennas) for the TE polarization. The link distance is d

_{link}= 100 μm and different values of the thickness d are considered, namely: (

**a**) d = 0.5 μm, (

**b**) d = 0.9 μm, (

**c**) d = 3 μm, and (

**d**) d = 4 μm. The antennas and the multilayer interfaces are denoted by the black lines. The wavelength is λ = 1.55 µm.

**Figure 11.**Normalized electric field (in logarithmic scale) calculated in the xz-vertical plane for y = 0 μm (i.e., in the middle of the antennas), for the TM polarization. The link distance is d

_{link}= 100 μm, and different values of the thickness d are considered, namely: (

**a**) d = 0.5 μm, (

**b**) d = 0.9 μm, (

**c**) d = 3 μm, and (

**d**) d = 4 μm. The antennas and the multilayer interfaces are denoted by the black lines. The wavelength is λ = 1.55 µm.

**Figure 12.**Normalized electric field (in logarithmic scale) calculated in the xy-vertical plane for z = 0 μm (i.e., in the middle of the antennas) for the TE polarization. The link distance is d

_{link}= 100 μm, and different values of the thickness d are considered, namely: (

**a**) d = 0.5 μm, (

**b**) d = 0.9 μm, (

**c**) d = 3 μm, and (

**d**) d = 4 μm. The antennas are denoted by the black lines. The wavelength is λ = 1.55 µm.

**Figure 13.**Normalized electric field (in logarithmic scale) calculated in the xy-vertical plane for z = 0 μm (i.e., in the middle of the antennas) for the TM polarization. The link distance is d

_{link}= 100 μm, and different values of the thickness d are considered, namely: (

**a**) d = 0.5 μm, (

**b**) d = 0.9 μm, (

**c**) d = 3 μm, and (

**d**) d = 4 μm. The antennas are denoted by the black lines. The wavelength is λ = 1.55 µm.

**Figure 14.**Transmittance in dB, which is calculated at the receiver waveguide as a function of the link distance for different values of the cladding refractive index: (

**a**) TE and (

**b**) TM polarizations. The black curves denote the transmittance calculated by the Friis transmission equation for a point-to-point link in a homogeneous medium (with refractive index n

_{SiO2}= 1.445). The cladding thickness is d = 3 µm, and the wavelength is λ = 1.55 µm.

**Figure 15.**Transmittance in dB, which is calculated at the receiver waveguide as a function of wavelength for the TE (solid curve) and the TM (dashed curves) polarizations. The link distance is d

_{link}= 100 µm, and a multilayer structure with PMMA as cladding polymer and cladding thickness d = 3 µm is considered.

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## Share and Cite

**MDPI and ACS Style**

Calò, G.; Bellanca, G.; Fuschini, F.; Barbiroli, M.; Tralli, V.; Petruzzelli, V.
Polarization Effect on the Performance of On-Chip Wireless Optical Point-to-Point Links. *Appl. Sci.* **2023**, *13*, 3062.
https://doi.org/10.3390/app13053062

**AMA Style**

Calò G, Bellanca G, Fuschini F, Barbiroli M, Tralli V, Petruzzelli V.
Polarization Effect on the Performance of On-Chip Wireless Optical Point-to-Point Links. *Applied Sciences*. 2023; 13(5):3062.
https://doi.org/10.3390/app13053062

**Chicago/Turabian Style**

Calò, Giovanna, Gaetano Bellanca, Franco Fuschini, Marina Barbiroli, Velio Tralli, and Vincenzo Petruzzelli.
2023. "Polarization Effect on the Performance of On-Chip Wireless Optical Point-to-Point Links" *Applied Sciences* 13, no. 5: 3062.
https://doi.org/10.3390/app13053062