# 4 × 4 Integrated Switches Based on On-Chip Wireless Connection through Optical Phased Arrays

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## Abstract

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## 1. Introduction

- (1)
- The proposed 4 × 4 OWS configuration, based on the use of OPAs with seven antennas, increases the number of transmitters and receivers that can be connected by the same wireless switch. This adds a further building block for on-chip wireless interconnection networks, thus opening new possibilities for the network design space exploration.
- (2)
- The design criteria for the OPA are identified and the OWS performances are analyzed and optimized by the Finite Difference Time Domain (FDTD) numerical simulations.
- (3)
- The effect of multipath propagation in the multi-layer on-chip structure is evaluated, showing that the device performances can be optimized, in terms of insertion loss and crosstalk, by varying the cladding layer thickness.
- (4)
- The effect on the OWS behavior of a non-ideal distribution of the power in input to the OPA is investigated. For this purpose, we first report the results of the design of a 1 × 7 beam splitter, based on a Multi-Mode Interference (MMI) device. Then, the MMI output signals are considered in input to the transmitting OPA to evaluate the effect of the non-uniform distribution of the OPA input on the performances of the OWS. This analysis shows that the OWS performances are not significantly affected by a non-ideal distribution of power in input to the OPA.

## 2. 4 × 4 Optical Wireless Switch

_{i}with i = 1, 2, 3, 4) with four outputs (i.e., O

_{i}with i = 1, 2, 3, 4). A wavelength division multiplexing signal, with M channels associated with M different wavelengths, is launched in input to one of the OPAs (e.g., I

_{1}), and it is distributed to the seven antennas through a 1 × 7 beam splitter. Each antenna receives, in input, all the WDM channels, radiating them in the surrounding space.

#### 2.1. Optical Phased Array Radiation Diagram

_{T}= 130 nm) [34]. The distance between the antennas in the OPA is chosen to be equal to d = λ

_{m}, where λ

_{m}is the wavelength in the surrounding medium, where the radiation occurs. According to antenna theory, the distance d = λ

_{m}guarantees that the OPA exhibits only a main radiation lobe, which can be steered by suitably phase-shifting the antenna input signals [39]. In particular, considering a uniform linear array configuration, the phase shift α between two adjacent antennas is constant.

_{T}, with a corresponding decrease in the half-power beam width, i.e., the angular aperture of the radiated beam. Further details on the radiation characteristics of the single-taper antenna can be found in [37,38].

_{a}identical antennas can be obtained through the multiplication of the electromagnetic field radiated by the single antenna by the array factor (AF), expressed as [38,39]:

_{q}is the excitation amplitude of each element, and k = 2π n

_{m}/λ is the propagation constant in a homogeneous medium with the refractive index n

_{m}at the wavelength λ. The angle ϕ shown in the scheme of Figure 1 is defined considering the spherical coordinate reference system, where r is the modulus of the position vector

**r**that identifies the calculation point, θ is the inclination angle (between

**r**and the z axis), and ϕ is the azimuthal angle (angle of rotation from the x axis). The behavior of a one-dimensional array is well described considering the plane identified by the direction x of maximum radiation for the single antenna and the axis y of the alignment of the array. Therefore, in the following, the radiation characteristics of the OPA are reported considering the xy plane, and they are represented as a function of the angle ϕ.

_{a}= 7 taper antennas and for different values of the phase shift α. The distance between two adjacent antennas in the OPA is equal to d = λ

_{m}, whereas the taper length is L

_{T}= 2 μm. The gain G(θ, ϕ) is calculated as [39]:

_{in}is the total power in the input to the array, given by the sum of the power values in the input to each antenna waveguide.

_{a}, with p = 1, 2, 3, are chosen to steer the main beam on the same positions of the nulls of the broadside (α = 0°) array, thus minimizing the crosstalk. In Figure 2, each of the seven main lobes, highlighted by a different number, corresponds to an addressable receiver. As analyzed in [38], the magnitude of the main radiation lobes, for the different values of the phase shift α, follows the envelope of the single-antenna radiation diagram. Therefore, according to the single-antenna radiation characteristics, the taper length L

_{T}= 2 µm (i.e., short-taper condition) has been chosen to minimize the variation in the maximum gain of the steered beams and, therefore, the difference in the power received by the different output OPAs.

#### 2.2. 4 × 4 OWS Operation Principle and Performances

_{1}is transmitting, the receiver O

_{1}can be illuminated when α = 0°. Similarly, when α = +p360°/N

_{a}, with p = 1, 2, 3, the receivers O

_{i}, with i = 2, 3, 4, can be addressed.

_{2}can be connected to O

_{1}when α = −360°/N

_{a}= 51.4°, whereas it can be connected to O

_{2}when α = 0° and to the other receivers O

_{3}and O

_{4}when α is, respectively, α = +360°/N

_{a}= 51.4° and α = +2∙360°/N

_{a}= 102.8°.

_{i}transmitters with the four receivers O

_{i}.

_{Si}= 3.457), an overlying layer of silicon dioxide SiO

_{2}(with a height equal to 3 µm and a refractive index n

_{SiO2}= 1.445), and another layer of Si (220 nm-thick), where the standard waveguides and the antennas are patterned. A further thin layer of borophosphorous tetraethyl orthosilicate (BPTEOS) (of a height equal to 300 nm and a refractive index n

_{BPTEOS}= 1.453) was considered on top of the antennas to improve the homogeneity of the refractive index around the antennas. The BPTEOS is then covered with a UV26 polymer cladding layer (with a thickness t = 3.78 µm and a refractive index n

_{UV26}= 1.526). The last layer of the multilayer stack, considered in the simulations, is air. Both the bottom bulk Si layer and the top air layer are considered as semi-infinite by using Perfectly Matched Layer (PML) boundary conditions.

_{1}and the four receivers O

_{i}, with i = 1, 2, 3, 4, thanks to the symmetry of the radiation diagrams. Figure 3 shows the transmittances T

_{Oi}in dB, calculated as a function of the wavelength, at the receiving OPAs, i.e., O

_{1}, O

_{2}, O

_{3}, and O

_{4}, when the transmitting OPA I

_{1}is excited with phase shifts: (a) α = 0°, (b) α = 51.4°, (c) α = 102.8°, and (d) α = 154.2°. The link distance d

_{link}= 70 μm was arbitrarily chosen. Figure 3 agree with the connectivity table (Table 1), as the addressed receivers exhibit high transmittance values. Nonetheless, a small part of the signal is also received by the non-addressed outputs, thus originating crosstalk.

_{j}=−10∙Log

_{10}(T

_{Oj})

_{Oj}is the transmittance at the addressed output Oj, and we define the crosstalk as:

_{Oi}is the transmittance of a non-addressed port. The arrows in Figure 3 highlight, for each phase-shift, the curves from which the maximum XT

_{i,j}is calculated according to Equation (3).

_{4}is considered (Figure 3d). It is worth pointing out that the simulations take into account the propagation in the multilayer structure, which is affected by multiple reflections at the media interfaces. This phenomenon causes constructive or destructive interference that depends on the multilayer characteristics, such as layer thicknesses, refractive indices, and the OPA radiation diagram [41,42].

_{j}in dB, calculated as a function of the wavelength and of the cladding thickness t, at the receiving OPAs, i.e., O

_{1}, O

_{2}, O

_{3}, and O

_{4}, when the transmitting OPA I

_{1}is excited: (a) IL

_{1}, (b) IL

_{2}, (c) IL

_{3}, and (d) IL

_{4}.

_{1}, O

_{2}, and O

_{3}are considered, whereas it occurs around t = 3 µm for the receiver O

_{4}, which, in general, exhibits higher insertion loss values. Considering Figure 4, for many of the values of the thickness t, the variation in IL

_{j}with the wavelength is limited to less than 3 dB, thus confirming that a wideband operation of the OWS can be achieved. This is particularly relevant when WDM communication schemes are implemented. Therefore, the layer thickness can be optimized to reduce the insertion loss while ensuring broadband communication. In particular, the configuration that minimizes the insertion loss at the further receiver O

_{4}(i.e., insertion IL

_{4}< 2.8 dB in the whole wavelength range) corresponds to t = 1 µm.

_{1}, O

_{2}, O

_{3}, and O

_{4}, when the transmitting OPA I

_{1}is excited: (a) XT

_{21}, (b) XT

_{12}, (c) XT

_{23}, and (d) XT

_{24}. To ease the readability of Figure 5, the color scales have been adapted to the range of variation of the XT values. Considering the XT values shown in Figure 5, the crosstalk remains, in general, below −15 dB. For the thickness t = 1 µm, the worst-case crosstalk XT

_{23}is below −18 dB in the whole wavelength range.

_{π}necessary to achieve a π phase shift with thermo-optic phase-shifters based on TiN metal is equal to P

_{π}= 21.4 mW.

_{q}is the power required for phase shifting each antenna in the array (identified by the index q), the total power for steering the optical phased array with N

_{a}= seven antennas is ${\mathrm{P}}_{\mathrm{O}\mathrm{P}\mathrm{A}}={{\displaystyle \sum}}_{\mathrm{q}=1}^{{\mathrm{N}}_{\mathrm{a}}}{\mathrm{P}}_{\mathrm{q}}$.

_{q}depends on the chosen phase shifter technology and on the array requirements. The power required for achieving a generic phase shift γ can be roughly estimated as P

_{i}= P

_{π}γ/π, given the almost linear dependence of the phase shift on the thermo-optic heater power.

_{q}= (q − 1)α. If γ

_{q}is greater than 360°, the angle γ

_{q}can be converted into the corresponding angle in the [0°, 360°] range by the following equation:

_{a}, with p = 1, 2, 3, are chosen to steer the main beam on the same positions of the nulls of the broadside (α = 0°) array, thus minimizing the crosstalk. The power necessary to steer the optical phased array of the transmitter I

_{1}toward the receiver O

_{4}is ${{\displaystyle \sum}}_{\mathrm{q}=1}^{{\mathrm{N}}_{\mathrm{a}}}{\mathrm{P}}_{\mathrm{q}}$ = 128 mW. To guarantee efficient communication between I

_{1}and O

_{4}, it is also necessary to virtually steer the radiation diagram of the receiving array toward the transmitter. This can be accomplished by applying a corresponding phase shift −α also at the addressed receiver. Therefore, the connection of one transmitter and one receiver would require approximately P

_{tot}= 2∙P

_{OPA}= 256 mW. Similar values of the total power are obtained for the connection of the other transmitters and receivers.

## 3. Effect of Non-Uniform Power Distribution at the Transmitting OPA Antennas

#### 3.1. 1 × 7 Multi-Mode Interference Beam Splitter

_{T}= 1 µm. The distance between the output waveguides was arbitrarily chosen to be equal to d

_{A}= 1.50 µm, but in the design of an overall integrated circuit, it can be customized to meet the topological constraints, e.g., for fabrication. The width of the MMI region is chosen to be equal to w

_{MMI}= 7∙d

_{A}. The optimal length of the MMI can be estimated by the following equation [50]:

_{π}is defined as the beat length of the two lowest-order modes of the multimode region, N

_{A}is the number of outputs, and λ

_{0}is the design wavelength (i.e., 1.55 µm), whereas n

_{1}and n

_{2}are the effective refractive indices of the two lowest-order modes of the MMI.

_{MMI}= 28.6 µm, estimated by Equation (6), must be optimized by the simulation of the full device, taking into account the non-uniformity of the power at the seven outputs. The output power non-uniformity NU, which is a function of the wavelength, can be quantified as:

_{Ai}with i = 1, 2,…7 are the transmittances in dB calculated at the seven output ports of the MMI. Indeed, the non-uniformity is zero when the output transmittances T

_{Ai}are all equal, and it is greater than zero when the power distribution is non-uniform.

_{MMI}, was performed by three-dimensional FDTD simulations. Figure 7 shows the transmittances T

_{Ai}calculated at the output ports (in dB) as a function of the MMI length and at the wavelength λ

_{0}= 1.55 µm. Given the symmetry of the device with respect to the central output A

_{4}, only four curves are visible in Figure 7. Considering Figure 7, the MMI length that gives the lowest variation of the transmittances (i.e., calculated non-uniformity NU(λ

_{0}) = 0.44 dB at the design wavelength λ

_{0}= 1.55 µm) is equal to L

_{MMI}= 26.5 µm.

_{0}) calculated at the design wavelength λ

_{0}= 1.55 µm (dashed curve) and the maximum non-uniformity in the bandwidth (solid curve) calculated, for each value of L

_{MMI}, as:

_{MMI}give higher non-uniformity. Considering Figure 8b, the length value that gives the lowest non-uniformity in the whole analyzed wavelength range, i.e., NU(λ) < NU

_{max}with NU

_{max}= 2.46 dB, is L

_{MMI}= 28 µm. The corresponding non-uniformity at the design wavelength is NU(λ

_{0}) = 1.93 dB.

_{MMI}= 28 µm, the overall insertion loss of the 1 × 7 MMI, calculated by summing up the power coupled at the seven output waveguides, is about IL

_{MMI}= 1.27 dB. Moreover, the calculated back reflection at the input port of the 1 × 7 MMI is below −14 dB in the whole frequency range.

_{i}is equipped with an OPA that radiates the whole signal spectrum (i.e., all the WDM channels) toward the same addressed receiver. At the addressed receiver, all the seven antennas of the OPA contribute to the received power. If the proper phase relation is ensured, as assumed in this paper, the signals received by each antenna in the receiving OPA constructively sum up in the output waveguide. Therefore, the Nx1 combiner is intended to constructively add the signals received by the seven antennas in the receiving OPA and to deliver the resulting signal at the output waveguide.

_{OPS}< 0.01 dB).

#### 3.2. OWS Performance with Non-Uniform Input Power

_{MMI}= 28 µm. As mentioned above, this configuration exhibits a non-uniformity NU(λ

_{0}) = 1.93 dB at the design wavelength and NU(λ) < 2.46 dB in the whole wavelength range.

_{q}coefficients in the theoretical formula of Equation (1). The array factor AF is then multiplied by the far-field of the single-taper antenna, calculated by FDTD simulation.

_{q}coefficients have been chosen to be equal to the amplitudes of the MMI output signals, calculated at the wavelength λ

_{0}= 1.55 µm. Figure 9 shows the gain as a function of the angle ϕ for an array of N

_{a}= seven taper antennas calculated for the uniform (solid curve) and the non-uniform (dashed curves) input amplitude distributions. The four values of the phase shift α necessary for the description of 4 × 4 OWS operation are considered: (a) α = 0°, (b) α = 51.4°, (c) α = 102.8°, and (d) α = 154.2°. In Figure 9 the represented ϕ range was restricted between −90° and 90° to ease the readability of the curves.

_{0}= 1.55 µm, thus taking into account the non-uniform power distribution at the 1 × 7 MMI outputs. We have chosen to apply a straightforward simulation approach in which the amplitudes of the seven mode sources do not change with the wavelength.

_{1}, O

_{2}, O

_{3}, and O

_{4}, when the transmitting OPA I

_{1}is excited with uniform (solid curves) and non-uniform (dashed curves) input signals. The phase shift values considered in Figure 10 are: (a) α = 0°, (b) α = 51.4°, (c) α = 102.8°, and (d) α = 154.2°.

_{12}is found for the connection between the transmitter I

_{1}and the receiver O

_{2}(Figure 10b), which now corresponds to the worst-case crosstalk. Nonetheless, the crosstalk XT

_{12}is still below −18 dB in the whole wavelength range.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Scheme of the 4 × 4 Optical Wireless Switch (OWS), which connects four-input with four-output Optical Phased Arrays (OPAs). The signal in each of the seven antennas in the OPAs is suitably phase-shifted by Optical Phase Shifters (OPSs) to guarantee beam steering.

**Figure 2.**Gain as a function of the angle ϕ calculated for an array of N

_{a}= seven taper antennas and for different values of the phase shift α. The distance between two adjacent antennas in the OPA is equal to d = λ

_{m}, whereas the taper length is L

_{T}= 2 μm.

**Figure 3.**Transmittance in dB, calculated as a function of the wavelength, at the receiving OPAs, i.e., O

_{1}, O

_{2}, O

_{3}, and O

_{4}, when the transmitting OPA I

_{1}is excited with phase shifts: (

**a**) α = 0°, (

**b**) α = 51.4°, (

**c**) α = 102.8°, and (

**d**) α = 154.2°. The simulated device exploits reconfigurable OPAs made of N = seven taper antennas with a taper length L

_{T}= 2 μm. The link distance is d

_{link}= 70 μm, and the UV26 cladding thickness is t = 3.78 µm.

**Figure 4.**Insertion loss in dB, calculated as a function of the wavelength and of the cladding thickness, at the receiving OPAs, i.e., O

_{1}, O

_{2}, O

_{3}, and O

_{4}, when the transmitting OPA I

_{1}is excited: (

**a**) IL

_{1}, (

**b**) IL

_{2}, (

**c**) IL

_{3}, and (

**d**) IL

_{4}. The simulated device exploits reconfigurable OPAs made of N = seven taper antennas with a taper length L

_{T}= 2 μm. The link distance is d

_{link}= 70 μm.

**Figure 5.**Crosstalk in dB, calculated as a function of the wavelength and of the cladding thickness, at the receiving OPAs, i.e., O

_{1}, O

_{2}, O

_{3}, and O

_{4}, when the transmitting OPA I

_{1}is excited: (

**a**) XT

_{21}, (

**b**) XT

_{12}, (

**c**) XT

_{23}, and (

**d**) XT

_{24}. The simulated device exploits reconfigurable OPAs made of N = seven taper antennas with a taper length L

_{T}= 2 μm. The link distance is d

_{link}= 70 μm.

**Figure 6.**Scheme of the 1 × 7 MMI beam splitter. The waveguides are made of silicon, and the same multilayer of the OWS is considered in the simulations with the UV26 cladding thickness t = 1 µm.

**Figure 7.**Transmittances T

_{Ai}at the output ports in dB as a function of the MMI length (calculated values (dots) and polynomial fitting (solid curves)) at the wavelength λ = 1.55 µm. The same multilayer of the OWS is considered in the FDTD simulations with the UV26 cladding thickness t = 1 µm.

**Figure 8.**(

**a**) Non-uniformity NU

_{MMI}at the output ports calculated in dB as a function of the MMI length and of the wavelength; (

**b**) non-uniformity NU(λ

_{0}) at the design wavelength λ

_{0}= 1.55 µm (calculated values (dots) and polynomial fitting (dashed curve)), and maximum non-uniformity in the bandwidth NU

_{max}(calculated values (dots) and polynomial fitting (solid curve)) as a function of the MMI length. The same multilayer of the OWS is considered in the FDTD simulations with the UV26 cladding thickness t = 1 µm.

**Figure 9.**Gain as a function of the angle ϕ for an array of N

_{a}= seven taper antennas calculated for uniform (solid curve) and non-uniform (dashed curves) input power distributions. Different values of the phase shift α are considered: (

**a**) α = 0°, (

**b**) α = 51.4°, (

**c**) α = 102.8°, and (

**d**) α = 154.2°. The distance between two adjacent antennas in the OPA is equal to d = λ

_{m}, whereas the taper length is L

_{T}= 2 μm.

**Figure 10.**Transmittance in dB, calculated as a function of the wavelength, at the receiving OPAs, i.e., O

_{1}, O

_{2}, O

_{3}, and O

_{4}, when the transmitting OPA I

_{1}is excited with uniform (solid curves) and non-uniform (dashed curves) input signals. The phase shift values are: (

**a**) α = 0°, (

**b**) α = 51.4°, (

**c**) α = 102.8°, and (

**d**) α = 154.2°. The simulated device exploits reconfigurable OPAs made of N = seven taper antennas with a taper length L

_{T}= 2 μm. The link distance is d

_{link}= 70 μm, and the UV26 cladding thickness is t = 1 µm.

**Table 1.**Phase shifts α required for connecting the four I

_{i}transmitters with the four receivers O

_{i}.

Input\Output | O_{1} | O_{2} | O_{3} | O_{4} |
---|---|---|---|---|

I_{1} | α = 0° | α = 51.4° | α = 102.8° | α = 154.2° |

I_{2} | α = −51.4° | α = 0° | α = 51.4° | α = 102.8° |

I_{3} | α = −102.8° | α = −51.4° | α = 0° | α = 51.4° |

I_{4} | α = −154.2° | α = −102.8° | α = −51.4° | α = 0° |

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## Share and Cite

**MDPI and ACS Style**

Calò, G.; Bellanca, G.; Fuschini, F.; Barbiroli, M.; Bertozzi, D.; Tralli, V.; Petruzzelli, V.
4 × 4 Integrated Switches Based on On-Chip Wireless Connection through Optical Phased Arrays. *Photonics* **2023**, *10*, 367.
https://doi.org/10.3390/photonics10040367

**AMA Style**

Calò G, Bellanca G, Fuschini F, Barbiroli M, Bertozzi D, Tralli V, Petruzzelli V.
4 × 4 Integrated Switches Based on On-Chip Wireless Connection through Optical Phased Arrays. *Photonics*. 2023; 10(4):367.
https://doi.org/10.3390/photonics10040367

**Chicago/Turabian Style**

Calò, Giovanna, Gaetano Bellanca, Franco Fuschini, Marina Barbiroli, Davide Bertozzi, Velio Tralli, and Vincenzo Petruzzelli.
2023. "4 × 4 Integrated Switches Based on On-Chip Wireless Connection through Optical Phased Arrays" *Photonics* 10, no. 4: 367.
https://doi.org/10.3390/photonics10040367