# Polarization independent silicon grating antenna based on subwavelength metamaterials

Sarra Salhi, Xiaochen Xin, Daniel Benedikovic, Carlos Alonso-Ramos, Laurent Vivien, Delphine Marris-Morini, Eric Cassan, Winnie Ye, Daniele Melati

► To cite this version:

Sarra Salhi, Xiaochen Xin, Daniel Benedikovic, Carlos Alonso-Ramos, Laurent Vivien, et al. Polarization independent silicon grating antenna based on subwavelength metamaterials. 2024. hal-04557012

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# Polarization independent silicon grating antenna based on subwavelength metamaterials

Sarra Salhi, Xiaochen Xin, Daniel Benedikovic, Carlos Alonso-Ramos, Laurent

Vivien, Delphine Marris-Morini, Eric Cassan, Winnie Ye, Daniele Melati

► To cite this version:

Sarra Salhi, Xiaochen Xin, Daniel Benedikovic, Carlos Alonso-Ramos, Laurent Vivien, et al.. Polarization independent silicon grating antenna based on subwavelength metamaterials. Scientific Reports, 2025, 15, pp.13276. 10.1038/s41598-025-97833-3. hal-04557012v2

HAL Id: hal-04557012

https://hal.science/hal-04557012v2

Submitted on 26 Feb 2025

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entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
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Polarization independent silicon grating antenna
based on subwavelength metamaterials

Sarra Salhi¹,*, Xiaochen Xin²,*, Daniel Benedikovič²,³,
Carlos Alonso-Ramos ¹, Laurent Vivien ¹,
Delphine Marris-Morini¹, Eric Cassan¹, Winnie N. Ye²,
Daniele Melati ¹

¹Centre de Nanosciences et de Nanotechnologies, Université Paris-Saclay, CNRS, 91120 Palaiseau, France

²Department of Electronics, Carleton University, Ottawa, ON K1S 5B6, Canada

³Dept. Multimedia and Information-Communication Technology, University of Zilina, 01026 Zilina, Slovakia

Abstract

Optical antennas are key components of an optical phased array sys-
tem, enabling light coupling between the chip and the free space. In such
systems, surface gratings are commonly used as antenna elements, which
however suffer from a strong polarization sensitivity of their scattering an-
gle and efficiency. Here, we experimentally demonstrate a surface grating
antenna with polarization insensitive behavior on the 500 nm silicon-on-
insulator platform exploiting subwavelength metamaterials. The antenna
successfully achieves the same diffraction angle of 10° for both TE and
TM polarizations, an estimated scattering efficiency of -4 dB, and a dif-
ference in diffraction efficiency between the two polarizations smaller than
1 dB over a bandwidth of 31 nm. This antenna facilitates efficient light
coupling into and out of photonic integrated circuits.

1 Introduction

Optical Phased Arrays (OPAs) for on-chip beam forming and steering represent a promising alternative to traditional mechanically moving components in various applications, notably in light detection and ranging (LiDAR) and free-space optical communications [1–5]. Integrated optical antennas, which are responsible of emitting and receiving light into and from the free space, are the fundamental components of an OPA. Although recent literature demonstrated optical antennas based on metallic structures, dielectric pillars, fiber lenses, photonic crystals and ceramics [6–9], dielectric surface gratings are still the most popular
# Polarization independent silicon micro antenna based on a subwavelength metamaterial

Sarra Salhi<fnref n="1" />,*,+, Xiaochen Xin<fnref n="2" />,+, Daniel Benedikovič<fnref n="2" />,<fnref n="3" />, Carlos Alonso-Ramos<fnref n="1" />, Laurent Vivien<fnref n="1" />, Delphine Marris-Morini<fnref n="1" />, Eric Cassan<fnref n="1" />, Winnie N.Ye<fnref n="2" />, and Daniele Melati<fnref n="1" />

## ABSTRACT

Optical antennas are key components of an optical phased array system, enabling light coupling between the chip and the free space. In such systems, surface gratings are commonly used as antenna elements, which however suffer from a strong polarization sensitivity of their scattering angle and efficiency. Here, we propose a versatile approach to realize micro antennas based on surface gratings with a polarization insensitive behavior exploiting a subwavelength metamaterial in the silicon-on-insulator platform. In the experimental demonstration, the antenna successfully achieves the same diffraction angle of 10° for both TE and TM polarizations and an estimated scattering efficiency of -4 dB despite a very compact footprint of 6.4 µm x 2.9 µm. The difference in diffraction efficiency between the two polarizations remains smaller than 1 dB over a bandwidth of 31 nm.

## Introduction

Optical Phased Arrays (OPAs) for on-chip beam forming and steering represent a promising alternative to traditional mechanically moving components in various applications, notably in light detection and ranging (LiDAR) and free-space optical communications<fnref n="1" />⁻⁵. Integrated optical antennas, which are responsible for emitting and receiving light to and from free space, are the fundamental components of an OPA. Although recent literature demonstrated optical antennas based on metallic structures, dielectric pillars, fiber lenses, photonic crystals and ceramics⁶⁻⁹, dielectric surface gratings are still the most popular choice for OPAs because of their relative ease of fabrication and the possibility of achieving high efficiency¹⁰⁻¹⁴. Surface gratings with high diffraction performances for either transverse-electric (TE) or transverse-magnetic (TM) waveguide modes have been extensively reported in the literature¹⁵⁻²⁶, especially exploiting L-shaped diffraction elements to break the vertical symmetry and achieve high directionality¹⁸,²⁷⁻³⁰. Grating antennas with specially designed features such as an optimized radiation pattern, improved steerability, and reduced grating lobes have been reported as well³¹⁻³⁴. Micron-scale antennas are of particular interest for OPAs because the reduced footprint and broad radiated beam are fundamental to achieve large steering ranges³⁵. The main drawback of surface gratings is their strong polarization sensitivity, arising from the intrinsic birefringence of the grating Bloch mode which causes TE and TM polarized light to be diffracted at different angles and with different efficiencies³⁶,³⁷. The dependence of the optical behavior of the antenna on the polarization of the light can represent a significant challenge, for example in implementing polarization division multiplexing in optical communication systems or ensuring consistent and reliable coupling efficiencies of receiver devices. Polarization sensitivity is particularly pronounced in the high contrast, silicon-on-insulator (SOI) platform commonly used for the development of OPAs because of its strong waveguide birefringence. Nonetheless, optical antennas with a single feeding waveguide capable of effectively supporting both TE and TM polarizations would be extremely beneficial for enhancing the robustness and performance of OPA systems.

A polarization insensitive grating requires the TE and TM polarized Bloch modes to have the same effective index, a condition that brings to designs with low efficiencies in the 220-nm SOI platform³⁸. A recent design of a grating coupler for standard fiber coupling reported in³⁹ suggests (based only on simulations) that a considerable improvement could be achieved in the efficiency moving to a thicker silicon layer (500 nm) which allows to better guide the TM waveguide mode. Alternatively, subwavelength grating metamaterials (SWG) have also been explored in the literature as a promising path to increase the degrees of freedom available for the design of the grating and achieve a polarization insensitive behavior with higher scattering efficiencies⁴⁰⁻⁴³. Similarly to metasurface⁴⁴⁻⁴⁶ SWGs are realized by arranging their unit cells at a distance much smaller than

<footnote n="1">¹Centre de Nanosciences et de Nanotechnologies, Université Paris-Saclay, CNRS, 91120 Palaiseau, France</footnote>

<footnote n="2">²Department of Electronics, Carleton University, Ottawa, ON K1S 5B6, Canada</footnote>

<footnote n="3">³Currently, with the Dept. Multimedia and Information-Communication Technology, University of Zilina, 01026 Zilina, Slovakia</footnote>

<footnote>*sarra.salhi@universite-paris-saclay.fr</footnote>

<footnote>+these authors contributed equally to this work</footnote>
choice for OPAs because of their relative ease of fabrication and the possibil-
ity of achieving high efficiency [10–14]. Surface gratings with high diffraction
performances for either transverse-electric (TE) or transverse-magnetic (TM)
waveguide modes have been extensively reported in the literature [15–26], espe-
cially exploiting L-shaped diffraction elements to break the vertical symmetry
and achieve high directionality [18, 27–30]. Grating antennas with specially de-
signed features such as an optimized radiation pattern, improved steerability,
and reduced grating lobes have been reported as well [31–34]. Nonetheless, the
main drawback of surface gratings is their strong polarization sensitivity, which
cause TE and TM modes to be diffracted at different angles and with different
efficiencies [35]. The dependence of the optical behavior of the antenna on the
polarization of the light often represents a significant challenge, for example in
implementing polarization division multiplexing in optical communication sys-
tems or ensuring consistent and reliable coupling efficiencies of receiver devices.
Polarization sensitivity is particularly pronounced in the high contrast, silicon-
on-insulator (SOI) platform commonly used for the development of OPAs be-
cause of its strong waveguide birefringence. Nonetheless, optical antennas with
a single feeding waveguide capable of effectively supporting both TE and TM
polarizations would be extremely beneficial for enhancing the robustness and
performance of OPA systems. To overcome this limitation without moving to
a different platform or introducing additional materials, subwavelength grat-
ing metamaterials (SWG) has been explored in the literature as a promising
path [36–39]. SWGs are realized by arranging their unit cells at a distance
much smaller than the wavelength, resulting in an effective artificial material
whose optical properties can be controlled by modifying the geometry of the unit
cells [40]. For example, by exploiting the additional degree of freedom offered
by SWG metamaterials, a fiber grating coupler with a difference between TE
and TM coupling efficiencies smaller than 1 dB over a bandwidth of 12 nm was
experimentally demonstrated in [36] on an air-cladded, suspended membrane
waveguide.

In this work, we report on the design and experimental demonstration of an efficient and polarization insensitive grating antenna for free-space coupling based on SWG metamaterials and an L-shaped geometry. The antenna is realized on a 500-nm SOI platform, does not require the removal of the buried oxide, has an oxide top cladding, and a compact footprint of 6.4 µm x 2.9 µm. 3D FDTD simulations show that both TE and TM polarized modes are diffracted with the same scattering angle of 10° with an upward diffraction efficiency of -2.8 dB and -2.4 dB, respectively. The experimental characterization of the antenna, performed with a fiber-based setup, is in good agreement with simulations and demonstrates a difference in TE-TM coupling efficiency at 10° smaller than 1 dB over a 31 nm wavelength range, with an estimated free-space upward scattering efficiency of -4 dB.
<figure><img src="image_2.png" /><figcaption>Figure 1. Schematic of the micro antenna. (a) Perspective view and (b) cross-section.</figcaption></figure>

the wavelength, resulting in an effective artificial material whose optical properties can be controlled by modifying the geometry of the unit cells$^{47}$. For example, a grating coupler for standard fiber coupling with a difference between TE and TM coupling efficiencies smaller than 1 dB over a bandwidth of 12 nm was experimentally demonstrated in$^{40}$. However, the grating was based on a suspended membrane silicon waveguide that required removal of the buried oxide and made it difficult to implement the device using standard silicon photonics processes.

In this work, we report on an innovative approach to design polarization-insensitive micro antennas targeting free-space coupling and OPA applications. The antennas exploit surface gratings that are compatible with standard fabrication processes for silicon photonics. The antenna does not require the removal of the buried oxide and can be implemented with an oxide top cladding. The simultaneous use of an SWG metamaterial and L-shaped grating elements allows achieving the same scattering angle for TE and TM polarized light as well as a high scattering efficiency. In the proof-of-concept experimental demonstration reported here, the antenna has a minimum feature size of 120 nm and a very compact footprint of 6.4 µm x 2.9 µm (roughly 10 to 15 times smaller than common surface gratings designed for standard fiber coupling). A 500-nm SOI platform is chosen to ensure the best antenna performance but this does not compromises the generality of the device concept, which could also be implemented in a 300 nm platform, as discussed in section 1.1. 3D FDTD simulations show that both TE and TM polarized modes are diffracted with the same scattering angle of 10° and that, despite the compact size, the upward diffraction efficiency is as high as -2.8 dB and -2.4 dB for the two polarizations. The experimental characterization of the antenna is in a very good agreement with simulations and demonstrates a difference in TE-TM coupling efficiency at 10° smaller than 1 dB over a 31 nm wavelength range, with an estimated free-space upward scattering efficiency of -4 dB.

# 1 Design of the surface grating antenna

## 1.1 Antenna optimization

The diffraction angle of a surface grating can be calculated through the grating equation$^{42}$:

$$ \sin(\theta) = \frac{n_B}{n_C} + m \frac{\lambda}{n_C \Lambda_x} \qquad (1) $$

where $n_B$ is the effective index of the Bloch mode of the grating, $n_C$ is the refractive index of the cladding material, $\Lambda_x$ is the period of the grating (in the propagation direction x, as defined in Figure 1 (a)) and $\lambda$ is the wavelength, 1550 nm for the design considered here. In order for the TE and TM modes to be diffracted with the same angle, resulting in a polarization insensitive grating, it is required that $n_B$ be the same for the two polarizations. We achieve this objective by incorporating an SWG metamaterial into the grating unit cell to engineer the birefringence of the grating waveguide$^{48}$. The grating structure, as
# 2 Design of the surface grating antenna

## 2.1 Grating optimization

In order to design the antenna, we start by the diffraction angle of the grating, which can be calculated through the grating equation [38]:

$$ \sin(\theta) = \frac{n_B}{n_C} + m \frac{\lambda}{n_C \Lambda_x} \quad (1) $$

where $n_B$ is the effective index of the Bloch mode of the grating, $n_C$ is the refractive index of the cladding material, $\Lambda_x$ is the period of the grating (in the propagation direction x, as defined in Figure 1 (a)) and $\lambda$ is the wavelength, 1550 nm for the design considered here. In order for the TE and TM modes to be diffracted with the same angle, resulting in a polarization insensitive grating, it is required that $n_B$ be the same for the two polarizations, a condition that cannot be generally fulfilled in common SOI gratings. We achieve this objective by incorporating SWG metamaterials into the grating unit cell to engineer the birefringence of the grating waveguide [41]. The grating structure, as schematically represented in Figure 1 (a), includes two sections. The first one is an SWG metamaterial of length of $L_{SWG}$, with a transverse period in the y direction of $\Lambda_y$ and duty cycle $ff_y$. By adjusting the value of $ff_y$, it is possible to control the equivalent effective refractive index and the birefringence of the metamaterial, as represented in the cross-sectional view of Figure 1 (b). The second section is an L-shaped geometry, partially etched to 50% of the waveguide height for a length of $L_s$ and with an un-etched part of length $L_u$. The use of an L-shaped geometry is the key to achieve strong directionality and high upward diffraction efficiency [27]. The grating has a total period $\Lambda_x = L_{SWG} + L_s + L_u$ in the propagation direction x. The effective refractive index of the grating Bloch mode can be approximately computed as

$$ n_B = (n_{SWG} \frac{L_{SWG}}{\Lambda_x}) + (n_s \frac{L_s}{\Lambda_x}) + (n_u \frac{L_u}{\Lambda_x}), \quad (2) $$

where $n_{SWG}$, $n_s$ and $n_u$ are the effective indices of the fundamental 1-D modes that are supported in the corresponding sections of the unit cell for the polarization of interest, as shown in Figure 1(b). The effective refractive index $n_{SWG}$ of the SWG section can be changed by changing its duty cycle $ff_y$. To optimize the performance of the antenna, we define two convenient parameters:

$$ R_L = \frac{L_s}{L_s + L_u} $$

$$ ff_x = \frac{L_s + L_u}{\Lambda_x}, $$
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Combinations of $ff_y$ and $ff_x$ fill factors corresponding to polarization-insensitive antenna designs with different $R_L$ for 300 nm and 500 nm silicon thicknesses, $R_L$ and $ff_x$ are defined in Equations (3) and (4).</figcaption></figure>

schematically represented in Figure 1 (a), includes two sections. The first one is the SWG metamaterial of length of $L_{SWG}$, with a transverse period in the y direction of $\Lambda_y$ and fill factor $ff_y$. By adjusting the value of $ff_y$, it is possible to control the equivalent effective refractive index and the birefringence of the metamaterial, as represented in the cross-sectional view of Figure 1 (b). The second section is an L-shaped geometry, partially etched to 50% of the waveguide height for a length of $L_s$ and with an un-etched part of length $L_u$. The use of an L-shaped geometry is the key to achieve strong directionality and high upward diffraction efficiency$^{27}$. The grating has a total period $\Lambda_x = L_{SWG} + L_s + L_u$ in the propagation direction x. Accordingly, the effective refractive index of the grating Bloch mode can be approximately computed as:

$$n_B = (n_{\text{SWG}} \frac{L_{\text{SWG}}}{\Lambda_x}) + (n_s \frac{L_s}{\Lambda_x}) + (n_u \frac{L_u}{\Lambda_x}), \quad (2)$$

where $n_{\text{SWG}}$, $n_s$ and $n_u$ are the effective indices of the fundamental 1-D modes that are supported in the corresponding sections of the unit cell for the polarization of interest, as shown in Figure 1(b). These effective indices are calculated one by one using a mode solver and considering each section infinite in both the x and y directions. Silicon is used as core materials for the calculation of $n_s$ and $n_u$. For the SWG section, the equivalent refractive index of the core material (which characterizes the optical behavior of the SWG metamaterial) can be calculated from the pitch $\Lambda_y=300$ nm and duty cycle $ff_y$ of the SWG using the model described in$^{49}$. In order to optimize the performance of the antenna, we define two convenient parameters:

$$R_L = \frac{L_s}{L_s + L_u} \quad (3)$$

$$ff_x = \frac{L_s + L_u}{\Lambda_x}, \quad (4)$$

being $R_L$ the fill factor of the L-shaped geometry only and $ff_x$ the fill factor of the entire unit cell of the grating. We then exploited Equation (2) to estimate the Bloch effective indices of both TE and TM modes. For each value of $R_L$, we computed the grating fill factor $ff_x$ which is needed to obtain $n_B^{\text{TE}} = n_B^{\text{TM}}$ as a function of the SWG fill factor $ff_y$. With this approach, we obtained the curves shown in Figure 2 which represent a set of polarization insensitive designs for the grating. The results are reported for a silicon thickness of both 300 nm and 500 nm. The curves for a silicon thickness of 220 nm are not shown since not only the curves for different values are very close to each other, but all the points on the curves have $ff_x$ smaller than 0.1. This means that for a typical grating pitch in the range of a couple hundred nanometers, the smallest feature size of the L-shaped region is below 100 nm, which complicates fabrication. As detailed in the Supplementary material document, a preliminary analysis of $P_{\text{upward}}$ shows comparable results for the TE polarized mode between the two platforms, while the 500
<figure><img src="image_2.png" /><figcaption>Figure 1: Schematic of the grating antenna. (a) Perspective view and (b) cross section.</figcaption></figure>

being $R_L$ the duty cycle of the L-shaped geometry only and $ff_x$ the duty cycle of the entire unit cell of the grating. We then exploit Equation (2) to estimate the Bloch effective indices of both TE and TM modes. For each value of $R_L$, we computed the grating duty cycle $ff_x$ which is needed to obtain $n_B^{\text{TE}} = n_B^{\text{TM}}$ as a function of the SWG duty cycle $ff_y$. With this approach, we obtained the curves shown in Figure 2 which represent a set of polarization insensitive designs for the grating. The results are reported for a silicon thickness of both 300 nm and 500 nm. The curves for a silicon thickness of 220 nm are not shown since not only the curves for different values are very close to each other, but all the points on the curves have $ff_x$ smaller than 0.1. This means that for a typical grating pitch in the range of a couple hundred nanometers, the smallest feature size of the L-shaped region is below 100 nm, which complicates fabrication. We then compute the upward diffraction efficiency $P_{\text{upward}}$ for both polarizations for the different design possibilities reported in Figure 2 using 3D FDTD simulations. The grating periods $\Lambda_x$ of 800 nm and 680 nm were chosen for the 300 nm and 500 nm silicon thickness, respectively, to avoid second order diffraction. Simulation results as a function of $R_L$ and $ff_y$ are shown in Figure 3. $P_{\text{upward}}$ for the TE polarized mode shows comparable results between two platforms while the 500 nm silicon thickness has noticeable better performance over the 300 nm silicon for TM polarization. This is caused by the lower confinement of TM polarized light for thinner waveguides which results in less interaction with waveguide perturbations. It was also shown in [22] that it is difficult for thin grating structure to radiate large amount of TM polarized light. The fact that the performance of the grating for TE polarized light hardly further improves aligns with the observation made in [16]. As a result, 500 nm silicon is chosen as the platform for further optimizations. In particular, we sweep the three parameters $R_L$, $ff_y$ and $\Lambda_x$ in order to obtain the highest $P_{\text{upward}}$ for both polarizations simultaneously, considering a fixed buried oxide thickness $t_{\text{BOX}}$ =
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Diffraction efficiency of (a) TE mode, (b) TM mode, and radiation angle for (c) TE mode, and (d) TM mode with $R_L=0.45$</figcaption></figure>

nm silicon thickness has noticeable better performance over the 300 nm silicon for TM polarization. This is caused by the lower confinement of TM polarized light for thinner waveguides, which results in less interaction with waveguide perturbations. It was also shown in²² that it is difficult for thin grating structures to radiate large amount of TM polarized light. The fact that the performance of the grating for TE polarized light hardly further improves aligns with the observation made in¹⁶. As a result, 500 nm silicon is chosen as the platform for further optimizations. We use 3D FDTD simulations to compute the upward diffraction efficiency and diffraction angle for both polarizations for different design possibilities. We swept the parameter $R_L$ within the 0.40 – 0.55 range, $\Lambda_x$ between 600 nm and 800 nm, and $\Lambda_y$ between 0.2 and 0.9. The corresponding value of $ff_x$ can be retrieved using Figure 2. We consider a buried oxide thickness of 3 $\mu$m, a thickness of the upper cladding of 2.2 $\mu$m and a period of the SWG metamaterial $\Lambda_y = 300$ nm. Figure 3 reports the calculated $P_{upward}$ and diffraction angle for $R_L = 0.45$. The complete simulation results can be found in the Supplementary material document. The marker on the color maps points to the selected design $R_L = 0.45$, $ff_x = 0.6$, $ff_y = 0.62$ and $\Lambda_x = 643$nm which provides the same radiation angle 10° and diffraction efficiency around 55% for both polarizations. In this design, the smallest feature is represented by the etched sections in the SWG metamaterial, with a size of 120 nm. In addition to $P_{upward}$, one of the most important figures of merits of an antenna is its footprint, which puts constraints on its array integration and directly determines the beamwidth of the far-field (Fraunhofer) pattern through the antenna effective aperture size⁵⁰. The optimization of the antenna’s overall length and width involves adjusting the number of diffraction periods in both the x and y directions ($N_x, N_y$) to investigate their impact on the far-field beamwidth and the upward diffraction efficiency ($P_{upward}$). Figure 4 shows the results of the 3D FDTD simulations. As expected, increasing the number of periods in the propagation direction $N_x$ improves the diffraction efficiency up to the point where no undiffracted light remains in the grating. Likewise, a larger antenna (larger number of transversal SWG periods $N_y$) improves $P_{upward}$ by providing a better mode confinement until the effect of the grating lateral sidewalls becomes negligible. Conversely, a larger antenna causes a reduction of the beamwidth in the far field for both azimuth $\phi$ and elevation $\theta$ direction. We chose $N_x= 10$ and $N_y= 9$ as the optimal number of periods, ensuring a compact antenna footprint of 6.4 $\mu$m x 2.9 $\mu$m with a limited penalty on its efficiency.

## 1.2 Optimization of the injection waveguide

A rib waveguide with an etched depth of 250 nm is used as the input waveguide for the grating because this solution has been proven to effectively reduce back reflection at the grating interface¹⁵. However, the optimized grating antenna proposed here
<figure><img src="image_3.png" /><figcaption>Figure 2: Combinations of $ff_x$ and $ff_y$ duty cycles corresponding to polarization-insensitive antenna designs with different $R_L$ for 300 nm and 500 nm silicon thicknesses.</figcaption></figure>

3 µm, the thickness of the upper cladding $t_{TOX}$ = 2.2 µm and the period of the SWG metamaterial $\Lambda_Y$ = 300 nm. The parameter sweep allows to determine the values as $R_L$=0.45, $ff_y$=0.6 and $\Lambda_x$=643nm. In addition to $P_{upward}$, one of the most important figures of merits of an antenna is its footprint, which puts constraints on its array integration and directly determines the beamwidth of the far-field (Fraunhofer) pattern through the antenna effective aperture size [42]. The optimization of the antenna's overall length and width involves adjusting the number of diffraction periods in both the x and y directions ($N_x$, $N_y$) to investigate their impact on the far-field beamwidth and the upward diffraction efficiency ($P_{upward}$). Figure 4 shows the results of the 3D FDTD simulations. As expected, increasing the number of periods in the propagation direction $N_x$ improves the diffraction efficiency up to the point where no undiffracted light remains in the grating. Likewise, a larger antenna (larger number of transversal SWG periods $N_y$) improves $P_{upward}$ by providing a better mode confinement until the effect of the grating lateral sidewalls becomes negligible. Conversely, a larger antenna cause a reduction of the beamwidth in the far field for both azimuth $\phi$ and elevation $\theta$ direction. We chose $N_x$= 10 and $N_y$= 9 as the
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Optimization of the antenna footprint. (a,c) $P_{\text{upward}}$ as a function of the number of periods in the x ($N_x$) and y ($N_y$) directions. (b, d) Beamwidth in the elevation direction $\theta$ and the azimuth direction $\phi$ as a function of $N_x$ and $N_y$.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 5.** Overlap between the rib waveguide mode and the ideal grating excitation field for (a) the TE and (b) the TM fundamental modes. (c) Power coupling between the input and the output of the injection waveguide as a function of the inverse taper length.</figcaption></figure>

has an overall width of 2.9 µm and it is not practical to have a 2.9 µm-wide input waveguide while maintaining single mode operation since higher order transverse mode can easily be excited in practice. Therefore, we designed a rib-waveguide-based inverse taper as the input stage of the antenna to connect it with rest of the components on the circuit, as shown in Figure 1(a). Initially, the guided modes are confined in the rib region. As the rib becomes thinner, modes are pushed downward into the slab and then injected into the antenna. The initial width of the inverse taper $w_1$ needs to be properly designed such that only the fundamental TE and TM mode are guided. For the modes to be effectively guided in a rib waveguide, the mode effective indices must be greater than the effective index of the slab TE₀ mode⁵¹. For this reason, an $w_1$ of 500 nm is chosen. The final width $w_2$, on the other hand, has to be chosen to make sure that, at the end of the inverse taper, the modes in the rib waveguide have the best possible overlap with the ideal field excitations of the grating for both polarizations. The ideal excitation fields
<figure><img src="image_4.png" /><figcaption>Figure 3: Scattering efficiency $P_{\text{upward}}$ for points along the polarization-insensitive curves of Figure 2. (a) 300 nm silicon, TE mode, (b) 300 nm silicon, TM mode, (c) 500 nm silicon, TE mode, and (d) 500 nm silicon, TM mode.</figcaption></figure>

optimal number of periods ensuring a compact antenna footprint of 6.4 µm x 2.9 µm with a limited penalty on its efficiency.

## 2.2 Optimization of the injection waveguide

A rib waveguide with an etched depth of 250 nm is used as the input waveguide for the grating because this solution has been proven to effectively reduce back reflection at the grating interface [15]. However, the optimized grating antenna proposed here has an overall width of 2.9 µm and it is not practical to have a 2.9 µm-wide input waveguide while maintaining single mode operation since higher order transverse mode can easily be excited in practice. Therefore, we designed a rib-waveguide-based inverse taper as the input stage of the antenna to connect it with rest of the components on the circuit, as shown in Figure 1(a). Initially, the guided modes are confined in the rib region. As the rib becomes thinner, modes are pushed downward into the slab and then injected into the antenna. The initial width of the inverse taper $w_1$ needs to be properly designed such that only the fundamental TE and TM mode are guided. For the modes to be effectively guided in a rib waveguide, the mode effective indices must be greater than the effective index of the slab TE₀ mode [43]. For this reason, an $w_1$ of 500 nm is chosen. The final width $w_2$, on the other hand, has to be chosen to make sure that, at the end of the inverse taper, the modes in the rib waveguide have the best possible overlap with the ideal field excitations of the grating for both polarizations. The ideal excitation fields are defined
<figure><img src="image_7.png" /><figcaption>**Figure 6.** (a) Simulated scattering efficiency for both TE and TM polarizations. (b) Farfield radiation pattern for the TE and (c) the TM modes.</figcaption></figure>

are defined as the TE₀ and TM₀ mode fields of a 2.9 µm wide by 250 nm thick silicon waveguide on an SOI platform with oxide upper cladding. Field overlaps for different rib width w₂ for TE and TM are plotted respectively in Figure 5 (a) and (b). As expected, the best overlap occurs with small rib width. w₂ of 50 nm is chosen as a good compromise between ease of fabrication and device performance. For comparison, the obtained major electric field component for the two polarizations is plotted in the inset alongside with the ideal excitation. Finally, the length of the inverse taper L is optimized such that as much as power is coupled into the desired modes while the length is kept as short as possible. Simulations of power coupling at different taper lengths are performed by extracting the corresponding S-parameter using an Eigen Mode Expansion (EME) solver and the results are shown in Figure 5 (c). Taper efficiency for the TM mode is limited by substrate leakage that substantially increase losses for longer tapers. As a trade-off, a length of L = 11.8 µm is hence selected, resulting in estimated power couplings of 92% and 80% for TE₀-TE₀ and TM₀-TM₀ transitions respectively. It should be noticed that a rib waveguide structure is only used here for efficient light injection in the antenna. A transition to a fully etched waveguide⁵² could be used to ensure a better confinement and lower bend losses for general waveguide routing.

## 1.3 3D FDTD simulation results

Before proceeding to fabrication, the overall performance of the antenna (including the injection waveguide) were verified using 3D FDTD simulation centered at the desired wavelength of λ= 1550 nm. Simulation results for the upward diffraction efficiency are shown in Figure 6 (a). As can be seen, the antenna achieves a similar scattering efficiency $P_{upward}$ of 53% (-2.8 dB) and 58% (-2.4 dB) for TE and TM modes. Since the grating design was the result of a compromise between TE and TM performance at the wavelength of 1550 nm, the antenna achieves even better TM scattering efficiency above 65% for shorter wavelengths. Moreover, as shown by the far field projection of the scattered field in Figure 6 (b) and (c), the grating scattering occurs at an angle of 10° for both polarizations, confirming the polarization insensitive operation. The beamwidth is also the same for both polarizations, being equal to 9° in the elevation direction θ and 104° in the azimuth direction φ. These findings are also summarized in Table 1.

<table><caption>**Table 1.** Simulated performance of the designed grating antenna</caption><thead><tr><th></th><th>TE</th><th>TM</th></tr></thead><tbody><tr><td>Diffraction angle</td><td>10°</td><td>10°</td></tr><tr><td>Upward diffraction efficiency</td><td>53% (-2.8 dB)</td><td>58% (-2.4 dB)</td></tr><tr><td>Beamwidth (θ x φ)</td><td>9°x104°</td><td>9.5°x104°</td></tr></tbody></table>

## 2 Grating antenna fabrication and experimental results

In order to experimentally test the performance of our design, the grating antenna was fabricated on a SOI wafer with a silicon layer thickness of 500 nm and a buried oxide layer thickness of 3 µm. The fabrication process was completed in two steps. Firstly, the SWG metamaterial was created by electron beam lithography, followed by induced coupled plasma (ICP), resulting
<figure><img src="image_5.png" /><figcaption>Figure 4: Optimization of the antenna footprint. (a,c) $P_{\text{upward}}$ as a function of the number of periods in the x ($N_x$) and y ($N_y$) directions. (b,d) Beamwidth in the elevation direction $\theta$ and the azimuth direction $\phi$ as a function of $N_x$ and $N_y$.</figcaption></figure>

as the TE₀ and TM₀ mode fields of a 2.9 µm wide by 250 nm thick silicon waveguide on an SOI platform with oxide upper cladding. Field overlaps for different rib width $w_2$ for TE and TM are plotted respectively in Figure 5 (a) and (b). As expected, the best overlap occurs with small rib width. $w_2$ of 50 nm is chosen as a good compromise between ease of fabrication and device performance. For comparison, the obtained major electric field component for the two polarizations is plotted in the inset alongside with the ideal excitation. Finally, the length of the inverse taper L is optimized such that as much as power is coupled into the desired modes while the length is kept as short as possible. Simulations of power coupling at different taper lengths are performed by extracting the corresponding S-parameter using an Eigen Mode Expansion (EME) solver and the results are shown in Figure 5 (c). L = 11.8 µm is selected, which results in estimated power couplings of 92% and 80% for TE₀-TE₀ and TM₀-TM₀ transitions respectively.

## 2.3 3D FDTD simulation results

Before proceeding to fabrication, the overall performance of the antenna (including the injection waveguide) were verified using 3D FDTD simulation centered
<figure><img src="image_8.png" /><figcaption>**Figure 7.** Schematic representation of the experimental setup. In the inset, scanning electron microscopy top view picture of the fabricated grating antenna.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 8.** Experimental performance of the grating antenna. (a) Measured (solid lines) and simulated (dashed lines) fiber coupling efficiency for both TE and TM polarizations as a function of the wavelength. (b) Difference in TE-TM measured fiber coupling efficiency.</figcaption></figure>

in a 500 nm etch depth. Next, the partial etched regions in the grating and the rib waveguide were formed using electron beam lithography and ICP etching, achieving a 250 nm etch depth. Finally, we deposited PMMA as waveguide cladding. Following the spin-coating step, the PMMA cladding was cured by gradually increasing the temperature from 40°C to 180°C over a period of 3 minutes. PPMA was chosen because it has a refractive index similar to that of $SiO_2$ ($n_{PMMA}=1.49$) and allowed to speed up fabrication within our cleanroom but a regular oxide cladding could also be used with no changes to the design.

A scanning electron microscopy (SEM) image of the fabricated antenna is shown in the inset of Figure 7. Two antennas were placed in a back-to-back configuration, connected by a rib waveguide with a length of 5 mm. To facilitate the optical characterization, the scattering efficiency of the antenna was measured using two standard single mode fibers even if the design optimization was performed for free-space coupling. The characterization setup is schematically shown in Figure 7. It includes a tunable laser and a polarization controller to set the polarization of the light injected in the grating by the first fiber. 90% of the light collected by the output fiber is sent to the detector, while the remaining 10% is fed into a polarimeter. Both input and output fibers have a 10° angle to match the designed emission angle of the antenna. First, light polarization was set to TE using a reference grating with a polarization-dependent transmission realized on the same chip. We then characterized the designed antenna, obtaining the transmission spectrum shown in Figure 8 (a) with a solid blue line. The transmission was normalized to account for both setup losses and the propagation losses of the interconnecting waveguides, which were estimated as 2 dB/cm using an optical frequency domain reflectometry⁵³. A peak fiber coupling efficiency of -9 dB was achieved for a single
<figure><img src="image_6.png" /><figcaption>Figure 5: Overlap between the rib waveguide mode and the ideal grating excitation field for (a) the TE and (b) the TM fundamental modes. (c) Power coupling between the input and the output of the injection waveguide as a function of the inverse taper length.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 6: (a) Simulated scattering efficiency for both TE and TM polarizations. (b) Farfield radiation pattern for the TE and (c) the TM modes.</figcaption></figure>

at the desired wavelength of $\lambda$= 1550 nm. Simulation results for the upward diffraction efficiency are shown in Figure 6 (a). As can be seen, the antenna achieves a similar scattering efficiency $P_{upward}$ of 53% (-2.8 dB) and 58% (-2.4 dB) for TE and TM modes. Since the grating design was the result of a compromise between TE and TM performance at the wavelength of 1550 nm, the antenna achieves even better TM scattering efficiency above 65% for shorter wavelengths. Moreover, as shown by the far field projection of the scattered field in Figure 6 (b) and (c), the grating scattering occurs at an angle of 10° for both polarizations, confirming the polarization insensitive operation. The beamwidth is also the same for both polarizations, being equal to 9° in the elevation direction $\theta$ and 104° in the azimuth direction $\phi$. These findings are also summarized in Table 1.
grating at a wavelength of 1560 nm. We then changed the setup polarization to TM using the polarimeter as a reference and measure the normalized transmission spectra shown in Figure 8 (a) with a solid orange line. The same normalization used for TE is applied to TM transmission. In this case, a fiber coupling efficiency of -11.5 dB was obtained at 1560 nm (again for a single grating). Figure 8 (b) shows the difference in the fiber coupling efficiency between the TE and TM modes. A perfect polarization-independent operation is achieved at a wavelength of 1532 nm, with a 1-dB polarization insensitive bandwidth of 31 nm.

It should be noted that these results depend on both the upward diffraction efficiency $P_{upward}$ of the antenna and also on the overlap integral of the scattered field with the fiber mode, which was not considered for the design of an antenna for free-space applications. In order to better evaluate the experimental results, we hence simulate the antenna coupling efficiency with a standard single mode fiber with 3D FDTD for both polarizations. Results are reported in Figure 8 (a) with dashed lines and are in a very good agreement with the experiment. The difference between the experimental fiber transmission and the simulation prediction is smaller than 1 dB for both polarizations in the bandwidth of interest, likely due to fabrication tolerances. In the simulations, a perfect polarization insensitive coupling is obtained at a wavelength of 1538 nm, with coupling efficiency of -10.5 dB. Conservatively assuming that the additional 1 dB loss can be entirely attributed to the scattering efficiency and not to the modes overlap, allows to estimate a $P_{upward}$ of at least -4 dB (40%) for the fabricated antenna for both TE and TM modes.

## 3 Conclusion

In this work, we proposed an innovative approach to design micro antennas with a polarization insensitive behavior based on surface grating couplers. The incorporation of an SWG metamaterial in the grating structure was the key to obtain the same effective index for TE and TM grating Bloch modes and hence the same scattering angle. The use of an L-shaped section ensured at the same time a high diffraction efficiency. As a proof-of-concept, we designed and experimentally demonstrated a polarization insensitive antenna with a compact footprint of 6.4 µm x 2.9 µm on a 500-nm SOI platform that successfully achieved a 1-dB polarization insensitive bandwidth of 31 nm with an estimated scattering efficiency of about -4 dB (40%).

The demonstrated antenna is compatible with standard silicon photonics fabrication processes and offers a robust solution for efficient light coupling in integrated Optical Phased Arrays regardless of the polarization state. By enabling broadband operation, the antenna holds the potential to realize next-generation photonic applications in telecommunications and beyond.

## Acknowledgements

This work was partially funded by the European Union through the European Research Council (ERC) project BEAMS (Grant agreement No.101041131). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. The device fabrication was performed within the C2N technological platforms and partly supported by the RENATECH network and the General Council of Essonne.

## Data availability statement

The simulation and experimental data reported in the manuscript will be made available by the corresponding author upon reasonable request.

## Author contributions statement

X. X., D. B., and W. N. Y. conceived the devices and optimized the design of the antenna. S. S., C. A.-R., L. V., D. M.-M., and D. M. were responsible for the device fabrication and characterization. W. N. Y. and D. M. supervised the project. All authors contributed to writing and reviewing the manuscript.

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<table><caption>Table 1: Simulated performance of the designed grating antenna</caption><thead><tr><th></th><th>TE</th><th>TM</th></tr></thead><tbody><tr><td>Diffraction angle</td><td>10°</td><td>10°</td></tr><tr><td>Upward diffraction efficiency</td><td>53% (-2.8 dB)</td><td>58% (-2.4 dB)</td></tr><tr><td>Beamwidth (θ x φ)</td><td>9°x104°</td><td>9.5°x104°</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>Figure 7: Scanning electron microscopy top view picture of the fabricated grating antenna.</figcaption></figure>

## 3 Grating coupler antenna fabrication and experimental results

In order to experimentally test the performance of our design, the grating antenna was fabricated on a SOI wafer with a silicon layer thickness of 500 nm and a buried oxide layer thickness of 3 µm. The fabrication process was completed in two steps. Firstly, the SWG metamaterial was created by electron beam lithography, followed by induced coupled plasma (ICP), resulting in a 500 nm etch depth. Next, the partial etched regions in the grating and the rib waveguide were formed using electron beam lithography and ICP etching, achieving a 250 nm etch depth. Finally, we deposited PMMA as the cladding because it has a refractive index similar to that of SiO₂ ($n_{PMMA}$=1.49). A scanning electron microscopy (SEM) image of the fabricated antenna is shown in Figure 7. Two antennas were placed in a back-to-back configuration, connected by a rib waveguide with a length of 5 mm. To facilitate the optical characterization, the scattering efficiency of the antenna was measured using two standard single mode fibers instead of performing direct measurements in free space. The characterization setup is schematically shown in Figure 8. It includes a tunable laser and a polarization controller to set the polarization of the light injected in the grating by the first fiber. 90% of the light collected by the output fiber is sent to the detector while the remaining 10% is fed into a polarimeter. Both input and output fibers have a 10° angle to match the designed emission angle of the antenna. First, light polarization is set to TE using a reference grating with a polarization-dependent transmission realized on the same chip. We then characterize the designed antenna, obtaining the transmission spectrum shown in Figure 9 (a) with a solid blue line. The transmission is normalized to account for both setup losses and the propagation losses of the interconnecting waveguides,
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which are estimated as 2 dB/cm using an optical frequency domain reflectome-
try [44]. A peak fiber coupling efficiency of -9 dB is achieved at a wavelength of
1560 nm. We then change the setup polarization to TM using the polarimeter
as a reference and measure the normalized transmission spectra shown in Figure
9 (a) with a solid orange line. The same normalization used for TE is applied to
TM transmission. In this case, a fiber coupling efficiency of -11.5 dB is obtained
at 1560 nm. Figure 9 (b) shows the difference in the fiber coupling efficiency
between the TE and TM modes. A perfect polarization-independent operation
is achieved at a wavelength of 1532 nm, with a corresponding fiber transmission
of -11.5 dB for both TE and TM at this wavelength and a 1-dB polarization
insensitive bandwidth of 31 nm.

It should be noted that these results depend on both the upward diffraction
efficiency P_upward of the antenna and also on the overlap integral of the scattered
field with the fiber mode, which was not considered for the design of an antenna
for free-space applications. In order to better evaluate the experimental results,
we hence simulate the antenna coupling efficiency with a standard single mode
fiber with 3D FDTD for both polarizations. Results are reported in Figure 9 (a)
with dashed lines and are in a very good agreement with the experiment. The
difference between the experimental fiber transmission and the simulation pre-
diction is smaller than 1 dB for both polarizations in the bandwidth of interest,
likely due to fabrication tolerances. In the simulations, a perfect polarization
insensitive coupling is obtained at a wavelength of 1538 nm, with coupling effi-
ciency of -10.5 dB. Conservatively assuming that the additional 1 dB loss can
be entirely attributed to the scattering efficiency and not to the modes overlap,
allows to estimate a P_upward of about -4 dB (40%) for the fabricated antenna
for both TE and TM modes.

4 Conclusion

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<figure><img src="image_10.png" /><figcaption>Figure 9: Experimental performance of the grating antenna. (a) Measured (solid lines) and simulated (dashed lines) fiber coupling efficiency for both TE and TM polarizations as a function of the wavelength. (b) Difference in TE-TM measured fiber coupling efficiency.</figcaption></figure>

state. By enabling broadband operation, the antenna holds the potential to realize next-generation photonic applications in telecommunications, data centers, and beyond.

**Acknowledgements** This work was partially funded by the European Union through the European Research Council (ERC) project BEAMS (Grant agreement No.101041131). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. The device fabrication was performed within the C2N technological platforms and partly supported by the RENATECH network and the General Council of Essonne.

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