A compact polarization insensitive all-dielectric metasurface lens for Gaussian to tophat beam shaping in sub-terahertz regime

A compact polarization insensitive all-dielectric metasurface lens for Gaussian to tophat beam shaping in sub-terahertz regime

Journal Pre-proof A compact polarization insensitive all-dielectric metasurface lens for Gaussian to tophat beam shaping in sub-terahertz regime Afshi...

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Journal Pre-proof A compact polarization insensitive all-dielectric metasurface lens for Gaussian to tophat beam shaping in sub-terahertz regime Afshin Abbaszadeh, Mehdi Ahmadi-Boroujeni, Ali Tehranian

PII: DOI: Reference:

S0030-4018(20)30042-0 https://doi.org/10.1016/j.optcom.2020.125313 OPTICS 125313

To appear in:

Optics Communications

Received date : 24 October 2019 Revised date : 8 January 2020 Accepted date : 12 January 2020 Please cite this article as: A. Abbaszadeh, M. Ahmadi-Boroujeni and A. Tehranian, A compact polarization insensitive all-dielectric metasurface lens for Gaussian to tophat beam shaping in sub-terahertz regime, Optics Communications (2020), doi: https://doi.org/10.1016/j.optcom.2020.125313. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.

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A compact polarization insensitive all-dielectric metasurface lens for Gaussian to tophat beam shaping in sub-terahertz regime Afshin Abbaszadeh, Mehdi Ahmadi-Boroujeni* and Ali Tehranian Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran

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Abstract: In this paper, we present a Gaussian to tophat beam shaper (GTBS) based on an all-dielectric metasurface lens for sub terahertz (sub-THz) applications. In order to calculate the required phase profile of the GTBS, we use an analytical procedure based on the geometrical transformation technique. The calculated phase profile is then realized by a silicon (Si) metasurface lens consisting of rectangular-shaped pillars of subwavelength dimensions. Because of large solution domain relative to the operation wavelength, we combined the beam envelope and the finite element methods to simulate the structure with a high precision. By designing an anti-reflection metasurface made up of periodically arranged Si pillars of subwavelength dimensions at the back surface of the beam shaper, we reduced the reflection from the lens surface considerably. The proposed idea is firstly investigated in a two-dimensional (2D) structure composed of an array grooves in a Si substrate and then is extended to three dimensions (3D) by considering a 2D array of subwavelength pillars or holes. The 3D structure is shown to be polarization insensitive. The compactness, ease of fabrication, low transmission loss, polarization independence, and straightforward design of the proposed metasurface beam shaper lens make it a promising choice for the implementation of sub-THz quasi-optical elements especially for standoff imaging systems.

Keywords: Metasurfaces, Beam shaping, Sub-terahertz imaging

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1. Introduction

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Imaging is one of the most important applications of Terahertz (THz) radiation. The electromagnetic (EM) waves in this regime can penetrate into most of non-metallic materials providing numerous applications such as security imaging for the detection of concealed objects [1], quality control of electronic chips [2], and harmless THz medical imaging [3]. In most of these applications, quasi-optical elements such as lenses and mirrors are used for the illumination of object and focusing of the reflected wave on the detector. The development of THz detector arrays, also called THz cameras, has made the realization of focal plane array (FPA) imaging possible. In this imaging setup, the object plane is illuminated by a wide beam and the image is formed without mechanical scanning. Uniform illumination of the target plane with a low spill-over is crucial in such an imaging scenario. Design of a low-profile lens for the mentioned purpose is the main focus of this paper. Since the wavelength is much larger in THz band as compared to the optics regime, design of compact lenses is of high practical importance especially at sub-THz frequencies. In addition to reducing the dimensions, reducing the reflection from the lens surface and achieving a desired shaped-beam in the lens output comprise other design goals. In order to realize a low-profile lens in the THz regime, one can use metasurfaces [4], plasmonic and quasi-plasmonic structures [5, 6], photonic crystals [7, 8], or other structures based on dielectric materials [9]. In the optics regime, beam shaping has been used in various applications, such as lithography [10], optical processing [11], laser printing [12], camera optics [13], and holography [14, 15]. In the focused imaging systems, Gaussian beams are normally used. However, it has been shown that by illuminating an object with a uniform beam of sharp roll-off, hereafter called the tophat beam, the quality of the acquired image can be improved [16, 17]. By the use of a Gaussian to tophat beam shaper (GTBS), one can convert the Gaussian beam of conventional sources into a tophat beam. Various methods for the beam shaping have been introduced so far. One of the simplest methods is apodization and truncation [17], but the drawback of this method is its low transfer energy efficiency. Another method is optical beam integrator which is based on the use of two elements for beam shaping; the first element separates the incident beam to a cluster of sub-beams, and then, the second one directs these sub-beams in order to form the desired shaped beam at the output plane [18]. Another two-element based beam-shaping approach is optical amplitude and phase modulation [19]. In this method, amplitude of the incident wave is modulated by * Corresponding author. E-mail address: [email protected]

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first element and then the phase of the transmitted waves is modulated by the second element to obtain the desired beam shape. Because of the low energy transfer efficiency, difficult fabrication process of amplitude modulators, and alignment challenge of two-element-based beam shapers, these methods are not commonly used. Single optical phase filters introduced in [17, 19] are more promising for beam shaping owing to their high energy transfer efficiency, easy fabrication process and no need for alignment. Single optical phase filters have different categories; refractive elements, reflective elements, and diffractive elements or a combination of these functions [20-22]. Refractive or reflective phase elements are usually pseudo-spherical lenses. Computer generated holograms, diffraction gratings and diffractive optical phase plates are well-known diffractive phase only elements [23-25]. There are various methods to calculate the phase profile of a diffractive phase element. The geometrical transformation technique [26] and Grechberg-saxton and its modifications [27, 28] are two of the most commonly used methods. In a recent work [29], we have shown that the phase profile of the GTBS lens can be estimated by geometrical optics principles and a simple optimization method based on the full-wave simulation of the lens and the source antenna is suggested to tune the analytically extracted lens profile. The mentioned procedure has been applied to the design of a double curved Teflon lens and has been verified by measurement of a prototype lens at 100GHz. In this paper, we extend the mentioned design methodology and propose a compact all dielectric metasurface for the realization of the beam shaper lens. To have a compact, low cost and energy transfer efficient beam shaper, we use a metasurface lens which works as a phase-only element. Metasurfaces consist of subwavelength resonators which are periodically arranged on a surface and are capable of changing the characteristics of the EM waves [30]. Some examples of different applications of metasurfaces, especially in the THz regime, are as follows. In [31], a C-shaped metallic ring resonator-based metasurface was used to implement a broadband THz deflector. In [32], an ultra-thin metasurface composed of arrays of complementary V-shaped antennas in the planar gold films is introduced and used to implement a focusing lens in THz regime. An ultra-thin broadband beam-shaper consisting of a monolayer of metallic Nano rods operating at visible and near-infrared regimes was introduced in [33] which induces the required phase shifts by rotating the existing metallic rods. Huifang et al, introduced an all dielectric polarization insensitive metasurface with cylindrical silicon pillars for realizing vortex and Bessel beam generators in the THz regime [34]. In [35], an all-dielectric metasurface composed of cubic blocks is used for implementing a lens with application in THz imaging systems. All dielectric metasurface based on Si is adopted in this paper for the realization of the mentioned GTBS. The outline of this paper is as follows. In Section 2, we calculate the phase profile of a GTBS and extract the equivalent refractive index model of the beam shaper by the use of thin element approximation. In Section 3, we introduce and analyze a unit cell of a 2D all-dielectric Si metasurface to investigate its capability of providing 2π phase shift with a high transmission coefficient. In addition, we utilize the proposed metasurface to realize the phase profile of the GTBS. A metasurface-based anti-reflection layer is also designed and assessed to reduce the reflection of EM waves from the GTBS lens surface. In Section 4, we extend the beam shaper design to 3D structures by introducing two different metasurfaces that can realize the desired phase profile of the GTBS with no polarization sensitivity. Finally, we give some concluding remarks in Section 5. 2. The phase profile of a GTBS

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In the optics regime, the Gaussian profile is a widely used approximation for the lateral intensity distribution of collimated radiation sources. In the sub-THz regime and especially in standoff imaging systems, it is common to use dielectric lenses or parabolic mirrors to collimate the radiation of sources; hence, the Gaussian profile can be used as an approximate model for the radiated beam of such sources. In imaging scenarios where the object plane is illuminated by a single collimated beam, there is a tradeoff between the uniformity of illumination and the spill-over efficiency. To illuminate the object plane uniformly, one should adopt a wide Gaussian beam which spreads a considerable amount of power outside the desired field-of-view. Consider a 1D Gaussian intensity distribution with the waist diameter of wo centered on the origin along the x-axis; i.e., I(x)=Ioexp[-(2x/wo)2]. If this profile is used to illuminate an interval of width 2xo around the origin (|x|
Journal Pre-proof technique to extract the phase profile of the GTBS. The GTBS is designed to convert an incident Gaussian beam of waist diameter w1 into an output tophat beam of diameter w2 at the distance of d from the input plane. Using the geometrical transformation technique, the phase profile of the GTBS can be obtained as [17]:  ( x) =

2

d 

x

-D 2

  S ( x)  1 D −  − x   dx ; | x |  w2   2   S ( D 2 ) 2  

In which, D is the GTBS diameter, λ is the wavelength, and S ( x ) = 

x

−D 2

exp ( −8

(1) 2

2 w1 ) d  . The intensity

I out ( x ) 



+D 2 −D 2

I in ( x  ) e

− j ( x )

2   j exp  − ( x − x  )  dx   d 

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distribution of the resultant tophat beam at the distance of d can then be estimated by the Fresnel diffraction integral [38]: (2)

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Where, the input Gaussian intensity and the obtained tophat intensity profiles are denoted by Iin and Iout, respectively. As an example, at the wavelength of λ=3mm (f=100GHz) a Gaussian beam of diameter w1=8cm is transformed to a tophat beam of diameter w2=64cm at the distance of d=2m by a GTBS of diameter D=20cm. In Fig. 1(b), the field profile of the input Gaussian beam is illustrated. The extracted spatial phase profile of the GTBS is shown in Fig. 1(c) and the obtained field profile at the output plane is illustrated in Fig. 1(d). It is clear that the obtained profile is nearly tophat with a full-width half-maximum of w2≈64cm. In theory, the designed phase profile can be realized by a flat graded-index lens. The refractive index of the flat GTBS lens can be expressed as:   ur ( x )

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n ( x) = 1+

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(3)

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Where, h is the lens thickness and Φur represent the unwrapped phase profile of GTBS. For λ=3mm and thickness of h=8λ, the equivalent refractive index of a flat lens that realizes the GTBS is depicted in Fig. 2(a). Using the COMSOL software, the mentioned example is simulated. Fig. 2(b) shows the simulation setup in which the Gaussian beam is incident from the bottom-side to the flat GTBS lens and the resultant field is recorded at the distance of d=2m. The electric field magnitude is superimposed in this figure which demonstrates the beam shaping mechanism qualitatively. The obtained field profile in this simulation is compared to the calculated one in Fig. 2(c). The agreement between the presented results proves the validity and preciseness of the proposed technique for extracting the GTBS phase profile.

Fig. 1. (a) Spill over efficiency versus the non-uniformity in a Gaussian beams. (b) Normalized input Gaussian profile, (c) Calculated phase profile of the GTBS, (d) calculated normalized tophat profile at the output of GTBS at d=2m.

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Fig. 2. (a) The equivalent refractive index of the graded-index GTBS, (b) Simulation of the graded-index GTBS lens in COMSOL. The Gaussian beam is incident from the bottom-side to the GTBS lens located at y=0. The resultant output beam at y=2m is a tophat beam. (c) The electric filed amplitude at the output plane of the GTBS calculated analytically (solid line) and simulated by COMSOL (dashed line).

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3. Realization of the GTBS by an all-dielectric metasurface

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In practice, the proposed GTBS can be realized by either a conventional dielectric lens or a low-profile metasurface. In this section, we propose an all-dielectric metasurface composed of an array of subwavelength dielectric corrugations on a substrate to realize the phase profile of the GTBS. The proposed GTBS lens composes a metasurface for realizing the GTBS phase profile and another antireflection metasurface for reducing the surface reflection. Each of the mentioned metasurfaces is implemented on one side of a dielectric substrate. Here, we choose Si (n=3.45) for the metasurface structure because of its high refractive index, low attenuation constant and available fabrication processes. Firstly, we introduce the design of a 2D structure for realizing an arbitrary phase profile in one direction. The structure consists of rectangular corrugations on a Si substrate. Fig. 3(a) shows a unit cell of such structure. The lattice constant of the structure (p) is subwavelength to avoid higher diffraction orders and make the quantization of the required phase profile adequately fine. The height of corrugations (h) is fixed and is chosen in such a way that 0 to 2π phase shift can be achieved by only changing the width of corrugations (w). Hence, the required phase profile is quantized according to the lattice constant of the metasurface and is realized by an array of corrugations with variable widths. For realizing the GTBS phase profile at 100GHz, we choose a Si substrate of thickness t=1mm on which an array of corrugations of height h=1.5mm and period p=1mm is created. The relative phase shift and transmission coefficient of the mentioned structure for various corrugation widths is calculated using COMSOL and illustrated in Fig. 3(b). It is clear that the phase shift can be varied from 0 to 2π by changing the corrugation widths. As it is shown in Fig. 3(b), by varying the corrugation width, one can obtain phase shifts larger than 2π. The acceptable range of corrugation width is restricted by limitations of fabrication process for thin pillars and by low transmission coefficient of large pillars. Therefore, in Fig. 3(b) we marked two intervals for corrugation width variations from 0.05mm to 0.76mm and from 0.065mm to 0.875mm in case one is interested in using pillars with larger widths. The variation of the transmission coefficient versus corrugation width is also depicted in Fig. 3(b). It is worth mentioning that even though the effect of the Si substrate is considered in unit cell analysis, the transmission coefficient is relatively high and its variations is not considerable. Using the information of Fig. 3(b), we can calculate the width of corrugations for realizing the phase profile of the GTBS presented in Fig. 1(c). The width of corrugations within the diameter of the GTBS is shown in Fig. 4(a). The designed metasurface GTBS is simulated using COMSOL and the electric field magnitude is recorded. Fig. 4(b) shows the simulation setup in which the field magnitude is superimposed. It is apparent that the

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incident Gaussian beam is transformed to a tophat beam by the designed metasurface GTBS. The obtained normalized field magnitude is compared with the analytical result in Fig. 4(c). As the figure shows, there is a good agreement between analytical and simulated results that verifies the design of metasurface GTBS. Limited sampling accuracy of the phase profile by the lattice constant of the metasurface, small variations in the transmission coefficient of different pillars, multiple reflections happening inside of the structure, existing anomaly in the transmitted wave caused by abrupt change in the widths of the adjacent corrugations and coupling effects of adjacent corrugations of different widths which couldn’t be considered in the unit cell analysis are responsible for slight difference between analytical and obtained results. It is worth noting that because of the large distance between the input and the output planes, it is not possible to use FEM solver to accurately mesh the entire simulation area due to limited computational resources. Therefore, we divided the simulation region into two domains. Domain one is a small region around the metasurface structure and excitation line which is accurately meshed and solved by the FEM solver of COMSOL. Domain two is the remaining area between the metasurface structure and the output plane. To simulate the wave propagation in this domain, the beam envelope method is used. In this way, the performance of the GTBS can be simulated accurately with an affordable computational cost.

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Fig. 3. (a) A unit cell of the proposed 2D metasurface including a rectangular corrugation on a substrate. The structure is invariant along the z-axis and is excited by a z-polarized plane wave. (b) Simulated transmission amplitude and induced phase shift of the metasurface versus the corrugation width. Other parameters are introduced in the text.

Fig. 4. (a) Width of corrugations along the diameter of metasurface GTBS. (b) Magnitude of the electric field in the plane of the metasurface GTBS simulated by COMSOL. The GTBS is excited by a Gaussian beam form the bottom-

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The performance of the proposed metasurface GTBS can be improved by reducing the reflection of the incident wave and increasing the transmission coefficient. It can be achieved by integrating an anti-reflection (AR) metasurface in the proposed GTBS. As shown in Fig. 5 (a), the smooth side of the GTBS is replaced by a periodic one. In order to achieve maximum transmission amplitude at 100GHz, the height, width, and period of AR corrugations are chosen as 0.4mm, 0.25mm, and 0.6mm, respectively. The proposed structure is simulated and the electric field magnitude at the output plane is recorded in the presence and in the absence of the mentioned AR corrugations. This comparison is presented in Fig. 5(b). It is evident that the amplitude of the tophat beam is increased considerably by integrating the AR layer. Since the transmission efficiency is quite important to evaluate the performance of such devices, we have calculated the insertion loss defined as IL=10×log(Pout/Pin) for our designed metasurface GTBS, in which Pout is the average power of the EM wave at the target plane, and Pin is the input average power incident on the lens structure. Insertion loss for our designed metasurface GTBS when there is no anti-reflection layer attached to the back of the Si substrate is 3.24 dB, and is 0.5 dB in the presence of the AR layer which shows the anti-reflection layer improves the transmission efficiency remarkably. Hence, one can implement a high-performance low-profile metasurface GTBS by making customized corrugations on either side of a silicon substrate.

Fig. 5. (a) Schematic drawing of the metasurface GTBS integrated with an anti-reflection metasurface, (b) The electric field amplitude at the output plane (y=2m) in the presence (solid line) and in the absence of anti-reflection layer (dashed line).

4. 3D metasurface-based GTBS

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In the previous section, we proposed the application of an all-dielectric metasurface for the realization of the GTBS in one direction (the x-axis). In this section, we extend the proposed idea to two directions which is of more interest in practice. In other words, the possibility of realizing a 2D phase profile for the generation of a tophat beam from a rotationally symmetric input Gaussian beam is studied in the following. As a first step, the required phase distribution of the beam shaper can be calculated by the geometrical transformation technique explained in Section 2. The next step is the design of a 3D metasurface that can implement the required 2D phase profile. A 2D array of subwavelength dielectric pillars can be proposed for realizing the mentioned phase profile. In other words, the 2D GTBS studied in the previous section is extended to a 3D one by replacing the corrugations with pillars or holes. A unit cell of such metasurface can be a subwavelength cubic or cylindrical pillar on a substrate as shown in the insets of Fig. 6. Again, we choose silicon for the metasurface and design a unit cell that is capable of providing 0 to 2π phase shift. The height of pillars are fixed and the phase shift is changed by varying the lateral dimensions of pillars. To achieve, a polarization independent phase shift, the cross-section of pillars should be circular or square shaped. To show the feasibility of such polarization independent phase shift, we design and simulate a unit cell of a 3D Si metasurface at 100GHz. The thickness of the underlying silicon substrate, the height of pillars, and

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the lattice constant in both directions are assumed as t=0.5mm, h=2mm, and p=1mm, respectively. Then the relative transmission phase and amplitude are simulated for various diameters of pillars (w). To conduct the simulations, the frequency-domain solver of COMSOL Multiphysics is used. The obtained results for both x and y polarizations are illustrated in Fig. 6. Fig. 6(a) shows the results of cubic pillars on a rectangular grid and Fig. 6(b) illustrates similar results for the cylindrical pillars. It is seen that by varying the diameter of pillars from 0.13mm to 1mm for cubic pillars and 0.1mm to 0.84mm for cylindrical pillars, the phase shift is changed from 0 to 2π. It should be highlighted that the transmission coefficient shows negligible variation and both phase and amplitude responses are insensitive to the polarization. Another type of polarization-independent metasurface consisting of subwavelength cubic or cylindrical air holes in a Si slab arranged in a square lattice with lattice constant p=1mm is also introduced in Figs 6(c) and 6(d). By assuming the slab thickness as h=3.5mm and by varying the diameter of holes from 0.7mm to 1.1mm for cubic holes and 0.55mm to 0.9mm for cylindrical holes, 2π phase shift can be attained. A 2D array of pillars or holes can thus be exploited for realizing a low-profile GTBS. The phase profile of the GTBS is discretized in two directions according to the lattice constant of the metasurface and each of its pixels is realized by a pillar or a hole of certain dimension. Instead of a square lattice, one may prefer a hexagonal one but the overall performance is nearly the same.

Fig. 6. Simulated transmission coefficient and induced phase shift of the 3D metasurface unit cells for (a) square pillars and (b) cylindrical pillars on a silicon substrate and (c) square holes and (d) cylindrical air holes on a silicon slab versus the pillar or hole diameters in a tetragonal lattice.

To examine the proposed methodology, a 3D metasurface-based GTBS lens is designed and simulated. The metasurface-based GTBS consists of cylindrical pillars on a silicon substrate arranged in a tetragonal lattice. The GTBS lens is designed to convert a Gaussian beam of diameter w1=8cm into a tophat beam of diameter w2=64cm at the distance of d=2m at 100GHz. The diameter of the GTBS lens is assumed D=20cm. To make the computational cost of the simulations affordable, we assume an incident wave with a Gaussian profile along the x-axis and a uniform profile along the y-axis. Hence, the GTBS lens is composed of a row of pillars with

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varying diameters along the x-axis which is periodically replicated along the y-axis. The diameters of the pillars along the x-axis and a schematic of the designed metasurface-based GTBS are shown in Fig. 7 (a) and (b). By recording the phase of the transmitted field, the phase profile of the GTBS lens is extracted and is compared with the required phase profile in Fig. 7(c). It is evident that the realized GTBS lens modulates the phase of the incident wave correctly. The recorded field profile at the output of the GTBS lens is used to extract the transmitted beam at the distance of d=2m based on the Fresnel diffraction integral. Fig 7(d) shows the simulated and analytical beam profiles which are in close agreement. In the simulations, the sensitivity of the GTBS to the misalignment of the incident Gaussian beam and the lens axis is also studied. A lateral offset of d offset =2mm and 5mm is assumed between the axis of the input beam and the lens and the resultant output beam is also shown in Fig. 7 (d).

Fig. 7. Design and simulation of a 3D metasurface based GTBS: (a) diameter of cylindrical pillars, (b) schematic of a the designed GTBS, (c) analytical and simulated phase profile of the GTBS, (d) analytical and simulated output beam for doffset=0, 2mm, and 5mm.

We also investigated the effect of removing thin pillars in 3D structure. The output top-hat beam profile for the cases when pillars thinner than 0.3 mm and 0.4 mm in diameter are removed, is presented in Fig. 8(a), along with the case when all of the pillars are in place and analytical solution. According to the results, eliminating

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the thin pillars as small as 0.3 mm and 0.4 mm in diameter, would reduce the top-hat beam quality slightly. Thus, it is safe to remove these thin pillars in 3D structure which might be helpful if one wants to avoid fabrication challenges.

Fig. 8. (a) Output beam profile for when pillars with smaller diameters are removed in 3D structure. Black dashed line is analytical solution, blue solid line is for when all of the pillars are in place, red dotted line represents the case when pillars with diameters smaller than 0.3 mm are removed and purple dashed-dotted line is for when pillars with widths smaller than 0.4 mm are removed. (b) Sensitivity of the generated top-hat beam to the changes of frequency for 3D structure. Red dashed-dotted line, black dashed line and blue solid line are for input EM wave of frequencies 90, 100 and 103 GHz respectively.

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We have to consider that our proposed metasurface-based top-hat beam-shaper is designed based on a desired resonance frequency, therefore its performance deteriorates by changing the operation frequency. To investigate the sensitivity of the proposed metasurface GTBS to any change in the frequency of the input EM wave, we have studied its performance for different input wave frequencies. We changed the input frequency until the quality of the output tophat beam starts fading. The resultant output beam profiles are represented in Fig. 8(b). It is evident that when the input frequency ranges between 10 GHz lower or 3 GHz higher than the central frequency (100 GHz), the quality of the output beam profile remains well and outside of this range the beam profile begins to show undesirable ripples. 5. Conclusions

In this paper, we proposed a straightforward procedure for the design of a low-profile Gaussian to tophat beam shaper (GTBS) in sub-terahertz frequency regime. The proposed GTBS can be used in standoff imaging systems for uniform illumination of the target plane with a low spill-over. We used the geometrical transformation technique and thin element approximation to calculate the desired phase distribution of the GTBS and present a sample design at 100GHz. Then, the beam shaper is realized by using an all-dielectric metasurface-based structure made of silicon. At first, we realized a 1D GTBS and then we extended the concept to two directions. We obtained tophat beams at the output plane with three different approaches including analytical beam

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shaping, equivalent refractive index model of the beam shaper and metasurface-based beam shaping, all of which provide consistent results. It is shown that the surface reflection of the metasurface GTBS can be reduced by integrating another anti-reflection metasurface in the structure. In the 3D structure, we showed that polarization insensitive phase shift can be obtained by using either silicon pillars on a silicon substrate or a periodically perforated silicon slab. Our proposed metasurface-based beam shaper is more sensitive to the frequency of the input EM waves relative to conventional refractive-based beam shapers, but as an advantage, it has a total thickness of nearly λ which is so much less than that of refractive-based ones. This low-profile feature of our design is especially of interest for devices operating at sub-THz regime to prevent bulky and heavy structures of the conventional refractive-based devices. The proposed metasurface GTBS is promising for standoff imaging systems due to its compact and low-profile structure, high transmission coefficient, and high illumination efficiency.

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Afshin Abbaszadeh: Conceptualization, Methodology, Writing - Original Draft

Mehdi Ahmadi-Boroujeni: Writing - Review & Editing, Supervision, Validation

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Ali Tehranian: Writing - Original Draft, Investigation