A small-spot-size and polarization-insensitive flat lens employing dielectric metasurface in the terahertz region

A small-spot-size and polarization-insensitive flat lens employing dielectric metasurface in the terahertz region

Optics Communications 459 (2020) 125083 Contents lists available at ScienceDirect Optics Communications journal homepage: www.elsevier.com/locate/op...

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Optics Communications 459 (2020) 125083

Contents lists available at ScienceDirect

Optics Communications journal homepage: www.elsevier.com/locate/optcom

A small-spot-size and polarization-insensitive flat lens employing dielectric metasurface in the terahertz region Xiaorong Hong, Shuai Feng βˆ—, Honglian Guo βˆ—, Chuanbo Li School of Science, Minzu University of China, Beijing, 100081, People’s Republic of China

ARTICLE Keywords: Flat lens Dielectric metasurface Terahertz radiation


ABSTRACT A transmissive terahertz (THz) metasurface consisting of subwavelength silicon post resonators is proposed, and the performances of high efficiency (over 94%) and full phase shift (∼ 2πœ‹) are achieved through structural design. Based on the predominant dipole resonance characteristic of incident THz wave with the resonator elements, the hyperbolic THz wave phase profiles are generated, and the THz flat lens with a focal length of 1.80 mm supporting the y-polarized wave at 1.0 THz is achieved, whose focal spots along x and y directions of the focal plane are 0.66 πœ† and 0.44 πœ†, respectively. Due to the equal phase retardation in two arbitrary perpendicular directions of the post resonators, the lens also has the advantage of polarization-insensitive.

1. Introduction Optical metasurface, which is a two-dimensional (2D) artificial structure arranged in a planar space via subwavelength scale resonators, can manipulate the electromagnetic wave flexibly. The resonator elements can be analogized to β€˜β€˜meta-atom’’, which have a dipole resonance effect with the incident electromagnetic wave, thereby they can achieve the modulation of electromagnetic wave’s amplitude and phase [1]. Owing to the advantages of simple structure and light-thin, optical metasurfaces have been applied to many photonic devices, such as ultrathin lenses [2–5], optical vortex converters [6–8], optical wave plates [9–11], beam deflectors [12], polarization beam splitters [13]. Beyond above, they have also been employed to realize some optical processes, such as meta-hologram [14–16], the generation of photon spin Hall effect [17], the excitation of surface plasmon polaritons [18]. Terahertz (THz) radiation lies between the infrared and microwave bands. In recent decades, researchers have attracted more and more attention due to the unique properties in this electromagnetic band. Especially in the research and application of THz wave emission and receiving modules have been relatively mature. Nevertheless, for the traditional devices in the middle of THz system, the complexity of structure brings many disadvantages such as bulk and poor stability. In recent years, the application fields of metasurfaces have been expanded, for example, the THz imaging devices [19–21]. But these solutions are based on metallic resonator elements, which inevitably result in ohmic loss, and affect the modulating efficiency of the imaging devices. Furthermore, the incomplete symmetry of resonator elements leads to the polarization conversion in imaging lenses [22–25], which reduced the imaging quality to some extent. Consequently, it is particularly significant to design the metasurfaces composed of highly

efficient and polarization-independent resonator elements to achieve THz imaging. Based on our previous work, using a cross-typed resonator to achieve THz wave high-efficiency and full phase modulation under polarization-dependence [26], we employ transmissive THz metasurfaces consisting of high-efficiency and full phase modulation subwavelength silicon post resonators, which are obtained by parameters scanning and optimizing to generate hyperbolic THz wave phase profiles, and realize one-dimensional (1D) and 2D lenses for THz focusing. Moreover, the focal plane of 2D flat lens has a small spot size, and acquires high numerical aperture imaging. Since the phase retardations of post resonators in two arbitrary perpendicular directions are equal, phase modulation is polarization-insensitive, and the polarization conversion phenomenon is avoided. Based on the light-thin characteristic of the dielectric metasurface, the flat lens can be flexibly integrated in the optical equipments, for example, microscopes and some other laboratory tools. And the size of cameras, virtual reality headsets, and optical sensors for the internet of things can be significantly reduced. 2. Methods A schematic diagram of our proposed silicon post resonator element is shown in Fig. 1(a), which is consisted of a silicon post resonator (refractive index 𝑛𝑠𝑖 = 3.4), a benzocyclobutene (BCB) substrate (permittivity πœ€ = 2.67 and loss tangent 𝛿 = 0.012) [27] and top air layer. Here, D is the post diameter, h is the corresponding height, and P is the element period. We employ the numerical simulations based on finite element method (FEM) to optimize the parameters of resonator

βˆ— Corresponding authors. E-mail addresses: [email protected] (S. Feng), [email protected] (H. Guo).

https://doi.org/10.1016/j.optcom.2019.125083 Received 27 October 2019; Received in revised form 3 December 2019; Accepted 4 December 2019 Available online 9 December 2019 0030-4018/Β© 2019 Elsevier B.V. All rights reserved.

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Optics Communications 459 (2020) 125083

Fig. 1. (a) Schematic diagram of a single silicon post resonator element. (b) The transmission and phase of 16 resonator elements with non-periodic diameter change which are obtained by parameters scanning and optimization are modulated via 1.0 THz incident wave. And the phase is close to the range from βˆ’πœ‹ to πœ‹ (That is, the phase shift is almost full phase 2πœ‹). Simultaneously, the transmission maintains at an efficient distribution with above 94%. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

elements. Selecting carefully β„Ž = 148 ΞΌm, 𝑃 = 126 ΞΌm and keep them unchanged, while post diameter D is variable, Fig. 1(b) shows the parameter scan for the resonator element in Fig. 1(a) with the post diameter D as a variable at 1.0 THz, the transmission (red dotted line) and phase (blue dotted line) are obtained at a series of post diameters. After carefully selecting, 16 resonators with non-periodic change in post diameter are presented, where the gradient phase shift is πœ‹/8, so the total phase modulation is almost 2πœ‹ near linear change. What is more, the elements still maintain an efficient transmission efficiency of over 94% under full phase modulation. Simultaneously, we also give the resonant electric field distribution of 16 resonators with different diameters under the fold lines. Based on the dipole resonance theory, the incident THz plane wave and the resonant elements resonate with the electric dipoles, thereby the phase and amplitude of the electric field for transmitted waves are modulated. Besides, the shape of resonator is cylinder, so that the phase retardations of the elements in all directions are equal, and the phase difference between two arbitrary vertical directions is zero. That is, there is no polarization conversion for the incident wave. In order to verify the modulation effect of the resonators on phase for the incident THz wave shown in Fig. 1(b), we employ the FEM method for numerical simulation analysis. As shown in Fig. 2(a), in a waveguide composed of BCB substrate and air layer, an incident plane wave resonant at the frequency of 1.0 THz is utilized. It can be seen that the wave incident from the BCB substrate along z-axis direction transmits to air layer and continues to keep direction invariant for forward transmission. However, the 16 resonators obtained in Fig. 1(b) are placed at the junction of the substrate and air as shown in Fig. 2(b), according to the generalized refraction law [1]:

Fig. 2. Comparison of the phase distribution for THz wave deflection as there is no resonator element (a) and with resonator elements (b). (c) Schematic diagram of the THz flat metalens focusing principle under y-polarized wave incidence.

and the light polarization state can be intuitively and conveniently distinguished), transmits different lens resonator elements and dipole resonance effect is excited for different degrees. Thus, a gradient phase

πœ•πœ‘π‘‘ (1) πœ•π‘₯ Where, π‘˜i and π‘˜t are the wave vectors of incident and transmitted light, πœ•πœ‘ respectively. πœ•π‘₯𝑑 is the phase gradient introduced to transmitted light along x direction at the interface. According to Eq. (1), the incident THz wave irradiates vertically to the resonators to generate dipole πœ•πœ‘ resonance, and the phase gradient πœ•π‘₯𝑑 is obtained at the interface. Thus, we can notice that the phase distribution of transmitted wave in Fig. 2(b) is no longer parallel to the incident light wave. That is, the resonator elements modulate the incident wave phase well, so it is contributed to the realization of the deflection of transmitted THz wave’s forward direction. For clearly illustrating the working principle of the THz flat metalens, we designed a schematic diagram of the focusing principle for the lens and it is shown in Fig. 2(c). As the y-polarized THz wave is incident from left side of the metalens (the intensity distribution based on linearly polarized light depends on the polarization state,

delay is generated in radial direction of the lens so that the transmitted

π‘˜π‘‘ = π‘˜π‘– +

wave obtains parabolic phase profile to achieve focusing for THz radiation. According to Fermat’s principle, the parabolic phase profile of a transmitted wave can be expressed as follows: π›₯πœ‘ =

( ) 2πœ‹ √ 2 π‘Ÿ + 𝑓2 βˆ’ 𝑓 πœ†


Here, π›₯πœ‘ is the phase shift between an arbitrary point (x, y) on the lens √ and the central point O, πœ† is the wavelength in vacuum, π‘Ÿ = π‘₯2 + 𝑦2 is the distance from point (x, y) to central point O and f is the focal length of the lens. According to the given set focal length, we can calculate the phase distribution of each position on the lens via Eq. (2), so as to arrange the resonator elements reasonably, and finally realize the flat metalens for beam focusing. 2

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Optics Communications 459 (2020) 125083

Fig. 3. The focusing intensity distributions of the simple 1D single-focus lens at the frequencies of 0.8, 0.9, 1.0 and 1.1 THz (a), and the normalized intensity distributions along x direction at the corresponding focus position (b). The multi-focusing intensity distributions of the simple 1D multi-focus lens at the frequencies of 1.0 and 1.05 THz (c), and the normalized intensity distributions along x direction at the corresponding focus position (d). Table 1 Focal length and FWHM values of the simple 1D single-focus lens.

3. Results and discussion Now we employ the metasurface to achieve THz radiation focusing. Firstly, we study 1D single-focus and multi-focus lenses. The 16 resonators obtained in Fig. 1(b) are arranged symmetrically with a period of 𝑃 = 126 ΞΌm to obtain a simple 1D focusing lens, as shown in the bottom of Fig. 3(a) and (b). Via numerical simulations, as shown in Fig. 3(a), we obtained the focal intensity distributions of the plane wave at the frequencies of 0.8, 0.9, 1.0 and 1.1 THz, and S1, S2, S3 and S4 are the corresponding focal points at above four frequencies, respectively. It can be induced from the intensity distributions in Fig. 3(a) that the incident wave at above the four frequencies all achieve good focusing behavior. Our calculated results show that the light beam’s focusing quality is apparently depressed when the frequency moves away beyond above region. So the frequency width of good focusing behavior, π›₯𝑓0 , equals to 0.3 THz. It can be induced by the trend of connecting the focusing red line that the focal length of the lens becomes larger with the increasing of the working frequency 𝑓0 . Fig. 3(b) shows the normalized intensity distributions along the x direction at the focus positions of four focusing phenomena, from which the full width at half maximum (FWHM) of the focus size is obtained. Here, we list the focal length values and FWHM values at four frequencies in Table 1. It

𝑓0 (THz)

𝑓 (mm)

FWHM (πœ†)

0.8 0.9 1.0 1.1

1.16 1.90 3.00 4.85

0.80 0.94 1.07 1.27

shows that as the frequency of incident wave increases, the focal length and FWHM also increase. That is, the focus position is farther gradually from the lens and the focus size becomes larger gradually. Next, we shift the first eight and last eight elements of the simple 1D focusing lens and make them far away from the central sixteen elements by a distance of 0.3 mm, an optimized distance to generate two different hyperbolic phase profiles, and the multi-focus lens phenomena are observed in this simple 1D structure shown in the bottom of Fig. 3(c) and (d). The light intensity distributions at 1.0 and 1.05 THz are calculated and the multi-focus function (bi-focus B1, B2 and tri-focus T1, T2, T3) is achieved as shown in Fig. 3(c). Correspondingly, Fig. 3(d) shows the normalized intensity distributions in x direction at 3

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Optics Communications 459 (2020) 125083

Fig. 4. (a) 2D THz flat metalens structure and its phase distribution. (b) Focusing intensity distribution of the lens for y-polarized incident waves at the frequency of 1.0 THz. (c) The normalized intensity distribution on the focal plane xy and the curve distributions along x and y directions. Table 2 Focal length and FWHM values of the simple 1D multi-focus lens. 𝑓0 (THz)


𝑓 (mm)

FWHM (πœ†)


B1 B2

2.10 4.90

0.80 1.11


T1 T2 T3

0.90 3.30 7.45

0.65 1.30 1.46

numerical simulations. An incident y-polarized continuous wave with the single frequency of 1.0 THz travels from the substrate, and the spatial intensity distribution is shown in Fig. 4(b). It can be seen that the y-polarized wave passes through the flat lens and the hyperbolic wavefront is obtained, owing to the dipole resonance, thereby a good focusing behavior is achieved. Through measuring, the focal length is 1.80 mm. Similarly, to investigate the metalens’ focusing quality, we gained the normalized intensity distribution on the focal plane xy as shown in Fig. 4(c) and the curve distributions along x and y directions. We can find from the three-dimensional distribution that the intensity distribution of the focal plane xy is concentrated at the center of the plane, revealing that a good focusing effect is acquired. For quantitative analysis, the normalized intensity distributions in x and y directions are also given. The FWHM is 0.66 πœ† and 0.44 πœ†, respectively, indicating that the lens has a small spot size (meaning that a high numerical aperture). Comparing the intensity distributions along x and y directions, it is found that the intensity mainly distributes along y direction, judging that the transmitted waves remain y-polarized state (that is, the flat lens has polarization-insensitive characteristics). So far, a high-numericalaperture and polarization-insensitive THz flat metalens based on the dielectric metasurface has been realized. In the actual fabrication process, a size-error of the post resonator is existing, and this factor affects the size accuracy of the post resonators, thereby reducing the polarization insensitivity of the lens. Simultaneously, inadequate dipole resonance caused

each focus position. Similarly, the focal length values and FWHM values at two frequencies are listed in Table 2. From Table 2, it can be seen that the FWHM of the back-focus is wider than that of the front-focus. That is, the back-focus size is larger than the front-focus. Via above study of the simple 1D lenses, we extend the 1D lens into a 2D lens. Fig. 4(a) shows the 2D THz flat metalens structure and its phase distribution. For the convenience of research and lens size limitation, we only utilize one full phase periodic element (that is, 16-ring resonant elements of 16 resonators are arranged according to periodic P) to be arranged on the BCB substrate in the radial direction by a πœ‹/8 phase gradient. Above, the phase shift from the center of the flat lens to its boundary is exactly 2πœ‹. In order to verify the focusing characteristics of the lens, we employed the FEM method for 4

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Optics Communications 459 (2020) 125083

by size-error will also have an influence on the focusing quality and the transmittance. Here, in order to approximately evaluate the influence of the size error on the optical characteristics, we calculated that when the diameter of the post resonator is varying within the range of Β±5 ΞΌm, the transmittance change is about Β±1% and the phase change is about Β±0.4 rad. Hence, we can roughly judge that the influence of size error is acceptable within a certain range, and it also shows that our design is meaningful for practical fabrication.

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4. Conclusion In summary, we have realized a small-spot-size and polarizationinsensitive THz flat lens employing the transmissive metasurface consisting of the subwavelength silicon post resonators. Moreover, 1D single-focus broadband lens and multi-focus lens are realized by employing the metasurface in terahertz band, this will provide a meaningful reference for achieving broadband and multi-focus lenses. The flat lens is capable of producing hyperbolic THz wave phase profiles, achieving the 1.80 mm focal length focusing and supporting THz radiation of y-polarized beam at 1.0 THz. The FWHMs for the light intensity distributions along x and y directions of the focal plane are 0.66 πœ† and 0.44 πœ†, respectively, indicating that the lens has a high numerical aperture, this feature enables the lens to achieve high-quality imaging. And the phase difference between two arbitrary perpendicular directions on cylindrical resonator is zero, ensuring that the lens also has polarization-insensitive characteristics. Our proposed device has potential applications in some other THz devices, such as beam deflectors, optical vortex converters and flat lens arrays. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Xiaorong Hong: Software. Shuai Feng: Conceptualization, Methodology. Honglian Guo: Validation. Chuanbo Li: Formal analysis. Acknowledgments This work is supported by the National Natural Science Foundation of China with Grant Nos. 61775244, 61675068, 61974170, 61934007 and 61675195, and the National Key Research and Development Program of China with the No. 2018YFB2200500. References [1] N. Yu, P. Genevet, M.A. Kats, F. Aieta, J.P. Tetienne, F. Capasso, Z. Gaburro, Light propagation with phase discontinuities: generalized laws of reflection and refraction, Science 334 (2011) 333–337. [2] F. Aieta, P. Genevet, M.A. Kats, N. Yu, R. Blanchard, Z. Gaburro, F. Capasso, Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces, Nano Lett. 12 (2012) 4932–4936.