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Design of polarization-independent reflective metalens in near infrared waveband

Zhang Yuhui Yang Bowei Li Yiting Zhao Yuanzhi Fu Yuegang

张玉慧, 杨博伟, 李轶庭, 赵元埴, 付跃刚. 近红外波段偏振无关型反射超透镜的设计[J]. 红外与激光工程, 2020, 49(6): 20200048. doi: 10.3788/IRLA20200048
引用本文: 张玉慧, 杨博伟, 李轶庭, 赵元埴, 付跃刚. 近红外波段偏振无关型反射超透镜的设计[J]. 红外与激光工程, 2020, 49(6): 20200048. doi: 10.3788/IRLA20200048
Zhang Yuhui, Yang Bowei, Li Yiting, Zhao Yuanzhi, Fu Yuegang. Design of polarization-independent reflective metalens in near infrared waveband[J]. Infrared and Laser Engineering, 2020, 49(6): 20200048. doi: 10.3788/IRLA20200048
Citation: Zhang Yuhui, Yang Bowei, Li Yiting, Zhao Yuanzhi, Fu Yuegang. Design of polarization-independent reflective metalens in near infrared waveband[J]. Infrared and Laser Engineering, 2020, 49(6): 20200048. doi: 10.3788/IRLA20200048

近红外波段偏振无关型反射超透镜的设计

doi: 10.3788/IRLA20200048
详细信息
  • 中图分类号: O436.3

Design of polarization-independent reflective metalens in near infrared waveband

Funds: National Natural Science Foundation of China (NSFC) (11474041); National Natural Science Foundation of China (NSFC) (61805025); “111” Project of China (D17017)
More Information
    Corresponding author: 付跃刚(1972-),男,教授,博士,主要从事光学设计及仿生光学等方面的研究。Email: fuyg@cust.edu.cn
  • 摘要: 近些年,超透镜受到了广泛关注。文中提出了一种基于金材料的近红外波段偏振无关型反射超透镜,该超透镜采用MgF2材料作为电介质层,利用FDTD软件实现仿真设计。仿真结果表明:超透镜在不同偏振光入射的情况下具有相同的聚焦效果,入射波长在700~850 nm 的范围内,具有较好的聚焦效果。入射波长在750 ~800 nm范围内单焦点聚焦效果最好。当入射波长为800 nm,该超透镜可以分别实现单焦点和多焦点聚焦,其单焦点、双焦点和三个焦点的焦距分别为9.6、6.6 和 4.7 μm。可以利用该超透镜的特点实现不同的聚焦要求。
  • Figure  1.  Schematic of proposed metalens. (a) Fragment; (b) Cross section view ; (c) Top view of proposed metalens

    Figure  2.  Phase shift and reflectance of reflected wave of (a) x-polarization incidence and (b) y-polarization incidence

    Figure  3.  Proposed metalens working for one focus. (a) Relationship between the position x and radius of each unit for x-polarization; (b) Simulated Poynting vector distributions for metalens for x-polarization; (c) Intensities of the focusing spots along x direction for x-polarization; (d) Relationship between position x and the radius of each unit for y-polarization; (e) Simulated Poynting vector distributions for the metalens for y-polarization; (f) Intensities of the focusing spots along the x direction for y-polarization

    Figure  4.  Simulated Poynting vector distributions for the metalens with incidence wavelength of (a) 650 nm, (b) 700 nm, (c) 750 nm, (d) 900 nm, (e) 850 nm

    Figure  5.  Intensities of the focusing spots along the x direction with the incidence wavelength of (a) 650 nm, (b) 700 nm, (c) 750 nm, (d) 850 nm, (e) 900 nm

    Figure  6.  Proposed metalens working for daul focus. (a) Relationship between the position x and the radius of each unit; (b) Simulated Poynting vector distributions for the metalens; (c) Intensities of the focusing spots along the x direction

    Figure  7.  Proposed metalens working for three focus. (a) Relationship between the position x and the radius of each unit; (b) Simulated Poynting vector distributions for the metalens; (c) Intensities of the focusing spots along the x direction

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出版历程
  • 收稿日期:  2020-02-16
  • 修回日期:  2020-04-01
  • 网络出版日期:  2020-07-01
  • 刊出日期:  2020-07-01

Design of polarization-independent reflective metalens in near infrared waveband

doi: 10.3788/IRLA20200048
    通讯作者: 付跃刚(1972-),男,教授,博士,主要从事光学设计及仿生光学等方面的研究。Email: fuyg@cust.edu.cn
基金项目:  National Natural Science Foundation of China (NSFC) (11474041); National Natural Science Foundation of China (NSFC) (61805025); “111” Project of China (D17017)
  • 中图分类号: O436.3

摘要: 近些年,超透镜受到了广泛关注。文中提出了一种基于金材料的近红外波段偏振无关型反射超透镜,该超透镜采用MgF2材料作为电介质层,利用FDTD软件实现仿真设计。仿真结果表明:超透镜在不同偏振光入射的情况下具有相同的聚焦效果,入射波长在700~850 nm 的范围内,具有较好的聚焦效果。入射波长在750 ~800 nm范围内单焦点聚焦效果最好。当入射波长为800 nm,该超透镜可以分别实现单焦点和多焦点聚焦,其单焦点、双焦点和三个焦点的焦距分别为9.6、6.6 和 4.7 μm。可以利用该超透镜的特点实现不同的聚焦要求。

English Abstract

    • Metamaterials have many unusual phenomena, including negative refractive index, giant chirality, and indefinite permittivity[1-4], which made them widely investigated in recent years. Metasurfaces, the two dimensional versions of metamaterials, have been demonstrated to be a novel approach to control electromagnetic wavefronts[5-6]. Since Capasso et al. first investigated beam steering in 2011[7], many kinds of structures have been reported on metasurfaces to achieve the functions of focusing lens[8-10] and anomalous reflection and refraction[11]. Among many kinds of metasurfaces, metalens can achieve the function of focusing and anomalous reflection by configuring different materials and shapes of units. Lots of models like nanoslit[12], nanohole[13-14], graphene ribbons[15-19] are introduced in metalens design, where 2π phase shift resulted by the designed antennas is needed in controlling the wavefront. Although much structures have been proposed in past reports, the function of metalens have not been fully investigated.

      In this paper, we proposed a new model based on Au and MgF2, which is independence of polarization[20-21]. x-polarized and y-polarized incidence are both have the same focusing effect. The proposed metalens can work well in the range of 700 - 850 nm for one-focus, and by configuring the resonance antenna, the proposed metalens can also achieves dual focus and three focus. When we use the incidence of 800 nm wavelength, the focal length of one focus, dual focus and three focus are 9.6, 6.6 and 4.7 μm, respectively. The focal length will decrease as the focus number increases. We believe that our findings are beneficial in designing new function controlling devices.

    • Figure 1 illustrates the schematic of the proposed lens, which is a metal-insulator-metal structure to form a Fabry-Perot cavity to enhance the interaction between light and resonance antenna. The resonance antenna and the bottom mirror are selected as Au with data acquired from reference [22]. The dielectric spacer is chosen as MgF2 with a refrative index of 1.892[23]. The thicknesses of Au antenna, MgF2 spacer and Au mirror shown in Fig.1(b) are set as ta=30 nm, td=50 nm and ts=130 nm, respectively. The top view of the unit cell of the metalens is shown in Fig.1(c). The period in x- and y-directions are px=pv=200 nm. The resonance antenna is a circle, which is independent of different polarized light. Thus, we can control the wavefront of the plane wave regardless of x-polarization or y-polarization incidences. The working mechanism of the proposed metalens is shown in Fig.1(a). For numerical analysis, all simulations are carried out by using the finite-difference time-domain (FDTD) software.

      Figure 1.  Schematic of proposed metalens. (a) Fragment; (b) Cross section view ; (c) Top view of proposed metalens

      Generally, the resonant antenna is a circle, it has the same effect on different polarized light. To explore this, we choose the working wavelength as 800 nm. It shows the phase shift and reflectance of the reflected light for x-polarization incidence in Fig.2(a) and y-polarization incidence in Fig.2(b). A near 2π phase shift can be acquired when the radius r increases from 10 nm to 90 nm. As we can see, the change in the radius of the resonant antenna has the same effect on x-polarization incidence and y-polarization incidence.

      Figure 2.  Phase shift and reflectance of reflected wave of (a) x-polarization incidence and (b) y-polarization incidence

    • To design metalens to focus incident light, the phase profile of the metalens should follow the expression[24]:

      $$\varphi (x) = \frac{{2{\text{π}}}}{{{\lambda _0}}}(\sqrt {{x^2} + {F^2}} - F)$$ (1)

      where x is the horizontal position from the center of metalens; ${\lambda _0}$is the wavelength of the incident; F is the focal length. Based on Eq.(1), we calculated the phase distribution curves for F=10 μm, and show them in Fig.3(a).

      Figure 3.  Proposed metalens working for one focus. (a) Relationship between the position x and radius of each unit for x-polarization; (b) Simulated Poynting vector distributions for metalens for x-polarization; (c) Intensities of the focusing spots along x direction for x-polarization; (d) Relationship between position x and the radius of each unit for y-polarization; (e) Simulated Poynting vector distributions for the metalens for y-polarization; (f) Intensities of the focusing spots along the x direction for y-polarization

      According to the expression, we selected the radius of the resonant antenna from Fig.2(a) and Fig.2(b) to design metalens. The focal length is designed as 10 μm and the size of the metalens is designed as 12 μm (60 units). The relationship between the position x and the radius of each unit for x-polarization and y-polarization are shown in Fig.3(a) and Fig.3(d) respectively. We simulated the metalens with 800 nm wavelength of the incident light. The Poynting vector distributions for incidence for x-polarization and y-polarization are shown in Fig.3(b) and Fig.3(e) respectively, (d) and the simulated focal lengths are both 9.6 μm, which agree well with the designed values. The intensity distributions along x-direction for x-polarization and y-polarization are shown in Fig.3(c) and Fig.3(f) respectively and the FWHM (Full Wave at Half Maximum) values for the focal lengths are both 0.67 μm. The results show that x-polarization and y-polarization have exactly the same focusing effect. The small deviations among the simulated focus length and the designed value are because the phase shift does not cover 2π, and we made the approximation when we selected the radius of the resonant antenna. On the other hand, the insufficient mesh accuracy may lead to deviations.

      Then we simulated the proposed metalens in other incident wavelengths for x-polarization, thats 650, 700, 750, 850 and 900 nm. Simulated results are shown in Fig.4 and Fig.5. The poynting vector distributions for 650, 700, 750 , 850 and 900 nm are shown in Fig.4(a)−(e), respectively. The intensity distributions for 650, 700, 750, 850 and 900 nm along x-direction are shown in Fig.5(a)−(e), respectively. As we can see, the proposed metalens can works well within a broadband wavelength that ranges of 700−850 nm, and it performs best in the 750−800 nm range.

      Figure 4.  Simulated Poynting vector distributions for the metalens with incidence wavelength of (a) 650 nm, (b) 700 nm, (c) 750 nm, (d) 900 nm, (e) 850 nm

      Figure 5.  Intensities of the focusing spots along the x direction with the incidence wavelength of (a) 650 nm, (b) 700 nm, (c) 750 nm, (d) 850 nm, (e) 900 nm

      Further more, the proposed metalens can achieve dual focus by configuring the resonance antenna according to the expression:

      $$a\left( x \right){{\rm {e}}^{ - i\varphi \left( x \right)}} = {a_1}{{\rm {e}}^{ - i\frac{{2{\text{π}}}}{\lambda }\left( {\sqrt {{{\left( {{{x - d} / 2}} \right)}^2} + {f^2}} - f} \right)}} + {a_2}{{\rm {e}}^{ - i\frac{{2{\text{π}}}}{\lambda }\left( {\sqrt {{{\left( {{{x + d} / 2}} \right)}^2} + {f^2}} - f} \right)}}$$ (2)

      where ɑ(x) is the nearest amplitude, d is the distance between the two focals and ɑ1=ɑ2=0.5. We designed two focus locate at x=−3, x=3 and the focal lengths are both 10 μm. The relationship between the position x and the radius of each unit is shown in Fig.6(a). We simulated the metalens with 800 nm wavelength of the incident light. The Poynting vector distributions for incidence and the intensity distributions along x-direction are shown in Fig.6(b) and Fig.6(c), respectively. The simulated focal lengths are 6.6 μm and the FWHM values are 0.95 μm. The simulated results are in good agreement with the designed values. Note that there are small deviations among the simulated focus length and the designed value, which due to the approximations in selecting the radius of the resonant antenna in configuring processes and the insufficient mesh accuracy.

      Figure 6.  Proposed metalens working for daul focus. (a) Relationship between the position x and the radius of each unit; (b) Simulated Poynting vector distributions for the metalens; (c) Intensities of the focusing spots along the x direction

      Then we designed three focus by the proposed metalens. According to the expression:

      $$\begin{split} a\left( x \right){e^{ - i\varphi \left( x \right)}} =\; & {a_1}{{\rm e}^{ - i\frac{{2{\text{π}}}}{\lambda }\left( {\sqrt {{{\left( {{{x - d} / 2}} \right)}^2} + {f^2}} - f} \right)}} +\\ & {a_2}{{\rm e}^{ - i\frac{{2{\text{π}}}}{\lambda }\left( {\sqrt {{{\left( {{{x + d} / 2}} \right)}^2} + {f^2}} - f} \right)}} + \\ &{a_3}{{\rm e}^{ - i\frac{{2{\text{π}}}}{\lambda }\left( {\sqrt {{x^2} + {f^2}} - f} \right)}}\end{split}$$ (3)

      where the a(x) is the nearest amplitude, a1=a2=a3=1/3. The designed three focus locate at x=−4, x=0, x=4 and the focal lengths are all 10 μm. We selected the radius of the resonant antenna according to Fig.7(a), which are the relationship between the position x and the radius of each unit. The Poynting vector distributions for incidence and the intensity distributions along x-direction of the simulated results are shown in Fig.7(b)and Fig.7(c). The focal lengths of Fig.7(b)are 4.7 μm and the FWHM values of Fig.7(c) are 0.86 μm. As can be seen from Fig.6 and Fig.7, the proposed structure also has a good focusing effect for multi-focus and the focal length will decrease as the focus number increases.

      Figure 7.  Proposed metalens working for three focus. (a) Relationship between the position x and the radius of each unit; (b) Simulated Poynting vector distributions for the metalens; (c) Intensities of the focusing spots along the x direction

    • In summary, we proposed the metalens based on Au and MgF2, which is independence of polarization. We simuated by using FDTD method. According to the simulated results, the proposed metalens can work well in the range of 700 nm to 850 nm and work best in the range of 750 nm to 800 nm for one focus. By configuring the resonance antenna, the proposed metalens can also work well for multi-focus. When the incidence wavelength is chosen as 800 nm, the focal length of one focus, dual focus and three focus are 9.6 μm, 6.6 μm and 4.7 μm, respectively. In conclusion, we can control the focus of the proposed metalens according to our requirements. We believe that our findings are beneficial in designing new function controlling devices.

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