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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.
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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。
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关键词:
- polarization-independent /
- metalens /
- one-focus /
- multi-focus
Abstract: Metalens has received extensive concern in recent years. Design of a polarization-independent reflective metalens was proposed baesd on Au in infrared waveband. MgF2 was chosen as the dielectric spacer of the metalens. All simulations were carried out by using the finite-difference time-domain(FDTD) software. Results show that the proposed metalens has the same effect on different polarized light and can work well in the range of 700 - 850 nm and one-focus works best in the range of 750 - 800 nm. When the incidence wavelength is chosen as 800 nm, the proposed metalens can also work well for one-focus and multi-focus. At that time, the focal length of one focus, dual focus and three focus are 9.6, 6.6 and 4.7 μm, respectively. Different focus requirements can be realized according to the characteristics of the metalens.-
Key words:
- polarization-independent /
- metalens /
- one-focus /
- multi-focus
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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
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