Doublet achromatic metalens for broadband optical retroreflector

Fig. 1. (a)–(c) Schematic of (a) a transmissive achromatic metasurface that enables a light source with a continuously changing wavelength to have (b), (c) the same focal point. (d)–(f) Schematic of (d) a reflective achromatic metasurface that bestows a twice tangential momentum to (e), (f) the incoming light source with continuously changed wavelength. (g)–(i) Schematic of a broadband retroreflector comprised of a transmissive achromatic metasurface combined with a reflective achromatic metasurface. (j), (k) Spectral phase profiles (left panel) for the central meta-unit and spatial phase profiles (right panel) along the radial direction for a (j) transmissive/(k) reflective achromatic metalens within an arbitrary wavelength range of $λ \in [λ_{\min}, λ_{\max}]$ .

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$(a), (b) Schematics of (a) the transmissive meta-units comprised of silicon square pillars and square holes, and (b) the reflective meta-units comprised of silicon square pillars and square holes on a gold film. (c) Theoretical transmission phase profiles for the transmissive metalens at r0=6.3 μm (red dashed line), 4.5 μm (azure dashed line), and 0 (black dashed line), associated with the simulated transmission efficiencies (red, azure, and black dotted lines) and phase profiles (red, azure, and black solid lines) of three meta-units with WpL=0.18 μm, WhL=0.34 μm, and WhL=0.10 μm, respectively. (d) Theoretical reflection phase profiles for the reflective metalens at R0=5.4 μm (red dashed line), 3.6 μm (azure dashed line), and 0 (black dashed line), associated with the simulated reflection efficiencies (red, azure, and black dotted lines) and phase profiles (red, azure, and black solid lines) of three meta-units with WpR=0.20 μm, WhR=0.32 μm, and WhR=0.18 μm, respectively. The lattice constants along the x and y directions are P=0.45 μm, and the thickness of silicon is H1=0.6 μm. The silicon layer is covered by SU-8 polymer, with the thickness and refractive index being H2=2 μm and 1.555, respectively, and the refractive indices of other materials are extracted from Ref. [34].$

Fig. 2. (a), (b) Schematics of (a) the transmissive meta-units comprised of silicon square pillars and square holes, and (b) the reflective meta-units comprised of silicon square pillars and square holes on a gold film. (c) Theoretical transmission phase profiles for the transmissive metalens at r₀ $= 6.3 μ m$ (red dashed line), $4.5 μ m$ (azure dashed line), and 0 (black dashed line), associated with the simulated transmission efficiencies (red, azure, and black dotted lines) and phase profiles (red, azure, and black solid lines) of three meta-units with $W_{p}^{L} = 0.18 μ m$ , $W_{h}^{L} = 0.34 μ m$ , and $W_{h}^{L} = 0.10 μ m$ , respectively. (d) Theoretical reflection phase profiles for the reflective metalens at R₀ $= 5.4 μ m$ (red dashed line), $3.6 μ m$ (azure dashed line), and 0 (black dashed line), associated with the simulated reflection efficiencies (red, azure, and black dotted lines) and phase profiles (red, azure, and black solid lines) of three meta-units with $W_{p}^{R} = 0.20 μ m$ , $W_{h}^{R} = 0.32 μ m$ , and $W_{h}^{R} = 0.18 μ m$ , respectively. The lattice constants along the x and y directions are P $= 0.45 μ m$ , and the thickness of silicon is H₁ $= 0.6 μ m$ . The silicon layer is covered by SU-8 polymer, with the thickness and refractive index being H₂ $= 2 μ m$ and 1.555, respectively, and the refractive indices of other materials are extracted from Ref. [34].

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Fig. 3. (a) Distributions of $|$ E $|^{2}$ in the x–z plane for the transmissive metalens of 13.95 µm in diameter under the illumination of x-polarized light waves with 0° and 16° at 1.35, 1.55, 1.75, and 1.95 µm. (b) Foci offsets and (c) focal lengths versus incidence angle for four wavelengths (1.35, 1.55, 1.75, and 1.95 µm). (d) Distributions of $|$ E $|^{2}$ in the x–z plane for the reflective metalens of 12.15 µm in diameter under the normal illumination of x-polarized light waves at 1.35, 1.55, 1.75, and 1.95 µm. (e) Focal length of the reflective metalens versus light wavelength.

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Fig. 4. (a) Distributions of the real part of E_ref,x for the broadband metasurface retroreflector under the illumination of x-polarized light waves for four wavelengths and three incidence angles (5°, 10°, and 15°). (b) In the upper semicircles, the normalized $| A_{x} (φ, k_{y} = 0, θ, λ) |^{2}$ (solid lines, with respect to its maximum value) versus spatial angle $φ$ and $\min [| r_{ret} (θ, λ) |^{2}, | r_{nor} (θ, λ) |^{2}] / \max [| r_{ret} (θ, λ) |^{2}, | r_{nor} (θ, λ) |^{2}]$ (dotted arcs) under the x-polarized incidence for different wavelengths and incidence angles: 5° (red), 10° (orange), and 15° (green). In the lower semicircles, the normalized $| Δ A_{x} (φ, k_{y} = 0, θ, λ) |^{2}$ (dashed lines, with respect to its maximum value) versus spatial angle $φ$ for different wavelengths and incidence angles: 5° (red), 10° (orange), and 15° (green).

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Fig. 5. (a) Reflection angles and (b) the difference between the reflection angles and the incidence angles versus incidence angle and wavelength under x- and y-polarized incidence. (c) Real and imaginary parts of the retroreflection coefficients r_ret $(θ, λ)$ versus incidence angles under x- and y-polarized incidence. (d) Values of $|$ r_ret $(θ, λ) |^{2}$ versus incidence angle and wavelength under x- and y-polarized incidence.