Achromatic Sparse Aperture Metalens Based on Wavefront Coding
Objective Optical sparse aperture technology is applied to the design and optimization of metalenses to reduce the lens processing area,increase the numerical aperture,and improve the resolution.Currently,optical sparse aperture metalenses are limited to a single wavelength,and thus are difficult to use in broadband imaging fields.There are two primary types of metalens phase modulation:transmission and geometric.Transmission phase modulation is wavelength sensitive,making it difficult to focus beams of all wavelengths simultaneously;therefore,this type of structure is unsuitable for application in wavefront-encoding achromatic metalenses.Alternatively,during geometric phase modulation,the phase delay is wavelength independent,which makes the optical system insensitive to the position of the focal plane.As a result,geometric phase wavefront-encoding technology can achieve achromatism by increasing the focal depth of the system for all wavelengths.In this study,the cubic-phase wavefront encoding method is introduced for the design of an achromatic donut-like optical sparse aperture(DOSA)metalens.After cubic phase modulation,the optical transfer function of the proposed metalens hardly changes with the defocus.Furthermore,we hope that the proposed achromatic optical sparse aperture metalens can achieve a resolution consistent with that of an ideal lens in the visible light band(400-700 nm).Methods An achromatic optical sparse aperture metalens was designed based on the wavefront encoding method and optical sparse aperture technology.The designed metalens employed a donut-like optical sparse aperture.After passing through a fused quartz substrate,the wavefront reaches a donut-like medium layer,and the phase is modulated by periodically arranged nanopillar structures in the layer.An optimized geometric nanopillar structure was adopted to achieve greater polarization conversion efficiency at various wavelengths.In addition,cubic phase encoding based on Fourier optics was applied to preset the wavefront phase of an incoherent imaging system.When adjusting the cubic phase encoding factor,the optical transfer function(OTF)of the designed metalens barely changed with the defocus.The surface phase of the designed metalens was obtained by combining the focusing phase of the DOSA metalens with the cubic encoded phase.In addition,Wiener filtering was employed to restore the degraded images after passing through the metalens.Results and Discussions The processing area of the designed metalens is reduced to 25％of the full-aperture transmittance metalens.Simultaneously,through the analysis of the modulation transfer functions(MTF)of the metalens at different wavelengths,the results show that the frequencies of the full-aperture and DOSA metalenses suffer severe losses at all wavelengths except 550 nm,leading to irreversible image blurring.Although the MTFs of the proposed achromatic DOSA metalens based on wavefront encoding decrease in the mid-frequency domain at all wavelengths,they are retained and can theoretically be restored(Fig.3).To further verify the imaging quality,image formation simulations are conducted on three types of metalenses.The restored images of the full-aperture metalens at 400 nm,470 nm,625 nm,and 700 nm exhibit extreme minutia loss(Fig.4).Similarly,the restored images of the DOSA metalens at 400 nm,470 nm,and 700 nm profoundly lose minutia(Fig.5).After wavefront encoding modulation,the quality of the restored image from the proposed metalens is basically the same at all wavelengths(Fig.6).Consequently,this achromatic DOSA metalens not only achieves broadband achromatism,but also reduces the processing area of large-aperture metalenses.Conclusions In this study,an achromatic DOSA metalens based on wavefront encoding is realized by the superposition of the cubic encoded phase and DOSA focusing phase,realizing achromatic imaging in the visible light band.During the imaging processes of the full-aperture and DOSA metalenses,chromatic dispersion caused by changes in the incident wavelength leads to poor image quality.To obtain more minutiae and achieve a higher resolution in the visible light band instead of at a single wavelength,cubic wavefront phase encoding is introduced to achieve the phase modulation of all wavelengths.Based on the above theories,a cubic-phase wavefront encoding DOSA metalens is designed using gallium nitride with an effective half aperture of 0.35 mm,internal radius of 0.303 mm,focal length of 7 mm,and a cubic phase encoding factor of 20.Finally,simulations including MTF and image restoration of the full-aperture metalens,DOSA metalens,and achromatic DOSA metalens are conducted at 400 nm,475 nm,550 nm,625 nm,and 700 nm.It is demonstrated that the DOSA metalens based on wavefront encoding can achieve achromatic imaging in the visible light band and theoretically achieve the same cut-off frequency as the ideal full-aperture metalens.Accordingly,it has excellent value in image acquisition owing to its low processing cost,large achromatic range,and high imaging quality.
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