Miniaturized and lightweight imaging systems are fast becoming integral to consumer electronics，industrial，medical，and automotive sectors^［1］. The optical lens，being the primary component of such systems，plays a crucial role in focusing light^［2］. The atmospheric window of 9-11.5 μm is particularly significant due to the peak of infrared radiation from room temperature object occurring at 10 µm，making this wavelength range vital for infrared imaging and detection^［3］. However，traditional infrared lenses tend to be bulky，intricate，and thus counterproductive to the portability and accessibility of long-wave infrared （LWIR） devices. To correct chromatic aberration，these lenses need multiple lens groups，which inherently limits both the depth of focus（DOF） and imaging resolution. It also impedes its broadband performance and actual imaging ability^［4］.

Metasurfaces，artificially arranged nanostructures with sub-wavelength patterned layers^［5，6］，have birthed a powerful new platform for light manipulation - the metalens. These metasurfaces control light characteristics such as amplitude，polarization，and phase ^［7-9］，enabling metalenses to potentially resolve these issues and thereby streamline numerous infrared applications. This results in thinner^［10］ ，easier-to-align and package lenses ^［11］，which in turn fosters a broad range of high-volume applications^［12］. Metalenses have been widely reported for use in polarization regulation^［13］，beam shaping ^［14］，holographic imaging^［15］，molecular fingerprint detection^［16］，integrated quantum devices^［17］ and more^［18］. Yet，the majority of these studies focus on the visible ^{［7，19-25］} and near-infrared^［26-29］ ranges，with mid-infrared and far-infrared metalenses still in their nascent stages of development ^{［2，30，31］}.

Contrary to the short-wave range，LWIR requires higher imaging tolerances due to its all-weather applicability in military and security sectors，necessitating a larger DOF ^［32-36］. However，no reported metalenses can function wideband in the LWIR spectrum with an large DOF，due to inherent large dispersion，requiring specific wavelength light sources for active imaging^{［37，38］}. Lenses with larger DOF are more practical for real-world applications^{［32，33］} and can gather more object information and exhibit superior performance in broadband application scenarios，while increasing the DOF of a metalens typically sacrifices resolution^{［39，40］}. The reported methodologies that ostensibly realize expanded depth of focus include Fresnel lens arrays （FLAs），axial lenses （AXLs） and light sword optical elements （LSOEs）^{［41，42］}.

Given the diverse and com plex requirements of long-wave infrared metalenses，including collecting more light for imaging，expanding the size of the metalens becomes essential^［3］. However，most currently reported metalenses are relatively small and have short focal lengths^［29］ due to the complex design ^［6］ and manufacturing precision required for larger sizes and longer focal lengths. These limitations necessitate the use of high-cost electron beam lithography for fabrication ^［1，43］. Further research has not been conducted on the potential wideband capabilities of existing LWIR metalenses^［44］. The reported designs of large-scale metalenses have not considered their imaging tolerance^［4，45］. Our research addresses these challenges and contributes to the development of long-wave infrared metalenses with large DOF and broad band operation.

In the present study，we introduce a metalens with extensive DOF for LWIR focusing. Such a metalens is designed based on propagation phase modulation with silicon and can be realized through a straightforward single-step UV lithography process，which is capable of performing in the 9- 11.5 μm wavelength range.

The design of the unit cell must balance the high refractive index and low absorption of the material in use. Many of the cells employed in recent work are complex media，reducing their process compatibility. Our solution to these challenges is a silicon cylinder structure relying on propagation phase modulation. As illustrated in Fig. 1（a），the metalens is composed of circular silicon nanopillars arranged in a square lattice. The cell period P and cylinder height h are 6 µm，with cylinder radius R ranges from 1 to 2.5 µm.

Simulations performed using finite-difference time-domain （FDTD） methods demonstrate that the propagation phase can be adjusted by modifying the radius of the subwavelength meta-atoms. The propagation phase versus radius is displayed in Fig. 1（b）. The silicon nanopillars showcase respectable transmission in the LWIR （9-11.5μm） region，as evidenced in Fig. 1（c）. The combination of low loss from the dielectric and an adept structural design allows for a superior overall transmittance at 10.5 μm. Fig. 1（d） illustrates the electric field distribution |E| of the silicon nanopillars with a diameter of 2 μm at wavelengths of 9-11.5 μm. The strong optical energy confinement within the nanopillar implies that wavefront manipulation using meta-atoms is a localized effect. This capacity for wavefront regulation is achieved through the phase accumulation of the electric field within the silicon column，although it decreases when the operating wavelength is shifted，still maintains sufficient adjustment potential.

The ideal phase distribution $\phi \left(x,y\right)$ of a metalens can be expressed as Eq. （1） ^［46］：

Here，（x，y） denotes the spatial coordinates of the unit structure， λ represents the free space wavelength，and f is the focal length of the metalens. It can be understood from this equation that with the same radial distance and wavelength，a higher focal length results in a smaller geometric phase difference. This implies a higher requirement for phase regulation accuracy，substantially increasing the fabrication complexity.

For the metalens to have sufficient phase control capability and focusing efficiency，it's necessary that the metalens' meta-atoms can cover a phase of 2π，and that each meta-atom exhibits high transmittance. Based on the optical response results displayed in Fig. 1（b-c），we select the optimal structure as the phase cell library. We employ interpolation between transmittance phase and size to choose the meta-atoms，aiming to enhance the focusing performance^［4］. Fig. S1 demonstrates the arrangement of our metalens units in a checkerboard layout，while Fig. S2 displays the phase distribution along the metalens radius.

The DOF of a lens can be generally expressed as per Eq. （2） ^［47］：

where NA = sin［arctan（D/（2f））］，and D is incident aperture. To augment the DOF of the metalens，one can either reduce the incident aperture or increase the focal length. However，reducing the incident aperture will compromise the metalens resolution，while a significantly larger focal length will enlarge the entire optical system. Therefore，continuous optimization is required to select the appropriate incident aperture and focal length. According to Huygens' principle，the phase gradient over the surface of a metalens determines the propagation direction of the transmitted light^［48］. We can manipulate the structural parameters of the meta-atom to subsequently alter its phase accumulation. By modifying the design of the metalens，it is feasible to induce more or less phase accumulation in some meta-atoms，facilitating the lengthwise broadening of focal spots. This configuration can be fabricated via a selective area etching effect.

We first designed a metalens structure with a central wavelength of 10.5 μm using the outlined method. Simulation results confirmed a commendable focusing effect and substantial DOF within the broadband range of 9-11.5 μm. Fig. 2（a-c） display the focusing impact of the metalens at wavelengths of 9 μm，10 μm，and 10.5 μm. Correspondingly，the FWHM at these different wavelengths are 16.5，16.3，16.2 μm，respectively. The NA and focal length are 0.442，0.445，0.447 and 1.15 mm，1.05 mm，1 mm，respectively，corresponding to the DOF of 131，126，124 μm. Additionally，the metalens，due to its substantial DOF，enables a focus with minimal chromatic aberration at a specific position. This is due to the large overlapping area of the focal spot at varying wavelengths.

Next，we studied the focusing deviation of the metalens during broadband operation. Fig. 2（d-f） compare the ideal phase distribution with the actual phase distribution of the designed metalens structure at wavelengths of 9 μm，10 μm，and 10.5 μm. As the deviation between the actual operating wavelength and the theoretical design center wavelength increases from 0 to 1.5 μm，the propagation phase error of the meta-atoms also escalates. We computed the propagation phase error levels for all meta-atoms of the metalens operating at different wavelengths and quantified the percentage of each element with varying error sizes，as depicted in Fig. S3. The maximum phase difference was observed to be 15%，signifying that the dispersion effect is minimal and broadband operation is feasible. We obtained similar results for 11 μm and 11.5 μm in Fig. S4，also with minimal phase error levels.

To enhance the practical application performance of the metalens，we designed a 4 mm diameter metalens with focal length of 4 mm and central wavelength of 10.5 μm. Fig. 4b presents the simulated focusing effect of the cross section of the focal spot at the focal plane，with FWHM of 11.6 μm and focusing efficiency value of 45.9%.

Subsequently，we fabricated the metalens via photolithography. The fabrication process involved direct utilization of pure silicon wafer to create samples with a substrate thickness of 625 μm. The process commenced with transferring the pattern from the mask plate onto the photoresist using ultraviolet lithography. This was followed by applying a chromium layer on the sample surface through magnetron sputtering. Afterward，we employed the lift-off process to wash off the photoresist，leaving behind the chromium pattern. Inductively coupled plasma （ICP） etching technology was used to create the metasurface and removed the remaining chromium using ceric ammonium nitrate. This process notably reduced the production budget and complexity as it employed only one-step UV lithography and ICP etching instead of low-temperature deep silicon etching. The process flow diagram is shown in Fig. 3（a）. Fig. 3（b-d） present photographs of the metalens sample we fabricated，along with SEM and microscopic images of its components. Fig. 3（b） demonstrates the high verticality of the cylinder. The SEM images reveal that the processed patterns have an excellent morphology that meets the design requirements. The maximum aspect ratio of the structure was observed to be 3，indicating the high robustness of the nanostructures. We discovered during the experiment that increasing the etching depth appropriately can also amplify phase accumulation in the unit structure. This，in turn，broadens the focusing spot along the longitudinal direction，thereby increasing the DOF，relevant details are presented in Fig. S10.

To validate the focusing effect and practical application capability of our metalens，we designed and conducted a series of test experiments. The experimental setup，as shown in Fig. 4（a），utilized a carbon dioxide laser as the light source with a wavelength of 10.55 μm. The spot pattern before passing through the lens group is depicted in Fig. S5. The imaging equipment was composed of a 40× reflective microscope objective （Thorlabs，LMM-40X-P01），achromatic doublet infrared lenses （Thorlabs，AC254-100-E），and an uncooled thermal imaging camera （Xenics Gobi+ 640）. This equipment was used to capture intensity images and assess the focusing performance of the metalens. A motorized stage assembly moved along the longitudinal direction （z axis） in 2.5 μm steps for the measurements. The reference position，i. e.，the device plane （z = 0），was set when the camera can clearly capture the image of the samples. Fig. S6 displays the shot of the optical path. Through the motorized stage，we measured the focal length of the metalens to be 4.05 mm，which agrees well with the designed result. Fig. 4（c） shows the cross-section of the spot at the focal plane，and Fig. 4（b） presents the focal spot image of the metalens simulated by FDTD for comparison. Tests on the focused spot，as shown in Fig. 4（d），revealed a nearly diffraction-limited FWHM of 12.6 μm. Additionally，measured Strehl ratios of the metalens is 84.1%.

Focusing efficiency is defined as the ratio of integrated power within the circle having radius 1.5 × FWHM to the incident power on the metalens［49］. The focusing efficiency value for the metalens is 41.8%. When comparing the experimental performance with the simulation and theoretical performance，slight deviations from the simulation results were observed. These data were accurately computed with the aid of a Gaussian fitting function，with the focal spot after Gaussian fitting presented in Fig. S7. The deviations were attributed to discrepancies between the experimental light source and the simulated light source. In the DOF measurement，the DOF was defined as the axial distance when the maximum FWHM of the focusing spot is reduced to half. The measured DOF was approximately 11 times of the focus wavelength. Detailed results are provided in Fig. 4（e）.

Subsequently，we used the metalens for passive imaging. The experimental setup involved removing the lens of the traditional infrared camera and replacing it with our metalens. The distance between the metalens and the detector plane was adjusted，and the camera's signal was directly input into the computer for reading. The optical path diagram of the imaging experiment is given in Fig. S8. We tested different targets （at the same distance） and observed good results. Fig. 5 （a-d） illustrate the infrared imaging effects of a monitor，face，palm，and candle. The camera was able to clearly capture the swinging palm and shaking individuals at 1 m distance. Owing to the large DOF，we can observe clear images even when the target was moved forward or backward over a large range of 0.4 m without refocusing. The results are presented in Fig. S9.

Our successful implementation of the infrared imaging experiment demonstrates the versatility of our design. As these metalens are made of pure silicon，they are compatible with the complementary metal-oxide semiconductor （CMOS） platform and additional devices. This compatibility simplifies the building of the light path，making system miniaturization achievable.

In conclusion，this letter presents the design and fabrication of a metalens structure with a substantial DOF and broad band operation. We have demonstrated the LWIR focusing capability of an all-silicon metalens through using the thermal infrared spontaneous broadband radiation of the target to achieve passive imaging experiments. This research opens up numerous possibilities for various applications such as low-visibility imaging，robot guiding systems，and portable military detection etc. We are confident that the 9-11.5 µm metalens can be successfully integrated into optical systems，thereby paving the way for extensive applications in infrared imaging.

Supplement materials and experimental details can be obtained by email from the authors.