Ultra-compact visible chiral spectrometer with meta-lenses

Recent advances in nanoscience have led to the development of new technologies for diverse areas of applications, ranging from disease diagnostics to environmental monitoring and energy storage.^1–4 Its broad appeal is centered on three aspects: improvement in performance, miniaturization and reduction of system complexity, and addition of new functionalities. In the context of optics, the development of metasurfaces comprising of sub-wavelength scatterers at an interface^5,6 has given rise to an impressive host of applications ranging from planar lenses,^7–12 wave-plates,¹³ holograms,^14–18 beam deflectors^19–24 to even cloaking²⁵ and analog computing devices.²⁶ 

On a system level, a basic but essential tool for many optical instruments is the spectrometer. The ability to decode changes to the spectrum of light in response to external stimuli is central to applications such as environmental monitoring of pollutants and the detection of specific antibodies in disease diagnostics.^1–4 Furthermore, advanced techniques such as circular dichroism spectroscopy are widely used to obtain additional circular polarization (CP) information in order to distinguish between optical isomers during the manufacture of many pharmaceutics and agrochemicals.^27,28

Conventional approaches to acquire spectral and circular polarization information require cascading multiple components such as non-polarizing beam splitters, waveplates, and polarizers, or composite prisms comprised of naturally birefringent crystals (e.g., Fresnel rhomb)²⁹ paired with a spectrometer. These spectrometers usually consist of focusing mirrors and a grating turret.³⁰ They suffer from insufficient grating dispersion to allow for large spatial separation within a short (e.g., mm to cm) light propagation distance, which places a lower limit on their physical size in order to achieve sufficient spectral resolution. The necessity of using a turret to mount gratings with different dispersions in order to tune/adjust spectral resolutions also adds significant complexity and bulkiness to the system. While handheld and miniaturized spectrometers do indeed exist,^31–34 they are typically limited to a single, fixed spectral resolution and lack polarimetric capabilities. Similarly, while there have been efforts to utilize metasurfaces for spectroscopy, these devices typically suffer from these same limitations or a low spectral resolution.^35–37 

These are strong motivations to develop compact spectrometers capable of good spectral performance and helicity-resolving capabilities, i.e., distinguishing right/left circularly polarized (RCP/LCP) light. Recently we have demonstrated silicon based off-axis meta-lenses at near-infrared wavelengths.³⁸ These meta-lenses can provide high spectral resolution beyond what is achievable by conventional gratings. However, their efficiency is significantly reduced in the visible range due to intrinsic material losses; additionally they were not designed to provide polarization information. Here we present off-axis meta-lenses operating at visible wavelengths with the added functionality of resolving the helicity of incident light. This is made possible using a recently developed titanium oxide (TiO₂) atomic layer deposition (ALD) process.³⁹ TiO₂ is lossless across the visible spectrum and possesses a moderately high refractive index to provide strong light confinement. This ALD process enables the fabrication of high quality nano-structures with minimal roughness and vertical sidewall profiles, which are essential to realize highly efficient metasurface devices. Earlier works typically made use of reactive ion etching (RIE) processes which limited the steepness of the sidewall profile and aspect ratio of fabricated structures.⁴⁰ This translates into inaccuracies in the resultant phase profile, which can be significant despite having only a small amount of tapering.⁴¹ By integrating multiple off-axis meta-lenses with different parameters (focal length, spatial size, position, and focusing angle) onto the same substrate, a highly versatile ultra-compact spectrometer with variable resolution, spectral range, and minimal spatial footprint can be achieved. Due to the intrinsic CP sensitivity of meta-lenses based on the geometric phase, such a spectrometer is also capable of resolving the helicity of light in a single measurement. We call it a chiral spectrometer by virtue of this functionality. Finally, their CMOS-compatible fabrication process is amenable to monolithic integration with camera sensors and large-scale production.

The building block of all metasurface elements in this work is a TiO₂ nanofin on a glass substrate (Fig. 1(a)) which acts as a birefringent waveguide. Phase control is achieved by geometric rotation of the nanofins, resulting in phase acquisition equal to twice the rotation angle (Pancharatnam-Berry phase).^42,43 The latter is accompanied by a conversion of the incident light helicity. We experimentally and numerically demonstrate this concept by first designing a meta-grating. A scanning electron microscope (SEM) image is shown in Fig. 1(b). The meta-grating diffracts the incident light into the +1 and −1 orders for RCP and LCP, respectively. The diffraction angle follows that of a conventional grating $sin−1(λ/P)$⁠, where λ is the wavelength and P is the period. Here the design wavelength for maximum conversion efficiency was determined to be 500 nm, and the period was 1 μm. Efficiencies as high as 70% and extinction ratios up to 16 dB were measured in the vicinity of the design wavelength, as shown in Fig. 1(c). We observe a difference (particularly at shorter wavelengths) between the experimental and simulated efficiency curves due to deviations in the size of the nanostructures from the intended design. This likely arises from the fabrication process, such as proximity effects during electron beam lithography, which cause the peak efficiency to be redshifted compared to the simulation. The efficiency is defined as the ratio of optical power in the desired order to that of incident light. The latter is measured after passing it through an aperture of the same size as the grating (here 250 μm × 250 μm) on the same substrate. The extinction ratio is calculated as the ratio of measured power for two different helicities of light in the same diffracted order. We also theoretically studied the dependence of the efficiency with grating period for the same nanofin parameters, where the unit cell and nanofin sizes are kept constant (Fig. 1(d)). As expected from the Nyquist sampling criteria, with decreasing grating period (or equivalently, increasing diffraction angle), the efficiency drops since there are less phase levels per period.

Compared to conventional grating spectrometers (Fig. 2(c)) whose focusing elements are achromatic due to the use of reflective optics, the aforementioned longitudinal focal length change of the off-axis meta-lenses can be exploited to further increase the dispersion of a compact spectrometer. In conventional spectrometers, the focal length change is negligible so that any contribution to the dispersion arises solely from the change in grating diffraction angle. Furthermore, in conventional gratings, the diffraction angle is limited to approximately a few tens of degrees, due to shadowing effects. These factors significantly limit the dispersion that can be achieved in such spectrometers.

For general spectroscopic applications, which require a large working wavelength range and high resolving power within a spectrum of interest, we integrate several off-axis meta-lenses on the same substrate to provide spatially separated focal spots in the same field of view of a camera. Each meta-lens possesses different spectral resolutions and spectral ranges and selectively focuses light with opposite CP states. In this way, we can realize in a single device within an area of less than 2 cm × 1 cm, the equivalent of multiple distinct gratings (with different wavelength ranges and resolutions), focusing lenses, and CP elements.

A representative SEM image of an off-axis meta-lens is shown in Fig. 3(a). For the final device (Fig. 3(b)), we fabricated four meta-lenses: two at large (⁠$α=60°$⁠) focusing angles with a NA of 0.1 for high spectral resolution (R1 and L1) and two at small focusing angles of 25° with a NA of 0.022 for a larger spectral range (R2 and L2). The two meta-lenses fabricated for each NA are sensitive to opposite helicities of incident circularly polarized light: as a result of the use of the geometric phase in the design, any one single meta-lens would focus light of a chosen handedness while defocusing the other. Note that these meta-lenses are designed according to the phase profile dictated by Equation (1), with care taken to avoid spatial overlapping of focal spots from different meta-lenses by proper placement on the substrate. The final shape of our meta-lenses is rectangular instead of circular to keep the focal spots within the active region of the camera; this results in the asymmetrical shape of the focal spots. The primary focusing/dispersion direction is along the horizontal axis of Fig. 3(c).

We first characterized the focal spots using a narrow line width (ȣpm) diode laser (Quantum Optics) at the design wavelength of 532 nm. The laser beam is coupled into a fiber and subsequently collimated (Thorlabs RC04APC-P01) before being incident on the meta-lenses. An objective lens (Mitutoyo M Plan Apo 10×, NA 0.28) paired with a tube lens of focal length f = 200 mm and a CMOS camera (Edmund EO-5012) with a small pixel size of $1.67μm$ were used for accurate characterization. Measured results are in good agreement with theory: we observe close to diffraction limited focal spots with full-width half maximum (FWHM) of $2.3μm$ and $11.6μm$ for the high and low NA meta-lenses, respectively (Figs. 3(c) and 3(d)). Similar values were obtained for meta-lenses designed for the opposite helicity. Additionally, we observe from Fig. 3(c) that the divergent light of opposite helicity introduces negligible background noise to the system.

To build a compact spectrometer, we paired the meta-lenses with a CMOS camera (Thorlabs DCC1545M) (Fig. 4(a)). It has a pixel size of $5.2μm$ and an active area of 6.66 × 5.32 mm². The camera plane is placed so that the quality of the focal spots (i.e., shape and symmetry) is optimized for two distinct wavelengths (λ = 532 nm and λ = 660 nm). The images of the focal spots corresponding to the NA = 0.1 and NA = 0.02 meta-lenses under linearly polarized light at λ = 532 nm, as well as their horizontal cuts, are shown in Fig. 4(b). Note that here the FWHM of the focal spot profiles are limited by the camera’s pixel size, in contrast to the characterization shown in Fig. 3(c).

One often cited concern about metasurface focusing and dispersive elements is chromatic aberration. Since the required phase profile is wavelength dependent, at wavelengths different from the design, the focal spot will be aberrated and its position will be shifted both laterally and longitudinally (along the focusing axis). These aberrations are more pronounced for higher NA lenses due to the smaller focal spot size. In general, in order to maintain high spectral resolution for as wide a range of wavelengths as possible, the focal spot quality (i.e., its size and shape) should be preserved for that range. This requires both a suitable NA in terms of lens design and appropriate placement of the detector plane such that it intersects with the focal spots within their depth of focus. Here, we specifically designed the small diameter meta-lenses (labelled R2 and L2 in Fig. 3(b)) for a large spectral range while maintaining a reasonable spectral resolution. Ray-tracing simulations of their performance at 470 nm, 532 nm, and 660 nm are shown in Fig. 5(a). These simulations provide a guideline to identify the optimal position of the camera plane for minimizing the focal spot simultaneously at different wavelengths within the working range. This range is defined as the spectrum over which the focal spots are still close to diffraction-limited along the dispersion direction. This criterion is more stringent than typically used in the industry, but we nevertheless find, under this definition, the spectral range of our meta-lenses to be almost 200 nm.

The aforementioned focal spot sizes are computed using a commercial software OpticStudio (Zemax LLC). Figures 5(b)–5(d) show the spot diagrams corresponding to the intercept points on the camera plane (black dashed line in Fig. 5(a)) for rays passing through the meta-lens. The colors of the spots correspond to their wavelength, i.e., 470 nm (blue), 532 nm (green), and 660 nm (red). To visualize the spreading of the points, the ideal Airy disk at each chosen wavelength is plotted as a reference. These were calculated by using the Huygens–Fresnel principle to propagate the complex electric fields at the meta-lens to its corresponding focal plane. For wavelengths away from the design wavelength $λd$ = 532 nm, the focal plane is defined by a normal vector and a point, corresponding to the propagation direction of the chief ray (the normal vector) as well as the intersection of the chief ray and paraxial rays (the point). This definition was used in the calculations since due to chromatic aberrations, not all rays have a common intersection at wavelengths different from the design wavelength. From Figs. 5(b)–5(d), it is clearly seen that the focal spots within 470–660 nm lie mostly within their Airy disk along the dispersion direction. Deviations are within the pixel size of our camera $(5.2μm)$⁠. Note that this only applies to the primary focusing direction of the meta-lenses (horizontal axis in Figs. 5(b)–5(d)).

Subsequently, we used a supercontinuum laser (SuperK Varia, NKT photonics) with its bandwidth set to 5 nm for wavelengths ranging from 480 nm to 780 nm in steps of 10 nm to characterize the performance of our meta-spectrometer and compare it against that of a commercial handheld spectrometer (OceanOptics USB4000 UV-VIS). The known center wavelengths of the supercontinuum laser input are used to calibrate our system and account for the slight non-linear dispersive effects across this broad wavelength range (Fig. S1 of the supplementary material). Figures 5(e) and 5(f) illustrate the measured spectrum by the meta-spectrometer and the commercial spectrometer, respectively. Camera images of the focal spots are shown in Figure S2. We observe close to identical spectral lineshapes with FWHM between 5 and 8 nm across the visible. This validates the claim for the working range of the low NA meta-lenses; additionally, we do not observe any significant linewidth broadening effects with the increase in wavelength within our previously defined working wavelength range from 470 nm to 660 nm. Beyond this range, due to aberrations in the focal spots, one can observe a significant, consistent increase in FWHM which is larger than the commercial system (Figure S3 of the supplementary material). This is in good agreement with our previously discussed theoretical results in Figs. 5(b)–5(d). These results also offer further evidence^9,10,38 that by a proper design a planar meta-lens can achieve comparable or even superior performance to traditional lenses.

We next quantified the dispersion and thus the spectral resolution of the meta-spectrometer. Figure 5(g) plots the measured peak intensity positions of the focal spots as a function of wavelength for both high and low NA meta-lenses about their design wavelength of 532 nm. These dispersion values are calculated by tracking the change in these positions as the wavelength is varied with higher precision in steps of 1 nm. As expected and consistent with the earlier calibration results in Fig. S1 of the supplementary material, the observed dispersions are approximately linear within a range of 30-40 nm. We find their values to be $59μm$/nm and $24μm$/nm for meta-lenses with NA of 0.1 and 0.022, respectively. Using Eq. (3), we determine the intrinsic experimental spectral resolution achievable to be 0.05 nm and 0.46 nm for meta-lenses with corresponding NAs of 0.1 and 0.022. In practice, for this meta-lens spectrometer, the spectral resolution is limited by the pixel size of the camera $(5.2μm)$⁠; the detector-limited attainable spectral resolution therefore becomes (Eq. (4)) 0.31 nm and 1.11 nm, respectively. It is important to note that the values achieved here are a proof of concept, given various experimental constraints. In principle, by using a suitable camera with a larger active region, one can significantly improve the working range while retaining high spectral resolution. As an example, it is possible to design meta-lenses of similar sizes (R2 and L2 in Fig. 3) with a spectral range covering the entire visible (400-800 nm) where all the focal spots lie within their respective diffraction limited Airy disk. Further details and simulated results are presented in Fig. S4 of the supplementary material.

Finally we characterize the CP resolving capability of the meta-spectrometer. A complete description of any arbitrary polarization state can be made using the Stokes parameters S₀, S₁, S₂, and S₃ which correspond to the intensities of incident, vertically polarized, 45° polarized, and circularly polarized light, respectively. Here, we focus on S₃ because the chiral optical response (circular dichroism) of most materials is weak compared to its linear counterpart. Furthermore, conventional approaches to measuring S₃ as a function of wavelength using a single planar device are challenging due to the requirement of separating light in both spectral and polarization domains. Although various nanostructures are known to behave as miniaturized CP filters, they lack the ability to resolve spectral information.^44–46 By using the off-axis meta-lenses based on rotated nanofins, the resulting phase profile intrinsically focuses one helicity while defocusing the other. This functionality thus enables us to resolve the helicity of incident light in a single measurement by having two separate meta-lenses to focus RCP and LCP on the same chip.

Figure 6(a) illustrates the variations in intensities of the focal spots upon changing incident light polarization (from RCP to linear to LCP). Differences in the intensities of the focal spots for RCP and LCP light arise from fabrication errors since they originate from different meta-lenses (R1 and L1 versus R2 and L2, as shown in Fig. 3(b)). To control the polarization of the incident light, we placed a polarizer (Thorlabs GTH10) and a zero-order single wavelength (532 nm) quarter waveplate (Thorlabs WPQ05M-532) in the collimated beam path right before the meta-lenses. Next, we obtained various S₃ Stokes parameters (normalized to incident light intensity S₀) at different wavelengths using the meta-lenses and compared them to the results of a commercial polarimeter and analytical calculations (Fig. 6(b)). These various elliptically polarized states at different wavelengths are generated by changing the wavelength of input light (SuperK Varia). Due to the deviation in optical retardance of the single wavelength (532 nm) quarter waveplate (characterized and provided by Thorlabs), various elliptical polarization states can be generated across a broad range in the visible. Measured values upon appropriate calibration (following the approach in Ref. 47) are seen to be in good agreement with both the values measured by a commercial polarimeter (Thorlabs TXP) and analytical predictions based on known retardance data. For wavelengths close to λ = 532 nm where the retardance of the waveplate is almost exactly $λ/4$⁠, the measured values are slightly greater than unity (approximately 1.01) likely due to experimental noise (e.g., pixel noise and limited dynamic range of the camera) in the measurements.^48,49 Details of these calculations are provided in Sec. VI. Although here we only obtained S₃/S₀ due to the chiral response of the meta-lenses designed with the geometric phase, in principle, by adding linear grating elements, the full Stokes parameters can be resolved.^50,51

In summary, we have demonstrated an ultra-compact meta-spectrometer based on integrating multiple planar off-axis meta-lenses at visible wavelengths. This has several advantages over its traditional grating based counterparts: first, it combines the functions of a focusing and dispersive element in a single planar structure, which eliminates the need for rotating turrets or focusing mirrors. Second, in terms of performance, it surpasses conventional blazed grating elements as one can achieve extremely large dispersions which are otherwise unattainable. In addition, the integration of several meta-lenses with different NAs on one substrate allows for multiple different spectral resolutions and a flexible working wavelength range with no further increase in system bulk or complexity. Finally, the meta-lenses can provide extra information about the circular polarization state of incident light, which is not attainable for conventional devices without the use of additional optical elements (e.g., polarizer and waveplates). The use of dielectric TiO₂ as the working material also renders it compatible with existing CMOS processes where large scale production could take place in a single lithographic step or be monolithically integrated with sensor technologies. We envision numerous potential applications in health care, environmental sensing, and related areas for this technology.

See supplementary material for additional figures (PDF).

This work was supported in part by the Air Force Office of Scientific Research (MURI, Grant Nos. FA9550-14-1-0389 and FA9550-16-1-0156) and Thorlabs, Inc. W.T.C. acknowledges postdoctoral fellowship support from the Ministry of Science and Technology, Taiwan (Grant No. 104-2917-I-564-058). A.Y.Z. thanks Harvard SEAS and A*STAR Singapore under the National Science Scholarship scheme. R.C.D. is supported by a Charles Stark Draper Fellowship. This work was performed in part at the Center for Nanoscale Systems (CNS), a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the National Science Foundation under NSF Award No. 1541959. CNS is a part of Harvard University.