Key Points:
- There are two primary types of efficiency for metasurfaces: transmission efficiency and focusing (or diffraction) efficiency
- Definitions of focusing (or diffraction) efficiency vary, often depending on the size of the region over which an intensity distribution is integrated. Material selection is critical for both of these metrics and presents some design tradeoffs
- Efficiency is a useful albeit incomplete metric. It’s important to consider it in combination with other metrics such as the modulation transfer function, image quality, and/or signal-to-noise ratio to obtain a more holistic evaluation of system-level performance
Overview
A key metric in many optical systems is efficiency, and this is true for meta-optics as well. What does efficiency mean though and how important is it? In this article, we aim to describe how efficiency is defined for metasurfaces, how it’s typically calculated, and when and how this metric is important.
Broadly speaking, the efficiency of a metasurface refers to what fraction of light arrives at the destination where the designer would like it be. Typically, for most metasurfaces, this is separated into two multiplicative terms. The first of these is the transmission efficiency, which is the simpler of the two. Transmission efficiency is simply the ratio of optical power on the transmitted side to the incident side. This is a function of multiple factors but often depends heavily on the metasurface material itself (e.g., is it a metal or high extinction coefficient dielectric that absorbs light at the measured frequency?), the substrate and Fresnel reflections, and any associated antireflective coatings.
In well-optimized meta-optical systems based on transparent dielectrics, it’s common to achieve transmission efficiencies in excess of 90%, and with appropriate antireflective coatings and well-optimized nanofabrication, this can reach 98% or higher. This is on par with efficiencies of refractive elements. Note that for metasurface designs that operate in reflection, rather than in transmission, you can define an analogous reflection efficiency.
Varying Definitions of Focusing Efficiency
The other primary type of efficiency is the focusing efficiency, or more generally, the diffraction efficiency. This metric captures the notion of how much light is actually sent in the direction the designer wants it to go, given how much was already transmitted by the meta-optic. Light that is diffracted elsewhere can be considered a form of stray light, which in imaging systems can reduce contrast. Unfortunately for this efficiency metric, there are many different definitions and a mix of conventions used within the metasurface community.
Some of these definitions are used because others used them before, whereas others have made their own definitions, perhaps to suit their own purposes. As such, what really matters often times is using a consistent metric that captures the relevant physics for the problem at hand. For example, a measure of the power located within the focal spot out to some fixed encircling radius is only fair if compared against other components that were measured under similar conditions and with the same sized encircling radius in the calculation.
Further complicating the focusing, or diffraction efficiency, is that for some meta-optical systems, there is no well-defined focus. For example, a component could be used in a non-imaging application. As such, a useful definition would be to define an aperture or other mask in k-space, and evaluate the overlap between the meta-optic’s angular spectrum and the k-space function for the ideal case. In any case, this treatment should be consistent to enable fair comparisons across design variants.
Imaging Systems
For imaging systems in particular, how much light is concentrated within the focal spot is usually a reasonable measure of the light throughput, one just needs to settle on what is the relevant area to integrate over (i.e., should it be a 5-micron disk, 10 micron-disk, or something else?). The answer to this will usually depend on the f/# as well as to some degree what comparable systems have used, such that there is a fair benchmark for comparison.
More broadly for imaging systems, however, the signal-to-noise (SNR) ratio may be a more useful metric. Efficiency is implicit in the calculation of SNR, as lower light throughput will reduce image intensity relative to any associated sensor readout noise or other noise sources. However, efficiency by itself does not capture the totality of the relevant physics at hand. Even if a lens has high efficiency, it may still introduce other artifacts associated with aberrations to its point spread function that reduce contrast and thus the modulation transfer function (MTF).
At any given spatial frequency, the MTF gives an indication of how efficiently information from an object is transferred to information in an image. So any evaluation of a lens will entail combining the efficiency measurement with an MTF. If images captured by a camera are heavily corrupted by noise, the total MTF (including the effect of the sensor) will be attenuated.
Considerations Beyond Just “Efficiency”
While metasurfaces tend to be inefficient when compared to refractive optics, there are additional considerations when thinking about light throughput, especially depending on the scale of the lens. If, for example, one is considering small lenses on the order of 10’s of microns in size (e.g., in applications for microlens arrays or miniaturized cameras), it’s challenging to make refractive optics that are very low f/#. So while a refractive may be more efficient, it may not be feasible to realize as low an f/# as a metasurface counterpart.
With this in mind, in some cases a less “efficient” metasurface could actually enable higher light throughput and thus SNR compared to a refractive alternative that is limited in f/# reduction, as a faster lens produces a brighter image. Note that this is a special case, though an important one as size-constrained applications are an area where the benefits of meta-optics tend to shine relative to refractives.
Material Selection
Material selection in metasurface design is also critical for meeting efficiency targets and this process can introduce several tradeoffs. Ideally, the material for the meta-atoms in a design will have a high refractive index while maintaining an extinction coefficient of zero. These two requirements are often at odds with one another, the degree to which also depends on the material options for the target wavelength range. In the visible range, a variety of materials with moderate refractive indices in the 2.0 to 2.5 range do exist with low extinction, but diffraction efficiencies increase with refractive index, whereas transmission tends to decrease owing to higher k. As such, this presents a counterintuitive design opportunity, wherein a much higher refractive index material (e.g., crystalline silicon or other high-index materials, which have high n and nonzero k) could be used to enhance diffraction efficiency but at the expense of reducing overall transmission.
This may or may not make sense to do, depending on the application; however, if high diffraction efficiency is critical (e.g., if it’s important to keep stray light to a minimum) and a moderate reduction in overall light throughput is tolerable, then this is a potentially viable design option. This has some equivalence to designing an imaging system with the goal of maximizing SNR, where the signal of interest is not based solely on the image brightness, but also depends on the contrast.
Summary
As such, efficiency on its own is a useful albeit incomplete metric, particularly for imaging lenses. It provides useful information quantifying performance, but from a systems perspective, especially when considering image quality, it’s less in isolation. When evaluating performance of a single component, or troubleshooting changes in nanofabrication processes to ensure process compatibility, efficiency can be a very critical metric that’s straightforward to measure. So it’s okay to harp on the efficiency of metasurfaces, but it’s important to understand that it’s an incomplete and sometimes misleading metric depending on what convention one’s using and the context in which it’s being referenced.
Additional References
Khorasaninejad, Mohammadreza, et al. “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging.” Science 352.6290 (2016): 1190-1194.
Arbabi, Amir, et al. “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays.” Nature communications 6.1 (2015): 7069.
Yang, Jianji, and Jonathan A. Fan. “Analysis of material selection on dielectric metasurface performance.” Optics express 25.20 (2017): 23899-23909.
Bayati, Elyas, et al. “Role of refractive index in metalens performance.” Applied optics 58.6 (2019): 1460-1466.
Fröch, Johannes E., et al. “Full color visible imaging with crystalline silicon meta-optics.” Light: Science & Applications 14.1 (2025): 217.