Peer review of: A hybrid achromatic metalens (2020)

Reviewers' comments: 

Reviewer #1 (Remarks to the Author): 

The manuscript by Balli et al presents a hybrid achromatic metalens (HAML) comprised of the 
usual nanostructures (here, nanopillars) on top of a phase plate made by multiphoton lithography. 
Thus the HAML more closely represents a multi-level lens, with higher measured efficiencies 
compared to existing single level metasurface lenses. 

Overall I believe that this work should be published, notwithstanding the fact that one could argue 
over the feasibility and practicability of combining nanostructure fabrication methods with 
multiphoton lithography. The authors should rephrase the manuscript to address the following: 

1. Multiphoton lithography is typically limited in their resolution due to e.g. the scanning galvo 
mirror, which limits the minimum feature size and resolution of the phase plate, which then in turn 
limits the resolution and working wavelength of the metalens. So there appears to be an 
incongruence of marrying a high-resolution technique (nano pillar fabrication, via either deep UV 
or beam lithography) to a lower-resolution one (multiphoton). Based on current technology, is it 
even possible to make a HAML operating in the visible? 

In this sense I feel that the authors should not imply that multiphoton or direct write systems are 
the only possible avenues for achieving HAMLs; they represent a possible way, and the inevitable 
tradeoffs are between resolution/minimum working wavelength vs ease of fabrication. For e.g., it 
is possible to e.g. obtain multi level meta lenses by using multistep lithography and etching 
processes with a sufficient number of masks. 

2. I might have missed it, but how many phase levels (different heights) are there for the phase 
plate? Also, the authors seemed to have calculated the phase shifts provided by the phase plate 
and nanopillars separately; I question if this is accurate, because the electromagnetic mode within 
the nanopillars should be affected by the presence of the phase plate, and especially since the 
height of the latter is not constant. 

3. In Fig. 4b one clearly sees that the side lobes are higher than the theoretical Airy pattern. This 
should translate to aberrations/lower resolution than expected for imaging. I suggest the authors 
quantify this via the Strehl ratio, rather than simply measuring the FWHM which often does not tell 
the whole story in lens/image characterization. 

4. (Minor point) I strongly suggest that the schematic and some other parts of Fig. 3a be brought 
forward to figure 1 to make the overall manuscript clearer. 



Reviewer #2 (Remarks to the Author): 

Balli et al. propose an approach to design polarization-insensitive large bandwidth achromatic 
metalens based on a hybrid approach that utilizes a phase plate fused with a multilevel 
subwavelength nanopillar array. Authors experimentally demonstrate their approach by realizing 
Hybrid Achromatic Metalens (HAML) using multiphoton lithography techniques and claim that this 
design scheme provides marked improvements in focusing efficiency (on average 60 to 80%) and 
bandwidth (1000-1800 nm wavelength range in the near-infrared) over which the achromatic 
correction can be maintained compared to recent demonstrations of similar devices which fall 
under the category of optically thin lenses. To that end, they characterize HAMLs of different 
diameters and NA and validate their claim by comparing figure of merits of the designed lenses 
with design schemes based on conventional binary metasurface that utilize some form of 
dispersion engineering using high index dielectric materials and with multilevel diffractive lenses 
which utilizes grayscale optical lithography to define multilevel surfaces on low index polymers. 
However, given the current state of the paper, I cannot recommend this paper for publication in 
this journal for the following reasons: 

1) This paper lacks novelty. This design scheme that uses two or more diffractive phase elements 
to correct for chromatic aberration utilizing the recursive raytracing approach for optimization has 
been rigorously described in: 
Michael W. Farn, Joseph W. Goodman, “Diffractive doublets corrected at two wavelengths”, J. Opt. 
Soc. Am. A,Vol. 8, No. 6, (1991) 
and other works cited by the authors. This work does not add any improvements to that approach. 

2) The authors also haven’t developed any special nanofabrication techniques to fabricate their 
HAMLs. This might not be a negative on its own, but the authors didn’t explore the extent of 3D 
design space afforded by their chosen method of fabrication to determine the limits of achievable 
focusing efficiencies and bandwidth. They only mention that complex designs can be explored to 
allow for higher NA and lens diameter combinations. Further studies into such designs even limited 
to just simulations might have provided instructive information to this community. 

3) The paper listed in 1) also theoretically compares different methods for chromatic aberration 
when using diffractive elements and concludes that when compared to the method the authors 
have utilized for their HAMLs, hybrid refractive-diffractive lenses provide better performance in 
terms of chromatic aberration correction. Such lenses are far simpler in design with refractive 
focusing power determined by the radii of the refractive element, which is balanced by diffractive 
focusing power provided by appropriate spatially varying phase gradient of the diffractive element. 
Such a device could be just as easily fabricated using the same fabrication technique the authors 
have chosen for fabricating their HAMLs. It must be noted that, even this hybrid refractive-
diffractive device will still demonstrate residual chromatic aberration [see Geary, J. M. Introduction 
to Lens Design: With Practical ZEMAX Examples; Willmann-Bell: Richmond, VA, 2002]. Such an 
aberration can only be corrected by integrating metasurfaces that allow for group delay and group 
delay dispersion response engineering. 

4) The authors do not clearly mention that the chromatic aberration correction in this scheme is 
done exactly for only two wavelengths, whereas in the approaches that utilizes binary 
metasurfaces with dispersion (group delay and group delay dispersion) engineering, the correction 
is done for the entire wavelength range under consideration. As such the achromatic correction is 
usually better in the latter case. 

5) Comparisons of any figure of merit of the HAMLs and other metasurface or diffractive platforms 
should be done for lenses with identical specs, i.e, same NA and lens diameter and wavelength 
range of operation. The focusing efficiency and bandwidth of chromatic correction is directly 
related to these lens parameters. Higher NA and lens diameter combination provide significant 
challenges for metasurface design and fabrication and therefore those devices will display reduced 
efficiencies. Authors claims of improved maximum focusing efficiency over metasurface design in 
the near-infrared is not valid given that they compare an HAML of diameter of 80 microns and 
0.06 NA with a metasurface lens with a larger diameter of 100 microns and 0.24 NA which is 4 
times the NA of their HAML. This is not a slight difference in NA. 

Similar comparisons are done with metasurfaces and diffractive lenses operating in the visible 
wavelengths. Such comparison in my opinion are invalid because there is significantly more 
scattering losses due to fabrication for metasurface operating in the visible wavelength region that 
reduces the focusing efficiency when compared to near-infrared. The authors comparison therefore 
results in an overestimation of their devices performance. 

6) In my opinion, it is also unfair to compare HAMLs with 3D design space with binary metasurface 
with only 2D design space. As such, only a significant improvement in overall figure of merits 
should be considered a novel and impactful work when such a comparison is to be made. 

I would only recommend this paper for publication in this journal if the following additions are 
made to the paper: 
1) Explore the entire 3D design space afforded by the fabrication method and report the 
theoretically achievable figure of merits and limitations. Experimental demonstration of a novel 
design (for example larger spacing between phase plate and the nanopillars layer and/or using 
design where ray crosses optics axis) based on that study might be considered a major 
improvement. Authors might find the following papers instructive: 
a. Simon Thiele, Christof Pruss, Alois M. Herkommer, and Harald Giessen, 3D printed stacked 
diffractive microlenses, Optics Express Vol. 27, Issue 24, pp. 35621-35630 (2019) 
b. Timo Gissibl, Simon Thiele, Alois Herkommer & Harald Giessen, Two-photon direct laser writing 
of ultracompact multi-lens objectives, Nature Photonics volume 10, pages554–560(2016) 

2) Authors only make valid comparisons between their design and the works reported before by 
experimentally demonstrating HAMLs with same NA and diameter as the other works. I do not 
think authors should make comparisons with visible metasurfaces unless they plan to also 
demonstrate HAMLs working on the same wavelength range. 

3) A discussion of dispersion engineering of the nanopillars and its utility in further improving the 
figure of merits will also be instructive.