Peer review of: Independent phase modulation for quadruplex polarization channels enabled by chirality-assisted  (2020)

REVIEWER COMMENTS 

Reviewer #1 (Remarks to the Author): 

This paper introduces a chirality-based degree of freedom to enable more flexible control of the 
phase changes when a microwave propagates through a metasurface. A metasurface has four 
output channels, namely RHCP output under LHCP or RHCP input and the LHCP output under the 
LHCP or RHCP input. The major claim of this paper is that by introduce the chirality-based phase 
change, one can control the phase changes of the four channels independently. 

While the motivation is sound, the idea of using multiple layers to introduce more degree of 
freedom (and its mathematical derivation) is straightforward. I therefore have reservation about 
its novelty. 

I also have a concern. It seems that the four degrees of freedom to control the phase changes of 
the four output channels rely on the control T_{LL}, T_{LR}, T_{RL}, and T_{RR}. The derivation 
of Eq. (S5c) shows that the phase change introduced by T_{LR} and T_{RL} are the same. If they 
are the same, then according to Eq. (2), t_{xy}-t_{xy} may vanish, and you loose one degree of 
freedom. I understand that due to the cross-layer coupling, T_{LR} and T_{RL} are not the same. 
But to me, this is a limitation: First, I'm not sure to what extent T_{LR} and T_{RL} are different 
due to coupling. Secondly, it is unclear how to precisely control the difference between T_{LR} and 
T_{RL} by changing the system parameters. 

I have another concern about the fabrication of the multi-layer metasurface. This work 
demonstrates it in microwave so the antenna is relatively large. But when applying it to make 
optical metasurfaces, manufacturing these layers and the alignment across multiple layers of 
optical metasurfaces can be a serious hurdle, as far as I know. This would largely limit the 
applicability of the proposed method. 

Minor comments: 

I think the authors need to proof read their draft more carefully. There are quite a few typos or 
grammar issues. here are a few examples (among others): 
- Line 81: meatsurfaces -> metasurfaces 
- Line 114: to decouple inherent consistent -> to decouple inherent consistency? 
- Line 58 of supplementary: the subscripts of α should be 1, 2, 3. 
- In eq. (S3), I believe the bra and ket in each line should be switched. 
- Line 64 of supplementary: "amplitude of co-polarized and cross-polarized are" not grammatically 
correct. 
- Line 77 of supplementary: "independent perfect wave plates" you mean "perfectly independent 
wave plates"? 



Reviewer #2 (Remarks to the Author): 

While past work has demonstrated arbitrary symmetry and unitary Jones matrices operating in 
transmission mode, the authors demonstrate extended functionality by including chirality to 
construct Jones matrices that are not symmetric. They show that by controlling the propagation 
phase, geometric phase, and chirality, the phase of four distinct channels of circularly polarization 
transmitting through the device may be controlled. The results and approach are non-obvious and 
impressive, and of great interest to the community. The presentation of the results is excellent, 
though the English could use some work. The explanation lacks clarity in places, has a few 
inaccuracies, and is burdened by poor notation, meaning the pedagogical worth of the paper is 
lacking. Assuming these issues and the following two major corrections are addressed, I am happy 
to recommend this work for publication in Nature Communications. I detail major and minor issues 
below. 

Major issues whose resolution I consider necessary for publication: 
1. The assumptions on the form of the (4x4) scattering matrices of each meta-atom being 
achieved here should be stated explicitly. It appears from their description that the authors 
assume a reciprocal, lossless, matched system. In this case, the scattering matrix is symmetric 
and unitary, and there is negligible reflection (impedance matched). If this is true, two statements 
the authors make are demonstrably false. If this is not true, the authors should clarify and address 
how this resolves the following problems: 

(a) The authors claim that the four transmission coefficients in the Jones matrix are totally 
independent. This is not true if the system is reciprocal (passive elements only), lossless (no 
material losses), and matched (i.e. no reflection losses either). It is easy to show that abs(txx) = 
abs(tyy) and abs(txy) = abs(tyx) in this case. The phases of each component, however, are 
indeed independent in principle (the complex Jones matrix need not be symmetric). In 
transmission mode, reciprocity constrains the phase of txy from side 1 to 2 to be the same as tyx 
from side 2 to 1, but does not constrain the phases of txy and tyx when incident from the same 
side. This inaccuracy does not change the authors’ results, since they focus on phase manipulation 
and choose all of these amplitudes to be equal to each other anyways. Therefore, this is easily 
fixed by clarifying the relevant passages to specify that the phases are independent. 

(b) The authors claim that the feat can be achieved in Reflection mode as well (where the matched 
assumption is omitted, of course, and presumably a mirror eliminates the transmission-side ports). 
This is not true if the system is reciprocal, because rxy = ryx in this case. In other words, the 
complex Jones matrix is symmetric in reflection mode by reciprocity. That is, both the amplitude 
and phase of the off-diagonal components of the reflected Jones matrix are identical. There simply 
aren’t four independent phases to control in a reciprocal mirror with one diffraction order. Again, 
this does not change the authors’ results for transmission mode. However, it is a basic inaccuracy 
that should be remedied before publication. 

2. The relationship between dependent and independent degrees of freedom is not made 
completely clear, even after reading the main text and supplementary several times. For a 
reciprocal, lossless, matched system, there are 5 degrees of freedom in the transmitted Jones 
matrix: four phases, and one relative amplitude (ratio between a diagonal component and an off-
diagonal component). The authors vary four geometric degrees of freedom: px, py, internal angle, 
and external angle. By using one of these degrees of freedom, one may easily set the amplitude of 
diagonal and off-diagonal components to be equal. It is implied that the degree of birefringence is 
fixed to set the amplitude to be equal, and the uninquisitive reader is thereby led to believe that 
this is achievable for any choice of the four phases. But this constraint uses up a degree of 
freedom (e.g. it fixes py for a choice of px and internal angle). This means there are three degrees 
of freedom remaining to control the desired four phases (in each the LL,RR,LR,RL channels), which 
is not feasible even in principle. 

Alternatively, the constraint on equal amplitude may be relaxed so that the four phases may be 
controlled independently. In supplementary section S5, the authors briefly discuss how the 
transmission amplitude of each component is not, in fact, perfectly equal. The authors explain this 
by the fact that the underlying phase-control mechanism is a resonance, which does not have 
constant amplitude as a function of px and py. However, this complication notwithstanding, it is 
not discussed in the manuscript whether the amplitudes can be equal even in principle (e.g. by 
using dielectric structures which impart phase in a non-resonant manner). The simple degrees-of-
freedom argument above suggests that it is not possible without a fifth degree of freedom. 

This limitation should be clarified explicitly, and the impact on achievable devices should be 
discussed. The fact that the amplitude of each channel is not independent of the chosen phases is 
highly relevant to experts in the field. Great effort was made in the initial metasurface works (e.g., 
the classic Ref [8]) to maintain constant amplitude, so that the phase response alone controls the 
local diffraction efficiencies across the device. This is a key assumption behind the Generalized 
Snell’s Law (Ref [8]), used by the authors in Equation (3), wherein a single diffraction order is 
selected for locally. A direct result of this amplitude limitation in the authors’ case is that the 
diffraction efficiencies into the desired channels may not all simultaneously be 50% (the ideal case 
for the authors) for arbitrary phase functions even in principle. The impact on diffraction 
efficiencies due to amplitude variations may partially be compensated, as briefly mentioned by the 
authors in the supplementary section S5, but not perfectly. 

I personally do not think this limitation of the design is enough to warrant rejection from Nature 
Communications, though it means the claims of the paper need to be clarified. In my view, the 
results speak for themselves: reasonable control over four output channels is achievable, which is 
in my view a significant advance to the field. It is well-known that phase is more important than 
amplitude in diffractive devices, so the variance of amplitude as a cost of control of 4 phase is a 
worthwhile, if somewhat limited, achievement. However, the implied assumption behind the vast 
majority of metasurface works is that the efficiencies could be ideal in principle, and are limited in 
practice by various imperfections in the control of optical responses and fabrication errors. Future 
work solving these practical and engineering imperfections are then immediately inheritable. Here, 
on the other hand, the efficiencies are limited by construction: it is a limitation in the design 
approach itself. This difference is a crucial to spell out, and a paper that hides it rather than 
clarifies it should be rejected. I think it is appropriate to say that future work can add that 5th 
degree of freedom to fully control the light, while the current manuscript represents a step to that 
final goal. 

Minor issues that I suggest resolving to improve the manuscript: 

1. In Figure 5, the use of a black background to organize the data is inappropriate if black is 
included in the colormap representing the data. It is sometimes difficult to tell where the data ends 
and where the background starts. A drawn border indicating these edges would also fix this issue 
without changing the background black color. 

2. The notation (e.g. E_(LHCP,inc)^(out-co)) is needlessly cumbersome, and hinders 
comprehension. Why not use E_LL,E_RL,E_LR,E_RR instead? This immediately tells the reader all 
the relevant information. It is readily apparent that E_RL,E_LR are cross-polarized components 
while E_LL,E_RR are co-polarized components. 

3. The matrices T1 and T2, defined in Equation (1), are never again referred to. 

4. Related to point 2 in the “major issues” list above, the co and cross phase terms in Equation S5 
appear as separate, while the discussion around Equation S2 specifically mentions that they are 
the same. Why do they appear separate in Equation S5? 

5. Relatedly, a closed-form relating the phases of E_LL,E_RL,E_LR,E_RR to the phases of txx and 
tyy, and the internal and external angle, would be highly valuable. Derivation of such a 
relationship would also show the amplitude variation discussed in point 2 above. 

6. Bold typeface appears to be used for both matrices and the elements of matrices, which is non-
standard. 

7. In Fig 5b the data is misaligned in the vertical direction. 

8.The title’s phrase of “full wavefront modulation” is non-specific and not accurate given the 5th 
remaining degree of freedom being uncontrolled. 

Adam Overvig