Dielectric multi-momentum meta-transformer in the visible

Metasurfaces as artificially nanostructured interfaces hold significant potential for multi-functionality, which may play a pivotal role in the next-generation compact nano-devices. The majority of multi-tasked metasurfaces encode or encrypt multi-information either into the carefully tailored metasurfaces or in pre-set complex incident beam arrays. Here, we propose and demonstrate a multi-momentum transformation metasurface (i.e., meta-transformer), by fully synergizing intrinsic properties of light, e.g., orbital angular momentum (OAM) and linear momentum (LM), with a fixed phase profile imparted by a metasurface. The OAM meta-transformer reconstructs different topologically charged beams into on-axis distinct patterns in the same plane. The LM meta-transformer converts red, green and blue illuminations to the on-axis images of “R”, “G” and “B” as well as vivid color holograms, respectively. Thanks to the infinite states of light-metasurface phase combinations, such ultra-compact meta-transformer has potential in information storage, nanophotonics, optical integration and optical encryption.

6. I'm wondering if in the paper describing fully classical properties of light it is important to use somewhere Plank's constant adjusted to the photon spin? Isn't the conversion of spin from +h toh simply the RCP-LCP conversion?

Communications
We would like to thank all reviewers for the careful and detailed reviewing of this work. The valuable comments have allowed us to significantly improve the manuscript. The detailed point-by-point response to the reviewers' comments is attached below. All changes have been highlighted in purple color in the revised manuscript.

Comments
Optical metasurface devices, ultrathin inhomogeneous media with planar nanostructures that can manipulate light propagation in a desirable manner, leading to the development of many optical devices with unusual functionalities. Jin and colleagues propose and experimentally demonstrated a multi-momentum metasurface transformer based on the combination of intrinsic multi-phase of light, orbital angular momentum (OAM) and linear momentum. Although much efforts have been put in the generation, detection and manipulation of OAM beams, this work is interesting and can stimulate new thinking. The results presented in the manuscript seem to be correct, the experimental evidence provided support the conclusions, the manuscript is mostly clear. Regarding the significance of the results, I believe this manuscript will be of interest to specialists within the relevant fields.

Response
Thanks a lot for the positive comments! Comments Thus, it seems to me that the manuscript can be accepted in this journal if the comments below can be fully addressed. 1. In Fig.2b, the calculated efficiency of the metasurface is very high. However, the signal-to-noise ratio in the Fig. 3b is very bad. I am not sure about the experimental value.
Response 1.1 The high conversion efficiency in Fig. 2b is from experimental results. The lower signal-to-noise ratio is caused by smaller phase difference between the incident vortex beams and encoded more OAM states. The details are discussed in the Response 1.2.
Comments 2. The performance of the devices. In Fig. 2d, the experimental results are better than those in Fig.3b. Is this related to the selection of the OAM? For example, the two topological charges with same absolute values but opposite signs (l=-5 and +5) are better than two positive values (1 and 3) or negative values.
Response 1.2 The qualities of experimental results are related to the difference of the encoded OAM topological charges but not limited to be conjugate state (same absolute values but opposite signs).
The performance of OAM meta-transformer can be improved with the increase of the phase difference among the incident vortex beams ∆ . The topological charges difference requires the phase difference 10 ( 0 , 0 ) in Fig. 2d but 3 ( 0 , 0 ) in Fig. 3b. Therefore, the experimental results in Fig. 2d has better performance than those in Fig. 3b.

Comments
3. The crosstalk issue. In Fig.3b, I can see other patterns in the OAM selective patterns. How many patterns can be encoded in the metasurface? I am sure there is a limit.
Response 1. 3 The capability of a single meta-transformer is affected by many conditions, such as the number of unit cell and momentum-state region. To have a more specific and valid discussion on this issue, we restrict some conditions: the number of unit cell is fixed at 600×600; OAM states ( ) range from -8 to 8; and LM states are in visible region. Under the given conditions, a single meta-transformer is able to support 5 OAM states or 6 LM states. By introducing the polarization-dependent response of TiO2 nano-fins, the capability of a meta-transformer can increase to 9 OAM states or 11 LM states. In the revised manuscript, we have discussed these results in detail on the Page 11 as follows: In manuscript: The capability is a critical issue for the multi-tasked metasurface. Based on the multi-momentum phase retrieval algorithm provided in this work, a single meta-transformer is able to support 5 OAM states ranging from -8 to 8 or 6 LM states in visible region (Supplementary note 8). With the help of the polarization-dependent response of TiO2 nano-fins, the number of patterns encoded in a meta-transformer can increase to 9 for OAM or 11 for LM. Furthermore, the capability of a meta-transformer can also be improved by increasing the number of units, and widening the multi-momentum state region. Besides, by considering the donut shapes of vortex beams, introducing random phase mask, and combining the LM and OAM simultaneously in the phase retrieval algorithm, the multi-momentum metatransformer has the potential to remarkably increase the carried information states.

In supplementary information:
8. The capability of multi-momentum meta-transformer In this simulation, the number of units in a phase profile is fixed at 600×600.

Supplementary Figure 5| The capability of an OAM meta-transformer. (a)
The OAM meta-transformer designed for the beam with RCP. This metatransformer encodes 5 states and ( ) are from -8 to 8 with step 4. (b) The OAM meta-transformer designed for the beam with CP. With the help of polarization, a single OAM meta-transformer is able to reconstruct 9 patterns with ( ) ranging from -8 to 8.

Supplementary Figure 6| The capability of a LM meta-transformer. (a)
The LM meta-transformer designed for the beam with RCP. In the visible region, a single LM meta-transformer is capable of supporting 6 LM sates. (b) The LM meta-transformer designed for the beam with CP. The capability of a single LM meta-transformer can be increased to 11 LM states.