Peer review of: Higher-order quantum spin Hall effect in a photonic crystal (2020)

Reviewers' Comments: 
 
Reviewer #1: 
Remarks to the Author: 
The authors took responsibility to answer the comments and described their position very well. I am thankful for 
the complete and visual answer that shows the serious approach of the authors. The authors revised their 
manuscript and added necessary information for readers. Also, I was very inspired by the proposed possible 
application. Unfortunately, the authors did not include any possible results confirming the real applications (and 
advantages) of the topological system in hand as a device in the revised version of the manuscript, thus focusing 
only on fundamental aspects. 
 
In terms of fundamental aspects, and in general, in terms of novelty, I still have some reservations regarding this 
manuscript. 
 
In the paper [J.Noh et al., Nat. Photon. 12, 408, 2018] higher-order topological corner states were observed 
experimentally for honeycomb. Furthermore, chiral eigenvalues were calculated for all types of corners in the 
system, showing different chirality and opposite signs of the topological index at the adjacent corners. 
Consequently, it seems that the novelty (in terms of authors' "first time" and "brand new concept") of the author's 
work concludes in the experimental demonstration of this chirality. That is an important achievement, but rather 
technical. The second comment is regarding the HO-QSHE. It seems that polarized coupling of topological corner 
modes goes through evanescent "tails" of topological edge states. 
 
I see the work quite interesting from the experimental point of view, and I would recommend this paper to be 
published in a more specialized photonics journal. 
 
 
 
Reviewer #2: 
Remarks to the Author: 
This paper reports the first observation of the pseudospin degree of freedom in higher order topological insulators. 
This effect is carefully characterized its potential applications are evident. Thus, this work expands the field of 
topological optics and will find application is topological insulators with different types of excitation. The impact of 
this work is well described in the conclusion. I therefore support the paper for publication in Nature 
Communications. 
 
I still feel the work needs careful editing. I illustrate this with some comments on the concluding paragraph: 
 
- In conclusion, we theoretically propose and experimentally realize a spinful higher-order photonic topological 
insulator in which both 1D edge states and 0D corner states are observed 

In conclusion, we theoretically propose and experimentally realize a spinful higher-order photonic topological 
insulator with both 1D edge states and 0D corner states. 
 
- We achieve a directional localization of pseudospin polarized corner states of microwaves, denoted as the 
photonic higher-order version of the QSHE. 

- We achieve the directional localization of pseudospin polarized corner states for microwave radiation, which are the 
photonic higher-order version of the QSHE. 
 
- are inﬂuenced by the ﬁnite size effect and quality and the precision of the fabricated samples. 

-are inﬂuenced by the ﬁnite size and the precision of the fabricated samples 
 
- The difference in the frequencies between the simulation and experiment are induced by the ﬁnite height of the 
dielectric rods in the experiment. 

The differences in the frequencies between the simulation and experiment are due to the ﬁnite height  of the 
dielectric rods in the experiment. 

- Our work paves the way 

Our work opens the way 
 
- The directional localization of 0D microwaves 

The directional localization of microwave radiation in 0D 
 
- Moreover, since our implementation is simple and based on the dielectric material, it can be directly extended to 
optical frequencies by using silicon-based coupled resonator optical waveguides and femto-lasing direct writing 
methods. 

Since our implementation is simple and based on the dielectric material, this work can be extended to optical 
frequencies using silicon-based coupled resonator optical waveguides written with femto-second lasers. 
 
- When quantum optics are considered, the single photons or multi-photons may have anomalous quantum 
behaviors which are related to the pseudospin degree of freedom such as the spinful quantum walk, spinful 
quantum correlations and entanglements 

It would then be possible to explore the quantum behavior of single or multiple photons which are related to the 
pseudospin degree of freedom, such as the spinful quantum walk, spinful quantum correlation and entanglement. 
 
- If we couple our system to quantum emitters, the spinful corner states may support chiral emission of photons 
and potential applications in quantum simulations. 

When coupled to quantum emitters, the spinful corner states may support chiral emission of photons with potential 
applications in quantum simulations. 
 
- Although our implementation is based on photonic crystals, we expect to observe a similar effect in other classical 
wave systems such as the phononic crystals, surface polariton plasmon, and electric circuit. {there is a lack of 
parallelism in the items listed} 

Although our implementation is based on photonic crystals, we expect to observe a similar effect in other periodic 
classical wave systems, such as the phononic crystals, and with excitations such as, surface polariton plasmon, and 
in electronic circuits.