This letter is intended as a Reply to the Comment by Meiler, Frank, and Giessen directed to one previous paper [1] proposing the use of plasmonic structures to dynamically tailor optical skyrmion lattice. Better understanding of the creation and control of optical skyrmion structures is of great recent interests to the community considering its potential applications.

First of all, we would like to thank the authors for taking interests in the subject and greatly appreciate the comments and discussions. We agree with the Comment that the perpendicular magnetic field is missing under the current configuration. In this case, the magnetic structure is a pure vortex and more rigorous treatment should have been carried out to confirm skyrmion architecture.

The key point we tried to make in [1] was to show the capability of dynamically tailoring optical skyrmion lattices through controlling the illumination with respect to the plasmonic structure. This is confirmed for the skyrmion structures for the electric field components. We would like to show that the perpendicular (longitudinal) component of magnetic field can also be generated with the configuration through adjusting the illumination. There are mainly two electromagnetic wave contributions in the near field, i.e. the diffraction component arising from polarization in parallel with the slit and the SPP waves arising from polarization perpendicular to the slit. Through adjusting the polarization orientation of excitation (Fig. 1), it is possible to generate prominent Hz component.

 

Fig. 1. Six spots illuminate each slit normally from the back side. The angle between the polarization orientation of the illumination and the corresponding slit is 10°, and the distance between any parallel pair of slits is 2 um.

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For example, Fig. 2 shows the magnetic field distribution when the angle between the polarization direction of the incident beam and the slit is 10° in the plane and the distance between any groups of symmetric slits is 2 µm. It can be seen from Figs. 2(a)–2(c) that the amplitude of the perpendicular component Hz is on the same order of magnitude as the transverse component Hx. The corresponding vector distribution is shown in Figs. 2(d) and 2(e).

 

Fig. 2. The distribution of the magnetic field at the center of the structure. (a) Re(H), (b) Re(Hx), (c) Re(Hz), (d) top view of vector distribution for the magnetic field, (e) perspective view of (d).

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In this modified excitation configuration, the perpendicular component Hz exists and will play a role in the construction of magnetic skyrmions. And such magnetic skyrmions can also be dynamically tailored as demonstrated in [1]. In addition, more degrees of freedom can be introduced to tailor the magnetic field structure. For example, symmetry of the structure and/or the polarization orientation of the illumination can be further exploited. However, as the authors of the Comment pointed out, the skyrmion structure and number for the magnetic field should be carefully analyzed by integrating the magnetic field in each unit cell [2]. Details of the subject study will be carried out and reported in the future.