# Generation of a Focused THz Vortex Beam from a Spintronic THz Emitter with a Helical Fresnel Zone Plate

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{ilφ}, where l is the topological charge (TC) and φ is the azimuthal angle [4,5]. TVBs have potential applications in high-speed THz communication, THz imaging, and atom trapping [6,7,8,9,10], and the generation of a TVB has been an important topic in the past few years [11]. Recently, by introducing electromagnetically induced transparency coupling to control nonlinear THz generation, a TVB with a different OAM was achieved [12]. Lu et al. reported that a hybrid nonlinear plasmonic metasurface incorporating indium tin oxide can be used to generate a TVB [13]. By designing all-silicon dielectric metasurfaces, Zhang et al. fabricated three TVB generators [14]. During these studies, to detect and characterize these generated TVBs, focusing and collimating are necessary [15,16]. However, traditional THz lenses are bulky and costly, and the generation and focus of a TVB, which are integrated into a single device, are an effect way to overcome this problem.

**j**

_{s}will be induced, and then it will transform into an ultrafast charge current

**j**

_{c}due to the inverse spin Hall effect. The ultrafast charge current will radiate a THz wave with an electric field of

**E**

_{THz}∝ γ

**j**

_{s}×

**M**/(|

**M**|), where γ is the spin Hall angle and

**M**is the magnetization of the FM layer, which can be changed by an external applied magnetic field [24]. Hence, by selecting NM layers with comparable magnitudes, but with opposite signs, two THz waves with a π phase difference can be generated.

## 2. Theoretical Design

_{2}substrate [15]. Then, two helical NM layers (W and Pt) with the same thickness of 4 nm are deposited on the CoFeB film, and they are adjacently arranged. Here, we select W and Pt as the NM layer, because they almost have the same magnitude of γ, but their signs are opposite [26].

## 3. Results and Analysis

**j**

_{c}is proportional to the intensity of the local pump beam [21], and we assume that the generated

**j**

_{c}emits a THz wave with an electric field of 1 V/m, its polarization, which is perpendicular to the direction of the external magnetic field H, is along the x-axis. To reduce the time and computational memory costs while guaranteeing accurate simulations [27], an adequate three-dimensional geometry is modeled in COMSOL Multiphysics, and the scattering boundary conditions are adopted. The focal length of the STE-HFZP is f = 1 mm and its radius is R = 2.5 mm, corresponding to NA = [1 + (f/R)

^{2}]

^{−1/2}= 0.93 [28]. The working frequency of the ST-FZPE is 1 THz, corresponding to λ = 300 μm. Figure 2 shows the calculated results, and Figure 2a,d,g shows the field intensities of the three electric components (E

_{x}, E

_{y}and E

_{z}) in the y = 0 mm plane. We find that the generated THz wave is focused and the largest electric field is E

_{x}at about 45.6 (V/m)

^{2}. Although the polarization of the generated THz beam is x polarization, the y and z components can also be found near the designed focus (z = 1 mm). However, most of the electric components in the focal plane is E

_{x}. In addition, the z component is larger than the y component, and it is comparable to the x component. These characteristics conform well to the tight focusing conditions of a high NA lens [29,30]. We can also estimate that the size of the focal spot is sub-wavelength (~300 μm). Figure 2b,e,h shows the intensities of the three electric components in the z = 1 mm plane, and we can find the x component has a donut shape, which is very similar to a vortex beam. Then, we calculate its phase profile (Figure 2c), and we can see that it has a helical wave front with a phase of e

^{iφ}. Hence, we can say that the STE-HFZP can directly emit a focused TVB with a TC of l = 1. We also calculate the intensities and phase profiles of the y and z components in the focal plane, as shown in Figure 2e,f,h,i, and these two components do not have a well-defined OAM due to their eccentric field distribution.

^{−iφ}, corresponding to a TC of l = −1. Like Figure 2f,i, the y and z components do not have well-defined OAMs as well, and their intensities are both lower than the x component. Therefore, E

_{x}with an OAM has a decisive effect on the light–matter interaction.

_{x}in the y = 0 mm plane and z = 1 mm plane, respectively, and we can find they also have a donut shape. Compared with Figure 2, we can find the radius of the ring is increased. The focused x component also has a helical wave front with a phase of e

^{i2φ}, as shown in its phase profile in Figure 4d, and its TC is l = 2. The electric field and phase profile of the other two components of the focused THz wave can be found in Figure A2 in Appendix A. We can see that they are weaker than the x component, and they do not have well-defined OAMs as their phase profiles show. If we selected l = −2 in Equation (1), the direction of the two helical cantilevers will be reversed, as shown in the inset in Figure 4e, and a focused TVB with a TC of l = −2 is generated, as shown in the phase profile in Figure 4e. The field intensities of the three components are the same as the STE-HFZP with l = 2, and are not shown, while their phases are opposite, as shown in Figure A2 in Appendix A.

^{i3φ}, corresponding to a TC of l = 3 as shown in Figure 4i. Figure 4g,h shows the distribution of E

_{x}in the y = 0 mm plane and the z = 1 mm plane, respectively. Compared with Figure 4c, the radius of the ring is further enlarged. More importantly, E

_{x}is also larger than the other two components, which do not have a well-defined OAM. When the helical direction of the three helical cantilevers of the STE-HFZP is reversed, as shown in the inset in Figure 4j, a focused TVB with a TC of l = −3 is generated, as shown in the phase profile in Figure 4j. We should point out that the field intensities of the three components are the same as the STE-HFZP with l = 3, and they are neglected. Similarly, the phase profiles of the other two components are opposite to l = 3, as shown in Figure A3 in Appendix A. To generate TVBs with higher TCs and change the focus of the target frequency, we only need to change the pattern of the STE-HFZP according to Equation (1).

_{x}| increases. To quantitatively analyze the radius of the ring, the line scans of the center of |E

_{x}| in the z = 1 mm plane are plotted and shown in Figure 5. The insets show the helical wave front of the focused E

_{x}with TCs of l = ±1, ±2 and ±3, respectively. These TVBs all have donut shapes, while their phases are opposite. It is clearly shown that the radii of the three rings are about 123 μm, 175 μm and 243 μm, respectively. This phenomenon is in good agreement with the property of a conventional vortex beam, where the ring size has a strong dependence on the TC [31].

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**The field intensities of the three electric components with l = −1 in the y = 0 mm plane (

**a**–

**c**) and the designed focal plane (z = 1 mm) (

**d**–

**f**).

**Figure A2.**The intensities of electric fields E

_{y}and E

_{z}of the focused THz with l = 2 in the y = 0 mm plane (

**a**,

**e**) and the z = 1 mm plane (

**b**,

**f**). The phase profiles of E

_{y}and E

_{z}. The insets in figure (

**c**,

**d**,

**g**,

**h**) show the corresponding STE-HFZPs, and (

**c**,

**g**) correspond to l = 2 and (

**d**,

**h**) correspond to l = −2.

**Figure A3.**The intensities of electric fields E

_{y}and E

_{z}of the focused THz with l = 2 in the y = 0 mm plane (

**a**,

**e**) and the z = 1 mm plane (

**b**,

**f**). The phase profiles of E

_{y}and E

_{z}. The insets in figure (

**c**,

**d**,

**g**,

**h**) show the corresponding STE-HFZPs, and (

**c**,

**g**) correspond to l = 3 and (

**d**,

**h**) correspond to l = −3.

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**Figure 1.**(

**a**) Schematic of the STE-HFZP to generate a TVB with a TC of l = 1. H: the applied external magnetic fields along the y axis. The inset shows the wave front of the generated TVB. (

**b**) Detail of the STE-HFZP. Here, the NM layers are selected as W and Pt, which are deposited on the FM layer (CoFeB) and arranged adjacently.

**Figure 2.**Calculated field intensities of the three electric components in the y = 0 mm plane (

**a**,

**d**,

**g**) and the designed focal plane (z = 1 mm) (

**b**,

**e**,

**h**). (

**c**,

**f**,

**i**) show the phase profiles of the three electric components in the z = 1 mm plane.

**Figure 3.**(

**a**) Schematic of a STE-HFZP to generate a TVB with a TC of l = −1. (

**b**) The phase profiles of the three electric components in the z = 1 mm plane.

**Figure 4.**The STE-HFZP that generates TVBs with TCs of l = 2 (

**a**) and 3 (

**f**), respectively. The field distribution of the x component in the y = 0 mm plane (

**b**,

**g**) and z = 1 mm plane (

**c**,

**h**). The phase profile of the focused TVB (

**d**,

**e**,

**i**,

**j**). The insets in (

**e**,

**j**) show an STE-HFZP with l = −2 and −3, respectively.

**Figure 5.**The line scans of the center of |E

_{x}|

^{2}in the z = 1 mm plane with l = ±1, ±2 and ±3, respectively. The insets show the helical phase front of focused E

_{x}.

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## Share and Cite

**MDPI and ACS Style**

Zhang, X.; Xu, Y.; Hong, B.; Zhang, F.; Wang, A.; Zhao, W.
Generation of a Focused THz Vortex Beam from a Spintronic THz Emitter with a Helical Fresnel Zone Plate. *Nanomaterials* **2023**, *13*, 2037.
https://doi.org/10.3390/nano13142037

**AMA Style**

Zhang X, Xu Y, Hong B, Zhang F, Wang A, Zhao W.
Generation of a Focused THz Vortex Beam from a Spintronic THz Emitter with a Helical Fresnel Zone Plate. *Nanomaterials*. 2023; 13(14):2037.
https://doi.org/10.3390/nano13142037

**Chicago/Turabian Style**

Zhang, Xiaoqiang, Yong Xu, Bin Hong, Fan Zhang, Anting Wang, and Weisheng Zhao.
2023. "Generation of a Focused THz Vortex Beam from a Spintronic THz Emitter with a Helical Fresnel Zone Plate" *Nanomaterials* 13, no. 14: 2037.
https://doi.org/10.3390/nano13142037