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*Ceramics*
**2018**,
*1*(1),
139-144;
doi:10.3390/ceramics1010012

Article

Tantalum Arsenide-Based One-Dimensional Photonic Structures

^{1}

Department of Nanochemistry, Istituto Italiano di Tecnologia (IIT), via Morego, 30, 16163 Genova, Italy

^{2}

Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

^{3}

Center for Nano Science and Technology@PoliMi, Istituto Italiano di Tecnologia, via Giovanni Pascoli, 70/3, 20133 Milan, Italy

^{*}

Author to whom correspondence should be addressed.

Received: 11 July 2018 / Accepted: 10 August 2018 / Published: 13 August 2018

## Abstract

**:**

Weyl semimetals can be described as the three-dimensional analogue of graphene, showing linear dispersion around nodes (Weyl points). Tantalum arsenide is among the most studied Weyl semimetals. It has been demonstrated that TaAs has a very high value of the real part of the complex refractive index in the infrared region. In this work we show one-dimensional photonic crystals alternating TaAs with SiO

_{2}or TiO_{2}and a microcavity where a layer of TaAs is embedded between two SiO_{2}-TiO_{2}multilayers.Keywords:

photonic crystals; Weyl semimetals; tantalum arsenide; high refractive index materials## 1. Introduction

Tantalum arsenide is a deeply studied Weyl semimetal [1]. Angle resolved photoemission spectroscopy measurements together with ab initio calculations demonstrated that fermions in TaAs can be described as massless chiral particles with spin ½ [2,3,4,5,6]. Recently, Wu et al. [7] have measured a very intense nonlinear optical response of TaAs together with other monopnictide Weyl semimetals, while Weber et al. [8] have studied the ultrafast dynamics of TaAs. Buckeridge et al. [9] have calculated several properties of TaAs, including the dielectric function of the material. Owing to the tetragonal symmetry, an anisotropy of the optical properties arises, with two different dielectric functions when the oscillating electric field is parallel to the a and b axis or parallel to the c axis. In the c direction, at photon energies below 1 eV, the imaginary part of the refractive index decreases significantly, while the real part of refractive index has values above 6. Thus, TaAs can be exploited as a high refractive index material in the infrared region.

For this reason, we want to demonstrate in this work the implementation of tantalum arsenide as a layer in a one-dimensional (1-D) multilayer photonic crystal. One-dimensional photonic crystals are the simplest case of photonic crystals that are materials in which the alternation of high and low refractive indices has a length scale of the light wavelength. In these materials, light is not allowed to propagate for certain photon energies, in correspondence with the so-called photonic band gap [10,11,12,13]. One-dimensional multilayer photonic crystals can be fabricated with many fabrication techniques such as sputtering, spin coating, pulsed laser deposition, chemical etching, and molecular beam epitaxy [14,15,16,17,18]. These structures are useful for several applications, for example lasing [15,19], emission control [20,21,22], and sensing [23,24,25]. Herein, we show one-dimensional photonic crystals alternating TaAs with SiO

_{2}or TiO_{2}and a microcavity where a layer of TaAs is embedded between two SiO_{2}-TiO_{2}multilayers. We show that with very thin layers of TaAs, 16 nm in the photonic crystals and 8 nm in the microcavity, we can achieve very efficient photonic band gaps and cavity defects, due to the high real part of the refractive index of TaAs in the infrared region.## 2. Methods

To calculate the optical properties of the different photonic structures studied herein, we have employed the transfer matrix method [26,27]. In our study, the light impinges at normal incidence on a system composed of a glass substrate, the photonic structure, and air.

Briefly, the electric (magnetic) field in air, E
where x is the number of layers. M
${\varphi}_{j}$ is the phase variation of the light wave passing through the layer, and for normal incidence ${\varphi}_{j}=\left(2\pi /\lambda \right){n}_{j}{d}_{j}$, with n

_{0}(H_{0}), is related to the electric (magnetic) field in glass, E_{m}(H_{m}), through this expression
$$\text{}\left[\begin{array}{c}{E}_{0}\\ {H}_{0}\end{array}\right]={\displaystyle \prod}_{j=1}^{x}{M}_{j}\left[\begin{array}{c}{E}_{m}\\ {H}_{m}\end{array}\right]=\left[\begin{array}{cc}{m}_{11}& {m}_{12}\\ {m}_{21}& {m}_{22}\end{array}\right]\left[\begin{array}{c}{E}_{m}\\ {H}_{m}\end{array}\right]\text{}$$

_{j}is the characteristic matrix of the layer j
$$\text{}{M}_{j}=\left[\begin{array}{cc}cos\left({\varphi}_{j}\right)& -\frac{i}{{p}_{j}}sin\left({\varphi}_{j}\right)\\ -i{p}_{j}sin\left({\varphi}_{j}\right)& cos\left({\varphi}_{j}\right)\end{array}\right]\text{}$$

_{j}being the refractive index of the layer, d_{j}is the layer thickness, and ${p}_{j}=\sqrt{{\epsilon}_{j}/{\mu}_{j}}$ for a transverse electric wave (TE, taking into account that for normal incidence TE and TM show the same behaviour in 1-D photonic crystals).The transmission coefficient t and the transmission T are

$$\text{}t=\frac{2{p}_{s}}{\left({m}_{11}+{m}_{12}{p}_{0}\right){p}_{s}+\left({m}_{21}+{m}_{22}{p}_{0}\right)}\text{}$$

$$\text{}T=\frac{{p}_{0}}{{p}_{s}}{\left|t\right|}^{2}\text{}$$

We have studied the optical response of a TaAs/SiO

_{2}photonic crystal, of a TaAs/TiO_{2}photonic crystal, and of a (TiO_{2}-SiO_{2})_{7}-[SiO_{2}-TaAs-SiO_{2}]-(SiO_{2}-TiO_{2})_{7}microcavity in the range 0.2–1.1 eV with a step of 2.5 meV.## 3. Results and Discussion

In this work, we studied the optical properties of 1-D photonic crystals made with TaAs alternated with SiO

_{2}or TiO_{2}and of a microcavity in which TaAs was embedded between two SiO_{2}-TiO_{2}Bragg mirrors (seven bilayers), as sketched in Figure 1.In Figure 2, we show the light transmission spectrum of a photonic crystal made of seven bilayers of TaAs and SiO

_{2}. The thickness of each TaAs layer was 16 nm, while the thickness of each SiO_{2}layer was 1200 nm. n and k (real part and imaginary part of the refractive index) of TaAs, in the c direction of the crystal, have been taken from Reference [9]. The Sellmeier equation for the dispersion of the refractive index of silica is [28]:
$$\text{}{n}_{Si{O}_{2}}^{2}\left(\lambda \right)-1=\frac{0.6961663{\lambda}^{2}}{{\lambda}^{2}-{0.0684043}^{2}}+\frac{0.4079426{\lambda}^{2}}{{\lambda}^{2}-{0.1162414}^{2}}+\frac{0.8974794{\lambda}^{2}}{{\lambda}^{2}-{9.896161}^{2}}\text{}$$

The Sellmeier equation for the dispersion of the refractive index of titania, reliable for thin films in the range 0.2–1.1 eV, fits the data by Siefke et al. [29,30] and is

$$\text{}{n}_{Ti{O}_{2}}^{2}\left(\lambda \right)-1=\frac{4.181{\lambda}^{2}}{{\lambda}^{2}-{0.2133}^{2}}+\frac{5.068{\lambda}^{2}}{{\lambda}^{2}-{14.33}^{2}}$$

For thicknesses of TaAs above 16 nm, the light absorption of the material became very strong because of the high imaginary part of the refractive index.

If we used TiO

_{2}instead of SiO_{2}to be alternated with TaAs, we observed a photonic band gap in the same spectral position (i.e., 0.35 eV) with a thickness of the TiO_{2}layers of 765 nm, resulting in a thinner photonic crystal. In Figure 3, the light transmission spectrum of a photonic crystal made of TaAs and TiO_{2}is depicted.In the spectra in Figure 2 and Figure 3, the transmission valley around 0.65 eV was the second order of the photonic band gap of the photonic crystals. For photon energies above 0.8 eV, the imaginary part of the TaAs complex refractive index increased significantly, such that the transmission valley at 0.9–1.0 eV was mostly due to TaAs absorption [9].

The photonic band gap was less intense with a TaAs-TiO

_{2}unit cell (minimum at about 0.1) with respect to the one with a TaAs-SiO_{2}unit cell (minimum at about 0.03) because of the smaller refractive index contrast in the TaAs-TiO_{2}case.In Figure 4, we show the light transmission spectrum of a (TiO

_{2}-SiO_{2})_{7}-[SiO_{2}-TaAs-SiO_{2}]-(SiO_{2}-TiO_{2})_{7}microcavity. The TiO_{2}layers of the [TiO_{2}-SiO_{2}]_{7}Bragg mirrors were 377.78 nm thick, while the SiO_{2}layers were 590.28 nm thick. In this way, the TiO_{2}layers and SiO_{2}layers followed the condition n_{SiO2}d_{SiO2}≅ n_{TiO2}d_{TiO2}. The two SiO_{2}layers that sandwiched the TaAs layer in the cavity defect were 560 nm thick, while the thickness of the TaAs layer was 8 nm. The microcavity shows in the region 0.31–0.42 eV a photonic band gap with an intense defect peak at 0.376 eV. Since n_{SiO2}d_{SiO2}≅ n_{TiO2}d_{TiO2}, the second order of the microcavity photonic band gap was not observed.## 4. Conclusions

In this work, we have exploited the high refractive index of tantalum arsenide in the infrared region (in the region 0.2–1.1 eV), employing the material as a layer in the engineering of a 1-D multilayer photonic crystal and of a 1-D microcavity. We showed one-dimensional photonic crystals alternating TaAs with SiO

_{2}or TiO_{2}and a microcavity where a layer of TaAs was embedded between two SiO_{2}-TiO_{2}multilayers. It is worth noting that with thin TaAs layers, 8 to 16 nm thick, it is possible to build photonic crystals and microcavities in the infrared region with good efficiency. This can be promising for the fabrication of thin filters for this spectral region.## Author Contributions

I.K. and M.G. contributed with scientific discussions and the writing of paper. F.S. performed the calculations and guided the project.

## Funding

This project has received funding from the European Union’s Horizon 2020 research and innovation program (MOPTOPus) under the Marie Skłodowska-Curie grant agreement No. [705444], as well as (SONAR) grant agreement No. [734690].

## Conflicts of Interest

The authors declare no conflict of interest.

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**Figure 1.**Scheme of (

**a**) a TaAs/SiO

_{2}(or TaAs/TiO

_{2}) photonic crystal and of (

**b**) a (TiO

_{2}-SiO

_{2})

_{7}-[SiO

_{2}-TaAs-SiO

_{2}]-(SiO

_{2}-TiO

_{2})

_{7}microcavity.

**Figure 2.**Light transmission spectrum of a 1-D photonic crystal made using seven bilayers of TaAs and SiO

_{2}.

**Figure 3.**Light transmission spectrum of a 1-D photonic crystal made using seven bilayers of TaAs and TiO

_{2}.

**Figure 4.**Light transmission spectrum of a (TiO

_{2}-SiO

_{2})

_{7}-[SiO

_{2}-TaAs-SiO

_{2}]-(SiO

_{2}-TiO

_{2})

_{7}microcavity.

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