Reduction in Crosstalk between Integrated Anisotropic Optical Waveguides

Abstract

The minimization of waveguide crosstalk is a long-standing challenge for optical engineers. Nowadays, the most popular technique to suppress crosstalk is anisotropic nanostructures, realized as subwavelength stripes between waveguides. However, the influence of material anisotropy on the efficiency of such structures remains unknown. In this work, we consider MoS₂ waveguides separated by MoS₂ stripes because this material has the record value of optical anisotropy. We discover that the use of MoS₂ instead of Si results in a several-orders-of-magnitude-larger crosstalk distance. Therefore, we envision that by combining the extraordinary material properties with the known crosstalk-suppression methods, one can make the integration density of photonic devices close to electronics.

1. Introduction

Silicon is a bedrock material of modern photonics owing to its high refractive index and mature fabrication technology [1,2,3]. However, the integration density of photonic components based on silicon is still much less than that of its electronic counterparts [4]. To overcome this gap, researchers have developed inverse design methods [5,6,7,8,9,10,11], which allow one to maximize the performance of photonic structures while keeping their footprint small. This approach proves useful in numerous applications, including demultiplexers, waveguide turns, polarizing beam splitters and photonic waveguide crosshairs, to name just a few [5,6,7,8,9,10,11]. Nonetheless, despite tremendous progress in this area in recent years, silicon still faces the fundamental limitation of diffraction of light. To overcome this problem, multiple works [12,13,14,15,16,17] suggested the use of plasmonic structures, where light is coupled to electronic oscillations. Plasmonics enables subdiffractional light confinement, but at the expense of rising optical losses. The alternative solution is the use of anisotropic structures [18,19,20,21,22], which do not cause additional losses. Anisotropic effective dielectric function provides a unique opportunity to manipulate momentum and skin depth of evanescent waves owing to the generalized total internal reflection law [18]. In addition, this strategy is easily applicable within inverse design techniques. Examples include the introduction of two subwavelength stripes between two adjacent silicon waveguides [23] and the optimization of a varied number of stripes in the work of Yang and colleagues [24]. Likewise, numerous publications investigated uniform grating between waveguides [25,26,27]. Their results reveal an increase of several orders of magnitude in the crosstalk distance, compared to the classical scheme without stripes.

Meanwhile, recent reports [21,28,29,30,31] establish a high refractive index, transparency in the near-infrared and giant optical anisotropy in transition metal dichalcogenides (TMDCs), which are increasingly regarded as photonic materials beyond silicon [32,33,34]. Consequently, the suppression of TMDC waveguide crosstalk via inverse design methods is in high demand. In contrast to silicon, this problem requires taking into account the anisotropic tensor of TMDCs because of their giant optical anisotropy.

In this work, we resolve this challenge using the example of TMDC waveguides, separated by one or more stripes. For an exemplary TMDC, we chose molybdenum disulfide since it has one of the highest refractive indices among transparent photonic materials [21]. Nonetheless, our results are also applicable to all similar TMDCs, such as tungsten disulfide (WS₂), tungsten diselenide (WSe₂) and molybdenum diselenide (MoSe₂).

2. Results

We start with the analysis of a typical structure (Figure 1), consisting of a pair of MoS₂ waveguides, placed on top of a silicon oxide substrate. To make waveguides operate in a single-mode regime, we chose the following waveguide dimensions, which support only the fundamental transverse electric (TE) mode (height h = 220 nm, width w = 400 nm) and set the gap between waveguides to d = 400 nm. The relations between the dimension, effective refractive index and difference in effective indices of supermodes are collected in Figure A1 in the Appendix A section. Additionally, we noticed that anisotropy aids in the suppression of all modes except TE, giving anisotropic materials an unexpected advantage because the single-mode regime is preferable to prevent undesired losses and multimode interference [35]. The reason for that is a nonzero projection of the electric field perpendicular to MoS₂ layers, where the refractive index is relatively small (n ~ 2.5) for waveguide modes apart from fundamental TE mode. Conversely, fundamental TE mode has an electric field along MoS₂ layers, where the refractive index is large (n ~ 4.0).

The crosstalk between these waveguides arises as a result of waveguide mode overlap. Accordingly, it generates two supermodes, symmetric (even) and antisymmetric (odd), with propagation constants β₊ and β₋ (Figure 1b). The crosstalk distance L, i.e., the propagation distance required for a mode to transfer from one waveguide to the other one, is given by:

$$L=\frac{\pi }{2\Delta \beta }=\frac{\pi }{\left|{\beta }_{+}-{\beta }_{-}\right|}.$$

(1)

It is convenient to express β₊ and β₋ in terms of effective mode indices n₊ and n₋:

$${\beta }_{+/-}=\frac{2\pi n_{+/-}}{\lambda },$$

(2)

where λ is the free space wavelength of light. Then, crosstalk distance reads:

$$L=\frac{\lambda }{2\left|n_{+}-n_{-}\right|}.$$

(3)

Hence, to calculate L, one needs to find n₊ and n₋, which we performed using the finite element method eigenmode solver implemented in COMSOL Multiphysics software. The initial structure has a crosstalk distance of L₀ = 1.59 mm for the standard telecommunication wavelength λ = 1550 nm. This wavelength also belongs to the transparency range of MoS₂, where the extinction coefficient k is less than 0.001. Hence, we work under the assumption of negligible optical losses [21].

Next, we try to reduce the crosstalk by placing a single stripe between the waveguides. Since, in practice, waveguides are produced from a planar layer by lithography [36,37], we assume that the stripe height and material composition are identical to the waveguides. It is also worth noting that structure has reflection symmetry; hence, stripes need to be placed symmetrically to achieve the best performance. Therefore, a single stripe should be located in the center between waveguides, as shown in Figure 2a. Figure 2b shows the crosstalk distance as a function of the stripe width w₁. The maximum is reached at w₁ = 130 nm, with the corresponding L₁ = 9.4 mm, which is almost 6-times greater than for the initial configuration without the stripe (Figure 1a). For comparison, silicon waveguides with the same original crosstalk distance have L₀ = 1.57 mm (without a stripe) and L₁ = 3.16 mm (with a single optimized strip). It implies a several-times enhancement in crosstalk distance for MoS₂, compared to silicon. We attribute this fact to the high refractive index (n ~ 4) of MoS₂. High refractive index allows for a higher effective mode index of the fundamental mode. It also enhances the effective anisotropy of combined air/MoS₂ spacing between waveguides, contributing to the total internal reflection and the decay of the evanescent field outside the waveguides [18,19,20,21,22]. At the same time, giant intrinsic optical anisotropy of MoS₂ does not lead to a decrease in the effective mode index since the electric field in TE mode is mainly directed parallel to the atomic planes of MoS₂ and, therefore, is weakly influenced by the low out-of-plane component of the refractive index.

Aiming to further decrease waveguide crosstalk, we study the effect of insertion of two stripes between waveguides on the crosstalk distance. We computed a 2D heatmap (Figure 3) of crosstalk distance as a function of stripe width w₁ = w₂ (equality required by reflection symmetry) and stripe separation d₂ (see the inset in Figure 3). Note that the map is triangular because parameters should satisfy d₁ + d₂ + d₃ + w₁ + w₂ = 400 nm, equal to the initial gap between waveguides (inset in Figure 3). The absolute maximum in Figure 3 corresponds to L₂ = 6.9 m, achieved at w₁ = w₂ = 44 nm and d₂ = 59 nm. Of immediate interest is the significant ratio of L₂/L₁ ≈ 750 for MoS₂. For comparison (

Table 1. Comparison of the crosstalk distance enhancements with other works.

Criterion	Y. Yang et al. [23] Isotropic Model (Si)	Y. Bian et al. [24] Isotropic Model (Si)	This Work Anisotropic Model (MoS2)
L1/L0	2.0	2.0	5.9
L2/L1	5.0	4.3	734

), in the case of uniform stripes (w₁ = w₂ = d₂ = 46 nm), L₂/L₁ ≈ 100, which is still, by an order of magnitude, higher than for silicon with L₂/L₁ ≈ 5 [23]. Therefore, our inverse design analysis demonstrates that TMDCs, in particular MoS₂, provide an order-of-magnitude-higher integration circuit performance, in our case crosstalk distance, than silicon, despite only 15% higher refractive index.

In light of the recent advances in TMDC fabrication with atomic precision, subwavelength dimensions of the stripes (w₁ = w₂ = 44 nm and d₂ = 59 nm) can be realized with standard lithography techniques [38]. Still, modern synthesis techniques need further development to realize the nanostructures proposed in our work because, to date, researchers have fabricated thick TMDC films using an exfoliation method [27], which yields only, at best, tens of micrometers lateral size [39], so modern synthesis techniques require further development to realize the nanostructures proposed in our work. Nevertheless, the recent advances in molecular beam epitaxy open up prospects for defect-free TMDCs with excellent optical properties on a large scale [40,41].

3. Discussion

In summary, we demonstrated the effect of MoS₂ anisotropic optical response on the suppression efficiency of crosstalk between waveguides due to anisotropic nanostructures in the form of subwavelength stripes. We looked at numerous scenarios, including waveguides, separated with one or two stripes and without stripes. According to our calculations, adding even one stripe improves crosstalk by 6-times, while adding two gives an improvement of more than 4000, compared to original waveguides without stripes. This enhancement is 20-times better in comparison to silicon, which we attribute to the high refractive index and optical anisotropy of MoS₂. Moreover, we expect a similar situation for other van der Waals (vdW) materials, including WS₂, MoSe₂ and WSe₂, because of their similar dielectric tensor [21,28]. From a wider perspective, with recent advancements in fabrication [42,43,44] and nanostructure processing [33,38,45] of vdW materials, we envisage that our discoveries will be used in the next-generation integrated circuits, where vdW materials will complement or even replace the conventional material platforms, such as silicon [1,2] or gallium phosphide [46,47].