### Horizontal slot waveguide

#### Simulations

The horizontal slot waveguide (HSW) is the basis of the structure and it has to be optimized first. The influence of the parameters, i.e., the thickness of the layers, is determined using a mode solver based on the Fourier Modal Method [16,17,18]. Accurate mode profiles and confinement factors are calculated by Finite Difference mode solver, OptiWave [19, 20], in order to avoid ripples due to Gibbs phenomenon inherent to FMM. Our goal is to design a single-mode waveguide (for TM polarization) with the highest relative power confined in the slot.

Titanium dioxide is used as a high-refractive index material (TiO_{2}, \( {n}_{{\mathrm{TiO}}_2}=2.27 \)at *λ* = 1550 nm) and silicon dioxide as the low refractive index material for the slot (SiO_{2}, \( {n}_{{\mathrm{SiO}}_2}=1.44 \) at *λ* = 1550 nm). The cladding is air and the substrate material is SiO_{2}. These materials are chosen for their refractive index and their transparency in a wide wavelength range, but also for the deposition technique involved in the fabrication (see Methods). The calculations were performed for thicknesses *t*
_{b,t} and *t*
_{s} ranging, respectively, from 100 to 340 nm for the HI-layers and from 60 to 250 nm for the slot region. The normalized power (*P*
_{s}), also called the confinement factor in the literature, within the slot is chosen as a figure of merit and calculated using Eq. (1) [21].

$$ {P}_{\mathrm{s}}=\frac{\iint_{\mathrm{A}}{P}_z\left(x,y\right)\mathrm{d}x\mathrm{d}y}{\iint_{\mathrm{total}}{P}_z\left(x,y\right)\mathrm{d}x\mathrm{d}y}\kern0.5em , $$

(1)

where *P*
_{
z
}(*x*, *y*) = *ℜ*(**E**(*x*, *y*) × **H**
^{∗}(*x*, *y*)) ⋅ **e**
_{
z
} is the *z*-component of the Poynting vector, **E**(*x*, *y*) the electric field and **H**
^{∗}(*x*, *y*) the complex conjugate of the magnetic field, **e**
_{
z
} the unit vector in the *z*-direction, and A symbolizes the region where light has to be confined, i.e., the slot region.

Figure 2a summarizes in a map the normalized power in the slot with the variation of the HI-layers and slot thicknesses. It is evident from this figure that the HI-layers thickness should be set at a value around 200 nm. However, the power is monotonically increasing with the thickness of the slot. This comes from the evident thickness dependence of the confinement factor. To make a relevant use of the map presented in Fig. 2a, one has to consider also the characteristic length discussed in introduction. The hatched region in the figure represents the zone of excluded values, for which the characteristic length is shorter than *t*
_{s}, and therefore the structure is no more a *slot waveguide*.

Another measure of the efficiency of the structure is the intensity within the slot, which is the power per unit area *I*
_{s} = *P*
_{s}/(*w*
_{s}
*t*
_{s}). This allows taking into account the geometry of the structure. With this parameter, we see that the trend is reverse when the slot thickness is concerned, a thinner slot enables a larger intensity. Combined with the observation of the variation of power, these results yield a trade-off. One can now set a range of layer thicknesses for which both the power and the intensity are maximized inside the slot region.

The last figures of merit are the effective index and the effective index difference (*Δn*
_{eff}) for the mode propagating in the slab with and without a cladding material, i.e., the expected effective index contrast of the waveguide. It is important to introduce, already at this stage of the optimization, the loading-strip material, considered, at first, as a semi-infinite medium in the *y*-direction and invariant in the *xz*-plane. In this work the loading-strip material is a resist AZ-2070 from MicroChemicals and its refractive index is *n*
_{c} = 1.6. Results are presented in Figs. 2c and d, where the thickness of the HI-layers was varied for several slot thicknesses. The largest *Δn*
_{eff} was obtained for the thinnest HI-layers, for which the cladding material will influence more the effective index of the mode. It is evident from these calculations that we need a trade-off between good confinement, high intensity, and large* Δn*
_{eff}. Therefore, we chose as the central value, before the finest optimization, an 80 nm-thick LI-layer and 200 nm-thick HI-layers.

An ideal structure would be a slot waveguide suspended in air, leading to a nearly symmetric mode. In a realistic device the waveguide is deposited on a substrate that has to be taken into account in the optimization. In our case, the HI-layers have the strongest influence, among other parameters, on the shape of the slot mode in *y*-direction, i.e., on its symmetry. Depending on the application, one may prefer a slot mode with a profile shifted towards the top HI-layer or towards the bottom one. In this particular study, we are interested in observing the trends in order to show the possibilities offered by the SLSW platform. This is done by varying independently the two thickness of the HI layers around the value determined above. The *Δn*
_{eff} and the confinement factor are used as figures of merit. Results are presented in Fig. 3. Figure 3a shows the influence of the top and bottom HI-layers on the normalized power and Fig. 3b on the effective index difference. It is clear from these results that the bottom layer influences mainly the effective index difference while the top layer has a stronger influence on the field confinement inside the slot. The plots show an almost independence of the two parameters. Note that such a property is directly linked to the range of the parameters. For both HI-layer thicknesses, *Δn*
_{eff} varies linearly and *P*
_{s} in a parabolic manner. In the region around the central value (200 nm), *Δn*
_{eff} increases 4 times faster when *t*
_{b} decreases and the confinement factor increases 6 times faster when *t*
_{t} increases. In this work, we target the highest effective index difference while maintaining a reasonable confinement. We determined our targeted parameters for the further fabrication of the horizontal slot waveguide to be: *t*
_{s} = 80 nm, *t*
_{b} = 180 nm and *t*
_{t} = 200 nm.

#### Experimental verifications

One crucial constraint for the horizontal slot waveguide is the roughness at the interface between different materials. This roughness dictates the propagation losses in the structure. Therefore, we used atomic layer deposition (TFS-200, Beneq) for the fabrication of the different layers constituting the basis of the structure [22,23,24]. In addition of allowing very smooth and homogeneous layers, this technique provides an accurate control of the thickness over wafer-scale area (see Methods). Layer thicknesses were determined by ellipsometry (VASE, Woollam): *t*
_{s} = 76 nm, *t*
_{b} = 185 nm, and *t*
_{t} = 197 nm. Fig. 4a is an SEM picture of the cross-section of the horizontal slot waveguide.

With prism coupler measurements (Metricon M-2010), we confirmed the presence of a single TM mode in the horizontal slot, and determined its effective index \( {n}_{\mathrm{eff}}^{{\mathrm{TM}}_0}=1.63 \) at* λ* = 1550 nm. This value is in perfect agreement with our theoretical predictions. To push further our investigations, the influence of the cladding thickness, i.e., the loading-strip layer, was also studied on a test sample coated in the same batch. The sample was coated with an e-beam resist (AZ-2070, from MicroChemicals, *n*
_{c} = 1.6) by spin-coating and measured with the prism coupler. The resist layer was removed (using the development process involving the developer AR 300–47, AllResist) after each measurement to allow another spin coating with a different thickness. The experimental results, as well as the simulated curves, are presented in Fig. 4b. One can see the first order mode (TM_{1}) appearing after a thickness *t*
_{p} ≈ 550 nm. Note that this mode will correspond further to the TM_{01} mode in the channel waveguide. The measured effective indices are in good agreement (less than 0.2% difference) with the calculated ones for both the fundamental and first order TM modes. An important second conclusion about this graph is the invariance of the effective index of the fundamental mode after a certain resist thickness (here, *t*
_{p} ≈ 480 nm). This leads to even more relaxed constraints on the fabrication.

### Strip-loaded horizontal slot waveguide

#### Single-mode and multi-mode waveguides

The loading-strip geometry dictates the properties of the *channel* waveguide. Its width (*w*
_{p}) and thickness (*t*
_{p}) are simultaneously studied by FMM. The main figure of merit is the confinement factor of the field in the slot, under the loading-strip (region A). Results are presented in Fig. 5a, where the hatched region is the multi-mode operating zone of the waveguide, which has to be avoided. From the power calculations (Fig. 5a), one can clearly see that the confinement increases with the width of the loading-strip and reaches a maximum for *t*
_{p} ≈ 250 nm.

A mode extends to infinity, which means that the shape of the guided mode should not modify the losses. However, for integration purpose, the width of the mode is important to 1) determine the position of the neighboring waveguides; 2) estimate the width of the sample; 3) prevent the bend loss. The shape of the mode profile in *x*-direction depends on the loading-strip width as shown in Fig. 5b. For a narrow loading-strip, the profile tends to be Lorentzian, while it becomes Gaussian-like for wider strips. The full widths at half maximum are: 1.74 μm for a 500 nm-wide strip, 1.54 μm for 900 nm-wide strip, and 1.54 μm for a 1.2 μm-wide strip. This proves that the loading-strip becomes more efficient in terms of effective index increase when its width increases. These considerations drove us to choose *w*
_{p} = 1.2 μm and *t*
_{p} = 250 nm as the loading-strip width and thickness, respectively. For such a waveguide the confinement factor of light in the A region is 20%. It corresponds to an effective mode area of 0.45 μm^{2} [25], which is a good value compared to literature considering the low index contrast of the slot waveguide.

Figure 6a is an SEM picture (slightly tilted top view) of the end of the waveguide. In order to show the multi-mode behavior of the waveguide due to a too wide loading-strip, one observed the modes at the output of a 3 μm wide waveguide (Fig. 6b). By tuning the coupling of light in the waveguide, one can excite preferentially the fundamental or the first higher order quasi-TM mode. These observations confirm the above calculations. In Fig. 6b, the picture of the first higher mode shows a low contrast interference pattern on one side of the mode, where a neighboring waveguide is 200 μm away, while on the other side nothing appears (no other waveguide). This pattern is not seen for the fundamental mode proving its confinement and isolation from neighboring waveguides. This emphasizes the role of the shape of the mode, which must be considered during the design.

#### Propagation loss measurements

One of the main characteristics of optical waveguides is the propagation loss. Slot waveguides are known to be lossy structures, as already mentioned in the introduction, although significant efforts have been put to solve this problem [26,27,28].

We determined propagation losses of our single-mode SLSW by the well-known cut-back method [29]. We fabricated first a set of several 4 cm long waveguides (for statistical purposes) and cleaved them shorter and shorter. For each length the transmitted intensity was measured at* λ* = 1550 nm. A sketch of the optical setup is presented in Fig. 7a.

Although the injection is carefully optimized for each length and each waveguide, some errors may occur due, for instance, to the cleaving of the waveguide. It is thus crucial to measure several waveguides and average the values. More than 20 waveguides and 4 different lengths (from 4.1 cm to 1.1 cm) were investigated. The propagation losses were estimated at 1.4 ± 0.6 dB/cm [Fig. 7b]. This value, already far below standard values for slot waveguides, is still overestimated. Firstly, some stray light cannot be avoided from coupling and shorter the waveguide, stronger its influence on the transmitted intensity; secondly, the coupling is always slightly different and we took it into account with our statistical study.