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Slot waveguides are becoming more and more attractive optical components, especially for chemical and bio-chemical sensing. In this paper an accurate analysis of slot waveguide fabrication tolerances is carried out, in order to find optimum design criteria for either homogeneous or absorption sensing mechanisms, in cases of low and high aspect ratio slot waveguides. In particular, we have focused on Silicon On Insulator (SOI) technology, representing the most popular technology for this kind of devices, simultaneously achieving high integration capabilities, small dimensions and low cost. An accurate analysis of single mode behavior for high aspect ratio slot waveguide has been also performed, in order to provide geometric limits for waveguide design purposes. Finally, the problem of coupling into a slot waveguide is addressed and a very compact and efficient slot coupler is proposed, whose geometry has been optimized to give a strip-slot-strip coupling efficiency close to 100%.

Nowadays, rapid advancements in photonic technologies have significantly enhanced the performance of photonic biochemical sensors, particularly in the areas of light-analyte interaction, device miniaturization, multiple analysis and integration. Due to these reasons, optical biosensors are becoming essential in crucial areas of applications such as environmental monitoring, biotechnology, medical diagnostics, security, drug screening and food safety, to name but a few. Moreover, the more and more increasing demands for low cost, reliable and multi-function sensors has brought an extensive industrial and scientific interest in photonic sensors due to their high integration. To this purpose, an accurate choice of materials and device architectures assumes a very important role. High refractive index (HI) materials, such as silicon and other group IV materials, are very promising for integrated optical sensors for their capability to provide very high light confinement, low propagation losses and bend losses reduction in ring resonator-based sensors. On the other hand, low refractive index (LI) materials, such as water or other liquid substances, can be very useful for sensing purposes. For example, a number of chemical and biochemical species can be easily dissolved in the aqueous solution involving a change of the solution refractive index, directly related to the analyte concentration. In recent years, slot waveguides have attracted a lot of interest for their capability to combine the advantages of both HI and LI materials, resulting in a significant performance improvement compared to sensors based on standard photonic wire waveguides [

A wide variety of chemical species (analytes), dissolved in a proper solution or solvent, can be detected by taking advantage of the induced refractive index change of the solvent, which depends on the analyte concentration. This sensing mechanism is known as homogeneous sensing. In optical sensors the solution usually covers the whole photonic structure, acting as a cladding medium for the waveguide. Due to this reason, an analyte concentration variation can induce an effective refractive index variation of the waveguide propagating mode. According with variational theorem for dielectric waveguides, sensitivity in homogeneous sensing can be written as [_{0}_{eff}_{c}_{c}^{0}_{c}^{I} is the optical field intensity confinement factor in cladding region,

_{c}^{0}

Another very promising sensing scheme concerns the absorption principle. In fact, many dangerous gases or volatile organic contaminants, either in air or in aqueous solution, can be detected with ultra-high selectivity and immunity to electromagnetic interferences by optical absorption spectroscopy [

Slot waveguides are very promising devices for absorptive sensing purpose, since they are able to confine a very high field power percentage in the cladding medium. By this way, the optimization of the power confinement factor into the cladding medium becomes crucial.

It is very important to observe that, in general, optical field power (Γ_{c} in cladding region) and intensity (Γ_{c}^{I} in cladding region) confinement factors are different and can show different variations with respect to the cladding refractive index, due to the non-zero z-component of the electric field. Power and intensity confinement factors can be defined as:

A slot waveguide is a well known optical waveguide, formed by two high refractive index photonic wires very close to each other, surrounded by a low refractive index medium. Our analysis is based on Silicon-On-Insulator (SOI) technology, so we assume buried oxide substrate (_{s}_{w}_{c}

The design of an efficient slot waveguide sensor [_{j} as in _{c} or _{j}

Such a definition has been proved to work very well for several technological parameters. However, both Γ_{c} and _{ϑ} parameter), if a large angular range (between 0° and 10°) is considered. A more efficient definition can be found to be the slope of the line connecting the sensitivity values corresponding to _{max}_{max}_{max}_{ϑ} enables to predict well the influence of optimizing parameters in terms of fabrication tolerances.

When fabricating a slot waveguide, many parameters need to be optimized. In this work, both power confinement factor into the cladding region (Γ_{c}) and sensitivity (_{c}, the higher the percentage of optical power interacting with the substance to be analyzed (for example, a specific liquid solution, enzyme or gas).

It can be demonstrated that sensitivity and power confinement factor are related to each other by

Since both _{eff}_{z}_{c} and

Furthermore, slot waveguide performances are very closely related to the height of the two silicon wires. It is clear that the higher the silicon wires, the largest the refractive index discontinuity area, the largest the sensitivity and the power confinement factor. On the other hand, when silicon wires becomes too thick, several higher order TE-like guided modes (

We have performed an accurate analysis on both low and high aspect ratio (height/width ratio) slot waveguides, showing advantages and differences in terms sensitivity, power and intensity confinement factors and fabrication tolerances.

In this section, we focus on SOI slot waveguides with low aspect ratio, being the slot height _{c} as a function of photonic wires width (

The gap region has been varied in the range between 80 and 220 nm and the silicon wires width between 190 and 230 nm. The analysis shows that an optimum region for Γ_{c} exists, with values up to 50%, as shown in

About the gap region, it is intuitive that for larger values of _{c} will decrease. On the other hand, if the gap dimension becomes too small, the effective index of the slot waveguide mode increases approaching the value proper to a waveguide of width

It can be found from _{c} > 49% for

All the above discussed considerations refer to a slot waveguide without any silicon etching residue and with perfectly vertical silicon wire sidewalls. In fact, the possibility to have a silicon etching residue both inside and outside the gap region is an important aspect to be considered and a possible situation in the etching process, limiting the field confinement factor into the slot region. Then, the influence of a possible silicon residue of thickness _{1}_{2}

The result of this analysis shows that the influence of a silicon residue inside the gap region is typically stronger than the influence of a silicon residue outside the slot region (

In order to reduce the effect of the etching residue (_{2}_{t2} = −0.2648 %/nm, very close to the value obtained for _{c} decreases with respect to the ideal case (_{c} is reduced by less than 5.4% with _{ϑ} decreases for wider gaps. In particular, a gap of 100 nm guarantees Ψ_{ϑ} = −1.24 %/°, while a wider gap _{ϑ} = −0.75 %/°. It should be pointed out that these coefficients represent a worst case estimation. Obviously, the optimal design should depend on the available technology, anyway

Nowadays, waveguide sidewall roughness is an important aspect to be considered for reducing the optical losses, requiring critical control of technological process. Using optimized SOI technology processes, sidewall roughness with standard deviation as low as 1.5 nm and correlation length of 13 nm can be successfully achieved [_{ox}_{tox} coefficient is −0.4922 %/nm, calculated for

Then, the influence of a possible air bubble, embedded into the gap slot region with a height of _{air}

This effect is obviously related to the increase of the field attenuation coefficient in the _{air}_{air}_{tair} coefficients refer to the negative slope which occurs for t_{air} > 25 nm. For _{tair} coefficients are −0.0231 %/nm and −0.0240 %/nm, respectively.

In this paragraph, we focus our analysis on design criteria for

On the other hand, all discussed limitations regarding the lower limit for _{w}_{w}

Referring to slot waveguides, assuming a silicon wire width of 220 nm and a reference gap dimension of 120 nm, a very low sensitivity dependence with respect to ^{2}). As in case of confinement factor, fabrication tolerances have been calculated for the sensitivity with respect to several technological parameters. The optimizing parameter is

A sensitivity slope increase with slightly increasing both sidewall angles and gap dimensions can be noted. The effect of sidewall angle on sensitivity is twofold. Once fixed the slot gap _{w} = 3.476). As a result, the effective index of the slot mode tends to increase, simultaneously resulting in an increase of the field confinement factor into the silicon wires (Γ_{Si}). According with this consideration, the sensitivity should decrease. On the other hand, when slanted walls are considered, the gap

The average value of the gap is then reduced with respect to the value proper to a slot waveguide with vertical sidewalls, according to:

Due to this decrease, the field experiences an amplitude enhancement in the low index medium, which should lead to an increased sensitivity. Since the two effects discussed above act simultaneously, a peak in the graph in

_{ϑ}_{ϑ} = −0.009203 deg^{−1} for _{ϑ} = −0.00036 deg^{−1} can be achieved for

_{2}_{t2} = −0.00612 nm^{−1} and −0.00542 nm^{−1} have been calculated, respectively, so it is seen that gap dimension has a poor influence on silicon residue. In addition to _{2}_{ox}_{air}

Of course, the influence of both these parameters should be to reduce the sensitivity, for the same reasons discussed above in case of power confinement factor optimization.

Regarding the additional oxide layer, we have found a linear dependence between sensitivity and _{ox}_{tox}, in agreement with considerations for _{c}

For oxide layers less than 25 nm thick, a good choice for the gap width is _{tair}). Such a behavior again agrees with that shown for _{c}

In conclusion, a SOI slot waveguide optimized for sensing, simultaneously matching requisites of high sensitivity (

In this Section, an analysis of fabrication tolerances about slot waveguides with high aspect ratio (

An important issue for slot waveguide sensors is the single mode behavior, if an interferometer geometry is used. In order to define an analytical criterion to distinguish between TE-like, TM-like and hybrid modes, we have defined the parameters _{TE}_{TM}

The meaning of the symbols should be clear, considering that a TE-like mode has the E_{x} component as the major component, and a TM-like mode has the major component of the electric field oriented in the _{TE}_{TM}

In the design of a single mode slot waveguide with high aspect ratio, the choice of the gap width becomes critical. In fact, the smaller the gap, the higher the effective index of the waveguide modes, so a single mode behavior becomes extremely difficult to be achieved. On the other hand, sensor performances are significantly deteriorated for large values of _{c}

In region (1) of the contour maps of

The points on the dashed line are calculated points, so they own to the multimodal region. Region (3) is a region not covered by our simulations, having a resolution

A choice of

Since

_{c}.

The problem of coupling light into the slot waveguide is still a critical aspect for slot waveguide sensors [

Taking advantage from considerations made till now in terms of fabrication tolerances and sensitivity optimization, we have focused our work on low aspect ratio slot waveguides, optimized as in Section 3.2, with _{1}_{0}_{0}_{1}

The input width of both branches is _{1}/2_{1}

In order to estimate the coupling efficiency, we have considered a slot waveguide with both an input and output coupler (see the inset in _{in}_{out}_{min}_{min}_{min}_{min}_{min}

The FDTD power confinement factors have been calculated at the central z-section of the slot waveguide, while the FEM confinement factors have been calculated with a modal analysis performed on the slot waveguide cross section, regardless of the field shape and effective index at the lower z-sections. We have found a good matching with both FDTD and FEM results, confirming the high coupling efficiency of the proposed device. Thus, the strip-slot-strip coupling efficiency can approach 100%, while the one step strip-slot coupling efficiency is very close to 48%. The high confinement factors in cladding given by

In this paper, we have performed an accurate analysis of SOI slot waveguide fabrication tolerances, for both 220 nm thick and several hundred nanometers thick slot waveguides, demonstrating the fundamental role of the gap region dimension to obtain a robust design, simultaneously optimizing both cladding power confinement factor and sensitivity for either absorption or homogeneous sensing devices, respectively. An analysis of single mode behavior for high aspect ratio slot waveguides has been also performed, in order to provide geometrical limits for the design of the waveguide. Finally, a very compact and efficient strip-slot coupler has been investigated. The strip-slot-strip coupling efficiency of the proposed device has been demonstrated to be close to 100% with a very good feature for optical sensing purposes, while the power confinement factor in the cladding region (including slot) approaches the maximum theoretical value (48.4%), as predicted by 2D full-vectorial FEM analysis and confirmed by 3D FDTD. The design of the coupler has been performed by taking into account the technological parameters too, and very good fabrication tolerances have been demonstrated.

This work has been supported by Fondazione della Cassa di Risparmio di Puglia, Bari, Italy, under the Project “Studio di sensori fotonici di nuova concezione operanti nel medio infrarosso”.

_{3}and υ

_{2}+ 2υ

_{3}vibrational bands of methane

Schematic view of slot waveguide cross section. _{1}_{2}

(_{c} (%) _{c} (%) _{2}_{1}

(_{c} (%) _{c} (%) _{2}_{1}

(_{c} (%) _{ox}_{c} (%) _{air}

(_{w}_{w}

(

(_{Si}/d

(_{2}_{1}_{2}

(_{ox}_{ox}_{air}_{air}

Sensitivity (_{c} (

Sensitivity (blue curve) and Γ_{c} (green curve) _{ox}_{2}_{air}

Strip-slot coupler geometry. In the insets, E_{x} field distributions at the starting and ending section of the coupler are shown (calculated by FEM).

Coupling efficiency _{min}

Fabrication tolerances with respect to Γ_{c} for several technological parameters in case of

_{c} [%] |
_{ϑ} [%/°] |
_{t2} [%/nm] |
_{tox} [%/nm] |
_{tair} [%/nm] | |
---|---|---|---|---|---|

120 | 49.41 | −1.0220 | −0.2648 | −0.4922 | −0.0231 |

140 | 49.29 | −0.8721 | −0.2587 | −0.4173 | −0.0237 |

160 | 49.00 | −0.7534 | −0.2493 | −0.3601 | −0.0240 |

180 | 48.48 | −0.6442 | −0.2374 | −0.3149 | −0.0249 |

200 | 47.98 | −0.5555 | −0.2255 | −0.2781 | −0.0250 |

220 | 47.35 | −0.4661 | −0.2134 | −0.2474 | −0.0312 |

Fabrication tolerances with respect to

_{ϑ} [deg^{−1}] |
_{t2} [nm^{−1}] |
_{tox} [nm^{−1}] |
_{tair} [nm^{−1}] | ||
---|---|---|---|---|---|

120 | 0.7984 | −0.009203 | −0.00612 | −0.009356 | −0.001310 |

140 | 0.7847 | −0.006600 | −0.00598 | −0.008005 | −0.001324 |

160 | 0.7718 | −0.004752 | −0.00587 | −0.007005 | −0.001339 |

180 | 0.7574 | −0.003084 | −0.00573 | −0.006230 | −0.001348 |

200 | 0.7432 | −0.001650 | −0.00557 | −0.005613 | −0.001369 |

220 | 0.7294 | −0.000360 | −0.00542 | −0.005108 | −0.001387 |

Fabrication tolerances for _{c} (absorption sensing) for all considered technological parameters (Ψ_{ϑ} calculated with _{max}

| |||||
---|---|---|---|---|---|

_{ϑ} |
_{t2} |
_{tox} |
_{tair} | ||

0.91745 | −0.0077 deg^{−1} |
−0.0064 nm^{−1} |
−0.0099 nm^{−1} |
−0.000687 nm^{−1} | |

_{c} |
0.61775 | −2.78 %/ |
−0.35 %/nm | −0.69 %/nm | −0.047 %/nm |

Comparison between 3D FDTD and 2D Full-vectorial FEM calculated power confinement factors, for _{min}

_{min} |
_{c} |
_{Si} |
_{Ox} | |
---|---|---|---|---|

0 | Full-vectorial 2D FEM | 48.4% | 22.4% | 29.2% |

3D FDTD | 47.2% | 27.7% | 25.1% | |

50 nm | Full-vectorial 2D FEM | 48.4% | 22.4% | 29.2% |

3D FDTD | 47.5% | 27.7% | 24.8% |