In order to optimize the design of an EO modulator the maximum overlap of the RF electric field to the optical field must be achieved. In a Slot waveguide it implies the overlap must be achieved mostly into the slot region. Therefore, limiting to the optical field, the design must induce the highest confinement of the lightwave into the slot. Typical vaues reported for the optical confinement factor are in the order of 20%-30%. Nevertheless, some papers (e.g. Koos and Leuthold works) report also other optical confinement factors referring for instance to all the EO cladding in the case of EO polymer modulators. Which is the benefit of having light confined out of the slot ? In my opinion, even if the optical propagating wave spread out of the slot, with part of the power guided into the EO cladding or the Silicon arms, the "useful" light confinement to be addressed concerns with the slot. What is your opinion on that ?
Apart from your exact question, I found from literature that there is increase in confinement factor with decrease in slot width. Recently the highest confinement factor of 33% is obtained for d = 100 nm in the double slot configuration. It is 6% better than common slot configuration. I would suggest to read article on ," A hybrid electro-optic polymer and TiO2 double-slot waveguide modulator " by Feng Qiu et al.
Ref. http://www.nature.com/srep/2015/150224/srep08561/pdf/srep08561.pdf
In case of EO modulators the "useful" light is confined in the slot region. In case of sensor application one is interested in the light which interacts with the surounding material and therefore the confinement factor is considered for the slot and cladding region.
Conference Paper Silicon-On-Insulator Slot-Waveguide Design Trade-Offs
Actually EO modulation with nonlinear polymer cladding is based on how much shift in effective index can be introduced by the induced electric field (E). In EO polymer the phase shift is local. And this shift increases with the strength of E, hence, it increases with stronger light confinement. Though you have to take the whole area of cladding EO polymer during calculation, the maximum contribution will come from the slot region (gap).
Please note that only 20% of light is confined insight the slot and up to 70% can be insight the whole cladding (depending on the rail width and height of the slot waveguide as well as on the refractive indices). But the main EO effect takes part insight the slot, where the EO material is interacting with the electric field. If you calculate now the phase shift (or refractive index change) it is better to consider only the slot region in order to get a conservative estimation.
In regular waveguides, the confinement factor is expressed as the fraction of the field power travelling in the core. In the same way, in slots it should express the amount of power travelling in the slot.
Thanks everybody for your kind feedback. So, do you agree that showing the confinement factor related to the whole EO cladding (including the slot) besides to the bare slot makes poor sense in terms of final application, as you can find in publications from Karlsruhe's group such as http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6579657 (see table at pag. 3) ?
Stefano, I disagree with that. It would depend on the amount of electrical field penetration outside the slot, into the cladding. If this field penetrates a lot (compared to the optical field in the cladding), then you need to include cladding. If penetration is very limited, the only include the slot.
These examples are limiting cases, of course. To calculate confinement factor, you should keep in mind that it is basically a surface integral, not a single number. We (= engineers) like to use easy, effective parameters. But we have to keep in mind that these are approximations.
If you want to be exact, you probably have to integrated the optical power over the complete polymer area, weighted with the applied index shift, or electrical field.
@Patrick: You are correct that you'll get an conservative estimation by only considering the slot, but that is a tricky approach. Yes, you are sure that you do not underestimate the required interaction length, but such estimations might lead to a number that looks prohibitive for using such modulators.
@Valentina: It is practically speaking not true what you are saying. Unfortunately you always have to check the exact definition the authors use. One striking example is the use of quantum wells. Sometimes these are averaged out with the barrier layers as an 'effective' active layer, and sometime they are considered separately. That leads to a factor of two (typically) difference. Obviously, the effective gain should be adjusted accordingly.
If one consider that the active part of the modulator is the polymer layer, the confinement factor must be calculated in this layer. Advantage of the slot mode is that the most part of the optical mode is localized in a thin layer with lower refractive index than the surounded high refractive index layers. As the refractive index of polymer is lower than silicon, slot configuration is a way to maximize the optical power in the active layer.
@ Martijn: You are correct that there is also a change of refractive index outside of the slot since the electric field is also located outside. This contribution is, however, very small compared to that one insight the slot if we assume the linear electro-optical effect (Pockels effect). This is because the Pockels effect needs a centrosymmetrical orientation of the NLO polymers or organic crystals. Because of that, the main part of the electric field which gives an contribution to the refractive index change is the x-component. The x-component is homogeneous insight the slot. Outside there is just a little projection of the x-component which contributes. However, your hint to weight it with the applied index shift is also very good.
@Patrick: Practically speaking you are very probably correct. However, since the original question did not include geometrical data, I formulated my answer as general as possible to avoid misunderstandings. The field of silicon photonics includes silicon thicknesses typically ranging from ~150 nm up to 5 µm, and uses wavelengths starting from 1.2 µm all the way up to the mid-infrared. That makes it hard to claim beforehand that one contribution can be ignored.
I thank you guys for the enlightening discussion.
Martin is right as I provided not enough details on my device assuming too much as given. When I said "in terms of final application" I meant the typical condition of a strip-loaded slot waveguided photonic modulator where usually the RF electrical field is strongly concentrated into the slot, so that one should aim to increase as much as possible the optical confinement into the slot to maximise the overlap of the RF and optical fields.
Martin is also right that typically we focus more on numbers, such as gamma in this case, without considering that it resumes a distributed physical quantity such as the optical field. This is a quite typical mistake for engineers :)
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