How does the thickness of the polysilicate layer influence the performance of the spherical microlenses?
Investigation of the effect of different thicknesses
In the end of question 5 we concluded that the spherical cells are the best option for biological micro lenses due to their orientation independence. Additionally, in question 6 we saw how the light scatters far from the lens. Also we assumed that most of the light refraction is happening due to the polysilicate layer because the difference on the refractive index of water and cell is very small.
All these studies generated the question of how the thickness of the polysilicate layer influences the properties of the proposed spherical microlens. To determine the impact of the polysilicate layer thickness on the the performance of the microlens a new study was performed. The effect of different thicknesses in the focusing of light and far field scattering is investigated through a series of simulations.
We performed two studies, again making use of COMSOL Multiphysics together with CST. First, the far field scattering of light compared to the polysilicate layer thickness was determined. Subsequently, we investigated the focusing effect for different polysilicate layer thicknesses. COMSOL is used for the far field effect where big domain is not necessary and CST is used in the focusing of light were we need bigger domain and it therefore more computational expensive.
For both the models all the parameters and materials were kept the same as in the previous studies and only the thickness was altered. The thickness was changed between \(20 nm\) and \(160 nm\) with steps of \(20 nm\).
Far Field scattering for different thicknesses
The 3D model used is the same as in the previous studies and it is displayed in figure 1. In COMSOL the ability to do parametric scans (sweeps) was implemented. The parameter we scanned as the t_sil (can be found in the parameters list in question 5 This basically means that the software does consecutive runs of the model keeping everything fixed except of the parameter selected for the parametric sweep .
For the visualization of the results the 2D plot of the far field was used as it allows as to overlap all the results in one graph. Figure 2 shows the results from the parametric sweep.
From figure 2 we can see that the shape of the main lobe is the same for all the thicknesses and it is very directional. This means that the scattering is not influenced by the thickness of the polysilicate layer. Additionally, the secondary lobes, back scattering and side scattering, are again negligible small meaning that even when we increase the thickness of the polysilicate layer we do not have back scattering or dispersion.
Focusing effect for different thicknesses
The second study is the influence of the thickness on the focusing effect of the microlenses. In order to complete this study, the software CST was used. Figure 3 demonstrates the 3D model used for this study.
The focusing effect is more interesting for this application so we extracted more data from those simulations.
Figure 4 below is an overlap of the plane passing from the center of the structure for all all the simulations. We can see how the focusing is evolving and it is going further away from the structure the thicker the polysilicate layer gets. Additionally, we can see that the intensity of the focusing are increases as the thickness increases. Those two effects can be better observed in figure 5 and figure 6.
Figure 5 illustrates the distance of the maximum focusing point for each thickness. It can be seen that the thicker the film gets the further the focal area is. This goes according to a previous assumption we made that the silicate layer is the component that is responsible for most of the scattering due to its high refractive index compared to water and the cell.
Figure 6 demonstrates the maximum electric field at the focus area. It can be seen that the relation between the thickness and the maximum electric field at the focusing point is linear.
We have simulated the same models for different thicknesses and observed the effect of the polysilicate layer thickness on the Far Field scattering and in the focusing. We saw that the scattering (far field) shape does not change with the thickness and we still have hardly any back or side scattering. Additionally, we can say that the focal area distance is increasing linearly with the thickness of the polysilicate layer and the maximum intensity of the focusing area increases with the thickness of the polysilicate layer as well. Concluding we can say that if we find a way to manipulate the thickness of the polysilicate layer we can use the same structure for applications that require different focal lengths, if we want to optimize for maximum focusing effect we should try and make the polysilicate layer as thick as possible. Further research into the enzyme expression and kinetics would be necessary for the directed design of biolenses with different focal distances.