Tabular dispersions might break Solver2x2

[MarJMue]

Using something like this Si_Palik.txt to generate a dispersion leads to rounding errors, where k varies around 0 in the IR and can become negative.

This breaks Solver2x2 as described in #130.

lbda = np.linspace(200, 1700, 10)
table = elli.Table(Si_Palik.index.values, Si_Palik["n"] + 1j * Si_Palik["k"])
table.get_refractive_index(lbda)

array([0.9151964 +2.75630140e+00j, 6.68599419+2.47306141e+00j,
       4.14435409+4.37175170e-02j, 3.78316134+1.26652976e-02j,
       3.64459034+2.26450024e-02j, 3.56345879+1.10329426e-02j,
       3.5193    -7.62329653e-21j, 3.50295359-2.04540250e-06j,
       3.47835012+3.04455261e-08j, 3.46418165+7.81489545e-09j])

Edit: I think the cubic interpolation leads to oscillations in this case. Setting it to linear fixes the issue, but i have no idea how we should handle this correctly.

[MarJMue]

Interpolation linear for comparison.

array([0.93614634+2.77121951j, 6.68401587+2.47180952j,
       4.1445037 +0.04452593j, 3.7830625 +0.0125625j ,
       3.65430495+0.0086344j , 3.57653854+0.00295387j,
       3.5193    +0.j        , 3.50127674+0.j        ,
       3.4782549 +0.j        , 3.46414615+0.j        ])

[domna]

Nice find. This is bad. Maybe there is an interpolation which is sign-safe, but I think we could also switch to linear per default. What do you think?

[MarJMue]

With the linear default we would lose accuracy in other ranges.
Alternatively we could implement a lower boundary which would be rounded to 0, but that would hurt high precission data from RII.
RII seems to use linear interpolation, too.

However I think we should make it configurable, but that might be clunky with the parameters...

[domna]

Do you think this would impact the accuracy much? I would expect that the values are close enough most of the time anyways.

I had a short look and it seems that linear interpolation is the only interpolation which is guaranteed to stay inside the data range. I would suggest we add an option to select different interpolations but set linear to the default value. This way we can always guarantee correct data but if users like more precision they are able to select a more accurate interpolation.

[MarJMue]

I agree. Linear interpolation should be good enough and is the simplest fix.
If someone needs something better there is always the possibility to use some formula dispersion.