Add Bruggeman EMA and depolarisation_factor property

[haydenrob]

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[haydenrob]

@andyfaff all tests in test_refellips.py passed locally for me, but test 11 fails on test_linux - I'm not sure why. Perhaps the way I've implemented warnings isn't correct for the Bruggeman approach?

[andyfaff]

Can you provide me with the equations/paper where the Bruggeman EMA is given? I'm not sure that you've implemented it correctly.

A clue to why that test is failing can be found here. The sqrt calculation on refellips/structureSE.py:1014 is being provided with an invalid value.
I then changed the code to print(slabs[..., 1:3]) just before the sqrt. It turns out that all the values in column 1 are negative. Pretty sure that refractive indices should be positive. Anyway, the sqrt operation is trying to take the sqrt of a negative number and it doesn't like it.

Which brings me to a further point, are we doing any of the EMA calculations correctly?? Let's consider the 'linear' EMA. The first thing we do is to square n and k separately:

>>> n = np.array([1, 2])
>>> n = n**2
>>> print(n)
[1 4]

However, this is totally different to:

>>> np.power(complex(1, 2), 2)
(-3+4j)

The averaging of the solvent and material is then done separately on n**2 (column 1) and k**2 (column 2), before taking the sqrt.

Should we be performing these calculations using the first or second forms?

I would hope that the test suite should detect this.

[haydenrob]

Just for reference, both EMA calcs are drawn from this paper.

• Maxwell-Garnett comes from Eq 34
• Bruggeman EMA comes from Eq 39

[haydenrob]

@andyfaff okay to merge?

[andyfaff]

It looks ok to me. I think a little refactor might be in order in a later PR. I'm thinking about introducing a MixedMaterialSlabSE class, and it would be nice to use the overall_RI function to do that.

[andyfaff]

I haven't checked the maths, relying on you to do that.

[andyfaff]

If you're happy then merge.

[haydenrob]

I like the idea of the MixedMaterialSlabSE, but definitely something to look at later. Maths should be all good, and it converges with WVASE calcs as well.