How are the fields components defined? in real space, lattice axes or reciprocal axes

Hello MPB specialist,

I've been working for sometime on reading the MPB fields (from hdf5 files), compared with the eigenvectors decomposition. I stumbled upon a problem that caused me to raised the question in the title.

I refer first to the 2D problem, say TE polarization where the magnetic field H has a single component in the direction perpendicular to the PhC plane - this will be the z direction. the PhC lattice axes form a set of coordinates x' and y', which can be different than x and y. I realized that mpb performs its computations relative to x' and y' for the space points, and in kx' and ky' (which can also be different than x and y) for the k vectors and G vectors (the spatial harmonics in the periodic decomposition of the dielectric and fields functions).

Up till now, I thought that the coordinates alone are affected by the transition to the lattice axes, which can be treated later with mpb-data to return to real x,y,z space. However, I looked through the mpb source code and found that, given a magnetic field vector H, the electric displacement D field is computed using the function maxwell_compute_d_from_H which (according to the comments) compute (k+G)xH. So my question is: are the components of D given in kx' and ky' coordinates? or is it x' and y'?

Or perhaps if I take the fields hd5 file after I pass them to mpb-data, then E will be in kx' and ky' and E-new will be in x and y?

Following this I need to ask what goes on with 3D PhC lattice, which field components are given in reciprocal axes / lattice axes?

Thank you very much in advance,

Amnon Willinger

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