Hello Andrea, I’m not 100% sure, so please correct me if I’m wrong. By introducing the line defect you keep the translational symmetry along one axis, the direction of the line. E.g. if you remove one rod with its axis along the x-axis, k_x still remains conserved. So I guess you should project the band diagram on that axis, having bands as omega(k_x). Of course I used k_x in terms of Cartesian coordinates, not the reciprocal ones. But you can do the transformation between both basis by MPB anyway. For a general example of the projected band diagram in 3D PhC I would recommend Chapter 6 in Photonic Crystals: Molding the Flow of Light<http://ab-initio.mit.edu/book/> by John D. Joannopoulos, Steven G. Johnson, Joshua N. Winn, and Robert D. Meade, but I guess you already had a look for that. A specific projected band diagram of a silicon woodpile can be found in the following:

Isabelle Staude, Christopher McGuinness, Andreas Frölich, Robert L. Byer, Eric Colby, and Martin Wegener, "Waveguides in three-dimensional photonic bandgap materials for particle-accelerator on a chip architectures," Opt. Express 20, 5607-5612 (2012) I hope I could help! Best regards, Max From: Andrea Locatelli<mailto:andrea.locate...@unibs.it> Sent: Tuesday, September 19, 2017 00:31 To: mpb-discuss@ab-initio.mit.edu<mailto:mpb-discuss@ab-initio.mit.edu> Subject: [MPB-discuss] Woodpile waveguide Hello MPB users, I'm going to simulate a waveguide consisting of a linear defect introduced into a woodpile photonic crystal. I had many doubts about the definiton of the irreducible Brillouin zone, but in the end I found an example that Steven posted here for the case of the perfect crystal which works fine (even if I used as some kind of black box). Now I must introduce the linear defect and other doubts come into my mind for what concerns the projected band structure, and in particular the correct definition of the direction of light propagation (and then the direction of projection of the band structure). Are there any examples concerning this very tricky case? Do you know any references that clearly illustrate this issue? Indeed, it's very difficult to find in the literature a complete projected band structure of a woodpile waveguide (or better, up to now I haven't found it). Regards, Andrea Informativa sulla Privacy: http://www.unibs.it/node/8155

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