triangular lattice irreducible brillouin zone

ahmet emin akosman <[email protected]>
Newsgroups gmane.comp.science.photonic-bands
Message-ID <[email protected]>
hi mpb users, 

 

i have seen several questions about the k-vectors of the irreducible brillouin zone of the triangular lattice, however there were not sufficient answers for them.

 

i have actually working on some photonic crystal structures that have C2v and C4v symmetries instead of higher symmetric crystals such as square and circular rods, so i have to change the edges of the irreducible brillouin zones however i could not realize the reciprocal lattice vectors of the triangular lattice example. 

 

i do not understand why the b2 reciprocal lattice vector has 45 degrees between the origin point, overall how can those two b1 and b2 vectors have 135 degrees between them? (for triangular lattice example of the mpb, M point is ( 0 1/3 0) and K point is (-1/3 1/3 0) ) is not there anything wrong about here? if it is not could you give some more specific explanation about it? (because in the photonic crystals: molding flow of the light book the reciprocal vectors are shown different than the vectors in the example, the situation is same for the mit open courses material of the nanophotonics lecture)

 

 

best regards 

 

ahmet akosman

 

tobb university of economics and technology/ Ankara-Turkey 
 		 	   		  
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