MPB has periodic boundary conditions, so the modes it calculates above the 
light line (which are not localized and hence "see" the artificial periodic 
boundaries in the direction orthogonal to the slab) are essentially artifacts 
of these boundary conditions.   So, when studying waveguides and PhC slabs with 
MPB, it is mostly only meaningful to look at the guided modes below the light 
line (which are localized and hence exponentially insensitive to the supercell 
boundary conditions).

To look at extended modes in an open system you need some kind of absorbing 
boundaries, such as the PML feature in Meep.   There are, of course, a 
continuum of solutions above the light line, so it's not clear to me which of 
these solutions you are interested in.   If you want to look at long-lived 
resonant ("leaky") modes above the light line, you can use harminv in Meep, as 
shown by this example:

        
https://meep.readthedocs.io/en/latest/Python_Tutorials/Resonant_Modes_and_Transmission_in_a_Waveguide_Cavity/#band-diagram
 
<https://meep.readthedocs.io/en/latest/Python_Tutorials/Resonant_Modes_and_Transmission_in_a_Waveguide_Cavity/#band-diagram>

> On Oct 15, 2020, at 5:09 AM, Juan Ramón D <deop...@hotmail.com> wrote:
> I am trying to simulate the band diagram and modes of a PhC slab with a 
> triangular lattice of air holes (similar to the one given in mpb examples).
> When I Increase the size of the supercell, the frequency of the guided modes 
> remains the same, but the frequency of the modes that fall inside the light 
> cone decreases.
> Does it mean I cannot get the extended modes in air and PhC using mpb? Is 
> there any way of getting the modes from the light cone either with mpb or 
> meep?
>  
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