Re: PhC Slab
"Steven G. Johnson" <[email protected]> Thu, 15 Oct 2020 08:18:54 -0400
| Newsgroups | gmane.comp.science.photonic-bands |
|---|---|
| Message-ID | <[email protected]> |
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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 Ram=C3=B3n D <[email protected]> =
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?
> =20
--Apple-Mail=_09EAF6DD-67B7-41CB-8F37-7C2914E1BD26
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<html><head><meta http-equiv=3D"Content-Type" content=3D"text/html; =
charset=3Dutf-8"></head><body style=3D"word-wrap: break-word; =
-webkit-nbsp-mode: space; line-break: after-white-space;" class=3D"">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).<div class=3D""><br class=3D""></div><div class=3D"">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:</div><div =
class=3D""><br class=3D""></div><div class=3D""><span =
class=3D"Apple-tab-span" style=3D"white-space:pre"> </span><a =
href=3D"https://meep.readthedocs.io/en/latest/Python_Tutorials/Resonant_Mo=
des_and_Transmission_in_a_Waveguide_Cavity/#band-diagram" =
class=3D"">https://meep.readthedocs.io/en/latest/Python_Tutorials/Resonant=
_Modes_and_Transmission_in_a_Waveguide_Cavity/#band-diagram</a></div><div =
class=3D""><div><br class=3D""><blockquote type=3D"cite" class=3D""><div =
class=3D"">On Oct 15, 2020, at 5:09 AM, Juan Ram=C3=B3n D <<a =
href=3D"mailto:[email protected]" class=3D"">[email protected]</a>>=
wrote:</div><div class=3D""><div class=3D"WordSection1" style=3D"page: =
WordSection1; caret-color: rgb(0, 0, 0); font-family: Helvetica; =
font-size: 12px; font-style: normal; font-variant-caps: normal; =
font-weight: normal; letter-spacing: normal; text-align: start; =
text-indent: 0px; text-transform: none; white-space: normal; =
word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: =
none;"><div style=3D"margin: 0in; font-size: 11pt; font-family: Calibri, =
sans-serif;" class=3D"">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).<o:p class=3D""></o:p></div><div =
style=3D"margin: 0in; font-size: 11pt; font-family: Calibri, =
sans-serif;" class=3D"">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.<o:p =
class=3D""></o:p></div><div style=3D"margin: 0in; font-size: 11pt; =
font-family: Calibri, sans-serif;" class=3D"">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?<o:p =
class=3D""></o:p></div><div style=3D"margin: 0in; font-size: 11pt; =
font-family: Calibri, sans-serif;" class=3D""><o:p =
class=3D""> </o:p></div></div></div></blockquote></div></div></body><=
/html>=
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