Re: Woodpile waveguide
Max Kellermeier <[email protected]> Tue, 19 Sep 2017 08:36:58 +0000
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--===============4116812846609939175== Content-Language: en-US Content-Type: multipart/alternative; boundary="_000_AM4PR0801MB270744F71A3048791AFD54719A600AM4PR0801MB2707_" --_000_AM4PR0801MB270744F71A3048791AFD54719A600AM4PR0801MB2707_ Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Hello Andrea, I=92m not 100% sure, so please correct me if I=92m wrong. By introducing the line defect you keep the translational symmetry along on= e 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 a= s omega(k_x). Of course I used k_x in terms of Cartesian coordinates, not t= he 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 recom= mend Chapter 6 in Photonic Crystals: Molding the Flow of Light<http://ab-in= itio.mit.edu/book/> by John D. Joannopoulos, Steven G. Johnson, Joshua N. W= inn, and Robert D. Meade, but I guess you already had a look for that. A sp= ecific projected band diagram of a silicon woodpile can be found in the fol= lowing: Isabelle Staude, Christopher McGuinness, Andreas Fr=F6lich, Robert L. Byer,= Eric Colby, and Martin Wegener, "Waveguides in three-dimensional photonic = bandgap materials for particle-accelerator on a chip architectures," Opt. E= xpress 20, 5607-5612 (2012) I hope I could help! Best regards, Max From: Andrea Locatelli<mailto:[email protected]> Sent: Tuesday, September 19, 2017 00:31 To: [email protected]<mailto:[email protected]> 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, bu= t 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 f= or what concerns the projected band structure, and in particular the correc= t 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 re= ferences that clearly illustrate this issue? Indeed, it's very difficult to= find in the literature a complete projected band structure of a woodpile w= aveguide (or better, up to now I haven't found it). Regards, Andrea Informativa sulla Privacy: http://www.unibs.it/node/8155 --_000_AM4PR0801MB270744F71A3048791AFD54719A600AM4PR0801MB2707_ Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable <html xmlns:o=3D"urn:schemas-microsoft-com:office:office" xmlns:w=3D"urn:sc= hemas-microsoft-com:office:word" xmlns:m=3D"http://schemas.microsoft.com/of= fice/2004/12/omml" xmlns=3D"http://www.w3.org/TR/REC-html40"> <head> <meta http-equiv=3D"Content-Type" content=3D"text/html; charset=3DWindows-1= 252"> <meta name=3D"Generator" content=3D"Microsoft Word 15 (filtered medium)"> <style><!-- /* Font Definitions */ @font-face {font-family:"Cambria Math"; panose-1:2 4 5 3 5 4 6 3 2 4;} @font-face {font-family:Calibri; panose-1:2 15 5 2 2 2 4 3 2 4;} /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {margin:0in; margin-bottom:.0001pt; font-size:11.0pt; font-family:"Calibri",sans-serif;} a:link, span.MsoHyperlink {mso-style-priority:99; color:blue; text-decoration:underline;} a:visited, span.MsoHyperlinkFollowed {mso-style-priority:99; color:#954F72; text-decoration:underline;} .MsoChpDefault {mso-style-type:export-only;} @page WordSection1 {size:8.5in 11.0in; margin:70.85pt 70.85pt 56.7pt 70.85pt;} div.WordSection1 {page:WordSection1;} --></style> </head> <body lang=3D"EN-US" link=3D"blue" vlink=3D"#954F72"> <div class=3D"WordSection1"> <p class=3D"MsoNormal">Hello Andrea,</p> <p class=3D"MsoNormal"><o:p> </o:p></p> <p class=3D"MsoNormal">I=92m not 100% sure, so please correct me if I=92m w= rong. </p> <p class=3D"MsoNormal">By introducing the line defect you keep the translat= ional symmetry along one axis, the direction of the line. E.g. if you remov= e one rod with its axis along the x-axis, k_x still remains conserved. </p> <p class=3D"MsoNormal">So I guess you should project the band diagram on th= at axis, having bands as omega(k_x). Of course I used k_x in terms of Carte= sian coordinates, not the reciprocal ones. But you can do the transformatio= n between both basis by MPB anyway. </p> <p class=3D"MsoNormal">For a general example of the projected band diagram = in 3D PhC I would recommend Chapter 6 in <span lang=3D"EN" style=3D"color:black"><a href=3D"http://ab-initio.mit.edu= /book/" title=3D"http://shop.barnesandnoble.com/booksearch/isbnInquiry.asp?= isbn=3D0691037442"><i><span style=3D"color:#3366BB">Photonic Crystals: Mold= ing the Flow of Light</span></i></a> </span>by John D. Joannopoulos, Steven G. Johnson, Joshua N. Winn, and Robe= rt D. Meade, but I guess you already had a look for that. A specific projec= ted band diagram of a silicon woodpile can be found in the following:<o:p><= /o:p></p> <p class=3D"MsoNormal"><o:p> </o:p></p> <p class=3D"MsoNormal" style=3D"margin-left:.5in"><span lang=3D"EN" style= =3D"color:#222222">Isabelle Staude, Christopher McGuinness, Andreas Fr=F6li= ch, Robert L. Byer, Eric Colby, and Martin Wegener, "Waveguides in thr= ee-dimensional photonic bandgap materials for particle-accelerator on a chip architectures," Opt. Express <b>20</b>, 5607-5612 (2012)<o:= p></o:p></span></p> <p class=3D"MsoNormal"><o:p> </o:p></p> <p class=3D"MsoNormal">I hope I could help!<o:p></o:p></p> <p class=3D"MsoNormal"><o:p> </o:p></p> <p class=3D"MsoNormal">Best regards,<o:p></o:p></p> <p class=3D"MsoNormal">Max<o:p></o:p></p> <p class=3D"MsoNormal"><o:p> </o:p></p> <p class=3D"MsoNormal"><o:p> </o:p></p> <div style=3D"mso-element:para-border-div;border:none;border-top:solid #E1E= 1E1 1.0pt;padding:3.0pt 0in 0in 0in"> <p class=3D"MsoNormal" style=3D"border:none;padding:0in"><b>From: </b><a hr= ef=3D"mailto:[email protected]">Andrea Locatelli</a><br> <b>Sent: </b>Tuesday, September 19, 2017 00:31<br> <b>To: </b><a href=3D"mailto:[email protected]">mpb-discuss@ab-= initio.mit.edu</a><br> <b>Subject: </b>[MPB-discuss] Woodpile waveguide</p> </div> <p class=3D"MsoNormal"><o:p> </o:p></p> <p class=3D"MsoNormal"><span style=3D"font-size:12.0pt">Hello MPB users,<o:= p></o:p></span></p> <div> <p class=3D"MsoNormal"><span style=3D"font-size:12.0pt">I'm going to simula= te a waveguide consisting of a linear defect introduced into a woodpile pho= tonic crystal. <o:p></o:p></span></p> </div> <div> <p class=3D"MsoNormal"><span style=3D"font-size:12.0pt">I had many doubts a= bout the definiton of the irreducible Brillouin zone, but in the end I foun= d an example that Steven posted here for the case of the perfect crystal wh= ich works fine (even if I used as some kind of black box).<o:p></o:p></span></p> </div> <div> <p class=3D"MsoNormal"><span style=3D"font-size:12.0pt">Now I must introduc= e the linear defect and other doubts come into my mind for what concerns th= e 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).<o:p></o:p></span>= </p> </div> <div> <p class=3D"MsoNormal"><span style=3D"font-size:12.0pt">Are there any examp= les concerning this very tricky case? Do you know any references that clear= ly illustrate this issue? Indeed, it's very difficult to find in the litera= ture a complete projected band structure of a woodpile waveguide (or better, up to now I haven't found it).<o:p></o= :p></span></p> </div> <div> <p class=3D"MsoNormal"><span style=3D"font-size:12.0pt"><o:p> </o:p></= span></p> </div> <div> <p class=3D"MsoNormal"><span style=3D"font-size:12.0pt">Regards,<o:p></o:p>= </span></p> </div> <div> <p class=3D"MsoNormal"><span style=3D"font-size:12.0pt"><o:p> </o:p></= span></p> </div> <div> <p class=3D"MsoNormal"><span style=3D"font-size:12.0pt"><o:p> </o:p></= span></p> </div> <div> <p class=3D"MsoNormal"><span style=3D"font-size:12.0pt">Andrea<o:p></o:p></= span></p> </div> <div> <p class=3D"MsoNormal"><o:p> </o:p></p> </div> <div> <div> <div> <div> <div> <div> <div> <p class=3D"MsoNormal"><o:p> </o:p></p> </div> </div> </div> </div> </div> </div> </div> <p class=3D"MsoNormal"><o:p> </o:p></p> <div> <p class=3D"MsoNormal"><o:p> </o:p></p> </div> <p class=3D"MsoNormal"><span style=3D"font-size:12.0pt;font-family:"Ar= ial",sans-serif">Informativa sulla Privacy: </span><span style=3D"font-size:14.5pt;font-family:"Arial",sans-s= erif"><a href=3D"http://www.unibs.it/node/8155" target=3D"_blank"><span sty= le=3D"font-size:12.0pt">http://www.unibs.it/node/8155</span></a><o:p></o:p>= </span></p> <p class=3D"MsoNormal"><o:p> </o:p></p> </div> </body> </html> --_000_AM4PR0801MB270744F71A3048791AFD54719A600AM4PR0801MB2707_-- --===============4116812846609939175== Content-Type: text/plain; charset="utf-8" MIME-Version: 1.0 Content-Transfer-Encoding: base64 Content-Disposition: inline X19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX19fX18KbXBiLWRpc2N1 c3MgbWFpbGluZyBsaXN0Cm1wYi1kaXNjdXNzQGFiLWluaXRpby5taXQuZWR1Cmh0dHA6Ly9hYi1p bml0aW8ubWl0LmVkdS9jZ2ktYmluL21haWxtYW4vbGlzdGluZm8vbXBiLWRpc2N1c3M= --===============4116812846609939175==--