http://ab-initio.mit.edu/wiki/index.php?title=MPB_Data_Analysis_Tutorial&action=history&feed=atomMPB Data Analysis Tutorial - Revision history2024-03-29T06:15:50ZRevision history for this page on the wikiMediaWiki 1.7.3http://ab-initio.mit.edu/wiki/index.php?title=MPB_Data_Analysis_Tutorial&diff=3143&oldid=prevStevenj: /* Important note on units for the diamond/fcc lattice */ link2008-06-25T16:44:57Z<p><span class="autocomment">Important note on units for the diamond/fcc lattice -</span> link</p>
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<tr><td> </td><td style="background: #eee; font-size: smaller;">=== Important note on units for the diamond/fcc lattice ===</td><td> </td><td style="background: #eee; font-size: smaller;">=== Important note on units for the diamond/fcc lattice ===</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">[<span style="color: red; font-weight: bold;">user-tutorial.html</span>#<span style="color: red; font-weight: bold;">units </span>As usual,] all distances are in the "dimensionless" units determined by the length of the lattice vectors. We refer to these units as ''a'', and frequencies are given in units of ''c/a''. By default, the lattice/basis vectors are unit vectors, but in the case of fcc lattices this conflicts with the convention in the literature. In particular, the canonical ''a'' for fcc is the edge-length of a cubic supercell containing the lattice.</td><td>+</td><td style="background: #cfc; font-size: smaller;">[<span style="color: red; font-weight: bold;">[MPB User Tutorial</span>#<span style="color: red; font-weight: bold;">A Few Words on Units|</span>As usual,<span style="color: red; font-weight: bold;">]</span>] all distances are in the "dimensionless" units determined by the length of the lattice vectors. We refer to these units as ''a'', and frequencies are given in units of ''c/a''. By default, the lattice/basis vectors are unit vectors, but in the case of fcc lattices this conflicts with the convention in the literature. In particular, the canonical ''a'' for fcc is the edge-length of a cubic supercell containing the lattice.</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">In order to follow this convention, we set the length of our basis vectors appropriately using the <code>basis-size</code> property of <code>geometry-lattice</code>. (The lattice vectors default to the same length as the basis vectors.) If the cubic supercell edge has unit length (''a''), then the fcc lattice vectors have length sqrt(0.5), or <code>(sqrt 0.5)</code> in Scheme.</td><td> </td><td style="background: #eee; font-size: smaller;">In order to follow this convention, we set the length of our basis vectors appropriately using the <code>basis-size</code> property of <code>geometry-lattice</code>. (The lattice vectors default to the same length as the basis vectors.) If the cubic supercell edge has unit length (''a''), then the fcc lattice vectors have length sqrt(0.5), or <code>(sqrt 0.5)</code> in Scheme.</td></tr>
</table>
Stevenjhttp://ab-initio.mit.edu/wiki/index.php?title=MPB_Data_Analysis_Tutorial&diff=3142&oldid=prevStevenj: /* Gaps and and band diagram for tri-rods */ link2008-06-25T16:44:30Z<p><span class="autocomment">Gaps and and band diagram for tri-rods -</span> link</p>
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<tr><td> </td><td style="background: #eee; font-size: smaller;"> Gap from band 4 (0.821658212109559) to band 5 (0.864454087942874), 5.07627823271133%</td><td> </td><td style="background: #eee; font-size: smaller;"> Gap from band 4 (0.821658212109559) to band 5 (0.864454087942874), 5.07627823271133%</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">The first five gaps are for the TM bands (which we ran first), and the last gap is for the TE bands. Note, however that the &lt; 1% gaps are probably false positives due to band crossings, as described in the [[MPB User Tutorial#Our First Band Structure|user tutorial]. There are no complete (overlapping TE/TM) gaps, and the largest gap is the 47% TM gap as expected (see [http://ab-initio.mit.edu/book our online textbook], appendix C). (To be absolutely sure of this and other band gaps, we would also check k-points within the interior of the Brillouin zone, but we'll omit that step here.)</td><td>+</td><td style="background: #cfc; font-size: smaller;">The first five gaps are for the TM bands (which we ran first), and the last gap is for the TE bands. Note, however that the &lt; 1% gaps are probably false positives due to band crossings, as described in the [[MPB User Tutorial#Our First Band Structure|user tutorial<span style="color: red; font-weight: bold;">]</span>]. There are no complete (overlapping TE/TM) gaps, and the largest gap is the 47% TM gap as expected (see [http://ab-initio.mit.edu/book our online textbook], appendix C). (To be absolutely sure of this and other band gaps, we would also check k-points within the interior of the Brillouin zone, but we'll omit that step here.)</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">Next, let's plot out the band structure. To do this, we'll first extract the TM and TE bands as comma-delimited text, which can then be imported and plotted in our favorite spreadsheet/plotting program.</td><td> </td><td style="background: #eee; font-size: smaller;">Next, let's plot out the band structure. To do this, we'll first extract the TM and TE bands as comma-delimited text, which can then be imported and plotted in our favorite spreadsheet/plotting program.</td></tr>
</table>
Stevenjhttp://ab-initio.mit.edu/wiki/index.php?title=MPB_Data_Analysis_Tutorial&diff=3141&oldid=prevStevenj: /* Gaps and and band diagram for tri-rods */ link2008-06-25T16:44:19Z<p><span class="autocomment">Gaps and and band diagram for tri-rods -</span> link</p>
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<td colspan='2' width='50%' align='center' style="background-color: white;">←Older revision</td>
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<tr><td> </td><td style="background: #eee; font-size: smaller;"> Gap from band 4 (0.821658212109559) to band 5 (0.864454087942874), 5.07627823271133%</td><td> </td><td style="background: #eee; font-size: smaller;"> Gap from band 4 (0.821658212109559) to band 5 (0.864454087942874), 5.07627823271133%</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">The first five gaps are for the TM bands (which we ran first), and the last gap is for the TE bands. Note, however that the &lt; 1% gaps are probably false positives due to band crossings, as described in the [<span style="color: red; font-weight: bold;">user-tutorial.html</span>#<span style="color: red; font-weight: bold;">sq-rods </span>user tutorial]. There are no complete (overlapping TE/TM) gaps, and the largest gap is the 47% TM gap as expected (see [http://ab-initio.mit.edu/book our online textbook], appendix C). (To be absolutely sure of this and other band gaps, we would also check k-points within the interior of the Brillouin zone, but we'll omit that step here.)</td><td>+</td><td style="background: #cfc; font-size: smaller;">The first five gaps are for the TM bands (which we ran first), and the last gap is for the TE bands. Note, however that the &lt; 1% gaps are probably false positives due to band crossings, as described in the [<span style="color: red; font-weight: bold;">[MPB User Tutorial</span>#<span style="color: red; font-weight: bold;">Our First Band Structure|</span>user tutorial]. There are no complete (overlapping TE/TM) gaps, and the largest gap is the 47% TM gap as expected (see [http://ab-initio.mit.edu/book our online textbook], appendix C). (To be absolutely sure of this and other band gaps, we would also check k-points within the interior of the Brillouin zone, but we'll omit that step here.)</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">Next, let's plot out the band structure. To do this, we'll first extract the TM and TE bands as comma-delimited text, which can then be imported and plotted in our favorite spreadsheet/plotting program.</td><td> </td><td style="background: #eee; font-size: smaller;">Next, let's plot out the band structure. To do this, we'll first extract the TM and TE bands as comma-delimited text, which can then be imported and plotted in our favorite spreadsheet/plotting program.</td></tr>
</table>
Stevenjhttp://ab-initio.mit.edu/wiki/index.php?title=MPB_Data_Analysis_Tutorial&diff=3140&oldid=prevStevenj: /* Triangular Lattice of Rods */ link2008-06-25T16:43:36Z<p><span class="autocomment">Triangular Lattice of Rods -</span> link</p>
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<tr><td> </td><td style="background: #eee; font-size: smaller;">== Triangular Lattice of Rods ==</td><td> </td><td style="background: #eee; font-size: smaller;">== Triangular Lattice of Rods ==</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">First, we'll return to the two-dimensional [[User Tutorial#Bands of a Triangular Lattice|triangular lattice of rods]] in air from the tutorial (see also [http://ab-initio.mit.edu/book our online textbook], ch. 5). The control file for this calculation, which can also be found in <code>mpb-ctl/examples/tri-rods.ctl</code>, will consist of:</td><td>+</td><td style="background: #cfc; font-size: smaller;">First, we'll return to the two-dimensional [[<span style="color: red; font-weight: bold;">MPB </span>User Tutorial#Bands of a Triangular Lattice|triangular lattice of rods]] in air from the tutorial (see also [http://ab-initio.mit.edu/book our online textbook], ch. 5). The control file for this calculation, which can also be found in <code>mpb-ctl/examples/tri-rods.ctl</code>, will consist of:</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">=== The tri-rods.ctl control file ===</td><td> </td><td style="background: #eee; font-size: smaller;">=== The tri-rods.ctl control file ===</td></tr>
</table>
Stevenjhttp://ab-initio.mit.edu/wiki/index.php?title=MPB_Data_Analysis_Tutorial&diff=3139&oldid=prevStevenj: /* Triangular Lattice of Rods */ link2008-06-25T16:43:24Z<p><span class="autocomment">Triangular Lattice of Rods -</span> link</p>
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<td colspan='2' width='50%' align='center' style="background-color: white;">←Older revision</td>
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<tr><td> </td><td style="background: #eee; font-size: smaller;">== Triangular Lattice of Rods ==</td><td> </td><td style="background: #eee; font-size: smaller;">== Triangular Lattice of Rods ==</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">First, we'll return to the two-dimensional [[User Tutorial#Bands of a Triangular Lattice|triangular lattice of rods] in air from the tutorial (see also [http://ab-initio.mit.edu/book our online textbook], ch. 5). The control file for this calculation, which can also be found in <code>mpb-ctl/examples/tri-rods.ctl</code>, will consist of:</td><td>+</td><td style="background: #cfc; font-size: smaller;">First, we'll return to the two-dimensional [[User Tutorial#Bands of a Triangular Lattice|triangular lattice of rods<span style="color: red; font-weight: bold;">]</span>] in air from the tutorial (see also [http://ab-initio.mit.edu/book our online textbook], ch. 5). The control file for this calculation, which can also be found in <code>mpb-ctl/examples/tri-rods.ctl</code>, will consist of:</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">=== The tri-rods.ctl control file ===</td><td> </td><td style="background: #eee; font-size: smaller;">=== The tri-rods.ctl control file ===</td></tr>
</table>
Stevenjhttp://ab-initio.mit.edu/wiki/index.php?title=MPB_Data_Analysis_Tutorial&diff=3117&oldid=prevStevenj: /* Diamond Lattice of Spheres */2008-06-25T16:21:36Z<p><span class="autocomment">Diamond Lattice of Spheres</span></p>
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<tr><td> </td><td style="background: #eee; font-size: smaller;"><blockquote> "Then were the entrances of this world made narrow, full of sorrow and travail: they are but few and evil, full of perils, and very painful." (''Ezra'' 4:7) </blockquote></td><td> </td><td style="background: #eee; font-size: smaller;"><blockquote> "Then were the entrances of this world made narrow, full of sorrow and travail: they are but few and evil, full of perils, and very painful." (''Ezra'' 4:7) </blockquote></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">Now, let us turn to a three-dimensional structure, a diamond lattice of dielectric spheres in air. The basic techniques to compute and analyze the modes of this structure are the same as in two dimensions, but of course, everything becomes more complicated in 3d. It's harder to find a structure with a complete gap, the modes are no longer polarized, the computations are far bigger, and visualization is much more difficult, for starters.</td><td>+</td><td style="background: #cfc; font-size: smaller;">Now, let us turn to a three-dimensional structure, a diamond lattice of dielectric spheres in air <span style="color: red; font-weight: bold;">(see [http://ab-initio.mit.edu/book our online textbook], ch. 6)</span>. The basic techniques to compute and analyze the modes of this structure are the same as in two dimensions, but of course, everything becomes more complicated in 3d. It's harder to find a structure with a complete gap, the modes are no longer polarized, the computations are far bigger, and visualization is much more difficult, for starters.</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">(The band gap of the diamond structure was first identified in: K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," ''Phys. Rev. Lett.'' '''65''', 3152 (1990).)</td><td> </td><td style="background: #eee; font-size: smaller;">(The band gap of the diamond structure was first identified in: K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," ''Phys. Rev. Lett.'' '''65''', 3152 (1990).)</td></tr>
</table>
Stevenjhttp://ab-initio.mit.edu/wiki/index.php?title=MPB_Data_Analysis_Tutorial&diff=3116&oldid=prevStevenj: /* Triangular Lattice of Rods */ links2008-06-25T16:20:41Z<p><span class="autocomment">Triangular Lattice of Rods -</span> links</p>
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<td colspan='2' width='50%' align='center' style="background-color: white;">←Older revision</td>
<td colspan='2' width='50%' align='center' style="background-color: white;">Revision as of 16:20, 25 June 2008</td>
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<tr><td> </td><td style="background: #eee; font-size: smaller;">== Triangular Lattice of Rods ==</td><td> </td><td style="background: #eee; font-size: smaller;">== Triangular Lattice of Rods ==</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">First, we'll return to the two-dimensional [<span style="color: red; font-weight: bold;">user-tutorial.html</span>#<span style="color: red; font-weight: bold;">tri-rods </span>triangular lattice of rods] in air from the tutorial. The control file for this calculation, which can also be found in <code>mpb-ctl/examples/tri-rods.ctl</code>, will consist of:</td><td>+</td><td style="background: #cfc; font-size: smaller;">First, we'll return to the two-dimensional [<span style="color: red; font-weight: bold;">[User Tutorial</span>#<span style="color: red; font-weight: bold;">Bands of a Triangular Lattice|</span>triangular lattice of rods] in air from the tutorial <span style="color: red; font-weight: bold;">(see also [http://ab-initio.mit.edu/book our online textbook], ch. 5)</span>. The control file for this calculation, which can also be found in <code>mpb-ctl/examples/tri-rods.ctl</code>, will consist of:</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">=== The tri-rods.ctl control file ===</td><td> </td><td style="background: #eee; font-size: smaller;">=== The tri-rods.ctl control file ===</td></tr>
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<tr><td> </td><td style="background: #eee; font-size: smaller;"> Gap from band 4 (0.821658212109559) to band 5 (0.864454087942874), 5.07627823271133%</td><td> </td><td style="background: #eee; font-size: smaller;"> Gap from band 4 (0.821658212109559) to band 5 (0.864454087942874), 5.07627823271133%</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">The first five gaps are for the TM bands (which we ran first), and the last gap is for the TE bands. Note, however that the &lt; 1% gaps are probably false positives due to band crossings, as described in the [user-tutorial.html#sq-rods user tutorial]. There are no complete (overlapping TE/TM) gaps, and the largest gap is the 47% TM gap as expected. (To be absolutely sure of this and other band gaps, we would also check k-points within the interior of the Brillouin zone, but we'll omit that step here.)</td><td>+</td><td style="background: #cfc; font-size: smaller;">The first five gaps are for the TM bands (which we ran first), and the last gap is for the TE bands. Note, however that the &lt; 1% gaps are probably false positives due to band crossings, as described in the [user-tutorial.html#sq-rods user tutorial]. There are no complete (overlapping TE/TM) gaps, and the largest gap is the 47% TM gap as expected <span style="color: red; font-weight: bold;">(see [http://ab-initio.mit.edu/book our online textbook], appendix C)</span>. (To be absolutely sure of this and other band gaps, we would also check k-points within the interior of the Brillouin zone, but we'll omit that step here.)</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">Next, let's plot out the band structure. To do this, we'll first extract the TM and TE bands as comma-delimited text, which can then be imported and plotted in our favorite spreadsheet/plotting program.</td><td> </td><td style="background: #eee; font-size: smaller;">Next, let's plot out the band structure. To do this, we'll first extract the TM and TE bands as comma-delimited text, which can then be imported and plotted in our favorite spreadsheet/plotting program.</td></tr>
<tr><td colspan="2" align="left"><strong>Line 141:</strong></td>
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<tr><td> </td><td style="background: #eee; font-size: smaller;">We can see several things from these plots:</td><td> </td><td style="background: #eee; font-size: smaller;">We can see several things from these plots:</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">First, the origin of the band gap is apparent. The lowest band is concentrated within the dielectric rods in order to minimize its frequency. The next bands, in order to be orthogonal, are forced to have a node within the rods, imposing a large "kinetic energy" (and/or "potential energy") cost and hence a gap. Successive bands have more and more complex nodal structures in order to maintain orthogonality. (The contrasting absence of a large TE gap has to do with boundary conditions. The perpendicular component of the displacement field must be continuous across the dielectric boundary, but the parallel component need not be.)</td><td>+</td><td style="background: #cfc; font-size: smaller;">First, the origin of the band gap is apparent. The lowest band is concentrated within the dielectric rods in order to minimize its frequency. The next bands, in order to be orthogonal, are forced to have a node within the rods, imposing a large "kinetic energy" (and/or "potential energy") cost and hence a gap <span style="color: red; font-weight: bold;">(see [http://ab-initio.mit.edu/book our online textbook], ch. 5)</span>. Successive bands have more and more complex nodal structures in order to maintain orthogonality. (The contrasting absence of a large TE gap has to do with boundary conditions. The perpendicular component of the displacement field must be continuous across the dielectric boundary, but the parallel component need not be.)</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">We can also see the deep impact of symmetry on the states. The K point has C<sub>3v</sub> symmetry (not quite the full C<sub>6v</sub> symmetry of the dielectric structure). This symmetry group has only one two-dimensional representation--that is what gives rise to the degenerate pairs of states (2/3, 4/5, and 7/8), all of which fall into this "p-like" category (where the states transform like two orthogonal dipole field patterns, essentially). The other two bands, 1 and 6, transform under the trivial "s-like" representation (with band 6 just a higher-order version of 1).</td><td> </td><td style="background: #eee; font-size: smaller;">We can also see the deep impact of symmetry on the states. The K point has C<sub>3v</sub> symmetry (not quite the full C<sub>6v</sub> symmetry of the dielectric structure). This symmetry group has only one two-dimensional representation--that is what gives rise to the degenerate pairs of states (2/3, 4/5, and 7/8), all of which fall into this "p-like" category (where the states transform like two orthogonal dipole field patterns, essentially). The other two bands, 1 and 6, transform under the trivial "s-like" representation (with band 6 just a higher-order version of 1).</td></tr>
</table>
Stevenjhttp://ab-initio.mit.edu/wiki/index.php?title=MPB_Data_Analysis_Tutorial&diff=1923&oldid=prevArdavan: /* The tri-rods.ctl control file */2005-10-17T18:42:52Z<p><span class="autocomment">The tri-rods.ctl control file</span></p>
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<td colspan='2' width='50%' align='center' style="background-color: white;">←Older revision</td>
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<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"> (set! num-bands 8)</td><td> </td><td style="background: #eee; font-size: smaller;"> (set! num-bands 8)</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"> </td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;"> </span></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"> (set! geometry-lattice (make lattice (size 1 1 no-size)</td><td> </td><td style="background: #eee; font-size: smaller;"> (set! geometry-lattice (make lattice (size 1 1 no-size)</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"> (basis1 (/ (sqrt 3) 2) 0.5)</td><td> </td><td style="background: #eee; font-size: smaller;"> (basis1 (/ (sqrt 3) 2) 0.5)</td></tr>
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<tr><td> </td><td style="background: #eee; font-size: smaller;"> (center 0 0 0) (radius 0.2) (height infinity)</td><td> </td><td style="background: #eee; font-size: smaller;"> (center 0 0 0) (radius 0.2) (height infinity)</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"> (material (make dielectric (epsilon 12))))))</td><td> </td><td style="background: #eee; font-size: smaller;"> (material (make dielectric (epsilon 12))))))</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"> </td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;"> </span></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"> (set! k-points (list (vector3 0 0 0) ; Gamma</td><td> </td><td style="background: #eee; font-size: smaller;"> (set! k-points (list (vector3 0 0 0) ; Gamma</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"> (vector3 0 0.5 0) ; M</td><td> </td><td style="background: #eee; font-size: smaller;"> (vector3 0 0.5 0) ; M</td></tr>
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<tr><td> </td><td style="background: #eee; font-size: smaller;"> (vector3 0 0 0))) ; Gamma</td><td> </td><td style="background: #eee; font-size: smaller;"> (vector3 0 0 0))) ; Gamma</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"> (set! k-points (interpolate 4 k-points))</td><td> </td><td style="background: #eee; font-size: smaller;"> (set! k-points (interpolate 4 k-points))</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"> </td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;"> </span></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"> (set! resolution 32)</td><td> </td><td style="background: #eee; font-size: smaller;"> (set! resolution 32)</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"> </td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;"> </span></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"> (run-tm (output-at-kpoint (vector3 (/ -3) (/ 3) 0)</td><td> </td><td style="background: #eee; font-size: smaller;"> (run-tm (output-at-kpoint (vector3 (/ -3) (/ 3) 0)</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"> fix-efield-phase output-efield-z))</td><td> </td><td style="background: #eee; font-size: smaller;"> fix-efield-phase output-efield-z))</td></tr>
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Ardavanhttp://ab-initio.mit.edu/wiki/index.php?title=MPB_Data_Analysis_Tutorial&diff=200&oldid=prevStevenj: /* Visualizing the diamond lattice structure and bands */2005-10-15T23:54:31Z<p><span class="autocomment">Visualizing the diamond lattice structure and bands</span></p>
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<tr><td> </td><td style="background: #eee; font-size: smaller;">[[Image:diamond-b3.gif|center]] [[Image:diamond-b3-eps.gif|center]]</td><td> </td><td style="background: #eee; font-size: smaller;">[[Image:diamond-b3.gif|center]] [[Image:diamond-b3-eps.gif|center]]</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><span style="color: red; font-weight: bold;">{{</span>Category:MPB<span style="color: red; font-weight: bold;">}}</span></td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">[[</span>Category:MPB<span style="color: red; font-weight: bold;">]]</span></td></tr>
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Stevenjhttp://ab-initio.mit.edu/wiki/index.php?title=MPB_Data_Analysis_Tutorial&diff=124&oldid=prevStevenj at 21:35, 15 October 20052005-10-15T21:35:31Z<p></p>
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<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">[[Image:diamond-b3.gif|center]] [[Image:diamond-b3-eps.gif|center]]</td><td> </td><td style="background: #eee; font-size: smaller;">[[Image:diamond-b3.gif|center]] [[Image:diamond-b3-eps.gif|center]]</td></tr>
<tr><td colspan="2"> </td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr>
<tr><td colspan="2"> </td><td>+</td><td style="background: #cfc; font-size: smaller;">{{Category:MPB}}</td></tr>
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Stevenj