Re: [MPB-discuss] About the lightcone and projected slab mode
On Fri, 16 Nov 2007, Ryan Hao wrote: I have used a non-orthogonal supercell for calvulating triangular lattice. That may be the problem. I chose the supercell like this: o o X o o This is partly my fault, because that is what I did in the line-defect.ctl example file. Non-orthogonal supercells work, of course, but doing projections is much easier with an orthogonal basis. ___ mpb-discuss mailing list mpb-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
Re: [MPB-discuss] About the lightcone and projected slab mode
Dear Prof. Steven, OKey! I got it. I have used a non-orthogonal supercell for calvulating triangular lattice. That may be the problem. I chose the supercell like this: o o X o o I will change it into orthogonal supercell (rectangle) when calculating slab mode. Professor, Thank you very much for your kind help~ Best wishes Yours, Ryan On Nov 16, 2007 7:19 AM, Steven G. Johnson [EMAIL PROTECTED] wrote: On Thu, 15 Nov 2007, Ryan Hao wrote: I know sent the supercell with no defect to calculate slab mode. But how to project it to the waveguide direction? Just plot it as a function of the waveguide-parallel k vector. The only thing you need to be careful of is to arrange your supercell so that one lattice vector points along the waveguide direction and one lattice vector is perpendicular. e.g. in a triangualr lattice you would use a supercell something like o o o o o o o o o ox o o o o x o o o o | o o o o o o o o o o| y (where o is a hole and x is the defect, for example, and the x direction is parallel to the line defect and y is perpendicular). Just a large supercell is enough? why? Could you please talk into it a little bit more in details? There are two ways to proceed. One is just to use a large supercell with no defect, in which the slab bands are folded many times...in the limit as the supercell becomes infinitely large, the slab bands will form a continuous region when plotted vs. k_x. More efficiently, use a small supercell (even just a single unit in the y direction), and compute the bands for many k_y values from 0 to 0.5. When plotted as a function of k_x, this will outline your continuum slab-band regions. In principle, you could also take the bands in the primitive non-orthogonal unit cell (for a triangular lattice) of the defect-free system and project them. This requires some care, however, as described in my paper Linear waveguides in photonic-crystal slabs, in Phys. Rev. B. 62, p. 8212 (2000). It is easier to use the supercell technique above to get an orthogonal unit cell. Regards, Steven G. Johnson ___ mpb-discuss mailing list mpb-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
Re: [MPB-discuss] About the lightcone and projected slab mode
On Thu, 15 Nov 2007, Ryan Hao wrote: I know sent the supercell with no defect to calculate slab mode. But how to project it to the waveguide direction? Just plot it as a function of the waveguide-parallel k vector. The only thing you need to be careful of is to arrange your supercell so that one lattice vector points along the waveguide direction and one lattice vector is perpendicular. e.g. in a triangualr lattice you would use a supercell something like o o o o o o o o o ox o o o o x o o o o | o o o o o o o o o o| y (where o is a hole and x is the defect, for example, and the x direction is parallel to the line defect and y is perpendicular). Just a large supercell is enough? why? Could you please talk into it a little bit more in details? There are two ways to proceed. One is just to use a large supercell with no defect, in which the slab bands are folded many times...in the limit as the supercell becomes infinitely large, the slab bands will form a continuous region when plotted vs. k_x. More efficiently, use a small supercell (even just a single unit in the y direction), and compute the bands for many k_y values from 0 to 0.5. When plotted as a function of k_x, this will outline your continuum slab-band regions. In principle, you could also take the bands in the primitive non-orthogonal unit cell (for a triangular lattice) of the defect-free system and project them. This requires some care, however, as described in my paper Linear waveguides in photonic-crystal slabs, in Phys. Rev. B. 62, p. 8212 (2000). It is easier to use the supercell technique above to get an orthogonal unit cell. Regards, Steven G. Johnson ___ mpb-discuss mailing list mpb-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
Re: [MPB-discuss] About the lightcone and projected slab mode
Dear Prof.Steven and others, Thank you for your answer. But my question is how to set the K path in calculating and projecting the slab mode? You known, projecting the slab mode needs to scan the full area of Brillouin zone, then project to the waveguide direction. Below is my code, Could you please have a look and tell me whether it is correct or not (I think there may something wrong in setting the reciprocal lattice and k path ): (define-param kymin 0) (define-param kymax 0.57735) (define-param k-interp 20) (define (do-stuff k k-hi k-inc) (if (= k k-hi) (begin (set! k-points (interpolate k-interp (list (lattice-reciprocal (vector3 k kymin 0)) (lattice-reciprocal (vector3 k kymax 0) (run-zeven ) (do-stuff (+ k k-inc) k-hi k-inc) ))) (do-stuff 0 0.5 0.1) Best wishes Ryan On Mar 28, 2007 2:20 AM, Steven G. Johnson [EMAIL PROTECTED] wrote: On Tue, 13 Mar 2007, Ryan Hao wrote: In the case of line defect waveguide in photonic crystal slab,I succeed in caculating the waveguide mode with MPB.but there still something left:I must find way to project the band strucure of the regular lattice of the slab(slab mode) and the lightcone?You can see in the below picture,the blue line represent for the lightcone,and the green line represent for slab mode. Projecting the light cone (for a uniform substrate/superstrate) is easy -- it is just the kmag output column divided by the substrate index. For projecting the modes of the unperturbed slab, the easiest thing to do is to use the same computational cell as your line-defect waveguide, but without the defect. (In fact, you can use a smaller supercell if you want, as long as you plot the slab bands for several values of ky from 0 to 0.5, where y is the direction perpendicular to your waveguide, assuming a rectilinear supercell.) Cordially, Steven G. Johnson ___ mpb-discuss mailing list mpb-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss -- === Best wishes Yours, Ryan Hao ___ mpb-discuss mailing list mpb-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
Re: [MPB-discuss] About the lightcone and projected slab mode
The easiest way to project the slab modes for a line defect is just to use a large supercell with no defect. On Thu, 15 Nov 2007, Ryan Hao wrote: Dear Prof.Steven and others, Thank you for your answer. But my question is how to set the K path in calculating and projecting the slab mode? You known, projecting the slab mode needs to scan the full area of Brillouin zone, then project to the waveguide direction. Below is my code, Could you please have a look and tell me whether it is correct or not (I think there may something wrong in setting the reciprocal lattice and k path ): (define-param kymin 0) (define-param kymax 0.57735) (define-param k-interp 20) (define (do-stuff k k-hi k-inc) (if (= k k-hi) (begin (set! k-points (interpolate k-interp (list (lattice-reciprocal (vector3 k kymin 0)) (lattice-reciprocal (vector3 k kymax 0) (run-zeven ) (do-stuff (+ k k-inc) k-hi k-inc) ))) (do-stuff 0 0.5 0.1) Best wishes Ryan On Mar 28, 2007 2:20 AM, Steven G. Johnson [EMAIL PROTECTED] wrote: On Tue, 13 Mar 2007, Ryan Hao wrote: In the case of line defect waveguide in photonic crystal slab,I succeed in caculating the waveguide mode with MPB.but there still something left:I must find way to project the band strucure of the regular lattice of the slab(slab mode) and the lightcone?You can see in the below picture,the blue line represent for the lightcone,and the green line represent for slab mode. Projecting the light cone (for a uniform substrate/superstrate) is easy -- it is just the kmag output column divided by the substrate index. For projecting the modes of the unperturbed slab, the easiest thing to do is to use the same computational cell as your line-defect waveguide, but without the defect. (In fact, you can use a smaller supercell if you want, as long as you plot the slab bands for several values of ky from 0 to 0.5, where y is the direction perpendicular to your waveguide, assuming a rectilinear supercell.) Cordially, Steven G. Johnson ___ mpb-discuss mailing list mpb-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss -- === Best wishes Yours, Ryan Hao ___ mpb-discuss mailing list mpb-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss ___ mpb-discuss mailing list mpb-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
Re: [MPB-discuss] About the lightcone and projected slab mode
Dear Prof.Steven, Thank you for your instant reply. I am sorry that I can't understand you. I know sent the supercell with no defect to calculate slab mode. But how to project it to the waveguide direction? Just a large supercell is enough? why? Could you please talk into it a little bit more in details? Professor, I know you are busy. If you have no time, Could you please be so kind to forward this question to one of your student who can answer me? Your instant reply will be greatly appreciated. On Nov 15, 2007 1:08 PM, Steven G. Johnson [EMAIL PROTECTED] wrote: The easiest way to project the slab modes for a line defect is just to use a large supercell with no defect. On Thu, 15 Nov 2007, Ryan Hao wrote: Dear Prof.Steven and others, Thank you for your answer. But my question is how to set the K path in calculating and projecting the slab mode? You known, projecting the slab mode needs to scan the full area of Brillouin zone, then project to the waveguide direction. Below is my code, Could you please have a look and tell me whether it is correct or not (I think there may something wrong in setting the reciprocal lattice and k path ): (define-param kymin 0) (define-param kymax 0.57735) (define-param k-interp 20) (define (do-stuff k k-hi k-inc) (if (= k k-hi) (begin (set! k-points (interpolate k-interp (list (lattice-reciprocal (vector3 k kymin 0)) (lattice-reciprocal (vector3 k kymax 0) (run-zeven ) (do-stuff (+ k k-inc) k-hi k-inc) ))) (do-stuff 0 0.5 0.1) Best wishes Ryan On Mar 28, 2007 2:20 AM, Steven G. Johnson [EMAIL PROTECTED] wrote: On Tue, 13 Mar 2007, Ryan Hao wrote: In the case of line defect waveguide in photonic crystal slab,I succeed in caculating the waveguide mode with MPB.but there still something left:I must find way to project the band strucure of the regular lattice of the slab(slab mode) and the lightcone?You can see in the below picture,the blue line represent for the lightcone,and the green line represent for slab mode. Projecting the light cone (for a uniform substrate/superstrate) is easy -- it is just the kmag output column divided by the substrate index. For projecting the modes of the unperturbed slab, the easiest thing to do is to use the same computational cell as your line-defect waveguide, but without the defect. (In fact, you can use a smaller supercell if you want, as long as you plot the slab bands for several values of ky from 0 to 0.5, where y is the direction perpendicular to your waveguide, assuming a rectilinear supercell.) Cordially, Steven G. Johnson ___ mpb-discuss mailing list mpb-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss -- === Best wishes Yours, Ryan Hao ___ mpb-discuss mailing list mpb-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss ___ mpb-discuss mailing list mpb-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss -- === Best wishes Yours, Ryan Hao Wuhan National Laboratory for Optoelectronics College of Optoelectronic Science and Engineering, Huazhong University of Science Technology, Wuhan, 430074, P.R.CHINA Phone: 86-027-87792242-809(O) Mobile: Fax: ___ mpb-discuss mailing list mpb-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
[MPB-discuss] About the lightcone and projected slab mode
Prof.steven and other MPB user: In the case of line defect waveguide in photonic crystal slab,I succeed in caculating the waveguide mode with MPB.but there still something left:I must find way to project the band strucure of the regular lattice of the slab(slab mode) and the lightcone?You can see in the below picture,the blue line represent for the lightcone,and the green line represent for slab mode. In the past,When I use Rsoft,this is easy .But now I don't know how to do it in MPB. Looking forward for your reply! Thank you very much! === Best wishes Yours, Ryan Hao Wuhan National Laboratory for Optoelectronics Institute of Optoelectronic Sinence and Engineering, HUST University Wuhan, 430074, P.R.CHINA Phone: 86-027-87792242-809(O) Mobile: Fax: attachment: slab.jpg ___ mpb-discuss mailing list mpb-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
