Large Out-of-plane component in 2D air-hole lattice
Max Kellermeier <[email protected]> Thu, 24 Aug 2017 11:16:41 +0000
| Newsgroups | gmane.comp.science.photonic-bands |
|---|---|
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Hello everyone,
I am a Master student working on photonic band gap structures for particle =
acceleration in my master project.
Currently, I try to reproduce the results by Lin [1] who studied the band s=
tructure of an air hole trigonal lattice in fused silica for varied out-of-=
plane component of the wavevector.
First I tried to simply compute the bands with MPB at such a kz value. But =
the first bands have much lower frequencies than the frequency range invest=
igated by Lin. So I used
(set! target-freq ..)
to change the freq. range of interest. But the iteration always fails due t=
o more than 10000 steps. (which appears a liitle bit too much to me)
Of course I raised the resolution a few times. But still the results don=92=
t show the band gaps around fa/c=3Dkz. I also increased the tolerance to ma=
ke sure the iteration limit of 10000 is not reached, although the result ma=
y be misleading as the tolerance should be lowered to resolve the bands.
Lin also mentioned the number of plane waves he used for the computation. I=
am not sure how the number of plane waves is set in MPB resp. where the Fo=
urier series is truncated in terms of reciprocal lattice vectors. I guess i=
t somehow depends on the discretization of the unit cell, doesn=92t it?
The bands at such a frequency are very thin. So probably I might have to se=
t num-bands quite large, but for a base line even with few bands I should g=
et the band gap at kz=3D8.2.
Thank you very much!
Best regards,
Max
[1] Lin, Xintian Eddie. "Photonic band gap fiber accelerator." Physical Rev=
iew Special Topics-Accelerators and Beams 4.5 (2001): 051301.
PS: This is what one of the configurations I used so far. I also raised the=
resolution to 128, changed the number of bands computed, the tolerance.
(set-param! num-bands 10)
(set-param! tolerance 1e-7) ; defaults
(define-param RADIUS 0.35)
(define-param EPSILON 2.13) ; Glass at optical Freq.
(define-param K_Z_MIN 6.0) ; Out-of-plane component
(define-param K_Z_MAX 10.0) ; Out-of-plane component
(define-param K_Z_NUM 20)
(define Glass (make dielectric (epsilon EPSILON)))
(set! default-material Glass)
(set! geometry-lattice (make lattice (size lattice-constant lattice-constan=
t no-size)
(basis1 (/ (sqrt 3) 2) 0.5)
(basis2 (/ (sqrt 3) 2) -0.5)))
(set! geometry (list (make cylinder
(center 0 0 0)
(radius RADIUS)
(height infinity)
(material air)
)))
(set-param! resolution 64)
(define (run-different-kz current_kz kmax dkz)
(if (<=3D current_kz kmax)
(begin
(set! target-freq current_kz)
(set! k-points (list (vector3 0 0 current_kz) ; Gamma
(vector3 0 0.5 current_kz ) ; M
(vector3 (/ -3) (/ 3) current_kz) ; K
(vector3 0 0 current_kz))) ; Gamma
(set! k-points (interpolate 9 k-points))
(run display-zparities display-yparities)
(run-different-kz (+ current_kz dkz) kmax dkz)
)
)
)
(run-different-kz K_Z_MIN K_Z_MAX (/ (- K_Z_MAX K_Z_MIN) K_Z_NUM ))
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<p class=3D"MsoNormal">Hello everyone,</p>
<p class=3D"MsoNormal"><o:p> </o:p></p>
<p class=3D"MsoNormal">I am a Master student working on photonic band gap s=
tructures for particle acceleration in my master project.</p>
<p class=3D"MsoNormal"><o:p> </o:p></p>
<p class=3D"MsoNormal">Currently, I try to reproduce the results by Lin [1]=
who studied the band structure of an air hole trigonal lattice in fused si=
lica for varied out-of-plane component of the wavevector.</p>
<p class=3D"MsoNormal"><o:p> </o:p></p>
<p class=3D"MsoNormal">First I tried to simply compute the bands with MPB a=
t such a kz value. But the first bands have much lower frequencies than the=
frequency range investigated by Lin. So I used</p>
<p class=3D"MsoNormal" style=3D"mso-margin-top-alt:12.0pt;margin-right:0in;=
margin-bottom:12.0pt;margin-left:0in;text-indent:.5in">
<span style=3D"font-family:"Source Code Pro"">(set! target-freq .=
.)<o:p></o:p></span></p>
<p class=3D"MsoNormal">to change the freq. range of interest. But the itera=
tion always fails due to more than 10000 steps. (which appears a liitle bit=
too much to me)</p>
<p class=3D"MsoNormal">Of course I raised the resolution a few times. But s=
till the results don=92t show the band gaps around fa/c=3Dk<sub>z</sub>. I =
also increased the tolerance to make sure the iteration limit of 10000 is n=
ot reached, although the result may be
misleading as the tolerance should be lowered to resolve the bands.</p>
<p class=3D"MsoNormal"><o:p> </o:p></p>
<p class=3D"MsoNormal">Lin also mentioned the number of plane waves he used=
for the computation. I am not sure how the number of plane waves is set in=
MPB resp. where the Fourier series is truncated in terms of reciprocal lat=
tice vectors. I guess it somehow depends
on the discretization of the unit cell, doesn=92t it?</p>
<p class=3D"MsoNormal"><o:p> </o:p></p>
<p class=3D"MsoNormal">The bands at such a frequency are very thin. So prob=
ably I might have to set
<i>num-bands </i>quite large, but for a base line even with few bands I sho=
uld get the band gap at k<sub>z</sub>=3D8.2.</p>
<p class=3D"MsoNormal"><o:p> </o:p></p>
<p class=3D"MsoNormal">Thank you very much!</p>
<p class=3D"MsoNormal"><o:p> </o:p></p>
<p class=3D"MsoNormal">Best regards,</p>
<p class=3D"MsoNormal">Max</p>
<p class=3D"MsoNormal"><o:p> </o:p></p>
<p class=3D"MsoNormal"><o:p> </o:p></p>
<p class=3D"MsoNormal">[1] <span style=3D"font-size:10.0pt;font-family:&quo=
t;Arial",sans-serif;color:#222222">
Lin, Xintian Eddie. "Photonic band gap fiber accelerator." <i>Phy=
sical Review Special Topics-Accelerators and Beams</i> 4.5 (2001): 051301.<=
/span></p>
<p class=3D"MsoNormal"><o:p> </o:p></p>
<p class=3D"MsoNormal">PS: This is what one of the configurations I used so=
far. I also raised the resolution to 128, changed the number of bands comp=
uted, the tolerance.</p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""><o:p> </o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro"">(set-param! num-bands 10)<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro"">(set-param! tolerance 1e-7) ; defaults<o:p></o:p></spa=
n></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""><o:p> </o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro"">(define-param RADIUS 0.35)<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro"">(define-param EPSILON 2.13) ; Glass at optical Freq.<o=
:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro"">(define-param K_Z_MIN 6.0) ; Out-of-plane compon=
ent<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro"">(define-param K_Z_MAX 10.0) ; Out-of-plane compo=
nent<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro"">(define-param K_Z_NUM 20)<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""><o:p> </o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro"">(define Glass (make dielectric (epsilon EPSILON)))<o:p=
></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro"">(set! default-material Glass)<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro"">(set! geometry-lattice (make lattice (size lattice-con=
stant lattice-constant no-size)<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> =
&nb=
sp; (basis1 (/ (sqrt 3) 2) 0.5)<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> =
&nb=
sp; (basis2 (/ (sqrt 3) 2) -0.5)))<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro"">(set! geometry (list (make cylinder<o:p></o:p></span><=
/p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> =
&nb=
sp; (center 0 0 0)<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> =
&nb=
sp; (radius RADIUS)<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> =
&nb=
sp; (height infinity)<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> =
&n=
bsp;(material air)<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> =
&nb=
sp; )))<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro"">(set-param! resolution 64)<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""><o:p> </o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro"">(define (run-different-kz current_kz kmax dkz)<o:p></o=
:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> (if (<=3D current_kz kmax)<o:p></o:p></span>=
</p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> (begin<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> (set! target-freq curre=
nt_kz)<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> (set! k-points (list (v=
ector3 0 0 current_kz)  =
; ; Gamma<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> =
&nb=
sp; (vector3 0 0.5 current_kz ) &n=
bsp; ; M<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> =
&nb=
sp; (vector3 (/ -3) (/ 3) current_kz) ; K<o:p></o:p=
></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> =
&nb=
sp; (vector3 0 0 current_kz))) &nb=
sp; ; Gamma<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> (set! k-points (interpo=
late 9 k-points))<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> (run display-zparities =
display-yparities)<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> (run-different-kz (+=
; current_kz dkz) kmax dkz)<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> )<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro""> )<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro"">)<o:p></o:p></span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:10.0pt;font-family:"So=
urce Code Pro"">(run-different-kz K_Z_MIN K_Z_MAX (/ (- K_Z_MAX K_Z_MI=
N) K_Z_NUM ))</span>
</p>
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