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
structure 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 investigated
by Lin. So I used
(set! target-freq ..)
to change the freq. range of interest. But the iteration always fails due to
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’t show
the band gaps around fa/c=kz. I also increased the tolerance to make sure the
iteration limit of 10000 is not reached, although the result may 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 Fourier
series is truncated in terms of reciprocal lattice vectors. I guess it somehow
depends on the discretization of the unit cell, doesn’t it?
The bands at such a frequency are very thin. So probably I might have to set
num-bands quite large, but for a base line even with few bands I should get the
band gap at kz=8.2.
Thank you very much!
Best regards,
Max
[1] Lin, Xintian Eddie. "Photonic band gap fiber accelerator." Physical Review
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-constant
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 (<= 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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