Propagation constant with find-k function again

Dear Steven,
  
     Thanks for your suggestion before. As you mentioned, I really need to fix a frequency first, but the wavelength equals to 0.5um, and the lattice period is 11um( I am now repeating a result from PRL paper), which makes the frequency 22 in MPB, too big to find the root? On the other hand, I am not sure about, since I define kdir in 'find-k' as (kx,ky,0) to find k-magnitude(since it's 2D, kz should be 0 here, am I right?) does the k-magnitude equal to kz(q)?
     I have attached my code below, I have also attached the band structure picture they got in attachment. Their values of q completely have no comparison with the results got from MPB, which makes me more confused now.
    So could you kindly give me some further suggestion to solve this problem? I really appreciate your help.

Best wishes
Yiling
========================================================================
; simulate the band structure in paper PRL-91-213906-2003-Two-dimensional Optical lattice soliton
; Sinusoidal lattice


(define pi (deg->rad 180.0))


; Define a function of position p (in the lattice basis) which returns
; the material refractive index at that position.
; This is periodic, and also has inverse symmetry.


; RI modulation is directly related to the voltage applied to the photorefractive crytal,
; which is called as index potential in paper-----V(x,y)                     
; For sinusoidal, V(x,y)=-(V0/2)[sin(pi*x)^2+sin(pi*y)^2]
; and the RI modulation is related to the normalized potential depth via V0=(2*pi*n0*a/lamda0)^2*delta.
; Then RI modulation: Delta=-(lamda0/2/pi/n0/a)^2*V0/2*[sin(pi*x)^2+sin(pi*y)^2]

(define n0 2.3)
(define a 11)
(define lamda0 0.5)
(define-param V0 21.6)
(define rad 3.5)
(define r (/ rad a))
(define (sinusoidal-func p)
  (make dielectric
    (index (+ n0 (* -0.5 V0 (sqr (/ lamda0 2 pi n0 a)) (+ (sqr (sin (* pi (vector3-x p)))) (sqr (sin (* pi (vector3-y p))))))))))



; The periodicity is 11um, and the radius is 3.5um for the dielectric-function.
(set! geometry (list
                (make cylinder
                    (center 0 0 0)
                    (radius r)
                    (height infinity)
                    (material (make material-function (material-func sinusoidal-func))))))
(set! default-material (make dielectric (index n0)))

(set! geometry-lattice (make lattice(size 1 1 no-size)))
(set! resolution 64)

; the wavelength is 0.5um, according to the implicit periodicity, omega shoule be a/lamda=22(???? is it too big)
(define-param omega 22) ;????it's too big to find the root
(define-param band-min 1)
(define-param band-max 5)

(define-param kdir (vector3 0.5 0 0))
(define-param tol 1e-4)
(define-param kmag-guess 0.5)
(define-param kmag-min -1.0)
(define-param kmag-max 1.0)
 
;(find-k p omega band-min band-max kdir tol kmag-guess kmag-min kmag-max)
(find-k NO-PARITY omega band-min band-max kdir tol kmag-guess kmag-min kmag-max)



    ****************************************************************************8
    MPB can certainly solve any problem of that form.  However, you still
    need a frequency in order to define your mode; given K (the in-plane
    wavevector with components kx and ky) and q (the z wavevector,
    although have switched the sign convention so that q = -kz) there are
    infinitely many eigenmodes with different frequencies.  Without a
    frequency your problem seems to be ill-posed.

    MPB solves the problem where, given (kx,ky,kz) you find the
    frequencies.  Alternatively, with find-k you can give (kx,ky) and the
    frequency and then solve for kz (q).

    Steven



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