Hi, Yang, thanks for your help. I had previously tried the case of turning
off eps-averaging,  and found it can only weaken but not completely avoid
the divergence if the run-time is more longer. The following is a new
example in which the run-time is 6553.6. When the eps-averaging is turned
off, it will be divergent at  5000. If eps-averaging is turned on, it will
be divergent earlier.

Best,

Deyin

(define-param n1 3.48)
(define-param eps (* n1 n1))
(define-param a 1)
(define-param r 0.2)
(define-param thick 0.3)
(define-param supercellhight 6)

(set! geometry-lattice (make lattice (size a a supercellhight)));the
computional cell
(set! eps-averaging? false)
(set! geometry
            (list
                 (make block
                          (center 0 0 -1.0)
                          (size a a 0.3)
                          (material (make dielectric (epsilon eps))))
                 (make block
                          (center 0 0 -0.9)
                          (size a a 0.1)
                          (material (make dielectric (epsilon
12.25))))
         (make cylinder
                  (center 0 0 -1.0)
                          (radius r)
                          (height thick)
                          (material (make dielectric (epsilon 1))))))
(define-param fcen 0.5) ; pulse center frequency
(define-param df 0.4) ; pulse width (in frequency)

(set! sources
    (list
     (make source
        (src (make gaussian-src (frequency fcen) (fwidth df)))
         (component Ey)
         (center 0 0 1.5)
;     (start-time 10)
;     (cutoff 100)
     (size 1 1 0))))

(set! k-point (vector3 0 0 0))
(set! pml-layers (list (make pml (direction Z) (thickness 1.0))))
(set-param! resolution 40)

(define (Eoutput)
         (print "Eoutput:, " (meep-time) ", "
         (get-field-point Ey (vector3 0 0 1.0)) ", "
        (get-field-point Ey (vector3 0 0 -1.8)) "\n"))

(run-until 6553.6  Eoutput (at-beginning output-epsilon))
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