Transmission through a one-dimensional Fibonacci sequence of function potentials Academic Article uri icon

abstract

  • We study transmission and reflection of a plane wave (with wave number k>0) through a one-dimensional array of N delta-function potentials with equal strengths v located on the Fibonacci numbers 1,1,2,3,5,8,. . . in the limit N-->∞. Our results can be summarized as follows: (i) For k∈piopen1[(1+ &surd;5 )/2] (a countable dense set on the positive part of the k axis), the system is a perfect reflector; namely, the reflection coefficient equals unity. (Physically, the system is an insulator.) (ii) For k=1/2(2N+1)pi (N=0,1,2,. . .) and 3 cospsi-1>0 with psi=arctan(v/k), the system may conduct. (The reflection coefficient is strictly smaller than unity.) (iii) For k=1/2(2N+1)pi (N=0,1,2,. . .) and 3 cospsi-1

publication date

  • January 1, 1990