Coupled Ring Resonators at Fibonacci Frequencies

Since the Middle Ages, Fibonacci (FB) numbers have attracted the interest of many scientists. In the recent years, a great research effort has been spent on the applications of FB numbers and sequences. It has been demonstrated that also some properties of resonant electronic systems are related to FB numbers. In this paper, an optical resonant device, with resonant frequencies spaced according to the FB series, is proposed, demonstrating the analogy with coupled electrical resonant cells. The proposed device consists of a silicon-based photonic coupled ring resonators, properly designed such that the resonant frequencies correspond to the sequence: 0.618·ω
_0,
..., ω
_0,
..., 1.618·ω
₀
, where ω
₀
is the operating angular frequency [rad/s]. These features make the device suitable for several applications, e.g. frequency-based quantum cryptography for the transmission of quantum information.