Controlled terahertz frequency response and transparency of Josephson chains and superconducting multilayers

A fundamental property of wave propagation is Anderson localization, which affects the transfer of information, energy, mass, and charge in disordered media. This localization can manifest itself via, e.g., the metal-insulator transition. We exactly map the behavior of a quantum particle moving in a potential with correlated disorder to the sub-terahertz wave propagation in either Josephson chains or superconducting multilayers. When the Josephson junction parameters vary randomly, the sub-THz electromagnetic waves cannot propagate through these Josephson structures due to localization. For parameter variations with long-range correlations, we predict sharp transitions from transparent to reflective frequency regions for Josephson plasma waves. With appropriate choices of the correlation function, frequency windows with targeted or designed transparencies for THz or sub-THz electromagnetic waves could be achieved. This could be useful for tailoring the electromagnetic wave spectrum of Josephson arrays within the THz frequency range, which is important for applications in physics, astronomy, chemistry, biology, and medicine.

Figure 1

(Color online) Schematic diagram of the parallel-coupled 1D Josephson junction array, known as discrete Josephson transmission line (a), and an artificial superconducting-nonsuperconducting multilayer (b). For both systems, disorder can be introduced by varying the Josephson critical currents $J_c^{\left(n\right)}=J_c(1+{\delta }_n)=J_c(1\pm \delta )$. These disordered Josephson transmission line (a) and artificial multilayers (b) can be mapped to a binary (dichotomic) chain with symbol “1” corresponding to $+\delta$ and “0” referring to $-\delta$.

Figure 2

(Color online) Controlling transparency windows in frequency-selective THz filters [Fig. 1a]. (a) The dimensionless transmission coefficient $T∕T_0=T∕T(\delta =0)=T\left(\omega \right)∕T(\omega ,\delta =0)$ versus dimensionless frequency $\omega ∕{\omega }_J$ for different lengths $N=L∕d$ of Josephson chains [Fig. 1a]. Blue dashed lines correspond to $T\left(\omega \right)$ for uncorrelated disorder, while the red solid curves correspond to $T\left(\omega \right)$ with disorder having correlation functions which are shown in panels (b) and (c). Spatial correlations associated with dimensionless $\xi \left(r\right)$ (normalized by $a$), shown in panel (b), produce correlations in the frequency domain: shown in the Fourier transform $\tilde{\xi }\left(E\right)$ with dimensionless $E$ [see panel (c)]. The parameters used here are: $a=0.5$; dispersion $\propto U_0^2={10}^{-2}$. It is clearly seen that varying the correlation function $\xi$ controls the transparency windows in $T\left(\omega \right)$.

Figure 3

(Color online) Controlling the transparency windows in frequency-selective THz filters [Fig. 1a]: Same as in Fig. 2, but with dimensionless correlation functions $\xi$ shown in (b) and (c). Comparing Figs. 2, 3, it is clearly seen that varying the correlation function $\xi$ controls the transparency windows in $T\left(\omega \right)$. Notice the sharp change in the correlation function $\tilde{\xi }\left(E\right)$ in both, Figs. 2c, 3c.

Figure 4

(Color online) Controlling transparency windows in angle-selective THz filters. (a) The dimensionless transmission coefficient $T∕T(\delta =0)$ versus the incident angle $\theta$ of THz radiation [see Fig. 1b] for different thickness $N=L∕d$ of artificial multilayers [Fig. 1b]. Blue dashed lines correspond to $T\left(\theta \right)$ for uncorrelated disorder in the Josephson critical currents between layers, while the red solid curves correspond to $T\left(\theta \right)$ with correlated disorder. Correlations are described by the dimensionless angular-correlation function $\tilde{\xi }\left(\theta \right)$ shown in panel (b). The parameters used here are ${\lambda }_{ab}∕{\lambda }_c=200$, $\delta ={10}^{-3}$, $({\omega }^2-{\omega }_J^2)∕{\omega }_J^2={10}^{-3}$, and $\epsilon =10$.