Reconfigurable nonreciprocity with a nonlinear Fano diode

We propose a dynamically tunable nonreciprocal response for wave propagations by employing nonlinear Fano resonances. We demonstrate that the transmission contrast between waves propagating in opposite directions can be controlled by an excitation signal. In particular, the unidirectional transmission can be flipped at different time of a pulse, resembling a Fano diode with dynamical reconfigurable nonreciprocity. The key mechanism is the interaction between a linear and a nonlinear Fano resonance that allows for the tunable unidirectional wave propagation and ultrahigh transmission contrast ratio. We further present a realistic photonic example which demonstrates the properties of nonreciprocity can be dynamically manipulated using a pump pulse, based on the general theoretical model.

Figure 1

Schematic view of the reversible nonreciprocal response based on the nonlinear Fano resonance. The arrows indicate the direction of the forward and backward transmission. The same system can support waves propagation predominantly either in one (a) or opposite (b) direction for different excitation signals. The color scale stands for the intensity of the field in each cite which are two particular solutions of Eq. (1). Nonlinear Fano defect is shown by a dashed ring while others are linear. Forward transmission means that the injection is from the left side, while backward transmission is corresponding to the excitation from the right side, as are indicated by the big arrows.

Figure 2

Linear transmission of the system presented in Fig. 1. Without loss of generality, we put here $N=1$, $E_{d1,d2}=0$, and $V_{1,2}=0.6$.

Figure 3

(a) Nonlinear transmission of opposite incident directions. Here $N=1$, $M=4$, $E_{d1,d2}=0$, $V_{1,2}=0.6$, $\lambda =1$, and incident power ${\left|I\right|}^2=0.05$. (b) The same plot as (a) except for ${\left|I\right|}^2=0.08$. Solid blue/dashed red color indicates the forward/backward incident direction throughout this paper, as is indicated in Figs. 1 and 3.

Figure 4

(a) The dependence of nonlinear transmission on the input power of the system for opposite incident directions (frequency $\omega =0.28$). Here, $N=1$, $M=4$, $E_{d1,d2}=0$, $\lambda =1$, and $V_{1,2}=0.6$. Solid lines represent the forward excitation, while dashed lines indicate the backward one. (b) The corresponding $T_{LR}/T_{RL}$ contrast ratio versus input power in (a). (c), (d) The same plots as (a) and (b) except for $\omega =0.45$. (a)–(d) share a similar $x$ label. The arrows indicate the transition directions between two stable states.

Figure 5

(a) Dynamics of the system at reversal incident direction with a Gaussian pulse with $I=I_{0}exp[-{(t-t_0)}^2/W^2]sin\left(\omega t\right)$, where $W=1400$ and $\omega =0.14$. The geometry parameters are similar with those in Fig. 4. The forward directions of the diode at specified pulse times are indicated by the insets. (b) Transmissions (thin lines) derived from (a) and the corresponding analytical results (thick lines). (c) Time evolutions of the nonlinear cavity excitations. (d) The effective pumping rates of the cavity. Solid lines stand for the forward excitation, while dashed lines represent the backward case.

Figure 6

(a) The FDTD results of the nonlinear transmission at reversal incident directions. A Gaussian pulse with a carrier frequency $f=0.378$ $2\pi c/a$ and 20-ps duration is used as an input probe signal. (b)–(e) are the corresponding instantaneous electric field ${\left|E\right|}^2$ distribution marked b–e in (a), respectively. The structure details of the PhCs are outlined by the green lines. The side-coupled cavity on the right is with Kerr nonlinearity. (b)–(e) are normalized with each maximum and are saturated for better visualization. The FDTD grid is nonuniform. The grid size near the defect is $a/100$ to tell the small feature, while the others are $a/50$. The computation domain is surrounded by perfect matching layers to absorb outgoing wave.

Figure 7

(a) The FDTD results of the pulse dynamics at reversal incident directions ($\omega =0.3782\pi c/a$). The input signal, which is used as a probe pulse to access the bistability, is shown by the dotted line. (b) Reconfigurable nonreciprocity driven by a pump pulse whose duration is comparable to the nonlinear cavity's lifetime. The maximum amplitude of the pump pulse is one third of the probe one. The pump pulse is superimposed upon the input Gaussian pulse, as is shown by the dotted line in (b). The carrier frequency of the pump pulse is the same as the probe pulse [23].