Figure 1

Excitation device (in dashed circle) connected to hopping transmission lines.Reuse & Permissions

Figure 2

Beam splitter for excitations. The device nodes are labeled with the integers 1 through 4. The transmission line nodes are indicated by pairs of numbers $r,m$ where the first labels the transmission line and the second labels a node along that transmission line. The hopping interaction coupling strengths between pairs of nodes within the device are labeled by $g_n$, where $n$ is 1 or 2. The hopping interaction coupling strengths between neighboring nodes along the transmission lines are all taken to be equal to $g$. The direction of propagation of the incoming $a_r^{\mathrm{in}}$ and outgoing $a_r^{\mathrm{out}}$ amplitudes for each of the transmission lines is also indicated.Reuse & Permissions

Figure 3

Power transferred to each port (a) and the corresponding phase (b) as a function of normalized frequency for the 50:50 beam splitter described in Fig. 2. The input from port 1 is evenly split in power between ports 3 and 4 at normalized frequency of 1. A 3-dB bandwidth in the unit of $0.2{\omega }_0$ is achieved. The phase difference between the two ports is ${90}^{°}$.Reuse & Permissions

Figure 4

(a) Schematic of a crossover splitter. The coupling strength between the adjacent nanoparticles is labeled on the transmission line connecting the nanoparticles. The power transferred to each port (b) and the corresponding phase (c) are calculated as a function of normalized frequency. The input from port 1 is transmitted to port 3 with an efficiency of $100\%$ at the normalized frequency of 1. The phase difference between the input and output is ${90}^{°}$ at the same frequency. The plot for port 2 overlaps with that of port 1 in the figure.Reuse & Permissions

Figure 5

Bandwidth of the crossover splitter as a function of coupling strength $g_3$, in units of ${\omega }_0$.Reuse & Permissions

Figure 6

(a) Schematic of a phase shifter consisting of a modified 50:50 beam splitter with two detuned nanoparticles. (b) Reflected power from port 1 and the transmitted power to port 2 as a function of normalized frequency. (c) Phase-frequency relation for the reflection from port 1 and the transmission to port 2. The power incident from port 1 shifted in phase by ${50}^{°}$ when it exits port 2. The output intensity is nearly unchanged for a bandwidth in the unit of 0.1 ${\omega }_0$.Reuse & Permissions