Resonant Guided Wave Networks

A resonant guided wave network is an optical materials design consisting of power-splitting elements arranged at the nodes of a waveguide network. The resulting wave dispersion depends on the network layout due to localized resonances at several length scales in the network. These structures exhibit both localized resonances with a $Q\sim 80$ at 1550 nm wavelength as well as photonic bands and band gaps in large periodic networks at infrared wavelengths.

Figure 1

(a) 2D RGWN plasmonic implementation and three possible resonant loop trajectories (dashed lines). Power-splitting properties of the emerging pulses in an $X$ junction: (b) intensity and (c) phase difference, relative to the exciting pulse. ${\lambda }_0=1.5\mu \mathrm{m}$.

Figure 2

Resonance buildup in a $2\times 2$ RGWN. (a) Two out-of-phase input pulses result in constructive interference in the same waveguides from which the pulses entered the junction ($+/-$ correspond to two $\pi$-shifted phase states of pulse). (b) Steady states of waves resonating in a $2\times 2$ network where each pair of pulses excites the $X$ junctions out of phase. MIM RGWN: (c) Schematics and snapshots of $H_z$ (normalized to the instantaneous maximal value) at the third to the seventh power-splitting events for a 2D-FDTD simulation. $d=0.25\mu \mathrm{m}$, $L=6\mu \mathrm{m}$. Channels RGWN: (d) 3D-FDTD of 2D topography of air channel waveguides network; two snapshots of the $H$ field in the parallel plane $0.1\mu \mathrm{m}$ underneath the Au-air interface ($z=0.9\mu \mathrm{m}$) and an inset showing the $H$-field distribution in the plane normal to the Au-air interface ($y=0$). ${\lambda }_0=1.5\mu \mathrm{m}$ and $E_x$-polarized excitation.

Figure 3

$Q$ factors of Au/air MIM $2\times 2$ RGWN resonator. (a) $Q$ factors from simulation results compared with those resulting from incoherent power splitting. The $Q$ factor contribution of the material loss is calculated from the attenuation coefficient [17]. (b) $Q$ factor vs the refractive index of a $1\mu \mathrm{m}$ long defect. $d=0.25$, $L=4\mu \mathrm{m}$, ${\lambda }_0=1.5\mu \mathrm{m}$.

Figure 4

Photonic band structure of an infinitely large periodic RGWN. (a) Optical DOS for a square periodic unit cell with $d=0.25\mu \mathrm{m}$, $L=3\mu \mathrm{m}$. (b) Dependence of photonic band III [at $\Gamma$ point at $\sim 180\mathrm{THz}$ in (a)] on $L$ for $d=0.3\mu \mathrm{m}$, and on $d$ for $L=4\mu \mathrm{m}$. (c) Photonic band gap formed in the optical DOS in rectangular periodic unit cell. In the $x$ direction: $d=0.24\mu \mathrm{m}$, $L=2\mu \mathrm{m}$; in the $y$ direction: $d=0.2\mu \mathrm{m}$, $L=1.2\mu \mathrm{m}$.

Figure 5

3D RGWN: (a) rendering of a 3D RGWN building block (6-arm junction). Optical DOS of an infinite 3D network spaced periodically with cubic periodic unit cell (b) $L=2\mu \mathrm{m}$ and (c) $L=2.2\mu \mathrm{m}$.