“Rainbow” Trapping and Releasing at Telecommunication Wavelengths

The reported “trapped rainbow” storage of THz light in metamaterials and plasmonic graded structures has opened an attractive new method to control electromagnetic radiation. Here, we show how, by incorporating the frequency-dependent dielectric properties of the metal, the graded grating structures developed for “trapped rainbow” storage of THz light in $\mu \mathrm{m}$ level can be scaled to nm level for telecommunication waves for applications in optical communication and various nanophotonic circuits.

Figure 1

Dispersion curves calculated for $d=200\mathrm{nm}$ and $p=400\mathrm{nm}$ with different groove depths ($h=140$ and 230 nm). Inset: a schematic of grating structures with a constant depth and graded depth. In this figure, the $x$ axis is the reduced propagation constant with a unit of $k_{x}p/2\pi$; the $y$ axis is the reduced frequency with a unit of $\omega p/2\pi c$, here $c$ is the light velocity in vacuum.

Figure 2

Trapped rainbow for telecommunication wavelengths obtained by using two-dimensional FDTD simulations: (a)–(d) correspond to the 2D field distribution at four different wavelengths of 1.33, 1.45, 1.55, and $1.65\mu \mathrm{m}$. The depth of the grating structure changes from 20 to 270 nm linearly in a $25\mu \mathrm{m}$ region. In these simulations, the period and width of the grating structure are 400 and 200 nm, respectively. Nonuniform mesh sizes are employed in this modeling: The edge grid sizes are $\Delta x=10\mathrm{nm}$ and $\Delta z=2\mathrm{nm}$, and body grid sizes are $\Delta x=20\mathrm{nm}$ and $\Delta z=20\mathrm{nm}$. The simulation time $T=2000\mu \mathrm{m}/c$, here $c$ is the light velocity in vacuum.

Figure 3

Dispersion curves calculated for $d=200\mathrm{nm}$, $p=400\mathrm{nm}$ and $h=70\mathrm{nm}$ with different temperatures. Inset: the temperature dependence of the refractive index of GaAs around $1.55\mu \mathrm{m}$ wavelength. Its thermo-optical coefficient is calculated with the fitting equation: $dn/dT=n(b_0+b_{1}T+b_2{T}^2+b{}_{3}T^3+b_4{T}^4+b_5{T}^5+b_6{T}^6)$. For GaAs at $1.53\mu \mathrm{m}$ wavelength, $b_0=-3.059\times {10}^{-5}$, $b_1=12.03\times {10}^{-7}$, $b_2=-6.442\times {10}^{-9}$, $b_3=1.820\times {10}^{-11}$, $b_4=-2.720\times {10}^{-14}$, $b_5=2.047\times {10}^{-17}$, $b_6=-6.086\times 10E^{-21}$. This equation is valid from 85 to 920 K [19].

Figure 4

(a) Lifetimes of the SPP modes for an incident wavelength of $1.70\mu \mathrm{m}$ calculated using Eq. (S4) in [15]. Inset: Dispersion curve for the flat silver/air interface calculated by Eq. (S2) (solid line) [15] and the FDTD method (dots). (b) Estimate of the SPP lifetime, $\tau$, at the wavelength of $1.70\mu \mathrm{m}$ along the grating surfaces for various depths. Blue dots are extracted raw data listed in Table S1 [15]. The dashed line is an exponential growth fit to guide the eyes.