Asymmetrical excitation of surface plasmon polaritons on blazed gratings at normal incidence

We present results of numerical simulations and preliminary experiments to investigate and characterize the effect of asymmetrical coupling of normally incident light to surface plasmon polaritons (SPPs) on metallic blazed gratings. Two types of blazed gratings are investigated, a two-dimensional (2D) area-coded binary grating and a one-dimensional (1D) slanted sinusoidal grating. The 2D blazed grating, which can be fabricated with standard $e$-beam lithography, is shown to have the same ability as the classical 1D blazed grating to enhance the strength of the $-1\text{st}\left(+1\text{st}\right)$ evanescent order over the $+1\text{st}\left(-1\text{st}\right)$ counterpart, which leads to the asymmetrical excitation of two counterpropagating SPP modes on the grating surface. The 1D blazed grating, as a reference, is also studied experimentally to verify the previous theoretical predictions. In our first experiments, the observed asymmetrical coupling effect is relatively weak compared with the optimal designs due to many practical limitations. However, good agreement between theory and experiment has been obtained, and physical insight concerning the observed SPP coupling phenomena has been gained. Further measures to realize stronger asymmetrical excitation of SPPs on blazed gratings at normal incidence are discussed.

Figure 1

(Color online) Geometries of (a) a BLACES and (b) a slanted sinusoidal grating. ${\text{SPP}}^{\pm 1}$ refer to the two SPP modes asymmetrically excited by the $\pm 1\text{st}$ evanescent orders at normal incidence (the lengths of arrows show the relative strength).

Figure 2

(Color online) Optimization of a BLACES with period $d=610\text{nm}$ under an $x$-polarized illumination with ${\lambda }_0=633\text{nm}$. (a) Amplitude ratio $r_{\pm 1}$ as a function of the transverse period $p$ and the grating layer thickness $h$. The white color shows the region with $r_{\pm 1}>500$. (b) Wavelength spectra of the BLACES with $p=312.5\text{nm}$ and $h=88\text{nm}$ corresponding to point A in (a). $H_{z\left(\pm 1\right)0}$ and $H_{z00}$ are amplitudes of the reflected $\pm 1\text{st}$ and zeroth orders normalized with the incident magnetic field amplitude. The total diffraction efficiency of all, reflected and transmitted, diffraction orders is also demonstrated.

Figure 3

(Color online) Distribution of the instantaneous $\mathbf{E}$ and $\mathbf{H}$ vectors as well as the time-averaged Poynting vector $⟨\mathbf{S}⟩$ in the $xz$ planes 1500–0 nm above the air-metal interface, as shown in (a)–(f). The arrow length is proportional to the magnitude of the vector.

Figure 4

(Color online) Amplitudes $\left|H_{zmn}\left(y\right)\right|$ of the $\left(m,n\right)\text{th}$ reflected orders normalized with the incident magnetic field amplitude (i.e., the incident magnetic field has unit amplitude). Note that the air-metal interface is at $y=h=88\text{nm}$.

Figure 5

(Color online) (a) Top-view SEM image of a fabricated BLACES sample. (b) Side-view schematic, corresponding to the dashed line in (a), of the sample in characterization with back-side illumination. ${\text{SPP}}^{\pm 1}$ have the same meaning as those in Fig. 1.

Figure 6

(Color online) Numerical spectra of the fabricated BLACES sample. The notations are the same as those in Fig. 2 except that the amplitudes are for the transmitted orders.

Figure 7

(Color online) Near-field strength (square root of the field intensity) scanned in $x$ direction across the illumination spot. The scan length is $100\mu \text{m}$ and the wavelength is changed from 1460 to 1580 nm with a step of 4 nm. The spot diameter is about $20\mu \text{m}$. (a) TE ($z$-polarized) incidence. (b) TM ($x$-polarized) incidence. The amplitude scale is in arbitrary units.

Figure 8

(Color online) $x\text{−}y$ scan of field intensity above the air-Au interface under TM illumination. (a)–(c): scans of the left side, across the central spot, and of the right side, respectively, at ${\lambda }_0=1484\text{nm}$. (d)–(f): the same as (a)–(c) but at ${\lambda }_0=1532\text{nm}$. The figure color representation is the same as that in Fig. 7. Note that in this figure the origin of $y$ axis is moved to the air-metal interface for the convenience of illustration.

Figure 9

(Color online) FFT analysis of the grating topography and the TM fields measured in the left and right regions indicated in Fig. 7b, for (a) ${\lambda }_0=1484\text{nm}$ and (b) ${\lambda }_0=1532\text{nm}$. Several key peaks are labeled with X for $k$ and Y for the amplitude.

Figure 10

(Color online) FFT analysis of the grating topography and the TM field measured on the left side of the spot with $L=100\mu \text{m}$, $N=512$, and ${\lambda }_0=1532\text{nm}$.

Figure 11

(Color online) Similar scan as Fig. 7 on the left side of the spot under TM illumination. The color scale is in arbitrary units.

Figure 12

(Color online) Optimization of the slanted grating with $d=1057.9\text{nm}$. (a) Diffraction efficiency of the zeroth reflected order; (b) amplitude ratio $r_{\pm }$ (in the central white region, $r_{\pm }>50$).

Figure 13

SEM images of (a) a slanted sinusoidal photoresist grating and (b) the final grating after Al deposition.

Figure 14

(Color online) Sketch of the SPPs far-field imaging system.

Figure 15

Far-field images of the excited SPPs on an Al slanted grating sample under (a) TM and (b) TE illuminations.

Figure 16

Far-field imaging of the SPP tails on the same sample mounted (a) as in Fig. 1b and (b) with the $\pm x$ directions reversed.

Figure 17

(Color online) Exponential fit to a measured right tail.