Mimicking electromagnetically induced transparency by spoof surface plasmons

We analytically show how an electromagnetically induced transparency (EIT)–like spectral response is attained by using spoof surface plasmons. We propose prism-coupled double-layer slit arrays to achieve this. The reflection spectrum from this system has a nonabsorbing window between the symmetric and antisymmetric spoof surface plasmon resonances due to the destructive interference of the spoof surface plasmons on over- and under-layer slit arrays. The optical pulse is significantly delayed inside this nonabsorbing window as it is in other EIT systems. Through the formal equivalence between the coupled spoof surface plasmons on slit arrays and the coupled whispering gallery modes inside the microspheres, the relation between our system and the coupled resonator induced transparency (CRIT) system is clarified.

Figure 1

Single-layer slit array with spacing $a$, thickness $h$, and period $d$. Origin of $x$ axis is at the center of the spacing and origin of $z$ axis is at the upper surface of the slit.

Figure 2

(a) Dispersion relations of spoof surface plasmons on single-layer slit arrays of two different thicknesses $h$. Red line indicates $h=300\mu \mathrm{m}$, and blue line indicates $h=600\mu \mathrm{m}$. Spacing $a=10\mu \mathrm{m}$ and period $d=200\mu \mathrm{m}$ are kept the same for two slit arrays. Solid lines indicate symmetric modes and dashed lines indicate antisymmetric modes. Dashed black line is the light line $\omega =ck$. Dashed yellow line indicates incident evanescent field $\omega =ck/\left(\sqrt{{\epsilon }_1}\sin \theta \right)$. Incident angle $\theta ={20}^{\circ }$ and permittivity of prism ${\epsilon }_1=11.56$ are same values as those used in Fig. 4. Wood-Rayleigh anomaly occurs at frequency where incident evanescent field crosses the light line (black circle). (b) Electromagnetic field distributions ($H_y$ and $E_x$) of a symmetric-mode spoof surface plasmon with frequency and wave vector represented by $f_{\mathrm{sym}}$ in the inset of (a) (black triangle).

Figure 3

(a) Schematics of a prism-coupled single-layer slit array. Spacing $a$, thickness $h$, and period $d$ are the same indexes as specified in Fig. 1. Distance between slit array and prism is denoted by $b$. Origin of $x$ axis is at center of slit spacing and origin of $z$ axis is at upper surface of slit array. Permittivity of the prism is denoted by ${\epsilon }_1$ and incident angle is denoted by $\theta$. (b) First term on the right side of Eq. (15) represents reflection from perfectly conducting plate as shown in this figure. (c) Under condition where Eq. (28) is satisfied, we can insert infinitely thin perfectly conducting plate at $z=-h$ interface without disturbing electromagnetic field distribution.

Figure 4

Reflection coefficients of prism-coupled single-layer slit arrays of two different thicknesses $h$. Black line is $h=250\mu \mathrm{m}$ slit array and the red line is $h=300\mu \mathrm{m}$ slit array. Spacing $a=10\mu \mathrm{m}$ and period $d=200\mu \mathrm{m}$ are kept the same for two slit arrays.

Figure 5

Schematics of double-layer slit arrays. Distance between two layers is denoted by $l$. Origin of $z$ axis is at upper surface of under-layer slit array. Spacing $a$, thickness $h$, and period $d$ are the same indexes as specified in Fig. 1.

Figure 6

(a) Dispersion relations of spoof surface plasmons on double-layer slit arrays. Dimensions of slit arrays are $a=10\mu \mathrm{m}$, $d=200\mu \mathrm{m}$, $h=300\mu \mathrm{m}$, and $l=100\mu \mathrm{m}$. Solid green line is symmetric mode and solid red line is antisymmetric mode. Dotted black line is the light line $\omega =ck$ and dashed yellow line is incident evanescent field $\omega =ck/\left(\sqrt{{\epsilon }_1}\sin \theta \right)$. ${\epsilon }_1=11.56$ and $\theta ={20}^{\circ }$ are same values used in Fig. 8. Blue lines are perfectly reflecting conditions calculated from Eq. (33) around the frequency of the incident evanescent field. f1 and f2 in inset correspond to resonance frequencies of symmetric and antisymmetric modes. f3 corresponds to the perfectly reflecting frequency. (b), (c) Electromagnetic field distributions ($H_y$ and $E_x$) of (b) symmetric and (c) antisymmetric mode spoof surface plasmons on double-layer slit arrays with frequencies and wave vectors represented by f1 and f2.

Figure 7

(a) Schematics of prism-coupled double-layer slit arrays. Origin of $z$ axis is at the upper surface of under-layer slit array. (b) If we regard the spoof surface plasmons as surface resonators (a) can be regarded as (b). (c) Schematics of CRIT system. Two microspheres are evanescently coupled with optical fiber.

Figure 8

Reflection coefficients of prism-coupled double-layer slit arrays. Dimensions of slit arrays are $a=10\mu \mathrm{m}$, $d=200\mu \mathrm{m}$, and $h=300\mu \mathrm{m}$. Distance between two layers was varied from $l=50\mu \mathrm{m}$ to $l=300\mu \mathrm{m}$ in steps of $50\mu \mathrm{m}$. f1 and f2 are symmetric- and antisymmetric-mode resonances. f3 is perfect reflection related to Eq. (33). Indexes f1, f2, and f3 correspond to indexes in inset of Fig. 6a. Red dotted lines are reflection coefficients of a single-layer slit array with the same dimensions [over layer was removed in Fig. 7a].