Online Supplementary Materials
Journal: Plasmonics
Title: Interaction between two perpendicular Fabry-Perot-like resonances of the antenna-dielectric-slit structure
and their influences on the transmission enhancement
Authors: Qiao Wang, 1 Xiaogang Wang, 1,2,* Shifa Wu1
Affiliations:
1
MOE Key Lab of Materials Modification by Beams, School of Physics & Optoelectronic Technology, Dalian
University of Technology, Dalian 116024, China
2
State Key Lab of Nuclear Physics and Technology and School of Physics, Peking University, Beijing
100871, China
*
Corresponding author. E-mail: xgwang@pku.edu.cn
Due to the page limit, the enhanced optical transmission (EOT) phenomenon under various exciting
wavelengths and the surface plasmon polariton (SPP) dispersion relation of the horizontal metal-insular-metal
(MIM) cavity with various geometric parameters presented in “The Dispersion Relationship of SPP
Wavelength in the Horizontal Cavity with Different Geometries” of the manuscript are shown here.
1. We set the wafer layer thickness tl = 50nm and vary the slit width ws and the film thickness t s .
1.1 With ws =30nm and t s =200nm, a series of incident light with wavelengths from 500 to 1000nm in
every 50nm is impinged from the top of the structure. The transmission efficiency of the nano-slit as a function
of the antenna width wa is shown below.
Figure S1 TE as a function of the antenna width
wa
with incident wavelengths from 500 to 1000nm in every
1
50nm, with ws =30nm, and
t s = 200nm.
Thus, we obtain from Fig. S1 the SPP wavelengths of sp (nm) = 218, 243, 281, 308, 308, 333, 363, 400,
425, 475, 436 for the incident wavelengths from 500 to 1000nm in every 50nm respectively shown in black
points in Fig. S2. The red solid line in the figure represents the theoretical result of the SPP dispersion
relationship derived from (A7) in Appendix.
Figure S2 Numerically simulated (black squares) and theoretical (red line) SPP dispersion relations with
and
ws =30nm
t s =200nm.
Formula (A7) indicates that the dispersion relation of SPP wavelength is a function of wafer thickness tl
only, for chosen materials. Therefore, with tl =50nm fixed, even the slit width ws and the film thickness t s
are varied, the theoretical red solid line remains the same as shown in Fig. 5(a).
1.2 The same as in Case 1.1 except for t s =100nm, the transmission efficiency of the nano-slit as a
function of the antenna width wa is shown below.
2
Figure S3 The same as in Fig S1, except for
t s =100nm.
Thus, we obtain from Fig. S3 the SPP wavelengths of sp (nm) = 210, 250, 291, 275, 308, 333, 363, 388,
413, 438, 463nm for the incident wavelengths from 500 to 1000nm in every 50nm respectively shown in black
points in Fig. S4. The red solid line in the figure again represents the theoretical result of the SPP dispersion
relationship derived from (A7) in Appendix.
It should be pointed out that with slit geometry of ws =30nm and t s =100nm in the 550nm wavelength,
the Fabry-Perot-like resonance phenomenon in the horizontal cavity is significantly weakened. Therefore, as
more coupling effect of slit and horizontal cavity takes into account, the MIM cavity model is not a good
approximation. Thus, we calculated the SPP wavelength in the horizontal cavity from the detailed magnetic
field distribution. It shows that the antenna widths of 150, 400, 650, 900, and 1150nm satisfy the
Fabry-Perot-like resonance condition in the horizontal cavity for the incident wavelength of 550nm.
Figure S4 The same as in Fig. S2 except for
t s =100nm.
1.3 The same as in Case 1.1 except for t s =300nm, the transmission efficiency of the nano-slit as a
function of the antenna width wa is shown below.
3
Figure S5 The same as in Figs. S1 and S3, except for
t s =300nm.
We then obtain from Fig. S5 the SPP wavelengths of sp (nm) = 210, 244, 258, 275, 300, 333, 363,
388, 413, 438, 462nm for the incident wavelengths from 500 to 1000nm in every 50nm respectively shown
in black points in Fig. S6. The theoretical result of the SPP dispersion relationship derived from (A7) in
Appendix is plotted as the red solid line in the figure.
Figure S6 The same as in Figs. S2 and S4 except for
t s =300nm.
1.4 The same as in Case 1.1 except for ws =40nm, the transmission efficiency of the nano-slit as a
function of the antenna width wa is shown below.
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Figure S7 The same as in Fig. S1, except for
ws =40nm.
Again from Fig. S7 we can obtain the SPP wavelengths of sp (nm) = 215, 250, 269, 292, 308, 338,
363, 400, 450, 412, 462nm for the incident wavelengths from 500 to 1000nm in every 50nm respectively
shown in black points in Fig. S8. The theoretical result of the SPP dispersion relationship derived from
(A7) in Appendix is also plotted as the red solid line in the figure.
Figure S8 The same as in Fig. S2 except for
ws =40nm.
1.5 The same as in Case 1.1 except for ws =50nm, the transmission efficiency of the nano-slit as a
function of the antenna width wa is shown below.
5
Figure S9 The same as in Figs. S1 and S7, except for
ws =50nm.
From Fig. S7 we obtain the SPP wavelengths of sp (nm) = 210, 250, 258, 283, 308, 350, 375, 388,
425, 425, 463nm for the incident wavelengths from 500 to 1000nm in every 50nm respectively shown in
black points in Fig. S10. The theoretical result of the SPP dispersion relationship derived from (A7) in
Appendix is also plotted as the red solid line in the figure.
Figure S10 The same as in Figs. S2 and S8, except for
ws =50nm.
2. We then set the slit width ws =30nm and film thickness t s =200nm respectively and vary the thickness
of wafer layer tl .
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2.1 With the thickness of wafer layer tl =80nm, a series of incident light with wavelengths from 500 to
1000nm in every 50nm is impinged from the top of the structure. The transmission efficiency of the nano-slit
as a function of the antenna width wa is shown below.
Figure S11 TE as a function of the antenna width
50nm, with ws =30nm,
wa
with incident wavelengths from 500 to 1000nm in every
t s = 200nm, and tl = 80nm.
Thus, we obtain from Fig. S11 the SPP wavelengths of sp (nm) =250, 275, 300, 325, 350, 375, 400, 425,
438, 575, 531nm for the incident wavelengths from 500 to 1000nm in every 50nm respectively shown in black
points in Fig. S10. For the incident wavelength of 900nm, the transmission peaks are not obvious in Fig. S11.
It is probably due to the poor confinement of SPP in the horizontal MIM cavity for thick dielectric layer at
near-infrared region. As a comparison, the theoretical result of the SPP dispersion relationship derived from
(A7) in Appendix is also plotted as the red solid line in the figure.
Figure S12 Numerically simulated (black squares) and theoretical (red line) SPP dispersion relations with ws =30nm,
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t s = 200nm, and tl = 80nm.
2.2 The same as in Case 2.1 except for tl =20nm, the transmission efficiency of the nano-slit as a function
of the antenna width wa is shown below.
Figure S13 The same as in Fig. 11 except for
tl = 20nm.
Then, we obtain from Fig. S13 the SPP wavelengths of sp (nm) =180, 157, 200, 225, 238, 258, 275, 300,
313, 338, 350nm for the incident wavelengths from 500 to 1000nm in every 50nm respectively shown in black
points in Fig. S12. As a comparison, the theoretical result of the SPP dispersion relationship derived from (A7)
in Appendix is plotted as the red solid line in the figure. It also shows that the transmittance can be enhanced
25 times with antenna width of 800nm in comparison to that without the antenna under excitation wavelength
of 650 nm.
Figure S14 The same as in Fig. S12, except for tl = 20nm.
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