Online SupplementaryMaterials
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:
1MOE 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:
Due to the page limit, the enhanced optical transmission (EOT) phenomenon under various exciting wavelengths andthe surface plasmon polariton (SPP)dispersion relationof the horizontal metal-insular-metal (MIM) cavitywith various geometric parameterspresented in“The DispersionRelationship of SPPWavelength in the Horizontal Cavity withDifferent Geometries” of the manuscriptare shown here.
1. We set the wafer layer thickness =50nm and vary the slit width and the film thickness .
1.1With =30nm and =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 widthis shown below.
FigureS1TEas a function of the antenna width with incident wavelengthsfrom 500to 1000nm in every 50nm, with=30nm, and = 200nm.
Thus,we obtain from Fig. S1 the SPP wavelengthsof(nm) = 218,243, 281, 308, 308, 333, 363, 400, 425, 475, 436for the incident wavelengths from 500 to 1000nm in every 50nm respectivelyshownin 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 S2Numerically simulated (black squares) and theoretical (red line) SPP dispersion relationswith=30nm and =200nm.
Formula (A7) indicates that the dispersion relation of SPP wavelengthis a function ofwafer thickness only,for chosen materials. Therefore, with =50nm fixed, even the slit width and the film thickness are varied, the theoretical red solid line remains the same as shown in Fig. 5(a).
1.2The same as in Case 1.1 except for =100nm, the transmission efficiency of the nano-slit as a function of the antenna width is shown below.
Figure S3The same as in Fig S1, except for=100nm.
Thus, we obtain from Fig. S3 the SPP wavelengthsof(nm) = 210, 250, 291, 275, 308, 333, 363, 388, 413, 438, 463nm for the incident wavelengths from 500 to 1000nm in every 50nm respectivelyshownin 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=30nm and =100nmin the 550nm wavelength, the Fabry-Perot-like resonancephenomenon 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 theFabry-Perot-like resonance condition in the horizontal cavityfor the incident wavelength of 550nm.
Figure S4The same as in Fig. S2 except for=100nm.
1.3The same as in Case 1.1 except for=300nm, the transmission efficiency of the nano-slit as a function of the antenna width is shown below.
Figure S5The same as in Figs. S1 and S3, except for=300nm.
We then obtain from Fig. S5 the SPP wavelengthsof(nm) = 210, 244, 258, 275, 300, 333, 363, 388, 413, 438, 462nm for the incident wavelengths from 500 to 1000nm in every 50nm respectivelyshownin 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 S6The same as in Figs. S2 and S4except for=300nm.
1.4The same as in Case 1.1 except for=40nm, the transmission efficiency of the nano-slit as a function of the antenna width is shown below.
Figure S7The same as in Fig. S1, except for=40nm.
Again from Fig. S7we can obtain the SPP wavelengthsof(nm) = 215, 250, 269, 292, 308, 338, 363, 400, 450, 412, 462nm for the incident wavelengths from 500 to 1000nm in every 50nm respectivelyshownin 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 S8The same as in Fig. S2except for=40nm.
1.5The same as in Case 1.1 except for=50nm, the transmission efficiency of the nano-slit as a function of the antenna width is shown below.
Figure S9The same as in Figs. S1 and S7, except for=50nm.
From Fig. S7we obtain the SPP wavelengthsof(nm) = 210, 250, 258, 283, 308, 350, 375, 388, 425, 425, 463nm for the incident wavelengths from 500 to 1000nm in every 50nm respectivelyshownin 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 S10The same as in Figs. S2 and S8, except for=50nm.
2. We thenset theslit width =30nmand film thickness =200nm respectively and vary the thickness of wafer layer .
2.1With the thickness of wafer layer =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 is shown below.
Figure S11TEas a function of the antenna width with incident wavelengths from 500to 1000nm in every 50nm, with=30nm, = 200nm, and = 80nm.
Thus, we obtain from Fig. S11 the SPP wavelengthsof(nm) =250, 275, 300, 325, 350, 375, 400, 425, 438, 575, 531nm for the incident wavelengths from 500 to 1000nm in every 50nm respectivelyshownin 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=30nm, = 200nm, and = 80nm.
2.2The same as in Case 2.1 except for=20nm, the transmission efficiency of the nano-slit as a function of the antenna width is shown below.
Figure S13The same as in Fig. 11except for= 20nm.
Then, we obtain from Fig. S13 the SPP wavelengthsof(nm) =180, 157, 200, 225, 238, 258, 275, 300, 313, 338, 350nm for the incident wavelengths from 500 to 1000nm in every 50nm respectivelyshownin 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. Italso shows that thetransmittance can be enhanced 25 times with antenna width of 800nmin comparison to that without the antenna under excitationwavelength of 650 nm.
Figure S14The same as in Fig. S12, except for= 20nm.
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