Fano Resonances in Ag-Air-SiO2 Nanostructure

LI Shu, LIU Huang-qing*, CHONG Gui-shu,CHEN Shu-guang, ZHAI Xiang, XIAO Shi-fang , ZOU Yang,2

(1. School of Physics and Electronics, Hunan University, Changsha 410082, China;2. Changsha No.1 Railway Middle School, Changsha 410001, China)

Abstract: Fano resonances in Ag-Air-SiO2 nanostructure were investigated by Finite-difference time-domain (FDTD). It could be observed a redshift with the growth of horizontal length l of silver film for the resonance peaks of the modes mj(j=2, 3). Fano resonance was related with the Ag-Air-SiO2 periodic structure and SiO2. The modes mj (j=2,3) presented a redshift and the Fano was becoming more and more obvious with the increment of transverse length L of SiO2. In addition, the Fano resonances were also closely related with the permittivity (negative value of the real part) of the silver film. The Fano resonances could be obtained when -ε′m=4 000 and -ε′m=6 000 in the aperiodic Ag-Air-SiO2 structure.

Key words: Fano resonances; Ag-Air-SiO2 ; nanostructure

1 Introduction

Surface plasmon polaritons (SPPs) can propagate along the surface of a metal-dielectric system and exponentially decay[1-2]. Recently, SPPs have been widely studied in optics[3-4]. Because of their unique properties, many nanoscaled devices have been simulated and experimentally confirmed, such as nanowaveguide[5-6], optical amplifiers[7-8]and optical switch[9-10]. Now, more and more nanostructures (such as nanofilm) have been prepared to observe some novel physical characters like electromagnetic induced Fano-type resonance[11-14]. In an asymmetric structure, two different kinds of interfere with each other generate a Fano-resonance. Because of its potential wide applications[15-16], Fano resonance has attracted wide attention both in theory and in experiment[11]. Fano resonance has the bright and dark modes[17-19]for the different excited ways under the incident light. The former can directly and strongly interact with the incident light while the latter is excited by the bright mode and mostly interacts with the incident light. In addition, asymmetric nanostructure is the most commonly used to cause Fano resonance[20]. As Fano resonance is dependent of material structure, such as three-dimensional size, dielectric constant and refractive index,etc. Søndergaardetal. studied the gap plasmon polariton optical resonators on rectangular Ag strip and obtained an increase of the length of strips equal to half the slow plasmon polaritons (PPs) wavelength resulting in a scattering resonance[21]. On the basis of our previous researches[22-23], we use the silver-air-silica structure to study Fano resonance. In this letter, we obtained Fano resonances by changing the size and permittivity of the material in a simpler metal-insulator-insulator (Ag-Air-SiO2) nanostructures.

2 Simulated Device

Fig.1 is the schematics of the simulated device. Periodic boundary conditions are applied along thexdirections. A plane wave with the electric field parallel to thexaxis illuminates normally the periodic structure. The upper layer is covered with Ag film. The lengthlis along thexdirection and the thicknessd1is along theydirection of the Ag film. The medium of the middle layer with the heightd2is air. The bottom layer is silicon dioxide with transverse lengthLand thickness of 300 nm. The position A monitored in the cavity with air was arbitrarily selected because some properties(such as electric field, magnetic field and transmission spectrum) here were independent of the thicknessd2whend2was no more than 50 nm[22]. Thus,d2was selected as 50 nm, which was far less than the wavelength of the incident light.

Fig.1 Schematics of the simulated device

The penetration depth of incident light(or SPPs) is related to the media on both sides of the interface[24]. For metal, the penetration depth of SPPs is

(1)

for the medium, the penetration depth of SPPs is

(2)

here,k0,ε′m,εdandλare wave vector in vacuum, complex permittivity of metal (or SiO2), permittivity of air and the wavelength of the surface plasma(approximate to wavelength of incident wave), respectively. In the simulation, we select the wavelength (λ) range of the incident light from 1 000 nm to 1 700 nm. For SiO2,ε′m=3 andεd=1,δd≈320-544 nm (>300 nm). In other words, near infrared light in this paper can completely pass through silica. Also, for Ag, whenε′m=-1000+10i andεd=1,δm≈5.1-8.6 nm. Because silver is a good conductor, the electromagnetic wave attenuates rapidly in it and the actual penetration depthδis smaller than the previousδm. The penetration depthδis expressed as[25]

(3)

Here,fis frequency of the electromagnetic wave. At the range of 1 000 nm to 1 700 nm, the penetration depthδwas about 3.7-4.8 nm.

Therefore, in the simulation of this paper, the thicknessd1of silver film is 10 nm. Thus, the transmission spectrum may be mainly derived from the diffraction of light at the two ends of the cavity. The simulation results showed that the wave entering the cavity was TM wave,i.e.Ez=Hx=Hy=0.

3 Results and Discussion

Fig.2 indicated the transmission spectra of Ag-Air-SiO2structure. The geometric parameters of the structure areL=1 800 nm,d1=10 nm andd2=50 nm, respectively. For comparison, the transmission spectrum of silver film with the same thicknessd1=10 nm was obtained by simulation. One resonant peak at about 1 093 nm can be observed for pure silver, which indicated that silver film has strong absorption at about 1 093 nm which is independent of the transverse lengthlof silver film. For Ag-Air-SiO2periodic structure, three resonant wavelengthsλspp, which is completely different from that of pure silver, could be observed at about 1 021 nm, 1 121 nm and 1 370 nm, corresponding to three kinds of modes mj(j=1, 2, 3), respectively. The peaks of the modes mj(j=2, 3) appeared a redshift with the growth of horizontal lengthl. It could be observed an obvious Fano resonance peak(especially whenl=1 300 nm and 1 320 nm), which was considered to be related with the Ag-Air-SiO2periodic structure and SiO2.

Fig.2 Transmission spectra of periodic Ag-Air-SiO2structure with different transverse lengthlof silver film and transmission spectrum of pure Ag. The geometric parameters areL=1 800 nm,d1=10 nm andd2=50 nm, respectively.

After changing the periodic condition to PML (perfect matching layer) by FDTD, the transmission spectra of Ag-Air-SiO2aperiodic structure with different transverse lengthlwere seen in Fig.3(a). It could be observed one transmission peaks at about 1 450 nm, corresponding to the mode m3in Fig.2, which exhibited a redshift and whose transmission decreased with the increment of transverse lengthlfrom 1 300 nm to 1 420 nm. Fig.3(b) indicated the reflection spectra of pure SiO2with different transverse lengthLfrom 1 300 nm to 1 700 nm. It could be observed one weak peak at about 1 020 nm and one obvious peak at about between 1 140 nm and 1 230 nm, which showed a redshift with the increment ofL. The above results showed that the mode m1in Fig.2 mainly originated from SiO2, the mode m2came from Ag and SiO2, and the mode m3was attributed to boundary reflection of Ag-Air-SiO2periodic structure. In other words, transmission spectra of Ag-Air-SiO2periodic structure were the result of a comprehensive effect from the transmission and the edge scattering of silver film, reflection of silicon dioxide and, plasma resonance excited by reflected light of SiO2and boundary reflection of Ag-Air-SiO2periodic structure on the lower surface of silver film.

Fig.3 (a)Transmission spectra of aperiodic Ag-Air-SiO2structure with different transverse lengthlof silver film. (b) Reflection spectra of pure SiO2with different transverse lengthL. The geometric parameters arel=1 300 nm,d1=10 nm andd2=50 nm, respectively.

Changing the transverse lengthL(L=100k,kis positive integers from 11 to 17) of SiO2whenl1=1 300 nm, the results of the simulation were shown in Fig.4. Three resonance modes could be observed in the transmittance spectra of various transverse lengthL. The modes mj(j=2, 3) presented a redshift and the Fano phenomenon was becoming more and more obvious with the increment of transverse lengthL, which showed that the modes mj(j=2, 3) had a strong dependence of transverse lengthL[24-26].

Fig.4 Transmission spectra of different lengthLof SiO2under constant transverse lengthl(1 300 nm) of silver film

The dielectric constantεm(ω) of metal is relative with incident light frequencyω, eigenfrequenciesωpof collective oscillations on surface charges of metals and damping frequencyγof the collective oscillation in the metal. The relationship among them was satisfied with modified Drude model[27-29]:

(4)

in the equation (4),ε∞=3.7,ωp=1.38×1016rad/s andγ=2.73×1013rad/s. As a result, the expression can also be written as

ε′m+ε″mi,

(5)

(6)

where,ε′mandε″mare the real part and imaginary part of the metal dielectric constantεm(ω). In this paper,ω=1.11×1015-1.88×1015rad/s,i.e,ω2≫γ2. Thus, -ε′m≈50.2-153.7 andε″m≈0.7-3.8 could be obtained, in other words, -ε′mis two orders of magnitude higher thanε″m, which is agreed with the result from the reference[30].

Fig.5(a) showed transmission spectra of Ag-Air-SiO2with different permittivityεm=-1000k+10i (k=1, 2, 3, 4 and 5) which was set according to the theoretical analysis above and the other length parameters are set asd1=10 nm,L=1 800 nm andl=1 300 nm. The modes m2could be observed when -ε′mwas no more than 2 000. The wavelengthλsppsof the surface plasmon resonance is related toε′mandε″mof the metal dielectric constant and dielectric permittivityεdof the medium (air), the expression between them is[22]

(7)

here,λ0is the wavelength of the incident wave. In the simulation of this article, -ε′m(=1 000k)≫ε″m(=10) andεd=1, the expression (7) is simplified to be

(8)

Fig.5 Ttransmission spectra of Ag-Air-SiO2with different permittivity. (a)εm=-1000k+10i(k=1, 2, 3, 4, 5). (b)-ε′m<1 000. The length parameters are set asd1=10 nm,L=1 800 nm,l=1 300 nm.

the eqution (8) showedλsppsis less than and close toλ0. And then, the change Δλof wavelength was

-0.85--0.25 nm,

(9)

thus,the maximum relative change Δλof wavelength is about 0.6 nm. Furthermore, according to the eqution (9), Δλis inversely proportional toε′m, namely, increment of dielectric constantε′mmeans reduction of Δλ(blueshift). Owing to -ε′m≥1 000 in the simulation, Δλ→0, namely, the change ofλ0is very small with the increment of the dielectric constant, as was shown in the mode m1of Fig.5(a), which also applies to the mode m1of Fig.5(b) with -ε′m<1 000. Δλof wavelength from Fig.5(b), for different modes mj(j=2, 3), their maximum value of wavelength change Δλis about 30 nm. That is to say, the results of the eqution (9) were great different from those of simulation. In addition, Fano resonance is easier to be realized when

-ε′m<1 000(especially -ε′m= 800) with respect to Fig.5(a).

4 Conclusion

Fano resonances in Ag-Air-SiO2nanostructure were obtained by FDTD in this letter. In a summary, Fano resonance was independent of the transverse lengthlof silver film and could be observed a redshift with the growth of horizontal lengthlof silver film for the resonance peaks of the modes mj(j=2, 3). Fano resonance was also related with the Ag-Air-SiO2periodic structure and SiO2. Changing the transverse lengthLof SiO2, Fano phenomenon was becoming more and more obvious with the increment of transverse lengthL. In addition, the Fano resonances were also closely related with the permittivity (negative value of the real part) of the silver film. The Fano resonances could be obtained when -ε′m=4 000 and -ε′m=6 000 in the aperiodic Ag-Air-SiO2structure. The structure has good filtering characteristics.