Ling-Xi Hu | Min Hu | Sheng-Gang Liu

Abstract—The simulation mechanism of surface plasmon polaritons (SPPs) and localized surface plasmon (LSP) in different structures was studied,including the Au reflection grating (Au grating),Au substrate with dielectric ribbons grating (Au substrate grating),and pure electric conductor (PEC) substrate with Au ribbons grating (Au ribbons grating).And the characteristics of the Smith-Purcell radiation in these structures were presented.Simulation results show that SPPs are excited on the bottom surface of Au substrate grating grooves and LSP is stimulated on the upper surface both of Au ribbons grating grooves and Au grating grooves.Owing to the irreconcilable contradiction between optimizing the grating diffraction radiation efficiency and optimizing the SPPs excitation efficiency in the Au substrate grating,only 40-times enhancement of the radiation intensity was obtained by excited SPPs.However,the LSP enhanced structure overcomes the above problem and gains much better radiation enhancement ability,with about 200-times enhancement obtained in the Au ribbons grating and more than 500-times enhancement obtained in the Au grating.The results presented here provide a way of developing miniature,integratable,tunable,high-powerdensity radiation sources from visible light to ultraviolet rays at room temperature.

Index Terms—Coherent radiation,high-power radiation,localized surface plasmon (LSP),micro-nano structure,Smith-Purcell radiation,surface plasmon polaritons (SPPs).

1.lntroduction

Surface plasmon polaritons (SPPs) have been observed in experiment more than 100 years[1]and the classical theoretical explanation work has also been done more than 50 years[2]-[4].Since 1944,the theoretical work of localized surface plasmon (LSP) has begun[5].The interaction size of SPPs and LSP is in nanoscale,which limits the practical application.Due to the improvement of nanotechnology and nanofabrication which leads to the physics and important applications,SPPs and LSP become research focus again in recent years.SPPs and LSP are widely used in near-field imaging[6]-[9],enhancement of optical transmission[10]-[13],biosensors[14]-[18],and enhancement of radiation[19]-[24].As a crucial means of tunable,broadband,nanoscale free electron light sources with a large radiation frequency range from the millimeter wave to deep ultraviolet,a large number of SPPs or LSP enhanced Smith-Purcell radiation structures have been studied[25]-[35].However,there is no clear explanation of the SPPs and LSP stimulation mechanism in a plenty of structures.

In this study,the excitation mechanism of SPPs and LSP in different structures was studied,including the Au reflection grating (Au grating),Au substrate with dielectric ribbons grating (Au substrate grating),and pure electric conductor (PEC) substrate with Au ribbons grating (Au ribbons grating) stimulated by one bunch of parallel electrons.Also the characteristics of the Smith-Purcell radiation in these structures were observed.When charged particles pass through a periodic structure,the Smith-Purcell radiation is emitted and the radiation wavelength satisfies the formula:λ=D(1/β-cosθ)/∣m∣,whereDis the grating pitch,mis the radiation order,β=ve/cis the relative velocity,veis the speed of excitation electrons,cis the light speed in vacuum,andθis the angle of emission measured from the direction of beam propagation[36],[37].The frequency range of SPPs and LSP in Au structures is the visible light region[38].In this work,the finite-difference timedomain (FDTD) simulation was employed to investigate the excited surface and radiation field.The 10.5-keV(β=0.2) electrons were applied in the whole work,and according to the Smith-Purcell radiation wavelength relationship and the frequency characteristics of excited SPPs and LSP,a 100-nm period grating was chosen in this research.The duty cycle was set as 0.2.In the Au substrate grating,the strongest surface plasmon field is excited on the upper surface of the Au substrate.As the grating depth increases,the frequency of surface plasmon decreases slightly.It meets the properties of SPPs in the layered metal-dielectric structure[28].In the Au ribbons grating,the strongest surface plasmon field is excited on the upper surface of Au ribbons,and as the grating depth increases,the frequency of surface plasmon significantly reduces.Due to the discontinuity of Au in this structure,only LSP can be excited in it.Thence,this surface plasmon mode is the LSP mode.The surface and radiation field characteristics in the Au grating are basically consistent with those in the Au ribbons grating.Although Au in this structure is continuous,only LSP is excited in this structure to enhance the Smith-Purcell radiation.The results show that compared with SPPs enhancement,LSP provides a stronger radiation enhancement capability in the Smith-Purcell radiation.And owing to more free electrons in the Au grating,the radiation in the Au grating is slightly stronger than that in the Au ribbons grating.The results presented here provide the theoretical guidance of developing miniature,integratable,tunable,high-power-density radiation sources from visible light to ultraviolet rays at room temperature.

Fig.1.Structure diagrams (D=100 nm and d/D=0.2):(a) Au substrate grating,(b) Au ribbons grating,(c) Au grating,and (d) PEC grating.

2.Model and Method

The schemes of the Au substrate grating,Au ribbons grating,Au grating,and contrast PEC reflection grating (PEC grating) are shown inFig.1.PEC is the pure electric conductor,which is an ideal conductor with infinite conductivity.The infinite conductivity in PEC leads to negative infinite permittivity and zero skin depth,thence,the total reflection occurs when the electromagnetic field is incident on the surface of PEC.When the operating frequency is much lower than the certain metal material plasma oscillation frequency,the metal can be regarded as PEC.The surface plasmon frequency of Au is in the visible light region,thence,the Smith-Purcell radiation in the visible light region is discussed in this study.Since the plasma oscillation frequency of Al is in the ultraviolet C radiation (UVC:The wavelength range is from 200 nm to 280 nm) region,it can be considered as PEC in the visible light region.The traditional Al grating is a PEC grating in this area.

One bunch of 10.5-keV Gaussian electron beams parallelly passes over the 20-nm position from the grating surface.Since the SPPs or LSP frequency in the Au structure is in the visible light region[38],and considering the Smith-Purcell radiation wavelength properties,a 100-nm period grating was selected in this study.The first-order radiation frequency in the Smith-Purcell radiation was from 500 THz to 750 THz.The duty cycle was 0.2 in the whole research.In the study,the grating depth changed in order to observe the properties of excited surface plasmon,which was used to determine whether it is SPPs or LSP.In this work,the FDTD simulation was employed to study the radiation and surface field characteristics.There were 200 cycles in the gratings,which meets the oscillation convergence condition of the Smith-Purcell radiation.In this study,SiO2was selected as grating ribbons in the Au substrate grating,and the relative permittivity was 2.19.The Drude model,which is a classical model proposed to explain the dielectric properties of metallic materials,was used to describe Au in this work,expressed as relative permittivity of the Au substrateεm=ε∞-/(ω2+jωγ)[39],[40]withωbeing the angular frequency.And the Drude parameters in this study are set as: The frequency infinity relative permittivityε∞=8.9128,the plasma resonance frequencyωp=1.208×1016rad/s,and the plasma collision frequencyγ=8.7894×1013Hz[38],[41].A series of observation probes was set at more than 5 times of the radiation wavelength from the grating surface to obtain the radiation far field information and the interval between observation points was 100 nm.The radiation observation probes are presented inFig.2 (a).In simulation,the spectrum envelope of all observation probes is the radiation spectrum in the Smith-Purcell radiation of the specific grating.The observation probes of the surface field were set at the surface in the middle of the grating.Taking the Au grating as an example,the observation schematic diagram is shown inFig.2.InFig.2 (b),the positions of surface field observation probes from bottom to top are the bottom (0),middle (h/2),upper surface of the grating groove (h),and a position twice the depth from the bottom surface of the grating (2h).

Fig.2.Schematic diagram of observation probes in simulation:(a) radiation far field (the interval between the observation points is about 5 times of the radiation wavelength) and (b) surface field (the distance between the observation probes and the bottom of grating grooves are 0,h/2,h,and 2h,respectively).

3.Results and Analysis

The normalized radiation spectra of the Au substrate grating in different grating groove depths are shown inFig.3 (a).The results show that as the groove depth increases,the radiation intensity decreases and the radiation peak frequency slightly decreases.Then,the normalized surface field spectra in the strongest radiation condition (D=100 nm,d=20 nm,andh=10 nm) are shown inFig.3 (b).It demonstrates that the surface plasmon field is excited on the Au substrate upper surface (the bottom surface of the grating groove)and due to the small depth of the grating,the surface wave of the grating is not excited in this structure.Afterwards,the normalized surface field spectra in different grating depths are presented inFig.3 (c).The frequency characteristics are basically the same as those of the radiation field shown inFig.3 (a),which proves that the excited surface plasmon field transforms into the coherent Smith-Purcell radiation.And the surface wave of the grating is not observed on the upper surface of the Au substrate.Due to the surface plasmon field stimulated on the bottom surface of the grating groove in the Au substrate grating,the smaller the grating depth,the smaller the distance between the electrons and the excited surface plasmon,and the stronger the excited field.While a low grating depth corresponds to low diffraction efficiency in the Smith-Purcell radiation,when the grating depth increases,the surface field intensity is reduced more significantly than that of the radiation field.Besides,the peak frequencies in different groove depths match the theory of the SPPs dispersion relationship in a layered metal-dielectric structure[7],[28],which is expressed as

Fig.3.Simulation results in the Au substrate grating:(a) normalized radiation spectra of the Au substrate grating in different groove depths;(b) normalized surface field spectra in the strongest radiation condition (D=100 nm,d=20 nm,and h=10 nm;in the legend,y is the distance between the observation probe and the grating groove bottom surface);(c) normalized surface field spectra of the Au substrate grating in different groove depths (the probe with y=0 is selected to observe the surface field);(d) normalized radiation intensities of the PEC grating and the Au substrate grating(D=100 nm,d=20 nm,and h=10 nm).

whereε2=d/D+εd(1-d/D) is the equivalent relative permittivity of the dielectric grating andεdis the relative permittivity of the dielectric material;the transverse propagation constant in the vacuum regionthe transverse propagation constant in the dielectric ribbons region;the transverse propagation constant in the Au substrate region;the vacuum wave vectork0=ω/c;kzis the propagation constant.In the dispersion calculation,the inhomogeneous region of dielectric ribbons approximates by the equivalent medium theory.Thence,the excited surface plasmon is confirmed as the SPPs mode in this structure.SPPs propagate along the metal/vacuum or metal/dielectric interface,and in this study,SPPs are excited by one bunch of parallel,uniform motion electrons,and the propagation constantkSPPs=2πfSPPs/ve,wherefSPPsis the frequency of SPPs.Finally,comparing with the Smith-Purcell radiation in the PEC grating,the normalized radiation intensities of the PEC grating and the Au substrate grating in the optimized condition are shown inFig.3 (d).The above results show that the Smith-Purcell radiation is coherently enhanced about 40 times by excited SPPs in the Au substrate grating.The radiation enhancement capability is basically the same as previously proposed structures.

Simulation results of the Au ribbons grating in different groove depths are presented inFig.4.

Fig.4.Simulation results in the Au ribbons grating:(a) normalized radiation spectra of the Au ribbons grating in different groove depths;(b) normalized surface field spectra in the strongest radiation condition (D=100 nm,d=20 nm,and h=30 nm);(c) normalized surface field spectra of the Au ribbons grating in different groove depths;(d) normalized radiation intensities of the PEC grating and the Au ribbons grating (D=100 nm,d=20 nm,and h=30 nm).

Owing to few free electrons existing in the Au ribbons grating with 10-nm grooves,the obvious surface plasmon is not stimulated.Thence,the contrast starts with a 20-nm depth grating.The results show that the optimized grating depth is 30 nm,and in this condition,the surface field characteristics are observed and the normalized spectra are shown inFig.4 (b).The peak frequency lower than 500 THz is the excited surface wave frequency of the grating.It demonstrates that the surface plasmon field is excited on the upper surface of the Au ribbons grating,hence,the distance between the electrons and excited surface plasmon does not change with the change of the groove depth.As the grating depth increases,the amount of free electrons raises,thence,the intensity of the excited surface plasmon field increases.These results are shown inFig.4(c).The radiation spectrum properties are basically the same as those of the surface plasmon field in different groove depths.This proves that the excited surface plasmon field transforms into the coherent Smith-Purcell radiation.In addition,as the groove depth increases,the radiation peak frequency obviously decreases,which is sensitive to the grating topography.Considering the discontinuity of the SPPs material in this structure and the consistent frequency change trend with LSP (the size of the morphology decreases and the frequency of LSP increases),the excited surface plasmon in this structure is verified as LSP.Finally,comparing with the Smith-Purcell radiation in the PEC grating,the normalized radiation intensities of the PEC grating and the Au ribbons grating in the optimized condition are shown inFig.4 (d).The results demonstrate that the Smith-Purcell radiation is coherently enhanced about 200 times by excited LSP in the Au ribbons grating,and the enhancement capability is significantly better than the SPPs enhancement structures.

Simulation results of the Au grating in different groove depths are presented inFig.5.

Fig.5.Simulation results in the Au grating:(a) normalized radiation spectra of the Au grating in different groove depths;(b) normalized surface field spectra in the strongest radiation condition (D=100 nm,d=20 nm,and h=20 nm);(c) normalized surface field spectra of the Au grating in different groove depths;(d) normalized radiation intensities of the PEC grating and the Au grating (D=100 nm,d=20 nm,and h=20 nm).

Fig.5shows that the optimized grating depth is 20 nm.In this condition,the surface field characteristics are observed and the normalized spectra are shown inFig.5 (b).The peak frequency lower than 500 THz is the excited surface wave frequency of the grating,which demonstrates that the surface plasmon field is also excited on the upper surface of the Au grating,hence,the distance between the electrons and excited surface plasmon does not change as the groove depth changes.As the grating depth increases,the amount of free electrons raises,thence,the intensity of the excited surface plasmon field enhances,the same as it in the Au ribbons grating.These results are presented inFig.5 (c).The radiation spectrum properties are nearly the same as those of the surface plasmon field in different groove depths.It indicates that the excited surface plasmon field transforms into the coherent Smith-Purcell radiation.And the frequency properties are similar to those of the Au ribbons grating,hence,the surface plasmon excited in the Au grating is also LSP.Because the discontinuous part interacts with the electron beam first,only LSP is excited in the Au grating to enhance the radiation.In the end,comparing with the Smith-Purcell radiation in the PEC grating,the normalized radiation intensities of the PEC grating and the Au grating in the optimized condition are shown inFig.5 (d).The results demonstrate that the Smith-Purcell radiation is coherently enhanced about 530 times by excited LSP in the Au grating.The radiation performance of the grating has been significantly improved by utilizing LSP in the surface plasmon material grating.

4.Conclusions

The above results show that the excited SPPs and LSP are the coherently enhanced Smith-Purcell radiation.In a 100-nm period,0.2 duty cycle grating excited by 10.5-keV parallel electrons,SPPs are excited in the Au substrate grating,obtaining about 40-times radiation enhancement.LSP is excited in both the Au ribbons grating and the Au grating,obtaining about 200-times and 530-times radiation enhancement,respectively.The perfect diffracted radiation requires a certain grating depth.As the grating depth increases,the SPPs excitation efficiency decreases.There is an irreconcilable contradiction between the grating diffraction efficiency and SPPs excitation efficiency,which limits the enhancement in the Au substrate grating.While LSP excited on the upper surface of the grating groove solves the above problem,the Smith-Purcell radiation is significantly enhanced.The results presented here provide the theoretical guidance of developing miniature,integratable,tunable,high-power-density radiation sources from visible light to ultraviolet rays at room temperature.

Disclosures

The authors declare no conflicts of interest.