Band diagrams and field distribution of squarely modulated slab metallic gratings

Band diagrams and field distribution of squarely modulated slab metallic gratings Band diagrams and field distribution of squarely modulated slab metallic gratings Jih Yin Lee and Yu Ju Hung Citation[.]

Band diagrams and field distribution of squarely-modulated slab metallic gratings

Jih-Yin Lee and Yu-Ju Hung

Citation: AIP Advances 6, 125117 (2016); doi: 10.1063/1.4973336

View online: http://dx.doi.org/10.1063/1.4973336

View Table of Contents: http://aip.scitation.org/toc/adv/6/12

Published by the American Institute of Physics

The optical transmission properties of squarely-modulated metallic gratings has been widely investigated This study used rigorous-coupled wave analysis (RCWA) to re-examine in detail the band structure of a laminated metal film with squarely-modulated metallic gratings located at the top The top structure was shown to modify the long-range surface plasmon polariton modes (LRSPP) at both interfaces of the thin metal film When the thickness of the intact metal film was altered, the coupling between the two interfaces presented intriguing behavior If the thickness of the metallic film was 30nm, the field achieved strong coupling similar to that of a two-level system When the thickness was decreased to 10nm, the band branch possessing negative group velocity was dominant Our results also verify that the first-order Fourier expansion of the gratings determined the energy position of bands at k||=0, whereas the second-order term caused band gap opening Introducing an asymmetrical component to the grating profile intensified the opening effect at k||=0 due to an increase in the amplitude of the

second-order Fourier component © 2016 Author(s) All article content, except where

otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/ ) [http://dx.doi.org/10.1063/1.4973336]

I INTRODUCTION

The extraordinary transmission (EOT) effect has attracted considerable attention over the past two decades.1Detailed computation of surface plasmon polariton (SPP) modes on a variety of grating structures has helped to elucidate the relationship between transmission, reflection, and absorption spectra with respect to the in-plane k vector k||.2 7This has helped to clarify the distinct characteristics

of Eigen modes on the metallic grating structures.8 Novel structures, such as sandwiched metal-oxide-metal,9 gap plasmonic devices, and T-shaped metal cap structures have been developed.10–12 Some of these designs are suitable for sensor-based devices,13,14while others are better suited to wide angle filters.15 A variety of structures have been developed to meet a range of application requirements Surface-Enhanced-Raman-Scattering (SERS) signals are enhanced by employing a structure of discrete metallic gratings in Ref.16 However, in this report, we found that a discrete metallic gratings on a continuous metal film are better suited to the detection of SERS The objective

in this study was to create metal gratings with a more effective design by revisiting the simple structure comprising a thin metal film with rectangular metallic gratings located at the top We first examined the band gap positions of the metallic gratings The pitch of the gratings determines the energy of the bands and produces a band gap under the effects of Bragg reflection However, the band folding branches and band gap created by the first-order grating component is negligible.17 – 23 Experimental data related to the band gap was obtained from the coupling between the first- and second-order Fourier component of the periodic gratings in Ref4,24 The +1/-1 SPP modes generated

by the first-order Fourier component were interfered each other to form degenerate standing waves

a Electronic mail: yjhung@mail.nsysu.edu.tw

2158-3226/2016/6(12)/125117/7 6, 125117-1 © Author(s) 2016

125117-2 J.-Y Lee and Y.-J Hung AIP Advances 6, 125117 (2016)

FIG 1 (a) Silver gratings on thin Ag film on glass substrate; (b) silver gratings on thin Au film on glass substrate; (c) asymmetrical cap structure on Ag grating substrate; (d) asymmetrical slot structure on Ag grating substrate.

However, the second-order term breaks the mirror symmetry of the first-order gratings, such that the two types of standing wave revealed different portions of the asymmetrical profile of the optical refractive index, thus the degeneracy of the two splits up.25 The second component also makes it possible to tune the gap.25–27This study deals with the process of band folding by a grating structure and the coupling between the two interfaces of continuous films of various thickness The two dispersion curves at the upper and lower interfaces began interacting when separated by a distance

of approximately 30nm When the thickness of the continuous film was reduced to zero, the discrete metallic stripes presented smaller corner field intensity comparing to that observed in LRSPP-assisted modes (i.e when the continuous film is 50nm thick) This is a clear indication that these experiments involving surface enhancement did not have a favorable effect on the structure of the discrete stripes The introduction of a phase-shifted grating embedded within the original grating (i.e., the second-order Fourier component of the periodic modulation), creates multiple corner field resonances which facilitate the surface enhancement experiments The insight provided by band diagrams and field distributions could facilitate the development of more effective devices using alternative approaches

to design

II SIMULATION OF STRUCTURES

Figure1presents the structures simulated in this study Fig.1(a)presents square Ag gratings

on a continuous Ag thin film (AgG-AgF) The lower substrate is glass and the medium above is air Thickness h1and h2of the metal structures varied from 0nm to 100nm and 50nm (both h1and h2) is picked to illustrate the band folding process The grating pitch is chosen as 600nm due to the proper bandgap position The grating duty cycle is 50% In this regime, planar SPP modes at both interfaces

of the continuous Ag film play a major role in the resulting reflection diagram Unlike in Ref.5, the thin Ag film here precluded the involvement of channel SPP mode within the metal slit To investigate the origin of the reflection bands, we included single Ag gratings without a complete film, as shown

in Fig.1(b) Fig.1(c)and1(d)illustrate the asymmetrical structural perturbation added to the basic structure Broadband white light source with TM polarization is incident from air All subsequent figures refer to the Hycomponent for simplicity

III RESULTS AND DISCUSSION

Figure2presents simulation results from the AgG-AgF structure where the thickness of both layers is 50nm Λ1 is the grating pitch as 600nm The overall reflection level is high, wherein the brighter curves represent dips under the corresponding conditions Fig.2(b)presents one sampling from zero incidence Groups 1 and 3 results are associated with coupling between gratings and the LRSPP mode at the lower Ag film/glass interface, whereas group 2 results are from coupling between gratings and the LRSPP mode at the upper Ag grating/air interface Fig.2(c)∼2(e)presents the field distribution of groups 1∼3 Clearly, the field could be categorized as upper and lower interface modes Fig.2(e)presents the second-order SPP mode at the lower interface

FIG 2 (a) Reflection diagram of AgG-AgF shown in Fig.1(a) ; (b) reflection spectrum at zero incidence; (c) the first mode

of the lower interface; (d) the first mode of the upper interface; (e) the second mode of the lower interface.

By unfolding the curves in Fig.2(a), the positions of the branching points (1.39, 1.92, and 2.49eV) indicate that the two dispersion curves at the air/Ag and glass/Ag interfaces are the basic elements constituting the band diagram.28 The transition between localized SPP and LRSPP modes on the periodic structure was discussed in Reference29 For the sake of simplicity, the periodic rectangular grating with periodicity Λ1can be approximated as follows:

f (x) = a sin(2π

Λ1)+ b sin(2 ∗2π

Where 2π/Λ1assists in coupling between the zero incidence and the LRSPP mode with forward (+1) and backward (-1) propagating waves forming two types of standing wave This interference created two types of standing wave located in different spatial positions, which differ in optical refractive index due to the effects of the periodic structure This is similar to the situation in Quantum physics,

in which two standing waves are associated with different portions of the periodic potential well, such that their eigen energies are different Naturally, the first-order Fourier component creates an energy gap.24 However, the experimental data in Ref 17–23,25presented very little evidence of band opening effect, which is referred to as a “mini gap” in Ref.24 The profile of the second-order term 2∗2π/Λ1breaks the mirror symmetry of the first-order surface profile, such that the two types

of SPP standing wave were affected by different portions of the non-symmetrical refractive index profile, such that they produced different resonance energies at zero incidence φ1 is an arbitrary phase term, as detailed in Ref.24 The folding procedure is illustrated in Fig.3(a) Groups 1 and

3 were obtained from the glass/Ag film curve, whereas group 2 was obtained from the air/Ag film curve According to Eq (2), SPP resonance is located at 2π/Λ1 whereas the first reciprocal lattice constant (π/Λ1) provides the lateral shift unit in the reduced zone picture The second component 2π/Λ2is primarily responsible for band gap opening (Λ2= Λ1/2) The branch folding position in the reduced zone of Fig.3(a)is consistent with the simulation values based on Equation (2), where the values are determined by the coupling of the grating to the SPP dispersion curves

k spp = k o sin θ ± n2π

The branches of each V-shape comprise two types of standing wave, located at edges and in the flat regions of the gratings, as shown in Figs.3(b)and(c) The second-order Fourier component of the gratings caused unequal perturbations in these two modes, which resulted in band gap opening

In the simulation in Fig.2(a), the duty cycle is 50%, such that the second-order term in Eq (1) is equal to zero In this case, the band gap opening effect is nearly invisible

125117-4 J.-Y Lee and Y.-J Hung AIP Advances 6, 125117 (2016)

FIG 3 (a) Image of the folding zone associated with the two reciprocal components from squarely-modulated metallic gratings; (b) one standing wave of branch 2 with the field located at the edges of the Ag gratings; (c) a different standing wave

of branch 2, wherein the field is resonant in the flat regions of the Ag gratings.

By altering the duty cycle of the metallic gratings, the position of branch 2 at zero incidence, (i.e., the upper interface mode), can be tuned without the duty cycle affecting bands 1 or 3 at the lower interface, as shown in Fig.4 Interestingly, the grating structure affects coupling locally, but not through the spacer layer (thin metal film) The effects of reflection band opening was unclear when the duty cycle was swept from 0 to 1 Prominent gap opening effect occurred when the mirror symmetry of the rectangular grating was destroyed, as discussed later in this paper

Varying the thickness of the continuous metal film revealed the coupling of the two interface modes Fig.5presents a reflection band diagram with films of various thickness h1 When h1=50nm, the folded bands presented no signs of coupling, as shown in Fig 5(a) When h1=30nm, strong coupling occurred between the upper and lower interfaces, as shown in Fig 5(b) When h1 was decreased further to 10nm, the branch of the negative group velocity was dominant, as shown in Fig 5(c) Lacking a continuous film, the bands became highly reflective and the band positions shifted slightly As shown inFig 5(d), unfolding the bands made it possible to fit the optical light lines (glass and air) rather than the dispersion lines of the planar surface plasmon modes The corresponding field strength of discrete grating stripes with kx=0 is only ∼5, due to a lack of LRSPP mode coupling,

as shown in Fig.6 When h1was decreased to 30nm, the splitting-out of coupling effects occurred only in bands above 2eV The dielectric constant of the metal revealed that the skin depth of Ag at higher photon energy exceeded that at lower photon energy levels Thus, the interaction strength of the planar surface plasmon modes was stronger at higher photon energy levels

FIG 4 Band positions versus duty cycle Trace 1 and 3 are modes of the lower interface while trace 2 is that of the upper interface The incidence angle is zero degree.

FIG 5 Reflection band diagrams obtained under various h 1 values: (a) h 1 =50nm (b) h 1 =30nm (c) h 1 =10nm (d) h 1 =0nm.

Including an additional object at the lobes of the standing fields in Figs.3(b)and(c)caused the two degenerate standing modes at zero incidence split out, as shown in Fig.7 The inclusion of an additional shifted cap or slot, as shown in Figs.7(a)and(d), destroyed the symmetrical field distribution at zero incidence Figs.7(a)∼7(c)present reflection, transmission, and absorption diagrams associated with cap geometry, whereas Figs.7(d)∼7(f)present the same for slot geometry The perturbation causing structure was on the upper interface; therefore, only branches associated with the air/silver interface were affected This situation is similar to that in which the duty cycle changes, wherein traces 1 and 3 remained unperturbed, as shown in Fig.4 The complimentary phenomenon in branches 2 and 4 will be investigated in future work A wide-angle absorption band at 3eV, similar to that shown in Fig.7(a), was reported in Ref 10–12 The field distribution induced by a complex cap structure includes numerous local corners for SPP resonance, which results in relatively robust excitation of the SPP modes at all incident angles The field distributions of the cap and slot structures are presented in Fig.8

A comparison of Figs.3(b)and(c)shows field strength ranging from 10 to 20, whereas the surface field resonance at multiple corners and slots in Fig.8ranges in strength from 15∼22 This could prove useful in the detection of materials presenting nonlinear optical responses or in Raman spectroscopy Conversely, the maximum field amplitude of the discrete gratings with kx=0 was only ∼5, as shown in Fig.6 This is a clear indication that a continuous metal film with metallic gratings is a more suitable approach to the enhancement of SERS than is the application of discrete metallic gratings on a glass substrate

FIG 6 The field distributions of discrete Ag gratings on glass substrate (a) and (b) are corresponding to points 1 and 2 respectively in Fig 5(d)

125117-6 J.-Y Lee and Y.-J Hung AIP Advances 6, 125117 (2016)

FIG 7 (a) Reflection diagram -band gap opening on cap structure; (b) transmission diagram; (c) absorption diagram; (d) reflection diagram -band gap opening on slot structure; (e) transmission diagram; (f) absorption diagram.

FIG 8 Field distributions of structures involved band gap opening at zero incidence (a) and (b) are for cap structure while (c) and (d) are for slot structure.

IV CONCLUSIONS

This paper presents reflection diagrams of squarely-modulated metallic gratings on a thin metal film substrate We discuss the band folding effect and the influence of the second-order Fourier component on the band gap opening mechanism The thickness of the intact metal film was reduced

to 30nm, the strong coupling between planar surface plasmon modes at the two interfaces caused band splitting effect When the thickness was reduced to 10nm, the band branch of negative group velocity was dominant Our results indicate that metallic gratings with asymmetric perturbations on a metallic film are better suited to field enhancement purposes than are simple discrete metallic gratings

ACKNOWLEDGMENTS

We would like to thank the Ministry of Science and Technology, R.O.C for the funding of project

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