Widening the Spectral Range of Ultrahigh Field Enhancement by

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Widening the Spectral Range of Ultrahigh Field Enhancement by Efficient Coupling of Localized to Extended Plasmons and Cavity Resonances in Grating Geometry Mohammad Abutoama, Shuzhou Li, and Ibrahim Abdulhalim J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b09756 • Publication Date (Web): 15 Nov 2017 Downloaded from http://pubs.acs.org on November 21, 2017

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The Journal of Physical Chemistry

Widening the Spectral Range of Ultrahigh Field Enhancement by Efficient Coupling of Localized to Extended Plasmons and Cavity Resonances in Grating Geometry Mohammad Abutoama1, Shuzhou Li*,2, Ibrahim Abdulhalim*,1,3 1

Department of Electro-Optic Engineering & Ilse Katz Institute for Nanoscale Science and Technology, Ben Gurion University of the Negev, Beer Sheva-84105, Israel 2 School of Materials Science and Engineering, Nanyang Technological University, Singapore, 639798 3

Singapore-HUJ Alliance for Research and Enterprise, NEW-CREATE Phase II, Campus for Research Excellence and Technological Enterprise (CREATE), Singapore 138602

ABSTRACT: Excitation of localized via extended plasmons was shown recently to reveal ultrahigh electromagnetic field (EM) enhancement when optimum coupling is obtained in the prism configuration. Using grating coupling one expects several advantages over the prism scheme such as being planar, more compact, and most important the possibility of tuning the spectral range over which the enhancement occurs. In this work we show that via gratings coupling the EM field enhancement can be up to 3 orders of magnitude higher than that obtained using free space excitation of localized surface plasmons (LSPs). Furthermore the spectral range over which the ultrahigh enhancement achieved becomes wider by tuning the grating parameters. The cavity resonances generated by thick enough gratings couple to the LSPs producing ultrahigh local enhancement and play an important role in widening the spectral range to cover the range 4002000nm. This is important for solar energy harvesting and improving the efficiency of infrared optoelectronic devices. Having the periodic NPs arrangement on top of the grating was found to be very significant not only under transverse magnetic (TM) polarization but also under transverse electric (TE) polarization; thus reducing the dependence on the polarization.

The requirement to achieve intense electromagnetic (EM) fields near nanostructures is one of the big challenges that have attracted large number of research groups during the last decade. This is attributed to the fact that using those intense fields one can significantly enhance many optical signals such as surface enhanced fluorescence (SEF), surface enhanced Raman scattering (SERS) and surface enhanced infrared 1-6 absorption (SEIRA). Using the same enhanced fields one can also enhance the efficiency of optoelectronic devices such as solar cells or photodetectors by locating the active material in 7-9 the nano-scale vicinity of nanostructures. Plasmonic assisted

enhancement of photoctalysis, up-conversion processes as well as solar water evaporation due to local heating are also 10 becoming active fields of research. Depending on the dimensions of the metallic structures with respect to the wavelength, two plasmonic waves can be supported, one is propagating or extended while the other is localized. Extended surface plasmon (ESP) is a compressional electromagnetic surface wave excited at and propagates along the interface between two dimensional metal and dielectric and decays evanescently along the normal to the interface. 11 This type of plasmon has been intensively used in biosensing

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and it can provide enhancement factor of

E

2

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25-26

at the surface

of the order of ˜×10-100. On the other hand localized surface 2,12 plasmon (LSP) is an EM wave which oscillates on the surface of metallic nanostructures such as metallic nanoparticles (NPs) with dimensions less than half the wavelength of the exciting EM wave. Similar to the ESP, the LSP can be used also in biosensing by following the resonance shift with the refractive index variations of the surrounding media. When the LSP condition is satisfied, a significant enhancement in the absorption and scattering cross sections is observed depending on the geometry of the nanostructure and the way the LSP is excited. The simplest case to achieve enhanced EM fields is to illuminate a single NP with direct plane wave excitation. Depending on the shape of the NPs (nanospheres, nanorodes, nanoprisms, nanostars or other possible shapes), one can achieve enhancement factor of ˜×102 - 103 . Metal NPs over 13-18 metallic film geometry have received wide attention due to their ability to generate higher enhancement of the EM fields (˜× 103 ) than single NP with direct plane wave excitation and more than in the case of metal NPs on dielectric substrate. The acceptable explanation for such enhancement was the coupling between the NPs and their mirror charge in the 16,19-20 metallic film. Another advantage of this configuration is the simple fabrication process which can be achieved by 13,16,21 depositing the NPs on the metallic film. These advantages of the metal NPs over metallic film configuration 4-6 make it very useful for SEF, SERS and other energy harvesting applications. The ESP and LSP modes have been separately investigated and used for few decades. During the last few years one of the hottest topics in this regard is the coupling between the ESP 5,14,16,22-27 and the LSP in what is called ESP-LSP mode. This mode of operation exhibits EM enhancement factor even more than the product of the two enhancement factors of the ESP and the LSP cases. In a more organized way of the distribution of the NPs over the metallic film, a high EM field enhancement was obtained using periodic array of metal NPs over metallic film. In this configuration the periodic array of the metal NPs acts as 2D grating to provide the needed momentum to the incident photons in order to excite the ESP waves on the silver film. The enhanced fields are obtained when the ESP resonance (ESPR) 22-23 coincides with the LSPR. In spite of the intensive use of the periodic array of metal NPs over metallic film, two main issues still need more careful investigation, the first one is the interparticle distance at small periodicities which was not 22-24 investigated. This is important because in this case a strong coupling between the neighboring NPs can be achieved. The second issue is the excitation methodology which means finding the optimum excitation conditions or methods that can lead to much higher enhancement factor. As mentioned before the ESP-LSP coupling mode gained a wide interest in the last few years, part of the works suggested to excite ESPs via LSPs 5,14,16 25-26 using metal NPs over metallic film while others suggested to excite LSPs via ESPs. The LSPs via ESPs excitation

showed huge potential in mode in the mentioned works terms of generating enhanced EM fields more than the ESPs via LSPs excitation mode. Although these works demonstrated the huge potential of this excitation mode; however there is still a need for work to reach the optimum conditions for LSPs via ESPs excitation. 27 In a recent work our group reported a novel methodology of exciting the LSPs on the surface of gold NPs via the ESPs of the underlying silver metallic film generated using the Kretschmann-Raether (K-R) or the prism coupling configuration. The K-R configuration allows coupling the incident light to the extended plasmons on the metallic film. It was shown that by providing the appropriate conditions for the ESP to LSP waves coupling, one can achieve enhancement factor of at least 1-3 orders of magnitude higher than the 27 direct plane wave excitations of the LSPs from free space. The simulations showed that the highest enhancement factor (2.5× 10 5 ) is achieved exactly when the illumination angle is at the ESP resonance angle of the metallic film and matching the 28 condition for LSP excitation. In reference the inter-particle distance and its influence on the hot spots generated between the neighboring NPs and at the gap between the NPs and the metallic film were investigated very carefully. In this configuration a squared array of gold NPs on a silver film was investigated as an example. The squared array of gold NPs can act as 2D grating to provide the needed momentum to the incident photons in order to excite the ESP waves of the silver film and then the ESPs can couple to the LSPs generating 28 27 intense EM fields. While in reference the NPs were randomly distributed over the metallic film, following the very careful investigation of the distribution of the NPs on the 28 metallic film that has been done in reference . It helped to 29 suggest a unique design which combined the two main observed conclusions: the excitation methodology and the inter-particle distance between the NPs. These conclusions significantly affect the hot spots and the enhancement factor 29 of the EM field. In reference a squared array of gold NPs on a 28 silver film was used, but in contrast to the excitation was 27 done using ESPs of the K-R configuration as in and not from free space. The generated ESP waves at the surface of the metallic film then hit the NPs and under the appropriate matching condition excite the LSPs; thus generating intense EM 29 fields at the gap between the NPs and the metallic film. In 27-29 the whole three works the size of the NPs was optimized to give the highest enhancement factor, as changing the NPs size controls the LSP resonance to match the ESP resonance for the best and most effective ESP-LSP coupling. Under these conditions one can roughly estimate the field enhancement factor to be determined by the product of the two separate enhancement factors: Fc = Fesp Flsp , the ones associated with the ESP ( Fesp ) and the LSP ( Flsp ) respectively. In reality even higher enhancement than this was obtained which is believed to be due to the fact that when the NP is close to the metal surface its response changes due to the mirror charge.


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In the present work we propose a unique configuration for the ESP-LSP modes coupling in which the ESP waves are first 29 excited using grating coupling instead of a prism and then couple them to LSPs on the NPs added on top of the grating. Using this coupling configuration, and when the gratings are thick enough additional modes are observed in the reflection spectrum of the grating corresponding to the cavity modes excited between two neighboring grating walls similar to the 30 Fabry-Perot mode. Hence additional coupling mode is available in our configuration, the cavity-LSP mode which also significantly contributes to reach the main goal of achieving high field enhancement over a wide spectral range that covers the whole solar spectrum. The planar nature of the grating is another advantage that makes the optical setup simpler than the one using the prism coupling. The number of resonances is controlled by increasing the grating thickness. The grating design was optimized to get a large number of resonances covering a wide spectral range (400nm-2000nm). The idea is then to decorate the top of the grating with NPs in a way to efficiently allow coupling of LSPs with ESPs and with cavity modes. By simply fine tuning the parameters of the NPs and their locations as well as the grating parameters such as the thickness, period, depth and aspect ratio, ultrahigh enhancement is achieved over the entire solar spectrum range.

METHODS

Reflectivity simulations from the structures as well as field calculations and distribution were done using COMSOL software which is based on finite element analysis (FEA) method. To get accurate results, the mesh size was considered to be extremely fine (~1nm-tetrahedral mesh) at the important regions (on the NPs and at the NPs-grating gap). The refractive indices and the dielectric functions of the materials were taken 31 from the database of Sopra.

ESP-LSP and cavity-LSP modes coupling can be achieved in a very efficient way. The distances between the neighboring NPs are shown in Figure 1. The performance of the structure was mainly tested under transverse magnetic (TM) but some checks were also done under transverse electric (TE) polarization for one case and both at normal incidence. We are not worried about obtaining similar enhancement for TE because this can be achieved easily by making the grating two dimensional. Increasing the incidence angle also increases the enhancement and the number of the gratings resonances; therefore we are not worried about the angular dependence either and therefore the results here are concentrated to normal incidence. The ambient medium (analyte for the case of sensing) is considered to be water to test the potential of the structure for sensing in water using enhanced spectroscopy and for plasmonic assisted water evaporation and hydrogen reduction applications.

DESCRIPTION, RESULTS AND DISCUSSION

General Geometry. The main goal behind this configuration is to achieve large field enhancement over a wide spectral range. To achieve that, our approach consists of first to design a structure that can produce a number of resonances as large as possible in which the highest field enhancement is obtained at these resonances. Metallic gratings are a preferred option for this task (due to ESP and cavity modes excitation). Figure 1 shows the proposed design, silver grating of 1000nm and 900nm period and linewidth respectively have been used on top of 100nm silver layer to avoid the transmission inside the SiO2 substrate. Two grating thicknesses have been used in the simulations; first we used 180nm and then to allow the excitation of additional resonances we increased it to 800nm. Gold NPs of 50nm radius were spread on top of the silver grating with a thin dielectric layer of thickness 2-4nm and refractive index (RI) of 1.6 is separating between them. The distribution methodology of the NPs over the dielectric layer is a main issue here in order to utilize the hot spots generated as a result of the ESP and the cavity modes excitation; hence the

Figure 1. A scheme of grating-NPs system for ESP and cavity modes to couple to LSP resonances. Water is used as an analyte.

Grating without NPs. The starting point is clearly illustrated in Figure 2 in which the reflection spectrum and maximum field enhancement from 180nm silver grating without NPs were calculated under TM polarization. Several resonances are observed in the reflection spectrum (Figure 2a) attributed to ESPR modes and some to cavity modes spread over a wide spectral range. One can observe in Figure 2b that the maximum field enhancement is obtained at the resonance wavelengths of the reflection spectrum. This was the motivation for increasing the number of the resonances over a wide spectral range, hence one can achieve enhanced EM field over wide range. Figure 2c shows the field intensity distribution at some resonances observed in the reflection spectrum. At 684nm a clear ESPR mode is observed while at 1748nm a clear cavity mode is observed in which most of the energy exists in the space between two neighboring grating lines. At the other wavelengths (538nm and 1235nm) a mixture of SPR and cavity modes are obtained. The ratio

I max / I 0

is the enhancement

factor of the maximum intensity of the total electric field. In addition to the maximum field enhancement calculation, the



average calculations are also important for the practical validation of the configuration since in the experiments the average field is measured and not the maximum field at specific point. Figure 3 shows two average calculations in two slices (see the dimensions in Figure 3) in which the maximum enhancement is also obtained at the resonance wavelengths of

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the reflection spectrum of the 180nm grating. The ratio

I av / I 0

is the enhancement factor of the average intensity of

the total electric field.

Figure 2. (a) Reflection and transmission spectra from the grating structure of Figure 1 but without the NPs and the grating and the dielectric spacer thicknesses are 180nm and 4nm respectively. The calculations were done under TM polarization. (b) Maximum field intensity enhancement versus wavelength. (c) Intensity distribution at some resonances observed in the reflection spectrum. The legends in the figures in (c) show the maximum intensity enhancement at the specific wavelengths.

Figure 3. Average field intensity enhancement versus wavelength under TM polarization. The grating and spacer thicknesses are 180nm and 4nm respectively. The boxes shown are the regions used for averaging in the two slices.

Centered NPs-Grating Configuration. After we achieved the ESP and the cavity resonances in the reflection spectrum of the grating alone, we started to deal with the ESP-LSP and cavity-

LSP modes coupling by locating gold NPs on the center of the dielectric spacer (which is located on top of the grating). At this point the dielectric spacer thickness was 4nm with 180 grating thickness under TM polarization. The configuration here is the one shown in Figure 1 but only the central NPs exist (no NPs on the edges of the grating lines), meaning in a xz cross section there is only one NP on each line located on the center. Figure 4a shows that by adding the NPs in this way we improved the maximum intensity enhancement factor in the visible range by around one order of magnitude in comparison to the case of the grating without NPs due to the ESP-LSP and cavity-LSP modes coupling. A strong coupling occurs using the visible wavelengths generating intense field at the NPs-grating gap. The enhancement at 616nm (additional peak in enhancement is obtained at 616nm in comparison to the case without NPs) is attributed to the fact that this is the LSPR wavelength of 50nm Au nanosphere embedded in water. One of the important advantages of the use of this coupling configuration is the flexibility of tuning the enhanced field at the wavelengths of interest. This can be done by optimizing the grating parameters as mentioned before and also by choosing the NP size to give LSPR at the wavelengths of interest and couple them to the grating resonances. This can significantly enhance the field at


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these wavelengths. Although we improved the enhancement factor in the visible range, one can see in Figure 4a that the central NPs are not contributing to the field enhancement at longer wavelengths and the enhancement factor is close to the one obtained by the grating without adding the NPs (see Figure 2b). This is due to the fact that the generated hot spots for the case of grating without NPs at the shorter wavelengths spread into the whole grating line area while at longer wavelengths it is mainly located in the grating spaces (between the grating lines) as it can be seen in the field distribution in Figure 2c. For example the coupling between the grating and the central NPs resonances at wavelengths close to 538nm and 684nm (more generally in the visible range) is strong. Therefore the added central NPs interaction with the field (generated by the grating without NPs) spreading along the whole grating line at these wavelengths is strong. On the other hand the added central NPs feel a very weak field close to the center of the grating line at the longer wavelengths (above 800nm). In fact, the small field enhancement and the weak coupling observed at wavelengths longer than 800nm can be related to three facts.

The first one is because the two resonances observed in the reflection spectra at wavelengths longer than 800nm (1235nm and 1748nm, see Figure 2c) are very broad leading to a small field enhancement. The second fact is that at these resonances the field is located mainly in the grating spaces which mean that adding the NP on the center of the grating line is not contributing to the field enhancement at these resonances. The third fact is that we used 50nm radius of the Au NPs (embedded in water) which have the LSPR wavelength at 616nm (dipole mode). The needed NP radius to get LSPR at wavelengths longer than 800nm is extremely larger than 50nm, but then higher LSP modes will appear (quadrupole, hexapole,…) and it is well known that the field at higher LSP modes is smaller than the one at the dipole mode. Intensity distribution at different wavelengths for the central NPs on top of the grating configuration is shown in Figure 4b.

Figure 4. (a) Maximum field intensity enhancement versus wavelength for the center NPs-grating configuration under TM polarization. The grating and spacer thicknesses are 180nm and 4nm respectively. (b) Intensity distribution at different wavelengths. The legends in the figures in (b) show the maximum intensity enhancement at the specific wavelengths.

We calculated the reflection spectrum for the 180nm grating thickness with the central NPs and noticed that in addition to the resonances that we obtained for the case of grating without NPs, additional resonance at 704nm was observed. This dip is attributed to the added central NPs array (satisfies the momentum matching equation for the ESPR excitation in 2D gratings) and it can explain the small peak at 704nm in the enhancement in Figure 4a. The existence of the central NPs array causes a small shift in the resonance wavelengths that we

obtained for the case of grating without NPs (Figure 2a). Edge/Center/Edge NPs-Grating Configuration. The next step was to improve the enhancement factor at wavelengths longer than the visible wavelengths by utilizing the whole hot spots generated at the whole resonance wavelengths for the case of the grating only without NPs which are attributed to the excitation of the ESP and cavity modes. By knowing the location of the hot spots, the improvement in the enhancement factor can be achieved by locating NPs at the



regions of these hot spots. This way an efficient ESP-LSP and cavity-LSP modes coupling can be achieved using the same configuration used in Figure 4 but with adding two additional NPs along the x-axis located close to the grating line edges (see Figure 1). Note that the added two NPs can now interact with the hot spots generated near the grating edges mainly by the cavity modes. Hence using the edge/center/edge NPs, an ESPLSP and cavity-LSP modes coupling in a wide spectral range can be obtained generating large enhancement factor over this range. Although we suggested to use the edge/center/edge NPs-grating configuration for mainly improving the enhancement factor at the longer wavelengths which was improved by factor of ˜×6-7 in comparison to the central NPsgrating configuration. In addition some improvement of the

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enhancement factor was obtained in the visible wavelengths as well as achieving one additional peak at 844nm which did not exist in the centered NPs-grating configuration; thus widening the enhancement region. All this can be attributed to the contribution of the dense NPs array in generating new resonances. The reflection spectrum for the 180nm grating thickness was calculated for the edge/center/edge NPs configuration showing the existence of the resonance at around 844nm. In the edge/center/edge NPs configuration with 180nm grating the resonance at 704nm in the reflection spectrum seen for the centered NPs/grating configuration get shifted to 734nm. This is due to the existence of the dense NPs array in the case of edge/center/edge configuration which can explain the peak at 734nm in the enhancement in Figure 5a.

Figure 5. (a) Maximum field intensity enhancement versus wavelength for the edge/center/edge NPs grating configuration under TM polarization. The grating and spacer thicknesses are 180nm and (2 or 4nm) respectively. (b) Intensity distribution at different wavelengths. The legends in the figures in (b) show the maximum intensity enhancement at the specific wavelengths.

The effect of the dielectric spacer thickness was also investigated and the maximum field intensity enhancement was calculated for 2nm spacer thicknesses in addition to 4nm. Figure 5a shows that an improvement of at least one order of magnitude is obtained in the enhancement factor at the spectral range between 530-950nm when 2nm spacer is used instead of 4nm due to the stronger ESP-LSP and cavity-LSP modes coupling. Note that using 2nm instead of 4nm spacer thickness, the peak at 844nm shifted to 870nm while those at

662nm and 734nm remain the same. The enhancement factor at the spectral range between 1300-2000nm was improved by factor ˜×3 as a result of using 2nm spacer. Note that the field at the spectral the range between 950-1300nm is always very small (for the three configurations with and without NPs) regardless the used spacer thickness (there is some improvement but it is still not enough) because of the very broad resonance in this spectral range (see the reflection spectrum in Figure 2a). This leads us to look for different mechanism to improve the field enhancement at this range.


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One way to do that is to increase the grating thickness which will be discussed in the next section. An example of the field distribution at different spacer thicknesses was performed at 600nm and is shown in the sub-figure of Figure 5a; one can observe the stronger field located at the NPs-grating gap in the case of 2nm spacer in comparison to the 4nm case. Intensity distribution at different wavelengths for the edge/center/edge NPs-grating configuration is shown in Figure 5b. The field distribution calculation showed that the coupling between the LSP mode of the edge NPs and the ESP or cavity mode is always stronger than the coupling between the LSP mode of the central NPs and the ESP or cavity mode. This causes more intense hot spots around the edge NPs as it can be seen in Figure 5b, a fact which is also demonstrated through the calculation of the average intensity enhancement over the entire NPs surfaces (see Figure 6b). To conclude, using the edge/center/edge NPs-grating configuration with 4nm spacer, an improvement of around one order of magnitude is obtained in the visible range in comparison to the case of using grating without NPs. Improvement in the SWIR wavelengths was also obtained (see Figure 5a) in comparison to the case of grating without NPs (see Figure 2b). Additional improvement of the intensity enhancement at the whole spectral between 4002000nm was achieved by using 2nm spacer instead of 4nm spacer (see Figure 5a). Hence the improvement we achieved in the enhancement factor was at least 1-2 orders of magnitude more than grating without NPs configuration (see Figure 2b) in a wide spectral range. This is important for many plasmonic assisted processes such as in solar energy harvesting, biosensing with enhanced spectroscopies, photocatalysis and improving the efficiency of infrared detectors and lasers. Figure 6a shows the average calculations of the enhanced intensity inside two regions called region 1 and region 2. In region 1 a box around the NPs with the dimensions shown in the figure was taken into account to show the average field in the vicinity of the NPs. In x-direction the whole grating period is considered, in y-direction 20nm distance from each side of the edge NPs edge is considered while in z-direction covers the dielectric spacer, the NPs and 20nm above them inside the analyte. Region 2 includes the following: in x-direction the whole grating period is considered, in y-direction the whole unit cell is considered (500nm length) while in z-direction covers the dielectric spacer, the NPs, the grating spaces and 20nm above the NPs inside the analyte. The idea is that region 1 will help to estimate the average field close to the NPs while in addition region 2 takes into account the field inside the grating spaces. This is important for applications in which the molecules can exist inside the grating spaces as well as for solar cell applications where the active material can be located in the grating spaces. Although the volume of region 2 is larger than that of region 1, we can see in Figure 6a that at wavelengths around 1750nm the average inside region 2 is larger than that inside region 1. This is due to the fact that region 2 includes the space where there is a significant contribution to the average field at these wavelengths. On the other hand Figure 6b shows the average calculations over the surfaces of NPs (Edge NPs and the central one). In contrast to the central NP, the edge NPs are contributing to the ESP-LSP

and cavity-LSP modes coupling in the whole spectral range, hence one can observe in Figure 6b that the average over the surface of the edge NPs is larger than the one over the surface of the central NP for the whole spectral range. Figure 6 indicates that molecules in the vicinity of the NPs surfaces will feel larger average field than the ones located far away from the NPs surfaces.

Figure 6. Average field intensity enhancement versus wavelength for the edge/center/edge NPs grating configuration under TM polarization. (a) In two different regions around the NPs. (b) Over the surfaces of the NPs. The boxes shown in (a) are the regions used for averaging in the two boxes, while the surfaces shown in (b) are the surfaces used for averaging over the two NPs surfaces. The grating and spacer thicknesses are 180nm and 2nm respectively.

Increasing the metallic grating thickness. Additional improvement of the configuration performance was achieved by increasing the thickness of the grating to 800nm while keeping the other parameters as the ones used in Figure 5 (with 2nm spacer) including the polarization, this leads to excite additional resonances as it can be observed in Figure 7a. The main contribution of increasing the grating thickness is the achievement of the relatively narrow resonance at 1340nm (in comparison to the one at 1235nm for the 180nm grating thickness case in Figure 2a). This helped to improve the field enhancement between 1300-1400nm. Hence Figure 7b shows additional enhancement of around one order of magnitude between 1300-1400nm in comparison to Figure 5a while at the other wavelengths the performances of the two configurations (edge/center/edge NPs configuration with 180nm and 800nm metallic grating thickness) are almost the same. Note that the enhancement is over the whole visible and near infrared (NIR) ranges, a fact which is very useful for SEF and SERS related



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applications. For the short wavelength infrared (SWIR) range the enhancement is partial but can be optimized and increased as per demand by mainly adjusting the grating parameters and by choosing larger NPs to achieve LSPR at longer wavelengths (higher LSPR modes). One more way to improve the enhancement in the SWIR range is to work at oblique angles. For example for the case of the 180nm grating, we made a quick calculation for 5˚ incidence angle showing that additional resonance appears at 1420nm in the reflection spectrum of the grating in comparison to 0˚ incidence angle. Higher incidence angles bring additional resonances and therefore the enhancement is expected to be large over a wide entire angular range. Figure 8 shows the same concept of average calculations as presented in Figure 6 (same configuration but for the 800nm silver grating thickness). Note that additional peak is obtained between 1300-1400nm in the average calculations in Figure 8.

Figure 8. Average field intensity enhancement versus wavelength for the edge/center/edge NPs grating configuration under TM polarization. (a) In two different regions around the NPs. (b) Over the surfaces of the NPs. The grating and spacer thicknesses are 800nm and 2nm respectively.

Structure performance test under TE polarization. In this study we tested the performance of the structure under TE polarization in an attempt to propose a structure with polarization independence performance. We took the same configuration from Figure 1 with 800nm and 2nm grating and spacer thicknesses respectively under TE polarization and calculated the reflection spectrum both with and without NPs to show the contribution of adding the NPs for the excitation of resonances that did not exist under TE polarization for the grating without the NPs case.

Figure7. (a) Reflection and transmission spectra from the grating structure of Figure 1 but without the NPs. The grating and the dielectric spacer thicknesses are 800nm and 4nm respectively. The calculations were done under TM polarization. (b) Maximum field intensity enhancement versus wavelength for the 800nm and 2nm grating and dielectric spacer thicknesses.

Figure 9. Reflection and transmission spectra from the grating structure of Figure 1 for both cases of with and without the NPs. The grating and the dielectric spacer thicknesses are 800nm and 2nm respectively. The calculations were done under TE polarization.


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Figure 9 shows the advantage of adding the NPs on top of the grating in order to produce new resonances that are located at the visible range which do not exist with only using the grating (without NPs) under TE polarization. This is due to the ability of the NPs array to act as a 2D grating to support the excitation of these resonances. Without NPs no considerable enhancement was obtained under TE polarization and the field was extremely small for the whole spectral range. Hence also under TE polarization the structure with edge/center/edge NPs provided enhancement improvement which was found to be larger by around 3 orders of magnitude than the case without NPs at least in the visible range (see the field enhancement in Figure 10). This is particularly important for solar energy harvesting as the solar light is mostly unpolarized. Figure 11 shows the same concept of average calculations as presented in Figure 8 (same configuration but under TE polarization). A noticeable improvement in the different average calculations was obtained by adding the NPs in comparison to the case without them. As mentioned before we are not worried about having similar field enhancements both at TE and TM polarizations because this can be easily achieved by using two dimensional grating structure, or two sets of grating lines oriented perpendicular to each other. In many lab experiments the polarization is important such as with polarized SEF and SERS, however when energy harvesting is considered from the sun, then polarization independence is important. Figure 11. Average field intensity enhancement versus wavelength for the edge/center/edge NPs grating configuration under TE polarization. (a) In two different regions around the NPs. (b) Over the surfaces of the NPs. The grating and spacer thicknesses are 800nm and 2nm respectively.

Figure 10. (a) Maximum field intensity enhancement versus wavelength for the grating structure of Figure 1 with edge/center/edge NPs on the grating. The dielectric spacer thicknesses are 800nm and 2nm respectively. The calculations were done under TE polarization. (b) Intensity distribution at some off and on resonance wavelengths. The legends in the figures in (b) show the maximum intensity enhancement at the specific wavelengths.

CONCLUSIONS

A unique strategy is proposed to achieve ultrahigh enhancement of local EM fields over a wide spectral range (400-2000nm). This enhancement is attributed to the coupling between the different resonance modes (ESP and cavity modes) generated by the silver grating with the LSPs on the dispersed gold NPs on top of the grating. The simulations showed that enhancement factor up to 3 orders of magnitude higher than the case with the LSPs excitation is from free space. A noticeable advantage of this configuration is the easy tuning of the enhanced spectral range by simply adjusting the parameters of the grating such as the period, thickness, depth and aspect ratio. The maximum enhancement is obtained when the LSPR coincides with the other resonance mode (ESP or cavity mode). One more way to control the enhanced spectral range is to choose the appropriate NPs size to match the LSPR with the other resonance modes generated by the grating. We used 50nm radius of the gold NPs which is more appropriate for the coupling in the visible and near infrared ranges. For solar energy harvesting or improving the efficiency of infrared detectors, there is a place for optimization of the NPs radius to match the longer wavelengths. The same is true for optimizing the gratings parameters. Depending on the application one can further optimize the NPs diameter, the gratings parameters to get even higher enhancement. The contribution of adding the NPs on top of the grating in terms of the field enhancement is found to be significant under TM and TE polarization states. Wherein the enhancement under TM



polarization is due to the coupling between the LSPs to the different resonance modes generated by the metallic grating (ESPs and cavity modes), the enhancement under TE polarization is mainly due to the ability of the NPs periodic array to generate new ESP resonances which do not appear without adding the NPs. This study highlights new strategy for obtaining ultrahigh field enhancements over wide spectral range, useful for solar energy harvesting and improving the efficiency of optoelectronic devices in the infrared range. One can think of many other types of periodic structures such as two and three dimensional, having different shapes of unit cells, combination of several orientations, depths and periods to extend the spectral range even wider, reduce the polarization and incidence angle sensitivity.

ASSOCIATED CONTENT Supporting Information Additional informative plots of the distribution of the intensity of the electric fields.

AUTHOR INFORMATION

Corresponding Authors *E-mail (Shuzhou Li): [email protected] (Tel: +6567904380) *E-mail (Ibrahim (Tel: +97286479803)

Abdulhalim):

[email protected]

ORCID ID Mohammad Abutoama: 0000-0002-4286-0434 Shuzhou Li: 0000-0002-2159-2602 Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS

This research is partially supported by the Israel-China binational research grant of the Ministry of Science Technology and Space of the State of Israel and the Ministry of Science and Technology of P.R. China. Mohammad Abutoama is funded by the Ministry of Science, Technology and Space, Israel (8753881) and the Kreitman Graduate School. This research is partially supported by grants from the National Research Foundation, Prime Minister’s Office, Singapore under its Campus of Research Excellence and Technological Enterprise (CREATE) programme.

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Widening the Spectral Range of Ultrahigh Field Enhancement by

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