Asymmetric light reflectance from metal nanoparticle arrays on dielectric surfaces

Asymmetric light reflectance associated with localized surface plasmons excited in metal nanoparticles on a quartz substrate is observed and analyzed. This phenomenon is explained by the superposition of two waves, the wave reflected by the air/quartz interface and that reflected by the metal nanoparticles, and the resulting interference effects. Far field behavior investigation suggests that zero reflection can be achieved by optimizing the density of metal nanoparticles. Near field behavior investigation suggests that the coupling efficiency of localized surface plasmon can be additionally enhanced by separating the metal NPs from substrates using a thin film with refractive index smaller than the substrate. The latter behavior is confirmed via surface-enhanced Raman spectroscopy studies using metal nanoparticles on Si/SiO2 substrates.

by including a thin film with optimized thickness. This behaviour provides a general method to enhance the LSPs coupling efficiency that may improve the performance of the LSPs based devices for a variety of applications.

Results
Far field behaviour. Figure 1(a-d) present the far field transmittance and reflectance spectra, respectively, of Au and Ag NP arrays on a quartz substrate. One can see from Fig. 1(a) that when light is incident normally from air to the air/Au NPs/quartz interface (designated as front incident), the transmission spectrum shows a valley at approximately 525 nm corresponding to the LSP resonance mode of the Au NPs. When light is incident normally from the quartz substrate (designated as back incident), the transmission spectrum is almost the same as that of front incident, agreeing with the principle of reciprocity. Similarly, a dip in transmittance near the LSP resonance wavelength and nearly identical transmission spectra for front and back incidence are observed for Ag nanoparticles, as seen in Fig. 1(b). However, the reflectance spectra when light is incident from different directions differ substantially, as shown in Fig. 1c for the structure with Au nanoparticles on quartz. At the LSP resonance wavelength, the reflectance spectrum measured from the front side shows a peak while the spectrum measured from the back side shows a valley. For the sample consisting of Ag NPs on quartz substrate, peaks are seen in the reflectance spectra when light is incident from both sides. However, when light is incident from back side, the peak intensity is smaller than that when light is incident from front side (Fig. 1d).
The behavior seen in Fig. 1 can be explained using a model based on modified Fresnel coefficients 23 . This model take into account excess current and charge densities present due to the discrete subwavelength metal NPs at the interface. For a plane wave propagating through a medium with refractive index n i toward an interface consisting of metal NPs against a medium with refractive index n t , the reflection coefficient r for a normally incident wave can be written as where V is the volume of the NPs, ω LSPR is the LSP resonance frequency, and L is a geometrical depolarization factor calculated by the image dipole theory 23,26 . For a hemisphere structure, one can obtain ≈ .
L 0 1. γ ≈ . × / rad s 2 5 10 0 13 are the width of resonance determined by the resistive Drude damping factor 25 and the factor ω = / F ah c L 9 LSPR 2 2 3 describes the radiative damping contribution that arises due to the finite size of the particle. Thus, one can see that when the frequency of the incident wave is equal to the LSP resonance frequency, i.e. ω ω = LSPR , the additional term arising from the localized surface plasmon, , is a positive real number. Equation (1) can then be written as One can see that when is the reflection coefficient for normally incident light when there is not any subwavelength metal NPs located at the interface. Thus reflectance | | r front 2 is greater than r 0 2 , which means that the reflectance spectrum measured from the front side exhibits a peak at wavelengths close to the localized surface plasmon resonance wavelength.
When > n n i t , which corresponds to the back incident situation, we obtain | = | , we see that < r r back 0 , and the reflectance spectrum will exhibit a valley at wavelengths close to the localized surface plasmon resonance wavelength as shown in Fig. 1 , we see that | | > | | r r back 0 , and the reflectance spectrum will contain a peak as shown in Fig. 1(d). However, regardless of the value of A LSPR , | | r back is smaller than | | r front . Thus when light is incident from the back side, the reflectance at wavelengths close to the localized surface plasmon resonance wavelength is smaller than that when light is incident from the front side. Figure 2 illustrates the mechanism leading to the asymmetric light reflectance phenomenon described above. For a plane wave propagating through a medium with refractive index n i toward an interface consisting of metal NPs against a medium with refractive index n t , the reflected wave can be regarded as superposition of two waves: the reflected wave from the interface without metal NPs on it and the reflected wave arising from the metal NPs. Thus the reflection coefficient arising from the metal NPs can be written as From Equation (3) one can see that r LSPR is a negative real number which indicates that a-phase shift of π is introduced when light is reflected by metal NPs. When light is incident from the medium with lower refractive index, the superposition of the two reflected waves leads to constructive interference. Thus the reflectance spectrum always shows a peak at wavelengths close to the localized surface plasmon resonance wavelength. When light is incident from the medium with higher refractive index, however, the superposition of the two reflected waves leads to destructive interference. Thus, when A LSPR is not too large, the reflectance spectrum exhibits a valley rather than a peak at wavelengths close to the localized surface plasmon resonance wavelength (Fig. 2a). One can see that, to a certain degree, this phenomenon is similar to the asymmetric light reflectance effect we have reported previously in AAO on glass 27 . However, the phenomenon observed here still has some major differences from previous report, which are described as follows. (i) This phenomenon is wavelength selective and can be regulated by the resonance wavelength of the LSPs. (ii) The two superposing waves come from metal NPs and dielectric interface which attach to each other rather than two separated interfaces. (iii) Metal nanostructure is not necessarily to be embedded into an optical film. Thus it is more suitable for further near field applications.
One can see both the volume and density of metal NPs will affect the value of A LSPR and therefore the reflectance intensity. If the diameter of the metal NPs is relatively small, peaks will not be present in the reflectance spectra when light is incident from back side even with relatively high NPs density. Figure 2b shows the simulated reflectance spectra of Au NPs (10 nm in diameter) with density as high as 2.9 × 10 3 μ m −2 , the reflectance spectra show peak and valley when light is incident from front and back sides respectively. When the diameter of metal NPs is relatively large, the far field behavior can be tuned by varying the densities of the NPs. In particular, when = − A n n LSPR i t , the reflection coefficient is zero at the the LSP resonance wavelength. Since A LSPR is a positive real number, zero reflectance can happen only when light is incident from the medium with high refractive index. Figure 2c-d show the simulated reflection spectra with different Au NPs densities. One can see that when the density of Au NPs (60 nm in diameter) equals to 80.2 μ m −2 ; the reflection spectra show peaks regardless the incident directions (Fig. 2c). For the large Au NPs with relatively low densities, the reflectance spectra show valleys when light is incident from the back side (Fig. 2d). One can see that when the density of Au NPs increases, the valley intensity decreases close to zero first and then increases. When the density of Au NPs equals to 28.9 μ m −2 , the reflection intensity at the LSP resonance wavelength can be as low as 0.15%. (3) also indicates that when light is incident from media with different refractive indices, the reflection coefficients associated with the metal NPs are not the same. The reflection by metal NPs can be regarded as arising from a portion of the light scattered by the metal NPs. Fig. 3b shows the simulated extinction spectra of a single hemisphere Au NP (60 nm in diameter) on quartz when light is incident from front and back sides. Extinction peaks at approximately 600 nm are present in both spectra regardless of the incident direction of the light. However, the peak intensities are different. When light is incident from the front side, the extinction peak intensity is smaller than that when light is incident from the back side. At the LSP resonance wavelength, the extinction peak intensity when light is incident from the back side is approximately 1.5 times that when light is incident from the front side.

Near field behavior. Equation
This behavior can be explained by the different local driving field intensities E d at the position of the Au sphere when light is incident from different directions. When light is incident to the air/NPs/substrate, the local driving field intensities can be regarded as superposition of field intensities of incident wave and reflecting wave as shown in Fig. 3a , where E dF and E dB are the local driving field intensities of LSPs when light is incident from front and back side respectively, n 1 and n 2 are the refractive indices of the materials above and beneath the Au sphere respectively. Despite the different LSP resonance wavelengths caused by the different effective refractive indices beneath the NPs, one can see from  28,29 . In this way, the efficiencies of the LSPs enhanced solar cells and the intensity of the surface-enhanced Raman scattering (SERS) signal have been significantly enhanced. However, if light is not generated from the devices, the energy loss by reflection , where h is the thickness of the thin film, and λ is the wavelength of the incident wave. One can see that when − > − n n n n 3 2 2 1 , the local driving field intensity of LSPs shown in Fig. 4b will be higher than that shown in Fig. 4a. Figure 4c shows the local driving field intensity of LSPs as a function of h, where A LSPR , n 2 and n 3 are set as 0.6, 1.5 and 3.5 respectively, λ equals to 532 nm. One can see that when , the local driving field intensity of LSPs is maximized. Figure 4d presents SERS results of R6G molecules using Au NPs/SiO 2 /Si as substrates. One can see that when the thickness of SiO 2 equals to 90 nm and 270 nm, the SERS signals are much larger than when the thickness of SiO 2 equals to 0 nm and 180 nm.

Discussion
In summary, we observed the asymmetric light reflectance phenomenon in metallic NPs fabricated on quartz substrate. The difference of the reflectivity when light is incident from different directions can be attributed to the superposition of waves reflected from metallic NPs and from the dielectric medium interface. A modified Fresnel coefficient model indicates that the phase shift of the wave reflected from metal NPs should be π . Thus the superposition between the reflected waves from metallic NPs and dielectric medium interface creates either constructive or destructive interference when light is incident from media with lower or higher refractive indices, respectively. Theoretical analysis and FDTD simulation suggest that this behavior can achieve zero reflectance via adjusting the density of metal NPs that can enhance the sensitivity of LSP sensors. Near field FDTD simulation shows that the ratio of the extinction peak intensities when light is incident from different directions equals the ratio of the refractive indices of two mediums beside the interface, implying that when light is incident from the medium with higher refractive index, metallic nanostructures would have higher coupling efficiency with the incident light. This behavior can be attributed to the different local driving field according to the Fresnel equation. Further investigating shows that the LSPs coupling efficiency when light is incident from air can be regulated by separating the metallic NPs from substrate using a low refractive index thin film. The highest LSPs coupling efficiency is achieved when the thickness of the thin film equals to , ( = , , , .....) . This work provides a general method to opti-

Methods
Sample Fabrication. Au and Ag NPs were fabricated on quartz wafers of 0.5 mm thickness. The quartz wafers were ultrasonically degreased in acetone, ethanol and then double deionized water for 3min each. Au and Ag films with thickness of approximately 2 nm were sputtered by using SCD005 (Balzers Union, Balzers, Liechtenstein). The sample was then annealed in N 2 ambient by using the RTA device at 450 °C for 60 s to form Au and Ag NPs. The average sizes of fabricated Au and Ag NPs are 28 and 20 nm respectively. The densities of Au and Ag NPs are 8.5 × 10 10 and 4.5 × 10 10 cm -2 respectively. For SERS measurement, SiO 2 /Si wafers with different SiO 2 thickness were used as substrates to fabricate Au NPs. The thickness of dry-oxidized SiO 2 layers was 0 nm, 90 nm, 180 nm and 270 nm respectively. Au film with thickness of approximately 2 nm was then sputtered and followed by annealing in N 2 ambient by using the RTA device at 700 °C for 60 s to form Au NPs.

Measurements and Simulations.
The optical characterizations of transmittance and reflectance spectra were performed using a UV-Vis-NIR spectrophotometer (Varian Cary 5000). All simulations in this work were performed with commercial Lumerical FDTD solutions (version 7.5) software. The incident plane wave propagated perpendicular to the interface of two media from z or -z directions with the same incident energy density. The polarization direction of incident wave is along the x-direction. The refractive index of quartz was set as 1.5. SERS spectra were acquired using a confocal Raman system (Xplora, Horiba) using 532 nm laser excitation. The laser power was 5mW for the SERS measurements. The typical exposure time for our measurements was 20 s. All the spectra are presented after baseline correction by a polynomial fitting method. The SERS analysis probe R6G was dissolved in DI water to a concentration of 10 −4 mol/L. The samples were soaked in the R6G solution for 1h. Then the samples were taken out and rinsed using DI water followed by drying in N 2 gas.