Experimental Demonstration of Surface Plasmon Polaritons Reflection and Transmission Effects

Special integrated photonic surface structures composed of a dielectric semicircle ridge and a dielectric block placed on a metal substrate are proposed for the investigation of surface plasmon polariton (SPP) reflection and transmission effects. A fabrication method called microscope projection photolithography was employed for the preparation of the structures. Leakage radiation microscopy was applied for the excitation and observation of surface plasmon polaritons (SPPs). It was observed that SPPs exhibit a remarkable decrease in intensity when impinging onto the rectangular dielectric block. Nevertheless, the transmitted wave out of the dielectric block was always observable. The propagation behavior of both the reflected waves at two boundaries (air/dielectric and dielectric/air) and the transmitted wave inside the dielectric block were demonstrated for different SPP incident conditions. The variation of the angles of reflection and transmission with respect to the incident angle was analytically and experimentally investigated. An agreement between the calculated results and the experimental results was obtained. Our findings might allow for novel applications in sensing and analytics once the structures will be functionalized.

In this paper, a novel integrated photonic surface structure (Figure 1a) was created with the purpose of investigating the reflection and transmission effects of propagating SPPs at the interface on two different media. The proposed structure, which was placed on a metal film, is composed of a dielectric semicircle ridge and a dielectric block as illustrated in Figure 1a. The ridge was used as a surface defect to excite SPPs by focusing a laser beam onto it and controlling the incident angle of the SPPs. The dielectric block was used to generate a space with a different dielectric constant from the surrounding air. The commonly used metals for the generation of surface plasmons are silver and gold. In this experiment, silver was used due to its longer SPP propagation length than gold [11]. The reflection and transmission of SPPs take place at the boundary between the air and the dielectric block as illustrated in Figure 1b. Additionally, SPPs can also be scattered into light waves propagating away from the metal surface, which decreases the intensity of the reflected and transmitted SPPs.
As to the preparation of samples, a silver film with the thickness of 60 nm was first spin-coated on a clean glass substrate. For the fabrication of proposed structures, the smoothness of the semicircle ridge and the lateral surface of the dielectric block has to be guaranteed in order to reduce the scattering of SPPs and thus improve the performance of the structure. With this consideration, a technique called microscope projection photolithography (MPP) [68], which is able to implement a fast fabrication process and achieve high structuring quality, was employed for the preparation of the proposed surface structure. Afterwards, leakage radiation microscopy (LRM) [69], which visualizes the propagating SPPs by collecting the waves leaked out of the substrate, was applied to excite and observe SPPs on the fabricated structures. A schematic diagram illustrating the principle of LRM for generating and visualizing SPPs is presented in Figure 1c. A detailed introduction of the system can be found in ref [69]. When the laser beam (the wavelength λ = 800 nm) is focused onto the ridge of the proposed structure, SPPs are excited and propagate to both the outer and inner radial directions of the ridge. Along the inner direction, SPPs propagate towards to the dielectric block. The reflection and transmission of SPPs at the boundaries between the air and the dielectric block can be observed using the LRM setup. By moving the laser focus along the semicircle ridge, the incident angle of SPPs striking onto the dielectric block can be varied. The dependence of the angles of reflection and transmission on the incident angle of SPPs is investigated and discussed both analytically and experimentally.

Theoretical Model
It is known that when a plane wave impinges onto a boundary between two homogeneous media with different dielectric constants, the plane wave can be split into a reflected wave and a transmitted wave, with the reflected wave propagating back to the first medium and the transmitted wave proceeding into the second medium [70]. The propagation directions of the reflected wave and the transmitted wave can be expressed using θ r = θ i (the law of reflection) and k t sin θ t = k i sin θ i (Snell's law) [70], with θ i indicating the angle of incidence, θ r the angle of reflection and θ t the angle of transmission, k i the wave number of the incident light and k t the wave number of the transmitted light. Both laws are deduced from the boundary conditions, which have to be satisfied for the existence of the reflected and transmitted waves. Therefore, the reflection and transmission of surface plasmon polaritons (SPPs) have to fulfil the boundary conditions at the interface between isotropic media with different dielectric constants.
A geometrical illustration of the reflection and transmission of SPPs at the boundary of two homogeneous media with the dielectric constants ε 1 and ε 2 is presented in Figure 1b. In this work, the dielectric block is made of ma-N 1405, which is a commercially available photoresist from micro resist technology GmbH and has a dielectric constant ε 2 = 2.64 at the wavelength of 800 nm. The dielectric constant of air is ε 1 = 1. With electromagnetic radiation at the wavelength λ = 800 nm, silver has the complex dielectric function ε Ag = −30.33 + 0.81i, which is calculated using the formula in the ref [11]. Here, we assume that the dielectric medium and Ag are in the region z > 0 and z < 0, respectively. At boundary 1 (see Figure 1a), x = 0. When SPPs propagate along the interface of Ag and a dielectric, the field of SPPs has a component ∝ e −iωt+i(k x x+k y y) in the interface plane and exhibits exponential decay away from the interface. The dispersion relations of SPPs can be expressed as [1,11]: where k spp1 and k spp2 represent the wave number of SPPs at the interface of Ag/air and Ag/ma-N 1405, ω indicates the angular laser frequency and c is the light velocity in vacuum. The angles of reflection and transmission are more related to the real component of the wave vector rather than its imaginary part, therefore only the real component of k spp is considered for the following calculation and discussion. Combining the above equations with the law of reflection and Snell's law [70], the angles of reflection (θ r1 and θ r2 ) and transmission (θ t1 and θ t2 ) at boundaries 1 and 2 (see Figure 1a) can be written as: At boundary 1 (ε 1 → ε 2 ), At boundary 2 (ε 2 → ε 1 ),

Results and Discussion
The proposed structures were fabricated by microscope projection photolithography (MPP). The commercial material ma-N 1405 (microresist technology GmbH) was employed for the fabrication. The refractive index of this material is approximately 1.625 at the wavelength of 800 nm. Figure 2 shows SEM images of fabricated structures obtained with an exposure time of 1000 ms. Structures with radii of r = 20, 25, 30 and 40 µm (see Figure 2) were fabricated, respectively. Smooth semicircle ridges and good surface quality dielectric blocks can be observed on each structure. With the exposure duration of 1000 ms, the height of the dielectric block is approximately 700 nm (Figure 2f).
When excited in the ridge, SPPs propagate along the radial direction at the boundary between Ag and air, with the wave vector k spp1 = ω c ε 1 ε Ag ε 1 +ε Ag . When striking onto the dielectric block, the transmitted wave proceeding into the dielectric then propagates at the interface between Ag and the dielectric, with k spp2 ≈ ω c ε 2 ε Ag ε 2 +ε Ag . The propagation lengths of SPPs along the interfaces of Ag/air and Ag/dielectric were calculated using L spp = 1 2k spp [11]. They are approximately 140 µm and 30 µm at the wavelength of 800 nm, respectively. The length of 140 µm is much greater than the obtained maximum radius of the semicircle (40 µm), and 30 µm is larger than the width of the dielectric block (10 µm). Therefore, all the structures could be used for the investigation of the SPP propagation behavior. In this work, the structure with r = 40 µm was employed for the experimental investigation for the purpose of ensuring better observation of SPPs in a relatively large space. By installing the sample into the leakage radiation microscopy (LRM) setup and focusing the laser beam onto the semicircle ridge, SPPs can be excited and propagate along the radial direction of the semicircle. Figure 3a is the LRM image of SPPs excited using the proposed structure. Surface plasmon polaritons are split into reflected wave and transmitted wave, when impinging onto the boundary between air and dielectric. The transmitted wave proceeds into the dielectric block and strikes onto boundary 2, where the wave propagates from a dense medium (dielectric) to a thin medium (air). In this case, the wave will be totally reflected when the incident angle θ i2 θ c , with θ c = arcsin k spp1 k spp2 = 36.73 • indicating the critical angle of total reflection. However, the total reflection does not occur at boundary 2, since the incident wave is exactly the transmitted wave at boundary 1, where SPPs proceed from air into the dielectric block. Based on Snell's law, the angle of transmission θ t1 , which equals the incident angle θ i2 , can not exceed θ c . In the image plane (Figure 3a), the transmitted wave out of boundary 2 is visible, while the reflected wave and transmitted wave at boundary 1 are only weakly observable. Consequently, an observation of propagating SPPs in the Fourier plane (Figure 3b) was performed, on which the propagation directions of the waves can be more explicitly visualized.  By moving the laser focus onto different positions on the semicircle ridge, the incident angle of SPPs impinging onto boundary 1 can be controlled. Here the reflection and transmission of SPPs with the variation of the incident angle θ i1 (in the range of 0-90 • ) at both boundaries 1 and 2 were observed. Figure 4 presents the images (in the image plane) of SPP propagation with different incident angles. The intensity of SPPs is greatly reduced when the waves hit onto the dielectric block. The reflected waves at those two boundaries and the transmitted wave into the dielectric block are weakly visible. Their existence can only be identified in the Fourier plane. Nevertheless, the transmitted waves out of boundary 2 are always observable in the image plane. Also, an intensity variation of the transmitted wave with respect to θ i1 can be seen. The angles of incidence (θ i1 ) and transmission (θ t1 and θ t2 ) can be measured in the figures obtained in the image plane. Additionally, observations of propagating SPPs in the Fourier plane were also performed, from where the angles of reflection (θ r1 ) for different incident angles are measurable. Here, the angle of reflection at boundary 2 (θ r2 ) is not taken into consideration due to the invisibility of the corresponding reflected waves within most of the incident angle range. For the purpose of improving the measurement accuracy of those angles, multiple measurements of each single angle (θ i1 , θ r1 , θ t1 and θ t2 ) under a fixed wave propagation direction were performed. An average of the multiply measured data for the same angle is taken as the experimental data point (see measured data in Figure 5). The measured data is presented together with an error bar, which is obtained based on the calculated standard deviation. Moreover, the variation of the angles of reflection and transmission with respect to the incident angle was also calculated analytically using Equations (3)- (6). The analytical and measured dependence of the angles of reflection and transmission on the incident angle is presented in Figure 5a indicating the results at boundary 1 and Figure 5b representing the results at boundary 2. Agreement between the analytical results and the experimental results is obtained. It has to be noted that the measurement error mainly results from the irregular form of the propagating SPP waves. Additionally, the weak light intensity for some directions might also affect the measurement results. Furthermore, it will be of significance to simulate and develop an effective approach to quantitatively characterize the intensity variation of propagating SPPs in the proposed structures for better control and optimization of their performance.

Conclusions
In conclusion, the reflection and transmission effects of SPPs at the boundaries between two different dielectrics are investigated. A special surface metallic structure with micrometer-and partially also nanometer-sized dimensions, which is composed of a dielectric semicircle ridge and a dielectric block, was designed and realized for this investigation. A microscope projection photolithography technique was applied for the fabrication of the proposed structures. The excitation of SPPs and experimental observations of their propagation behavior were realized using leakage radiation microscopy. The variation of the angles of reflection and transmission with respect to the angle of incidence was analytically estimated and experimentally measured. The validity of the law of reflection and Snell's law in surface plasmon polaritons (SPPs) is confirmed. The integrated structures reported in this work might lay the foundations for novel applications in sensing when functionalized. This will be part of our future work which will aim at measuring the dependence of the SPP behaviors depending on the environmental conditions.

Conflicts of Interest:
The authors declare no conflict of interest.

Abbreviations
The following abbreviations are used in this manuscript: SPPs Surface plasmon polaritons MPP Microscope projection photolithography LRM Leakage radiation microscopy