Optical Excitation of Surface Plasmons

The dispersion relations of SPPs on a planar metal/dielectric interface given by Equation (2.24) imply that at a given frequency, the in-plane wavevector of the SPP is always larger than that of the incident light. This means in general SPPs and light do not interact with each other because the energy and/or momentum mismatches. Therefore, it is not possible to excite SPPs on a flat metal surface by just illuminating it, nor can SPPs spontaneously decay into photons in such system.

There are several methods to couple light and SPPs, including attenuated total reflection (ATR) [36] [37], grating or surface roughness coupling [10] and end-fire coupling [48] [49].

The ATR method is also known as prism coupling; it employs an optically dense medium (e.g., prism) in the vicinity of the planar metal surface to generate an evanescent optical field near the metal via total internal reflection. This evanescent optical field increases the wavevector of the light in the direction parallel to the metal surface to match the wavevector of the

SPPs, resulting in SPP excitation on the planar metal surface. If the SPPs are excited on the interface of a dielectric medium with dielectric constant εd and a metal with dielectric constant εm = ε0m + iε00m, the condition for

light-SPP coupling becomes kx = ω c √ εpsinφ = ksp = ω c s εdε0m εd+ ε0m , (2.39)

where kx is the vector of light in the direction parallel to the metal/dielectric

interface; φ is the angle of incident of the light inside the prism; εp is the

dielectric constant of prism and εp > εd.

Figure 2.9 below illustrates two ATR based arrangements: the Otto configuration and the Kretschmann-Raether configuration. These schemes have been extensively used for studying the dispersion relation of SPPs and for measuring the dielectric constant of metals since the late 1960s. The occurrence of light and SPP coupling is captured by monitoring the spectral reflectance, using light of different wavelengths at a fixed angle of incidence or vice versa. A distinct, sharp dip appears in the reflection spectrum where light is coupled to SPPs. Close to 100% coupling efficiency can be achieved in these systems.

On the other hand, grating or surface roughness coupling methods utilize diffracting elements to provide additional transverse momentum to the photons for light-SPP interaction, such as shown in Fig. 2.10. In this case, the following dispersion relation is satisfied:

kx = ω c √ εdsinθ + ∆kx= ksp = ω c s εdε0m εd+ ε0m , (2.40)

where θ is the incident angle of the light; and ∆kx represents the contribution

§ 2. Background 28

Figure 2.9: Two ATR based arrangements. In Otto configuration the evanescent optical field couples with the SPPs on the inner metal surface; in Kretschmann-Raether configuration, the evanescent optical field couples with the SPPs on the outer metal surface. Here εp, εm and εdrefer to prism,

metal and air.

∆kx is the grating vector, which is defined as

kg = m

2π

P (m = ±1, ±2, ±3, . . . ), (2.41) where m is the diffraction order and P is the grating period. For surface roughness coupling, ∆kx is the roughness Fourier spectrum of the

metal/dielectric interface.

Figure 2.10: A grating coupling configuration for optical excitation of SPPs. In addition, corrugated metal surfaces were used together with the ATR method (Otto configuration) to decouple SPPs to free propagating light

in the early studies of SPPs [10]. Such systems generally consist of a prism, a photoresist grating prepared on the hypotenuse face of the prism and a thin metal film deposited on top of the grating surface. Recently, grating coupling has been extensively used in SP based applications due to its desirable compact arrangement. Thanks to the advanced micro/nano fabrication techniques, the periodic structures used for light-SPs coupling are no longer limited to the corrugated metal films. A wide variety of structures have been proposed to achieve light-SP interaction, such as metal films with subwavelength hole arrays [9], single apertures surrounded by periodic textures [50], metallic gratings with subwavelength slots [51] and planar/patterned multilayer systems [52] [53]. In this thesis, the grating coupling method was employed to achieve light-SPPs coupling.

The prism coupling and the grating coupling are both based on matching the in-plane wavevector component of the incident light to that of the SPPs. Conversely, the end-fire coupling method excites SPPs along a metal/dielectric interface by focusing light onto the end face of the metal- dielectric system that is normal to the interface [48], as illustrated in Fig. 2.11. The operation is based on overlapping the profile of the incident beam and the SPP field distribution on the end-face of the system, and the maximum SPP generation efficiency occurs when the width of the incident beam equals the penetration depth of SPPs at x = 0 plane. This scheme is considered to be an effective method to excite SPPs in SPP waveguides [54] [55] [49] [56].

It should be emphasized that, as opposed to the SPPs, optical excitation of LSPs does not require any special arrangement. As indicated by Equations (2.35) and (2.36), the momentum mismatch between SPPs and light does not exist at LSP resonances. Therefore, LSPs can be resonantly excited by light

§ 2. Background 30

Figure 2.11: Arrangement for optical excitation of SPPs by end-fire coupling. with appropriate polarization and wavelength, irrespective of the wavevector of incident light; they also can decay to freely propagating light naturally.