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Two superimposed gratings act to couple light to surface plasmon modes at a metal-air interface. A surface plasmon standing wave is created by generating two counter propagating plasmon waves. The wavelength and angle of incidence of the light that generates the surface plasmon standing wave can be selected by selecting the grating spacing of the couplers. The standing wave can then be out-coupled via the same gratings. In addition to affecting the transmission and reflection signals of the film the structure also enhances the light coupled into the forward- and the back-scattered direction.
©2006 Optical Society of America
1. Introduction
Resonant surface plasmons (SP) are electromagnetic modes propagating at a metal/dielectric interface. The fields are strong at the interface and die off exponentially as evanescent fields on either side. Light can be used to excite these electromagnetic modes but the coupling must not only satisfy the law of conservation of energy, it must also allow matching to the plasmon momentum along the direction of propagation. The coupling of light to the SP mode often is done via the evanescent wave generated by the internal reflection from a high index medium or by scattering using a structured surface. Coupling using gratings have seen renewed interest recently because of their role in photonic devices[1–5], surface enhanced Raman scattering[6–9], enhance transmission[10], and photonic band gaps[11–14]. Scattering involving two superimposed gratings has also recently been studied [12] because this can permit further control of the plasmon propagation properties. For example, one grating can be selected to couple light into the plasmon mode while another grating can be designed to produce a band stop (or bandgap) in the plasmon propagation curve. A similar use of multiple gratings to couple light into waveguide modes while modifying the mode dispersion curves have recently been presented [15,16] In some other applications the second grating couples light out from the structures[9] in desired directions. The control of the surface plasmon propagation and coupling is becoming of increased interest as the local high electric fields are used in sensor design.
Here we report a study where two surface gratings are superimposed on an azopolymer film that is then covered with a thin gold film. Both gratings act as couplers to generate surface plasmon traveling waves on the film at the gold/air interface. A proper selection of the structure and the incident light can result in the generation of a surface plasmon standing wave. In the present work we superimpose two surface gratings with grating spacing Λ1 and Λ2. The surface height, h(x), can be described by as the superposition of two sinusoidal functions given as
where h0 is the average surface height, Δh is the surface modulation amplitude and K1=2π/Λ1, K2=2π/Λ2, are the grating wave vectors.
For a light beam incident on the surface at an angle θ there are four plasmon waves generated by first order scattering with the following wave vectors along the surface of the film.
where =±ksp is the wave vector of the plasmon wave produced by light of frequency ωj that is scattered by the grating with grating vector K1 or K2. The surface plasmon wavevector satisfies the following dispersion relation
Consider K1>K2, then one can select a single frequency (ω2=ω3=ω) and angle of incidence such that =-=-ksp and two of the four plasmon waves have the same frequency (wavevector magnitude) and are generated by the two gratings at the same angle of incidence. These are however counter propagating and form a standing plasmon wave at the metal/dielectric interface. This situation is illustrated in Fig. 1.
Fig. 1. Generation of a surface plasma standing wave by counter propagating waves produced by two coupling gratings.
The energy stored in the standing wave can thus lead to a substantial increase in the local fields when the resonance condition is met. In addition the energy in the standing wave can be coupled out of the interface region by the same gratings that coupled the light into the SP. The light coupled out of the film will have the same frequency and will be coupled out (to first order) in four directions as illustrated in Fig. 2. The four directions are A(θout=θ) in the forward transmission direction, B(θout =180+θ) directly back scattered, C(θout=-θ) in the forward scattered direction and D(θout =180-θ) in the reflection direction.
The scattering of light by the two gratings can occur in multiple directions that satisfy the following scattering equation:
Where ni, no, mi, mo are the integer order of the scattering in and out by the gratings. Although the double grating can scatter light in many directions without the presence of the metal, we expect that the coupling to the surface plasmon standing wave by the first order scattering will significantly change the light scattered in these particular directions. The enhancement will only occur when SP are generated.
We note that the forward (C) and back scattered (B) beams involve coupling by both gratings to generate counter propagating waves so that they, in particular, will reflect the presence of a standing wave at the interface. The back scattered beam can be detected using a Littrow mount configuration.
2. Experiment
Surface gratings with spacings of Λ1=529 nm and Λ2=700 nm were produced on azopolymer films by sequential exposure of an interference pattern from two coherent light beams at 532 nm. The inscription technique permits control of both the spacing and depth of each grating. The gratings are formed by optically induced polymer movement as described elsewhere [15–17]. Here we have superimposed two sinusoidal gratings. An atomic force microscope (AFM) image of these superimposed sinusoidal surfaces is shown in Fig. 3.
3. Results and discussion
Pitches of the gratings on the doubly corrugated surface investigated were Λ1=529 nm and Λ2=700 nm, respectively. A typical reflectivity spectrum is presented in figure 4 for light incident on the sample at an angle of 2°.
Here we clearly see that the double grating structure can generate surface plasmons at four separate frequencies as predicted by equation 1. One can then obtain the SP dispersion curve from the reflection spectra at various angles of incidence as shown in Fig. 5.
Fig. 5. Reflectivity curves as a function of wavelength from 550 nm to 1000 nm for various incident angles. Counter propagating plasmons are generated at 8.5° and for λ~ 633 nm
Of particular interest for the present study is the condition for producing a plasmon standing wave with light incident at an oblique angle. Here we see that two counter propagating plasmons are generated for light at 633 nm at an angle of incidence of about 8.5° as was designed by superimposing the gratings with spacings of 529 and 700 nm. Of particular interest to observe the resonant coupling one can measure the signals in the forward scattered and back scattered directions. These are presented in the following figures.
In Fig. 6 we present the backscattered signal.
The difference in the s and p signals clearly emphasize the participation of the surface plasmon at the air-metal interface in the measured signal. The resonance occurs at 8.5° as expected. We also note that at that angle this backscattered beam is retro-reflected and is directed directly back towards the source.
The forward scattered beam is also another signal that is dominated by the presence of the SP, the signal is much smaller without the resonance. This is seen in Fig. 7. Again the resonance is at 8.5° and this signal shows a large increase (approximately a factor of 10 here) with respect to the signal off resonance.
4. Conclusion
Two superposed gratings can be used to couple light incident at an oblique angle into a surface plasmon modes to generate a standing wave at the metal-air interface. The conditions for resonance can be designed by selecting the grating spacing and depth. The surface plasmon can then re-emit light via the surface gratings and signal in four principle directions can be used to monitor the characteristics of the surface plasmon. The enhanced forward scattered and back scattered beams present interesting geometries for the development of plasmon mediated sensors.
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