Enhancing the yield in surface sum-frequency generation by the use of surface polaritons

The efficiency of sum-frequency generation at an air–metal interface can be enormously increased by coupling one of the input waves into a surface polariton. Experimental results for various configurations of input beams and couplers are discussed. PACS: 42.65.Ky; 41.60.Cr; 73.20.M Over the last ten years sum-frequency (SF) generation has developed into a standard tool for the study of surfaces and interfaces that are covered by molecular monolayers [1–4]. The vast majority of studies pertain to the wavelength range λ < 10 μm because of the ready availability of powerful tunable infrared sources at these wavelengths. The application of free-electron lasers to the field of sum-frequency spectroscopy has brought about a fundamental change here because these lasers are tunable over very wide wavelength ranges and reach into the far-IR [5–11]. Since SF studies with FELs are nontrivial from an experimental point of view, the use of table-top IR sources, even when they are somewhat less powerful, remains very appealing. In SF studies of monolayers, the flux of generated photons is quite small. On the one hand this is because nonlinear optical processes like SF generation are highly inefficient, on the other because the sample has essentially zero depth. In view of the signal-to-noise ratio it is then important to investigate methods to maximize the signal yield given the output power of the required visible and tunable IR laser sources. In theory the SF generation process can be made more efficient by increasing the flux density of the primary radiation. Given the output power of the sources, this can be implemented by reducing the spot size of both beams. Sample damage sets a limit to this approach. However, if only one of the beams is close to damage threshold there is another option: to employ field-enhancement techniques for the other input frequency. This will lead to a larger SF yield since one ∗ Present address: NMI, P.O. Box 654, 2600 AR Delft, The Netherlands of the driving fields is enhanced. Enhancement of the field at the interface of two media occurs for instance in a totalinternal-reflection (TIR) geometry just beyond the angle for total internal reflection, or when one excites a surface polariton at the interface [12]. Both these methods have been successfully employed in nonlinear optical experiments [13–17]. Whereas the TIR geometry is being applied in some instances to SFG from adsorbed monolayers [14–17], the possibilities offered by the application of surface polaritons to SFG of interfacial layers have remained unexplored until recently. In this article we summarize the results of our recent studies on the application of surface polaritons to sum-frequency generation at interfaces [18–20]. 1 Surface plasmon polaritons The possibility that electromagnetic waves can propagate on a surface or interface was first discussed by Sommerfeld in the context of the propagation of radio waves [21]. These solutions to Maxwell’s equations exist under welldefined conditions regarding the complex dielectric functions εa(ω) = ε′a(ω)+ ıε′′ a(ω) and εb(ω) = εb(ω)+ ıε′′ b(ω) of the media above (z > 0) and below (z < 0) the interface, respectively; either ε′a(ω) < 0 and ∣∣ε′a(ω)∣∣> εb(ω) or εb(ω) < 0 and ∣∣ε′b(ω)∣∣> ε′a(ω). The electric field is p-polarized and can be written as E(ω) = (Eax(ω)x+ E z (ω)z) exp [−αω a z− ıωt+ ıK SPPx] , (1) E(ω) = (Ebx(ω)x+ E z (ω)z) exp [−αω b z− ıωt+ ıK SPPx] , (2) where the surface excitation propagates along the x direction. Because of the continuity of the tangential component of the electric field and the normal component of the displacement field one has Ex(ω) = Ex(ω) and Ea z (ω) = (εb(ω)/εa(ω)) Eb z (ω). On both sides of the interface the amplitude of the wave decays away from the interface with the