Critical coupling layer thickness for positive or negative Goos-H'anchen shifts near the excitation of backward surface polaritons in Otto-ATR systems

摘要

A theoretical analysis of the lateral displacement (Goos-H\"anchen shift) ofspatially limited beams reflected from Attenuated Total Reflection (ATR)devices in the Otto configuration is presented when backward surface plasmonpolaritons are excited at the interface between a positive refractive indexslab and a semiinfinite metamaterial with negative refractive index. First, thestationary phase approximation and a phenomenological model based on theproperties of the complex poles and zeroes of the reflection coefficient areused to demonstrate that: i) the excitation of backward surface waves can leadto both negative and positive (and not exclusively negative) Goos-H\"anchenshifts, and ii) the sign of the shift depends on whether the value of thecoupling layer thickness is higher or lower than a critical valuecharacteristic of the ATR structure. Second, these findings are verifiedthrough rigorous calculations of the spatial structure of the reflected beam.For incident beams with a Gaussian profile, the lateral shift calculated as thefirst moment of the field distribution of the reflected beam agrees quite wellwith the predictions of approximate analysis. Near the resonant excitation ofthe backward surface plasmon polariton, large (negative or positive)Goos-H\"anchen shifts are obtained, along with a splitting of the reflectedbeam.