Ultrathin entirely flat Umklapp lenses

Abstract

We design ultra-thin, entirely flat, dielectric lenses using crystal momentum transfer, so-called Umklapp processes, achieving the required wave control for a new mechanism of flat lensing; physically, these lenses take advantage of abrupt changes in the periodicity of a structured line array so there is an overlap between the first Brillouin zone of one medium with the second Brillouin zone of the other. At the interface between regions of different periodicity, surface, array guided, waves hybridise into reversed propagating beams directed into the material exterior to the array. This control, and redirection, of waves then enables the device to operate as a Pendry-Veselago lens that is one unit cell in width, with no need for an explicit negative refractive index. Simulations using an array embedded in a slab of silicon nitride (Si3N4) in air, operating at visible wavelengths between 420 − 500THz demonstrate the effect.

Tailored elastic surface to body wave Umklapp conversion

“…Recently the importance of the Umklapp process has been solidified for electron-electron scattering through experimental verification, highlighting the fundamental role it plays in electrical resistance in pure metals 22 , along with the utility to probe electronic structures 23 . Further to this, new breeds of entirely flat lens devices have been theorised which incorporate Umklapp-scattering processes for surface waves on dielectric substrates 24 by virtue of abrupt, not adiabatic, gradings. Undeterred by its prevalence in quantum, discrete systems we demonstrate the efficacy of U-processes which can preside over purely passive, classical, continuous elastic devices.…”

“…1c), resembling an elastic leaky wave antenna 28 . This can be manufactured to take place at a desired position by either adiabatic or abrupt gradings 24 . A similar effect is observed when exciting along the opposite array direction; the grading experienced is then from high to low rods.…”

Surface corrugated laminates as elastic grating couplers: Splitting of SV- and P-waves by selective diffraction

“…There is no intersection with the construction line and the contours within the laminate, shown in Figure 4(f), and as such total reflection occurs at the interface. However when the corrugation is included, as in Figure 4(e), we see that incorporating momentum transfer by the grating by the subtraction of a reciprocal lattice vector G c = [0, 2π/a c ] (often attributed to the Umklapp mechanism 28,32 ) from the incident k s results in an intersection of the translated construction line with the laminate contours. This is shown in Figure 4(f).…”

Underwater Focusing of Sound by Umklapp Diffraction

“…Motivated by recent devices in electromagnetism and elasticity, which leverage so-called Umklapp diffraction [30,31], we apply these concepts to the setting of focusing underwater sound.…”