A Luneburg lens for spin waves

Abstract

We report on the theory of a Luneburg lens for forward-volume magnetostatic spin waves, and verify its operation via micromagnetic modelling. The lens converts a plane wave to a point source (and vice versa) by a designed graded index, realised here by either modulating the thickness or the saturation magnetization in a circular region. We find that the lens enhances the wave amplitude by 5 times at the lens focus, and 47% of the incident energy arrives in the focus region. Furthermore, small deviations in the profile can still result in good focusing, if the lens index is graded smoothly.It is often useful to manipulate a wave as it travels through a material, and this can be achieved by designing a suitable graded refractive index. This is a wellestablished field in optics [1], and the techniques have also been applied to other areas of wave physics.In magnonics [2,3], the study of spin waves, the theme of 'graded index magnonics' [4] has been gaining interest recently as we begin to explore the many parameters of magnetic materials that can be manipulated to confine [5,6], direct [7,8] or generate [9-11] spin waves.In graded index optics, one well-known profile is the Luneburg lens [12], a rotationally-symmetric refractive index profile designed to focus a plane wave to a point, or conversely, to convert a point source to a plane wave. This profile has been studied in many other areas of wave physics [13][14][15][16], due to its applications for use with antennas. As such, the Luneburg lens may have an important role in future wave-based computing circuitry, to launch plane waves from an antenna, or increase the amplitude of incoming plane waves to be read by the same antenna. To read/launch a plane wave from/to a different direction, one only needs to move the antenna to the corresponding point on the edge of the lens, without having to reconfigure the lens.In this work, we demonstrate theoretically how a Luneburg lens for spin waves may be realised in a magnetic thin film.The refractive index profile n(r) for a Luneburg lens is given bywhere r is the radial coordinate and R is the radius of the lens. This profile, along with the ideal operation of the lens, is shown in Fig. 1. For light propagation in an isotropic material, the refractive index is given by n = c/v, with c and v being the speed of light in vacuum and the medium, respectively. In a dispersive medium however, there is both a phase index, which relates to the phase velocity of light as before, and a group index, related to the group velocity. When these indices are the same, i.e. the dispersion relation for frequency ω as a function of wave-number k is approximately linear and there is no band gap in the ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� n(r) r/R (a) (b) Figure 1. (Color online) (a) The Luneburg lens, outlined by the black dashed line, focuses rays (red lines) to a diffractionlimited spot on the opposite edge of the lens. (b) Refractive index profile for the lens.spectrum, the graded index has the same spatial profile for different fre...

Optically Inspired Nanomagnonics with Nonreciprocal Spin Waves in Synthetic Antiferromagnets

“…Noteworthy, this picture is in agreement with a description analog to diffractive optics for the emission from a source of finite size, as shown in Figure g. The focusing is determined by the numerical aperture of the object, in our case the finite wall source, so that the minimum beam width can be estimated as w f = λ/[2sin(α)] = 363 nm, where λ = 330 nm is the experimental spin‐wave wavelength at f = 1.43 GHz and α = 27° is determined by the wall geometry.…”

Graded index lenses for spin wave steering

“…To change the wave number and thus the index for the given wave frequency, we need to change the dispersion relation by varying one of the bulk material parameters, or film thickness [11][12][13][14][15] . We then need to choose an isotropic dispersion relation that enables a large change in k, and thus n. This requirement is satisfied in the dipolar-dominated regime, in the forward-volume geometry, where the magnetization is directed normal to the film plane.…”

“…However, these waveguides may suffer from losses/scattering in bends, and usually have a large spatial footprint. An alternative solution is to steer spin waves via a graded refractive index [11][12][13][14] , which smoothly alters the wave trajectory with minimal reflections 15 . To achieve a graded index for spin waves, one must gradually change a magnonic parameter on a length scale much smaller than the wavelength.…”

Effective phase noise considerations in magnon based parametric excitations

“…In fact, a myriad of applications that rely directly on the magnon phase have been proposed in the recent past. The magnon-based paradigm of applications— magnonics —has emerged as one of the promising candidates for information transfer and data-processing technology; with the magnon phase playing an important role in notable novel applications like spin wave based logic circuits 4 , 5 , reservoir computing & machine learning 6 , spin wave conduits for interconnects 7 , spin wave lens 8 , 9 , spin-based majority gate 10 , and other waveguide applications 11 . They are also valuable for spintronic applications.…”