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...

We report an analytical theory of linear emission of exchange spin waves from a Bloch domain wall, excited by a uniform microwave magnetic field. The problem is reduced to a one-dimensional Schrödinger-like equation with a Pöschl-Teller potential and a driving term of the same profile. The emission of plane spin waves is observed at excitation frequencies above a threshold value, as a result of a linear process. The height-to-width aspect ratio of the Pöschl-Teller profile for a domain wall is found to correspond to a local maximum of the emission efficiency. Furthermore, for a tailored Pöschl-Teller potential with a variable aspect ratio, particular values of the latter can lead to enhanced or even completely suppressed emission.Wave generation is both an essential topic in wave physics and a prerequisite of any technology exploiting waves. Conventionally, waves are excited using an antenna, with their wavelength being limited by the antenna's size. Alternatively, we could use an inhomogeneity (either deliberately introduced, or naturally-occuring) in the medium and then apply a uniform, oscillatory external field to generate a wave. Small wavelength excitations require equally small antennas or inhomogeneities to generate them.In magnonics [1][2][3], the study of spin waves, we are fortunate that inhomogeneities with nanoscale dimensions naturally occur in magnetic materials: domain walls. These inhomogeneities are the transition regions between domains of uniformly aligned magnetization, and can have dimensions down to a few nanometers, depending on the material. Domain walls have been studied in great detail, due to a number of interesting properties: their magnetic field and current-driven motion [4,5], their ability to channel spin waves [6][7][8], and the unusual reflectionless behavior for spin waves passing through them [9]. Recently, there have also been numerical [10,11] and experimental [12,13] reports of pinned domain walls generating spin waves, with wavelengths down to tens of nanometers [14]. The origin of the observed spin wave emission has typically been attributed to the domain wall oscillations, generated by the applied microwave magnetic field [10][11][12][13] or spin-polarized current [14,15].In this letter, we report an analytical theory that demonstrates emission of exchange spin waves from a Bloch domain wall driven by a uniform microwave magnetic field, as a result of a linear process. The problem is reduced to that of the Pöschl-Teller potential in a Schrödinger-like equation -an exactly solvable model, of particular interest in quantum mechanics [16] and optics [17,18]. This potential is mostly known for its peculiar property of 100% transmission of incident waves at any frequency, for certain parameters of the potential [19]. While forming such a potential in other systems is difficult, serendipitously the reflectionless Pöschl-Teller potential exactly describes the graded magnonic index profile [20] due to a Bloch domain wall, allowing the peculiar behavior to be both investigated a...

We use micromagnetic modelling to demonstrate the operation of graded index lenses designed to steer forward-volume magnetostatic spin waves by 90 and 180 degrees. The graded index profiles require the refractive index to diverge in the lens center, which, for spin waves, can be achieved by modulating the saturation magnetization or external magnetic field in a ferromagnetic film by a small amount. We also show how the 90 • lens may be used as a beam divider. Finally, we analyse the robustness of the lenses to deviations from their ideal profiles. SUPPLEMENTAL MATERIAL List of Supplementary Animations and their CaptionsAnimation 1 (a) -Wave packet incident on 90 degree lens: Video corresponding to Fig. 6 (a) in the main text, showing the m x component of the wave packet moving through the 90 • lens. Animation 1 (b) -Wave packet incident on 180 degree lens: Video corresponding to Fig. 6 (b) in the main text, showing the m x component of the wave packet moving through the Eaton (180 • ) lens.Animation 2 (a) -90 degree lens as a beam divider: Video corresponding to Fig. 7 (a) in the main text, showing the 90 • lens acting as a ±90 • half-power beam divider. The m x component of the beam is shown. Animation 2 (b) -90 degree lens as a wave packet divider: Video corresponding to Fig. 7 (b) in the main text, showing the 90 • lens acting as a ±90 • half-power beam divider for an incoming wave packet. The m x component of the wave packet is shown.Each animation uses the parameters stated in the main text.

Starting from the general topic and fundamentals of magnonics, we discuss and provide demonstrations of exciting new physics and technological opportunities associated with the graded magnonic index and spin wave Fano resonances, highlighting them as the next big thing in magnonics research.

We report the photoluminescence study of low-energy, low-dose oxygen implantation induced compositional disordering of AlGaAs/GaAs quantum well structures. Significant disordering of both single and multiple AlGaAs/GaAs quantum wells has been achieved using low-energy (155 keV) oxygen ion implantation with doses as small as 5 × 1013 cm−2 after a moderate annealing step. These doses are significantly lower than those reported previously (500 keV and 1016 cm−2).