We show how the micro-focused BLS signal of forward volume spin waves is formed and why it remains observable despite symmetry-based "suppression" expectations. A reciprocity-theorem based model with vectorial diffraction-limited focusing identifies the nonnegligible longitudinal focal-field component as the key element responsible for BLS sensitivity in the forward volume geometry. We further demonstrate that full polarization analysis, implemented through polarizer-analyzer maps of coherently excited spin waves, provides information beyond the conventional crossed polarizer-analyzer readout. In a BiYIG thin film, the measured maps exhibit Stokes/anti-Stokes polarization asymmetries and nontrivial patterns that stem from quadratic magneto-optical coupling terms. Fitting the data with a model including Voigt and Cotton-Mouton contributions yields an effective Cotton-Mouton constant and shows that the quadratic response is comparable to the linear Voigt contribution.
We show how the micro-focused BLS signal of forward volume spin waves is formed and why it remains observable despite symmetry-based suppression expectations. A reciprocity-theorem based model with vectorial diffraction-limited focusing identifies the nonnegligible longitudinal focal-field component as the key element responsible for BLS sensitivity in the forward volume geometry. We further demonstrate that full polarization analysis, implemented through polarizer-analyzer maps of coherently excited spin waves, provides information beyond the conventional crossed polarizer-analyzer readout. In a BiYIG thin film, the measured maps exhibit Stokes/anti-Stokes polarization asymmetries and nontrivial patterns that stem from quadratic magneto-optical coupling terms. Fitting the data with a model including Voigt and Cotton-Mouton contributions yields an effective Cotton-Mouton constant and shows that the quadratic response is comparable to the linear Voigt contribution.
Brillouin light scattering (BLS) is among the most versatile optical methods of measuring condensed matter excitations, providing access to their frequency, wavevector, and phase via inelastic scattering of laser light. In magnetic systems, BLS directly measures thermal or externally driven spin waves (magnons) through Stokes (magnon creation) and anti-Stokes (magnon annihilation) processes. 1,2 From the experimental point of view, two BLS implementations dominate in magnonics research: (i) conventional, k-resolved BLS, where the in-plane magnon wavevector is selected by the scattering geometry; and (ii) micro-focused BLS (µBLS), where an objective with a high numerical aperture (NA) focuses the probing laser beam to a diffraction-limited spot, enabling spatially resolved mapping of spin-wave intensity and phase. 3 There are also recent nanophotonic approaches which further extend µBLS capabilities and allow interactions of spin waves with free space inaccessible light. [4][5][6][7][8] .
For a long time, the µBLS community had the intuition that with the optical axis normal to a magnetic film, the detection of spin waves in the forward volume (FV) configuration (uniform out-of-plane magnetization) is symmetry suppressed. In the simplified picture, the longitudinal focal-field component E z was often assumed negligible for rotationally symmetric illumination (analogous to the common paraxial neglect of longitudinal-field contributions 9 ), and the remaining transverse-field contribution was expected to cancel: in the FV geometry the dynamics is purely in-plane and the associated magneto-optical (MO) response carries an odd azimuthal symmetry that averages to zero when coherently integrated over the full aperture.
The key change in perspective comes from a full electro-magnetic description of the focusing: a high-NA objective does not generate a purely transverse field in the focal region. Instead, the focused field contains all three components (E x , E y , E z ), and the longitudinal component can be only a few times smaller than the dominant transverse component(s), rather than being negligible. 10,11 Consequently, the observability of FV spin waves depends on correctly accounting for the vectorial structure of the focused field and the subsequent MO coupling that transforms the incident field into the scattered field collected by the objective.
Experimentally, spin-wave modes in out-of-plane (or nearly out-of-plane) magnetized films have in fact been observed with µBLS in multiple contexts, 12,13 underscoring that FV detection is practically achievable even if certain idealized symmetry arguments predict its suppression. The modeling viewpoint therefore reframes the question: not can spin waves in the FV geometry be detected?, but rather which MO tensor terms and which electric field components dominate the FV signal under a given optical and magnetic configuration?
Another key aspect of magnon BLS is the polarization selectivity of the MO scattering process. In the simplest (and most commonly used) description, the polarization of the magnetically scattered light is rotated by 90 • with respect to the incident polarization 3 , which motivates the widespread use of crossed polarizer-analyzer detection to suppress the elastically scattered background and enhance the magnon signal. Most experiments record only the intensity projected onto the polarization orthogonal to the incident beam, rather than capturing the full polarization state of the scattered field.
Here we show that the polarization state of the scattered light contains additional information about the underlying FIG. 1. Schematics of the used micro-focused Brillouin light scattering setup. The polarization of the linearly polarized incoming laser can be rotated by motorized λ /2 plate. The beam then passes through two non-polarizing beam splitters and is focused on the sample by microscope objective with NA = 0.8. The scattered light then passes through a rotatable polarizer bef
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