The dipolar (magnetostatic) interaction dominates the behavior of spin waves in magnetic films in the long-wavelength regime. In an in-plane magnetized film, volume modes exist with a negative group velocity (backward volume magnetostatic spin waves), in addition to the forward surface-localized mode (Damon-Eshbach). Inside the film of finite thickness $L$, the volume modes have a nontrivial spatial dependence, and their two-dimensional dispersion relations $omega(mathbf{k})$ can be calculated only numerically. We present explicit perturbative expressions for the profiles and frequencies of the volume modes, taking into account an in-plane applied field and uniaxial anisotropy, for the regimes $lVert mathbf{k}L rVert gg 1$ and $lVert mathbf{k}L rVert ll 1$, which together provide a good indication of the behavior of the modes for arbitrary wavevector $mathbf{k}$. Moreover, we derive a very accurate semianalytical expression for the dispersion relation $omega(mathbf{k})$ of the lowest-frequency mode that is straightforward to evaluate using standard numerical routines. Our results are useful to quickly interpret and control the excitation and propagation of spin waves in (opto-)magnetic experiments.
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