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Fibrils in the solar chromosphere carry transverse oscillations as determined from non-spectroscopic imaging data. They are estimated to carry an energy flux of several $\mathrm{kW~m}^{-2}$, which is a significant fraction of the average chromospheric radiative energy losses. We aim to determine oscillation properties of fibrils not only in the plane-of-the-sky (horizontal) direction, but also along the line-of-sight (vertical) direction. We obtained imaging-spectroscopy data in $\mathrm{Fe~I}$, $\mathrm{Ca~II~IR}$, and $\mathrm{Ca~II~K}$ with the Swedish 1-m Solar Telescope. We created a sample of 605 bright $\mathrm{Ca~II~K}$ fibrils and measured their horizontal motions. Their vertical motion was determined through non-LTE inversion of the observed spectra. We determined the periods and velocity amplitudes of the fibril oscillations, as well as phase differences between vertical and horizontal oscillations in the fibrils. The bright $\mathrm{Ca~II~K}$ fibrils carry transverse waves with a mean period of $2.1\times10^2~$s, and a horizontal velocity amplitude of 1$~\mathrm{km~s}^{-1}$, consistent with earlier results. The mean vertical velocity amplitude is 1.1$~\mathrm{km~s}^{-1}$. We find that 77% of the fibrils carry waves in both the vertical and horizontal directions, and 80% of this subsample exhibits oscillations with similar periods in both horizontal and vertical directions. For the latter, we find that all phase differences between $0$ and $2\pi$ occur, with a mild but significant preference for linearly polarized waves (phase difference of $0$ or $\pi$). The results are consistent with the scenario where transverse waves are excited by granular buffeting at the photospheric footpoints of the fibrils. Estimates of transverse wave flux based only on imaging data are too low because they ignore the contribution of the vertical velocity., Comment: 12 pages, 12 figures

Broad-band images of the solar chromosphere in the Ca II H&K line cores around active regions are covered with fine bright elongated structures called bright fibrils. The mechanisms that form these structures and cause them to appear bright are still unknown. We aim to investigate the physical properties, such as temperature, line-of-sight velocity, and microturbulence, in the atmosphere that produces bright fibrils and to compare those to the properties of their surrounding atmosphere. We used simultaneous observations of a plage region in Fe I 6301-2 \r{A}, Ca II 8542 \r{A}, Ca II K, and H$\alpha$ acquired by the CRISP and CHROMIS instruments on the Swedish 1-m Solar Telescope. We manually selected a sample of 282 Ca II K bright fibrils. We compared the appearance of the fibrils in our sample to the Ca II 8542 \r{A} and H$\alpha$ data. We performed non-local thermodynamic equilibrium (non-LTE) inversions using the inversion code STiC on the Fe I 6301-2 \r{A}, Ca II 8542 \r{A}, Ca II K lines to infer the physical properties of the atmosphere. The line profiles in bright fibrils have a higher intensity in their K$_2$ peaks compared to profiles formed in the surrounding atmosphere. The inversion results show that the atmosphere in fibrils is on average $100-200$~K hotter at an optical depth log$(\tau) = -4.3$ compared to their surroundings. The line-of-sight velocity at chromospheric heights in the fibrils does not show any preference towards upflows or downflows. The microturbulence in the fibrils is on average 0.5 km s$^{-1}$ higher compared to their surroundings. Our results suggest that the fibrils have a limited extent in height, and they should be viewed as hot threads pervading the chromosphere.