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The formation of laser-induced periodic surface structures (LIPSS) on two different silica polymorphs (single-crystalline synthetic quartz and commercial fused silica glass) upon irradiation in air with multiple linearly polarized single- and double-fs-laser pulse sequences (τ = 150 fs pulse duration, λ = 800 nm center wavelength, temporal pulse separation Δt < 40 ps) is studied experimentally and theoretically. Two distinct types of fs-LIPSS [so-called low-spatial-frequency LIPSS (LSFL) and high-spatial-frequency LIPSS (HSFL)] with different spatial periods and orientations were identified. Their appearance was characterized with respect to the experimental parameters peak laser fluence and number of laser pulses per spot. Additionally, the “dynamics” of the LIPSS formation was addressed in complementary double-fs-pulse experiments with varying delays, revealing a characteristic change of the LSFL periods. The experimental results are interpreted on the basis of a Sipe-Drude model considering the carrier dependence of the optical properties of fs-laser excited silica. This new approach provides an explanation of the LSFL orientation parallel to the laser beam polarisation in silica—as opposed to the behaviour of most other materials.