  The non-linear propagation of the intense near-infrared (NIR) driving field
in wide bandgap materials pose a challenge and an opportunity to control the
spectral properties of high harmonic generation (HHG) in solids. Here, we have
investigated the non-linear propagation effects of the ultrafast intense
near-infrared (NIR) driving field at 800 nm of 40 fs pulse duration operating
at a repetition rate of 1 kHz focused on the wide bandgap dielectrics such as
MgO, Chromium (Cr) doped MgO (Cr: MgO), Sapphire (Sa) crystals and fused silica
(FS). Furthermore, we have generated second and third harmonic (TH) in these
materials to explore the non-linear response at a strong field. To quantify the
non-linear propagation effects, low-order harmonics have been generated in
reflection and compared with the harmonics generated in transmission. We
observe spectral shifts and broadening of the driving field spectrum which is
imprinted on the harmonics. We attribute these effects to strong
photoionization, generation of free-carrier density and self-phase modulation
effects. We have also studied the polarization dependence of second harmonic
generation (SHG) and TH in FS. The linear polarization dependence of below
bandgap harmonics in FS and Sa generated in reflection demonstrated the sharp
anisotropy than in transmission. This work shows the sensitivity to control the
spectral profile of harmonics by manipulating the driving field, showing the
possibility of new tailored solid-state XUV sources for optical diagnostics.
