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The creation of high energy density ($\gtrsim10^6$ joules per cm$^3$)over-critical plasmas in a large volume has essential applications in the studyof warm dense matter, being present in the hot cores of stars and planets. Itwas recently shown that femtosecond Bessel beams enable creating over-criticalplasmas inside sapphire with sub-wavelength radius and several tens ofmicrometers in length. Here, the dependence of field structure and absorptionmechanism on the plasma density transverse profile are investigated byperforming self-consistent Particle-In-Cell (PIC) simulations. Two { limiting}cases are considered: one is a homogeneous step-like profile, that can sustainplasmon formation, the second is an inhomogeneous Gaussian profile, whereresonance absorption occurs. Comparing experimental absorption measures toanalytical predictions allows determining the plasma parameters used in PICsimulations. The PIC simulation results are in good agreement with experimentaldiagnostics of total absorption, near-field fluence distribution, and far-fieldradiation pattern. We show that in each case an ambipolar field forms at theplasma surface due to the expansion of the hot electrons and that electronsound waves propagate into the over-critical region.

Femtosecond laser-induced sub-wavelength plasma inside dielectrics: I. Field enhancement