We investigate the nonlinear absorption of laser energy in the bulk of transparent dielectrics for femtosecond and picosecond laser pulses focused by a conical lens. We highlight the influence of the pulse duration, laser pulse energy, and cone angle on laser energy absorption in transparent dielectrics. We provide a semi-analytical model allowing the calculation of maps for the density of nonlinear absorption of energy in BK7 and in SiO2 as a function of the pulse duration and peak fluence in the focal region. The comparison of the density of nonlinear absorption of energy with the available energy density determines optimal pulse durations and Bessel beam cone angles compatible with uniform laser energy deposition in the Bessel zone. The results reproduce quantitatively the transmission measurements for experiments in BK7 with picosecond pulses and suggest that the loss of propagation invariance and uniform laser energy deposition is responsible for a previously reported transition between different types of damage morphology in SiO2 [M. K. Bhuyan et al., Appl. Phys. Lett. 104, 021107 (2014)].
