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Analytical descriptions of damage threshold of dielectric materials irradiated by femtosecond pulses

For a dielectric exposure to the femtosecond hyperbolic secant pulse, the electron dominated by collisional and multiphoton ionization has been studied. Analytical description of the temporal evolution of the electron density induced by the optical pulse has been given. As the result, at the damage threshold an explicit expression of the pulse width in terms of the pulse fluence has been derived.