Pulse-width-dependent critical power for self-focusing of ultrashort laser pulses in bulk dielectrics

Microscale filamentation of 0.25 NA-focused, linearly and circularly polarized 1030 nm and 515 nm ultrashort laser pulses of variable pulse widths in fused silica, fluorite, and natural and synthetic diamonds demonstrates the Raman-Kerr effect in the form of critical pulse power magnitudes, proportional to squared wavelength and inversely proportional to laser pulse width of 0.3-10 ps. The first trend represents the common spectral relationship between the quantities, while the second indicates its time-integrated inertial contribution of Raman-active lattice polarization, appearing in transmission spectra via ultrafast optical-phonon Raman scattering. The optical-phonon contribution to the nonlinear polarization could come from laser field-induced spontaneous/stimulated Raman scattering and coherent optical phonons generated by electron-hole plasma with its clamped density in the nonlinear focus. Almost constant product value of the (sub)picosecond laser pulse widths and corresponding critical pulse powers for self-focusing and filamentation in the dielectrics ("critical pulse energy") apparently implies constant magnitude of the nonlinear polarization and other "clamped" filamentation parameters at the given wavelength.