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

Abstract

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.

Nanohydrodynamic Local Compaction and Nanoplasmonic Form-Birefringence Inscription by Ultrashort Laser Pulses in Nanoporous Fused Silica

“…Our side-view optical microscopy studies of blue recombination plasma emission form the filamentary tracks [ 21 ] in the np-FS ( Figure 1 c, inset) enabled us to identify the critical powers P cr for self-focusing and filamentation in this material, corresponding to the bottom limit pulse energy (P cr τ) for the laser filamentation onset of the 1030-nm and 515-nm pulses at different pulsewidths. The entire pulse energy ranges (0.018–0.045 μJ (1030 nm) and 0.05–0.11 μJ (515 nm)) were below the corresponding critical energy P cr τ for the utilized pulsewidths of 0.3–3.8 ps ( Figure 1 c), thus representing the linear (geometrical) focusing regime with the proposed interferential mechanism of nanograting inscription [ 19 , 22 ].…”

“Stealth Scripts”: Ultrashort Pulse Laser Luminescent Microscale Encoding of Bulk Diamonds via Ultrafast Multi-Scale Atomistic Structural Transformations

“…High-order non-linearities are known to be related to multi-photon absorption (imaginary parts) and the generation of higher harmonics or wave-mixing (real parts), while low-order non-linearities emerge as laser beam Kerr self-focusing and filamentation (upstream non-linear focus), once the peak pulse power exceeds the critical one [ 36 ]. Critical powers for self-focusing on non-linear media are known to be wavelength-, polarization-, and even beam shape-dependent [ 36 , 37 , 38 ], while in diamonds the intra-gap OCs could function as intermediate resonances, enhancing such optical non-linearities [ 72 ].…”

“…Meanwhile, at higher peak laser powers >0.4 MW in the natural diamond and >3 MW in the HPHT diamond the longitudinal extension symmetry breaks, indicating the predominating extension of the PL tracks upstream (toward the pump fs-laser). Usually, if screening plasma shadow does not appear within the focal region in a bulk dielectric, such asymmetry could be considered as a solid indication of self-focusing and formation of non-linear focus prior to the geometrical (linear) one [ 36 , 38 , 74 ]. As a result, the critical power values P cr ≈ 0.4–0.5 MW for the natural diamond and ≈3 MW for the HPHT diamond can be derived at the 1030 nm wavelength [ 38 , 74 ] ( Figure 3 b) and compared to the previous measurements at the same and other vis-NIR wavelengths ( Figure 3 d).…”

“…First, in bulk transparent dielectric materials, high-power ultrashort laser pulses could propagate non-linearly, with polarization-, wavelength-, and pulsewidth-dependent χ ʒ -type Kerr self-focusing in the pre-focal region [ 36 ], as illustrated below in Section 2 . Higher-order non-linearities χ n in bulk dielectrics, responsible, e.g., for multi-photon EHP generation, could be also polarization-, wavelength-, and pulsewidth-dependent [ 36 , 37 , 38 ], while many dielectrics are yet unexplored. Furthermore, in natural diamonds with high OC concentrations (~10–10 3 ppm), the strong enhancement of optical non-linearities could be expected due to presence of intra-gap intermediate states, positively adding to the high linear refractive index of the material (≈2.4) during self-focusing and filamentation against the negative EHP contribution, but key self-focusing parameters in diamonds are OC concentration-dependent and thus very controversial.…”

Up/Down-Scaling Photoluminescent Micromarks Written in Diamond by Ultrashort Laser Pulses: Optical Photoluminescent and Structural Raman Imaging

“…Comparing to the Raman (428 nm) and N3 ZPL (415 nm) PL signals (Figure 3d-i), respectively, the acquired 3D image and the depth profiles of the much more intense, normalized green-red PL intensity variation (Figure 3a-c) allow measurement of the micromark length, diameter and PL contrast (normalized intensity) as a function of peak laser power and exposure (Figure 4a-c). Specifically, once the peak pulse laser power P exceeds the critical power for self-focusing, P cr , in the natural diamond at the 515 nm laser wavelength (P cr ≈ 0.5 MW [15,16]), the extended photoluminescent micromarks could be observed in the diamond bulk in front of the geometrical focal region (Figure 4a). This filamentary inscription regime (P ≥ P cr ) enables up-and down-scaling of the micromark lengths according to the square root dependence [17], as well as of micromark diameter and PL contrast (Figure 4a-c).…”