Tailoring the filamentation of intense femtosecond laser pulses with periodic lattices

We show numerically that by using periodic lattices the filamentation of intense femtosecond laser pulses, otherwise a result of competing nonlinear effects, can be well controlled with respect to its properties. The diffraction induced by the lattice provides a regularizing mechanism to the nonlinear self-action effects involved in filamentation. We demonstrate a new propagation regime of intense lattice solitons bridging the field of spatial solitons with that of femtosecond laser filamentation. The effective filamentation control is expected to have an important impact on numerous applications.

Figure 1

Comparison of peak intensities $I_{\mathrm{peak}}$ (r,z) for propagation (a,b) in air and (c,d) in a cylindrical lattice. The left column shows the linear propagation regime $P_{\mathrm{in}}={10}^{-6}{P}_{\mathrm{cr}}$, and the right column shows the nonlinear propagation and filamentation regime $P_{\mathrm{in}}=1.25P_{\mathrm{cr}}$. Lattice parameters are Λ$=$350 μm, $w$ $=$ 100 μm, and $\Delta n_o=-3.3\times {10}^{-7}$. Insets are graphic representations of the cylindrical lattice, where black represents lower refractive index.

Figure 2

Beam width as a function of the propagation distance $z$ (a) without lattice and (b) with lattice. Peak intensity $I_{\mathrm{peak}}$ as a function of the propagation distance $z$ for (c) lattice strengths $\Delta n_o$ of 0 (curve i), $-2\times {10}^{-7}$ (curve ii), $-2.5\times {10}^{-7}$ (curve iii), $-3.3\times {10}^{-7}$ (curve iv), and $-5.0\times {10}^{-7}$ (curve v) and (d) lattice periodicities Λ of $\infty$ (curve 1), 450 μm (curve 2), 400 μm (curve 3), 350 μm (curve 4), and 300 μm (curve 5). Insets are graphic representations of the cylindrical lattice, where black represents lower refractive index.

Figure 3

Peak intensity as a function of propagation distance, which reveals the transition dynamics between lattice solitons and lattice filaments. (a) The (2 $+$ 1)-dimensional (cylindrically symmetric) simulations. (b) The (3 $+$ 1)-dimensional (frozen time) simulations using a rectangular plasma lattice. Lattice soliton indicates the pulsed version of the cylindrical lattice soliton solution (taking into account only diffraction and Kerr effect). Lattice soliton (all effects included) indicates including GVD, multiphoton ionization, and plasma defocusing. Normal filament indicates typical filament in air from a Gaussian spatiotemporal pulse. Lattice filaments 1 and 2 indicate tailored lattice filaments for two different cases of lattice strength Δ$n$. Insets are graphical representations of the lattices used in each case, where black represents lower refractive index.