Observation and Optical Tailoring of Photonic Lattice Filaments

We demonstrate, for the first time, that photonic lattices support a new type of laser filaments, called lattice filaments (LF). The LF attributes (length, width, and intensity) can be tailored by both varying the photonic lattice properties and also dynamically through the interaction between filaments. This opens the way for extensive all-optical control of the nonlinear propagation of intense ultrafast wave packets. Our approach is generic and applicable to all transparent media, with potential strong impact on various photonic applications.

Figure 1

(a) and (b) Simulated and experimental SF propagation ($yz$ plane). (c) and (d) Simulated and experimental LF propagation. The input is an $80\mu \mathrm{m}$ wide Gaussian beam ($xy$ plane). The white arrow indicates the light propagation direction. The photonic lattice parameters are $\Delta n=-4\times {10}^{-4}$, $\Lambda =25\mu \mathrm{m}$, and $L=24\mathrm{mm}$. For the simulation, the inset shows the elliptical cross section. For the experimental visualization, the emitted fluorescence is collected by imaging the $yz$ plane on a CCD camera. Note that the $yz$ images size is $0.4\times 13\mathrm{mm}$. The inset shows a transverse view of the fs laser-induced structures. The white line corresponds to $30\mu \mathrm{m}$. (e) and (f) Corresponding intensity profiles versus the propagation length.

Figure 2

Fluorescence images for different input polarization ($P$) and lattice period ($\Lambda$): (a) $P=20°$, $\Lambda =25\mu \mathrm{m}$; (b) $P=60°$, $\Lambda =25\mu \mathrm{m}$; (c) $P=60°$, $\Lambda =35\mu \mathrm{m}$; and (d) $P=90°$, $\Lambda =25\mu \mathrm{m}$. (e) Corresponding longitudinal profiles (in log scale) compared to the SF profile (gray dashed line).

Figure 3

(a) Transverse profile of the LF for various configurations ($P$ and $\Lambda$, see Fig. 2) compared to SF (dashed curve and crosses). (b) Power measured at the output of the glass sample for different input power for the LF (filled circles) and the SF (crosses). For BK7, $P_{\mathrm{cr}}=3.7\mathrm{MW}$. The gray dashed line represents the linear propagation regime (i.e., no losses). The inset shows the output power for $5P_{\mathrm{cr}}$ input power in various configurations. The drop of the peak intensity and the increase of the propagation length is associated with a widening of the filament and, consequently, a more significant output power.

Figure 4

(a) Experimental setup. A delay line is used to separate in time the two pulses. One of the beam splitters (BS) is slightly rotated either around the $x$ (green arrows) or the $y$ axis (blue arrows) to spatially separate the two filaments. (b) Two SFs (SF1 and SF2) spaced by $50\mu \mathrm{m}$ (green arrow) overlapped in time ($\tau =0$, bottom) and not ($\tau \ne 0$, top). (c) Same as (b) for two LFs (LF1 and LF2). The top and the bottom filaments are labeled 1 and 2, respectively. The widening of the LF, waist increases the coupling and leads the two LFs to interact. (d) Total energy (integrated fluorescence intensity) of the LF1 (circles) and the LF2 (triangles) at both $\tau =0$ (opened symbols) and $\tau \ne 0$ (filled symbols) cases. An energy transfer occurs from LF2 to LF1. (e) Longitudinal profiles of the LF1 for $\tau =0$ (opened blue circle) and $\tau \ne 0$ (filled red circle) cases.

Figure 5

(a) Two SFs (SF1 and SF2) spaced by $20\mu \mathrm{m}$ (blue arrow) overlapped in time ($\tau =0$, bottom) and not ($\tau \ne 0$, top). (b) One SF and one LF at $\tau =0$ (bottom) and $\tau \ne 0$ (top). The SF is obtained by slightly shifting the top beam (blue arrow) to be out of the photonic lattice. (c) Same as (b) for longer propagation length (from 6.5 to 13 mm). (d) Transversal profile at $z=10\mathrm{mm}$ [white line of (c)] of a single LF (dashed gray curve), of both the SF and LF at $\tau \ne 0$ (filled red circle) and of both the SF and LF at $\tau =0$ (opened blue circle). The two gray lines represent the position of the SF (1) and the LF (2).