Energy Exchange between Femtosecond Laser Filaments in Air

We report on the energy exchange between femtosecond laser filaments in air. A traveling plasma grating formed at the intersection of the filaments is proposed to explain the energy transfer. In this moving plasma grating mediated mechanism the laser energy transfers from the lower frequency pulse to its higher frequency partner, while in a traditional Kerr nonlinearity mediated grating, energy transfer occurs in the opposite manner. Based on this mechanism, we demonstrate an energy transfer ratio as high as 50% for pulses with an energy of several millijoules.

Figure 1

Schematic experimental configuration with two interacting filaments. (a) Two focused pulse replica propagate from left to right and form two interacting filaments crossing under angle $\phi$. The laser polarizations are orthogonal to the plane formed by the two beams. The pulse energies after interaction are measured by detectors $d1$ and $d2$. (b) Photo of two interacting filaments, displaying the characteristic near UV luminescence of $N_2$ in air following ionization. (c) Schematic representation of the magnified area where the two plasma columns overlap, showing the interference pattern of the two laser fields traveling with a velocity ${\nu }_p$. The center of the overlapping area is chosen as the origin of the $x$ and $z$ axis.

Figure 2

Temporal and spatial distribution of laser intensity and refractive index modulation in the interaction region. (a) Temporal evolution of the laser interference intensity at $z=0$. Chirped pulse 2 of duration 200 fs is delayed by 100 fs with respect to chirped pulse 1. This corresponds to $\Delta \omega =10\mathrm{THz}$, see text. The origin of the time corresponds to the moment when the center of the overlapped pulses reaches $z=0$. The laser intensity modulation moves downward in the direction of ${\overrightarrow{K}}_g$ with a phase velocity ${\nu }_p$. (b) Temporal evolution of the refractive index modulation at $z=0$ induced by the rotational Raman response. The refractive index modulation also moves downward. A temporal retardation with respect to the laser interference pattern is apparent at the beginning and end of the time window. (c) Temporal evolution of the plasma induced refractive index modulation at $z=0$. This plasma grating travels downward during its production process ($-80$ to 40 fs). After 40 fs, the plasma density is constant because no decay mechanism is considered in the model. (d) Laser intensity (blue line, left ordinate), refractive index modulation due to Raman response (black line, right ordinate) and plasma (red line, right ordinate) at $\mathrm{\text{time}}=-20\mathrm{fs}$. The spatial phase shift between the laser intensity and the two index modulations is $1.2$ and $0.5\mu \mathrm{m}$, respectively.

Figure 3

Energy exchange of filaments in air (a),(b),(c) and argon (d),(e),(f). (a) Energy exchange of filaments in air as a function of delay (frequency difference $\Delta \omega$) between the chirped pulses with power $P=0.39$ $P_{\mathrm{cr}}$ and duration ${\tau }_p=220\mathrm{fs}$. Each point corresponds to the average from 100 measurements. (b) Same as in (a) except for $P=3.5$ $P_{\mathrm{cr}}$. (c) Maximum energy exchange ratio $S$ recorded at positive delay ${\tau }_d$ as a function of incident laser power in air. (d),(e),(f), similar as (a),(b),(c), except air is replaced by argon. In all cases, the focal lengths for both pulses are 2000 mm and the crossing angle is 0.9°.

Figure 4

(a) Ratio $S$ as a function of the incident laser power. The focal length for both pulses is $f=125\mathrm{mm}$. The crossing angle is 20°. Otherwise, same laser conditions as in Fig. 3. (b) Typical energy exchange between two pulses with power of 1.5 $P_{\mathrm{cr}}$. The experiment conditions are the same as in (a). (c) Ratio $S$ as a function of the interacting length $L$. The incident laser energy of both pulses is 1.15 $P_{\mathrm{cr}}$. The focal length for both pulses is $f=300\mathrm{mm}$.