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• Acoustic method was adopted to quantitatively measure the long-distance filamentation. • A simple physical model was presented to analyze the spatial distribution of filament. • The onset and length of filament can be conveniently obtained from the model. • The increase of the filament length can be obtained for longer pulse with more energy. The promising application of femtosecond laser filamentation in atmospheric remote sensing brings imperative demand for diagnosing and controlling the spatiotemporal dynamics of long-distance filamentation. Here, the acoustic method was adopted to quantitatively diagnose the long-distance filamentation of femtosecond pulses manipulated by energy and temporal domain. The onset and length of filament can be conveniently obtained from a simple analytic formula based on reasonable approximation and further demonstrated by the experimental results. The influence of pulse energy and initial pulse chirp under three different focal lengths (∼10 m, 20 m, and 30 m) on the filamentation in the air were studied experimentally. These findings provide a guiding significance for the optimal control of the long-distance propagation of filament, thereby laying a firm foundation for femtosecond laser-based atmospheric remote sensing. [ABSTRACT FROM AUTHOR]

• Large birefringence of THz wave inside a femtosecond laser filament was observed. • The birefringence is attributed to the strong confinement of THz wave inside the filament. • THz wave with arbitrary polarization orientation, ellipticity and chirality can be produced. Large birefringence of THz wave inside a femtosecond laser filament in air has been found in this work. By varying the laser pulse energy, the filament length is changed, inducing variation in the phase delay between two perpendicularly polarized THz pulses. The birefringence could be explained by the delayed rotational molecular wave packet of air molecules inside the femtosecond laser-induced filament. The newly discovered THz birefringence is essentially attributed to the strong confinement of the THz pulse inside the filament. This phenomenon has opened a new way to freely control the polarization of THz pulses emitted from an optical filament and significantly benefits polarization-sensitive THz spectroscopy and control of matter. [ABSTRACT FROM AUTHOR]