Filament refers to a plasma channel with high laser intensity and high plasma density formed by the propagation of intense femtosecond laser pulses in a transparent medium. Several literatures have shown that the cross-section image of an optical filament at a specific z usually contains abundant structural information such as filament diameter, length, and energy distribution, which is of great significance for the visualization study of the dynamic process of filament formation. Moreover, accurate acquisition of the spatial structure and energy deposition distribution of femtosecond optical filaments are also of great significance for the development of filamentation-based atmospheric applications. Nevertheless, it is also the inherent parameter most difficult to measure directly. To solve the problem, we introduce a new medical imaging method named photoacoustic tomography (PAT) for optical filament cross-section imaging. The feasibility of reconstructing monofilament and multifilament images by photoacoustic tomography is verified theoretically. Moreover, we also study the influence of the performance parameters of the ultrasonic transducers on the optical filament image reconstruction.

We adopt a forward simulation model based on the photoacoustic wave equation to simulate the acquisition process of ultrasonic signals induced by optical filaments in air. A circular-scanning-based PAT system is considered to obtain the cross-section image of the laser filament. To simplify the problem, we assume that the initial heat source distribution of the optical filament satisfies the Gaussian distribution form, which can represent both the small high-energy core of the optical filament and its weak background energy region with a larger range. Based on experimental measurements, the initial maximum energy deposition density is assumed to be in the order of 10 mJ/cm³, and the diameter of the heat source is assumed to be in the order of 100 μm. The simulated time series of the acoustic signal is then applied to reconstruct the transverse distribution of femtosecond laser filaments with delay and sum (DAS) algorithm. Moreover, we also analyze the influence of performance parameters of ultrasonic transducers such as center frequency, bandwidth, surface size, and detection surface sensitivity on the reconstruction of filament cross-sectional images. The back-projection amplitude distribution profile along the y-axis is leveraged to compare the effect of image reconstruction.

According to the time series of ultrasound signals generated by monofilaments and multifilaments recorded at different detection distances, the frequency of monofilament and multifilament induced by femtosecond laser with multi-millijoule pulse energy is mainly concentrated within 4 MHz (Fig. 2). The signal spectrum of monofilament is single-peak structure, while the acoustic signal spectrum of multifilament is multi-peak structure (Fig. 2). The amplitude value of sound pressure signal decreases rapidly due to the attenuation of air. As the center of the optical filament deviates further from the scanning center, the cross-section image of the optical filament reconstructed by the back-projection (BP) algorithm and the DAS algorithm appears an obvious "elongated" phenomenon in the tangential direction (y-axis), which is the so-called "finite aperture effect" (Fig. 3). For monofilaments, the maximum energy amplitude decreases significantly with the increase in the center frequency of the transducer, which may be related to the filtering out of more low-frequency signals (Fig. 4). The same method is adopted to reconstruct the image of multifilament. It is found that the reconstructed multifilament image appears serious deformation with the multifilament center position deviating from the scanning center (Fig. 5). When x₀=1.0 mm, the two monofilaments near the scanning origin side can still be distinguished, whereas the two monofilaments near the transducer side are fused and cannot be distinguished. Therefore, the secondary filaments around the multiple filaments are more susceptible to the "aperture effect" and the fuzzy deformation occurs. The fuzzy deformation effect will be more obvious when the distance becomes larger from the scanning center or the distance becomes smaller from the surface of the transducer. Therefore, compared with monofilament reconstruction, multi-filament image reconstruction is more affected by the "aperture effect". Especially, the blur deformation of the surrounding sub-filaments is more likely. In summary, the characteristics of the transducer have an obvious influence on the reconstruction of monofilament and multifilament cross-sectional images. A larger bandwidth of the transducer will cause a smaller surface diameter, a larger surface sensitivity parameter, and a better reconstruction quality of monofilament and multifilament images. The influence of the center frequency of the transducer on the optical fiber image reconstruction is very complicated. Therefore, it is necessary to select the transducer with the appropriate center frequency combined with the spectrum analysis of the acoustic signal in the actual measurement.

We utilize a novel medical imaging method named PAT to reconstruct cross-section images of femtosecond laser filament formed in an air medium. The results show that the acoustic signal induced by a single filament has a single-peak structure, while that induced by a multifilament has a multi-peak structure. The performance parameters of the transducer have an obvious influence on the reconstruction results. A larger bandwidth of the transducer will lead to a smaller surface diameter, a larger surface sensitivity coefficient, and a better reconstruction effect of energy deposition distribution of optical filament. Compared with monofilament, the reconstruction of the multifilament image is more susceptible to the "finite aperture effect". Our study can provide some theoretical support for the experimental measurement of the spatial deposited energy distribution of femtosecond laser filament transmission under real atmospheric conditions.