The risk of spacecraft damage caused by space debris is increasing. The ground-based laser space-debris removal (GBLSDR) is an effective method for removing centimeter-scale space debris in the low-earth orbit region. However, the problem of high-power laser beam propagation through the atmosphere will be encountered by the GBLSDR. For the application of GBLSDR, the beam power is well above the critical power of the self-focusing effect in the atmosphere. Until now, several studies have been carried out to analyze the influence of the self-focusing effect in the atmosphere on the beam quality at the debris target. It is shown that the intensity at the debris target decreases because of the self-focusing effect in the atmosphere. It is found that uniform irradiation at the debris target may be achieved because of the phase modulation caused by the self-focusing effect in the inhomogeneous atmosphere. In addition, the influence of the beam spatial coherence and the beam order on the self-focusing effect in the inhomogeneous atmosphere is also studied. However, these studies are restricted to the steady-state self-focusing effect in the inhomogeneous atmosphere, and they fail to consider the quasi-steady-state self-focusing effect. It is known that a pulsed beam is more suitable for the application of GBLSDR than a continuous wave (CW) laser beam. When the response time of media to the field is much shorter than the pulse width, the self-focusing effect can be called the quasi-steady-state self-focusing effect. Therefore, it is important to study the influence of the quasi-steady-state self-focusing effect in the inhomogeneous atmosphere on the beam quality at the target surface for the application of GBLSDR.

In general, under the standard paraxial approximation, the propagation of a high-power laser beam propagating from the ground through the atmosphere to space orbits can be described by the nonlinear Schr?dinger equation. In addition, the B integral is an important characteristic parameter to quantitatively describe the beam quality degradation due to the self-focusing effect. Based on the B integral of a high-power laser beam propagating vertically from the ground through the atmosphere to the debris target, the beam propagation model can be simplified as two stages, i.e., nonlinear propagation in the homogeneous atmosphere and linear propagation in a vacuum. According to the simplified beam propagation model, the influence of the quasi-steady-state self-focusing effect of a partially coherent light pulse (PCLP) propagating in the inhomogeneous atmosphere on the beam quality at the target surface is studied analytically.

In this study, the analytical expressions [Eq. (9), Eq. (10), and Eq. (12)] for the beam width, curvature radius, and actual focal length of a PCLP propagating from the ground through the atmosphere to the space orbit are derived, respectively. It is shown that the focal shift will take place because of the quasi-steady-state self-focusing effect, which results in an increase in the spot size on the debris target (Fig. 1). In order to suppress the quasi-steady-state self-focusing effect, the quasi-steady-state and steady-state modification methods are proposed. Furthermore, the analytical expression [Eq. (13)] for the modified focal length of the quasi-steady-state and steady-state modification methods is derived, and the applicable condition of the modified focal length is given [Eq. (15)]. It is shown that the spot size on the space-debris target decreases under the quasi-steady-state and steady-state modification methods, and smaller spot size on the space-debris target can be achieved by the quasi-steady-state modification method (Fig. 5).

In order to reduce the spot size and increase the laser intensity on the space-debris target (i.e., improve the beam quality on the target), the influence of the quasi-steady-state self-focusing effect of a PCLP propagating in the inhomogeneous atmosphere on the beam quality at the target surface is studied analytically in this study. The analytical expressions for the beam width, curvature radius, and actual focal length of a PCLP propagating from the ground through the atmosphere to the space orbit are derived, respectively. The focal shift takes place because of the quasi-steady-state self-focusing effect, which results in an increase in the spot size on the debris target. The quasi-steady-state and steady-state modification methods are proposed to suppress the quasi-steady-state self-focusing effect. It is found that a smaller spot size on the space-debris target can be achieved by the quasi-steady-state modification method. However, in practice, the steady-state modification method is easier to be performed than the quasi-steady-state modification method.