ABSTRACT
We analyze here a candidate system for correcting the wander of a self-channeled laser pulse using a fast-steering mirror along with a cooperative beacon imaged with a telescope. For our model system, the imaging telescope is coaxial with the propagation of the outgoing pulse. In the ideal case, any incoming light gathered from the beacon would be collimated, such that taking a centroid beacon image would yield the precise tip and tilt required for the self-channeled pulse to propagate back to the beacon on the reciprocal path. The degree to which reality differs from this ideal case determines the effectiveness of the wander correction. We simulate our system for a range of propagation and imaging conditions. We also show that in the absence of image noise (i.e., when the beacon power is arbitrarily high, and the signal-to-noise ratio is not an important consideration), the system exhibits its best performance when the receiving aperture diameter of the imaging system is close to the transverse size of the outgoing pulse, maximizing reciprocity. When realistic noise and finite beacon power are included in the simulation, however, we find that this reciprocity advantage may not be sufficient to compensate for the reduced photon count and resolving power of a small receiving aperture. In this case, the optimal aperture diameter will be the smallest possible, which allows for an acceptable signal-to-noise ratio.
ABSTRACT
A high-power laser beam propagating through a dielectric in the presence of fluctuations is subject to diffraction, dissipation, and optical Kerr nonlinearity. A method of moments was applied to a stochastic, nonlinear enveloped wave equation to analyze the evolution of the long-term spot radius. For propagation in atmospheric turbulence described by a Kolmogorov-von Kármán spectral density, the analysis was benchmarked against field experiments in the low-power limit and compared with simulation results in the high-power regime. Dissipation reduced the effect of self-focusing and led to chromatic aberration.
ABSTRACT
Adaptive optics (AO) systems rely on the principle of reciprocity, or symmetry with respect to the interchange of point sources and receivers. These systems use the light received from a low power emitter on or near a target to compensate phase aberrations acquired by a laser beam during linear propagation through random media. If, however, the laser beam propagates nonlinearly, reciprocity is broken, potentially undermining AO correction. Here we examine the consequences of this breakdown, providing the first analysis of AO applied to high peak power laser beams. While discussed for general random and nonlinear media, we consider specific examples of Kerr-nonlinear, turbulent atmosphere.
ABSTRACT
Thermal blooming of a laser beam propagating in a gas-filled tube is investigated both analytically and experimentally. A self-consistent formulation taking into account heating of the gas and the resultant laser beam spreading (including diffraction) is presented. The heat equation is used to determine the temperature variation while the paraxial wave equation is solved in the eikonal approximation to determine the temporal and spatial variation of the Gaussian laser spot radius, Gouy phase (longitudinal phase delay), and wavefront curvature. The analysis is benchmarked against a thermal blooming experiment in the literature using a CO2 laser beam propagating in a tube filled with air and propane. New experimental results are presented in which a CW fiber laser (1 µm) propagates in a tube filled with nitrogen and water vapor. By matching laboratory and theoretical results, the absorption coefficient of water vapor is found to agree with calculations using MODTRAN (the MODerate-resolution atmospheric TRANsmission molecular absorption database) and HITRAN (the HIgh-resolution atmospheric TRANsmission molecular absorption database).
ABSTRACT
Powerful, long-pulse lasers have a variety of applications. In many applications, optical elements are employed to direct, focus, or collimate the beam. Typically the optic is suspended in a gaseous environment (e.g., air) and can cool by convection. The variation of the optic temperature with time is obtained by combining the effects of laser heating, thermal conduction, and convective loss. Characteristics of the solutions in terms of the properties of the optic material, laser beam parameters, and the environment are discussed and compared with measurements at the Naval Research Laboratory, employing kW-class, 1 µm wavelength, continuous wave lasers and optical elements made of fused silica or BK7 glass. The calculated results are in good agreement with the measurements, given the approximations in the analysis and the expected variation in the absorption coefficients of the glasses used in the experiments.
