The signatures of turbulence in atmospheric laser propagation are examined, with a particular focus on the effects of non-Kolmogorov turbulence on laser scintillation and phase fluctuations. Non-Kolmogorov properties of the atmospheric index-of-refraction spectrum are outlined, and it is shown that it may be possible to reproduce these features through broadband power-law forcing of the velocity and temperature fields in turbulent flows. Numerical simulations of homogeneous isotropic turbulence subjected to power-law forcing are used to motivate a spectral model for the kinetic energy, which is then extended to address power-law forcing of passive scalars such as the temperature. A modeled non-Kolmogorov index-of-refraction spectrum for power-law forced turbulence is proposed, where the model spectrum consists of standard Kolmogorov and forcing-dominated contributions. This form could reproduce the experimentally observed signatures of atmospheric turbulence on laser propagation and it may provide insights into the origins of non-Kolmogorov turbulence in the atmosphere.