Theoretical analysis of the optical rotational Doppler effect under atmospheric turbulence by mode decomposition

The optical rotational Doppler effect associated with orbital angular momentum provides a new means for rotational velocity detection. In this paper, we investigate the influence of atmospheric turbulence on the rotational Doppler effect. First, we deduce the generalized formula of the rotational Doppler shift in atmospheric turbulence by mode decomposition. It is found that the rotational Doppler signal frequency spectrum will be broadened, and the bandwidth is related to the turbulence intensity. In addition, as the propagation distance increases, the bandwidth also increases. And when $C_n^2\le 5\times {10}^{-15}$ m^−2/3 and 2z ≤ 2 km, the rotational Doppler signal frequency spectrum width d and the spiral spectrum width d₀ satisfy the relationship d = 2d₀–1. Finally, we analyze the influence of mode crosstalk on the rotational Doppler effect, and the results show that it destroys the symmetrical distribution of the rotational Doppler spectrum about 2l⋅Ω/2π. This theoretical model enables us to better understand the generation of the rotational Doppler frequency and may help us better analyze the influence of the complex atmospheric environment on the rotational Doppler frequency.