Doppler effect is a classic physical phenomenon, belonging to one of the basic characteristics of waves. This effect originates from the relative motion between the wave source and the observer that gives rise to a frequency shift for the wave received by the observer, relative to the local frequency of the wave source. For not only mechanical waves, but also electromagnetic waves, one can retrieve the motion information of the observer relative to the wave source by extracting this Doppler shift. The Doppler effect has been widely applied in the realms of medical diagnosis, traffic flow monitoring, high-precision measurement, laser cooling, astronomy, aerospace, etc.
Light wave belongs to electromagnetic waves. Compared to mechanical waves, such as acoustic wave and water wave, light has distinct advantages of ultra-high speed, large bandwidth, good directionality and the ability of propagation in vacuum. Therefore, the development of optical Doppler effect has unparalleled advantages compared to other waves. For traditional beams with plane phase, if not considering the relativistic effect, the Doppler shift is produced, provided that the moving object has the relative motion component along the propagation direction of light beam, called the linear (or longitudinal) Doppler effect. In the past two to three decades, with the further understanding of the fundamental properties of light, more complex and diverse structured light beams have been studied beyond the simple beams with plane phase. Accordingly, the rotational (or transverse) Doppler effect based on structured light has also attracted more and more attention, which provides more measurable dimensions for optical Doppler metrology.
Throughout the discovery, development and application history of the Doppler effect, such effect is only based on the scalar properties of waves, that is, the Doppler shift is caused by continuous changes in phase (or intensity). For mechanical waves with low local frequency, usually the Doppler shift can be detected directly to determine the speed and direction of the moving object. For light (electromagnetic waves), due to its ultra-high local frequency, extracting Doppler shift requires optical interference with a reference light. Although the beating frequency can be extracted as the magnitude of Doppler shift, this implementation naturally loses the direction information, that is, it is impossible to distinguish between Doppler blue shift and red shift. Therefore, it is difficult to infer the direction information of the moving object by directly extracting the Doppler shift with interferometry, unless additional measurement methods are used, for example, heterodyne detection or dual-frequency detection. This undoubtedly leads to a major application limitation for optical Doppler metrology.
Light is the transverse wave. Apart from the degree of freedom of amplitude and phase, it also possesses the degree of freedom of polarization. The polarization of light describes the electromagnetic field resonance in the plane that is orthogonal to the direction of propagation. The polarization orientations of the traditional beams with plane phase are uniformly distributed in the cross section of the light beam. For a special kind of structured light, its polarization orientations are spatially and periodically distributed in the cross section, called vectorial polarized light. For this class of structured light, a recent research by Professor Wang Jian's group from Multi-Dimensional Photonics Laboratory (MDPL), Wuhan National Laboratory for Optoelectronics (WNLO), Huazhong University of Science and Technology (HUST), found that a moving particle within this class of structured light can produce a new Doppler effect, called vectorial Doppler effect. Different from the traditional Doppler effect based on scalar optical field (Doppler signal is characterized by time-varying one-dimensional intensity signals), for the vectorial Doppler effect based on the new vectorial structured light, its Doppler signal features time-varying two-dimensional polarization signals. This new Doppler polarization signal, not only carrying the magnitude information of velocity of the moving object, but also naturally carries the direction information of the velocity. Specifically, the Doppler polarization signals show different rotational chirality under opposite moving directions for the moving particle. In experimental or practical applications, one can easily distinguish the rotational chirality of the Doppler polarization signal by using two analyzers to measure the relative phase difference between two filtered optical intensity signals, and then directly determine the magnitude and direction information of velocity of the moving object.
From the study, the researchers also found that based on the vectorial Doppler effect with vectorial structured light, one could not only directly measure the full information of the particle's velocity vector (magnitude and direction), but also potentially track the instantaneous relative positions and instantaneous velocities of the moving particle. Furthermore, the measurement in the vectorial Doppler metrology does not need interference with a reference light, and thus has a high ability to resist the environmental interference. In addition, as for the anisotropic moving particles, theoretical analyses clearly show that even if the particles are rotating and meanwhile in the state of spinning around its mass center, it is also possible to simultaneously determine the particle's rotational velocity vector (magnitude and direction) and spin velocity vector (magnitude and direction) by analyzing the received Doppler polarization signals through either the standard Stokes analysis or simple usage of two polarizers. For more details, pleaseread the recent publication titled with “Vectorial Doppler metrology” in Nature Communications, July 7, 2021. In this work, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, is the first affiliation. Fang Liang as a postdoctoral fellow and Wan Zhenyu as a master student, both from Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technoogy, are the co-first authors, Professor Andrew Forbes from University of the Witwatersrand, also the honorary professor of Huazhong University of Science and Technology, is the co-author, and Professor Wang Jian from Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, is the corresponding author. This work is a breakthrough in the traditional Doppler effect based on scalar optical fields, which greatly enriches the contents of Doppler metrology. Moreover, it is of great scientific significance for the basic research and extended application research of vectorial structured light fields.
Liang Fang, Zhenyu Wan, Andrew Forbes, Jian Wang*, “Vectorial Doppler metrology,” Nature Communications, 12, 4186 (2021).
https://www.nature.com/articles/s41467-021-24406-z
Figure 1. Conceptual diagram of vector Doppler effect
Figure 2. Vectorial Doppler effect based on the vectorial structured light used for motion vector (magnitude and direction) determination of a moving particle.(a)(c) A schematic diagram of the moving particle with opposite moving directions interacting with the local polarization within the vectorial polarization field (represented by HE31). (b)(d) The two-dimensional Doppler polarization signals sampled, reflected or scattered by the moving particle show different chirality under opposite moving directions of the particle. These two-dimensional Doppler polarization signals carry both the magnitude and direction information of velocity of the moving particle, which is not available in traditional one-dimensional Doppler intensity signals based on scalar optical fields.
