Linear Doppler Effect Research Articles

Fourier-transform spectroscopy based on the rotational Doppler effect

We propose a new Fourier-transform spectroscopy technique based on the rotational Doppler effect. The technique offers an application for optical vortex frequency combs, where each frequency component carries a unique amount of orbital angular momentum (OAM). Here, we emulate a vortex comb using a tunable single frequency laser and a collection of spiral phase plates, generating up to 11 distinct OAM modes. Unlike in traditional Fourier-transform spectroscopy based on the Michelson interferometer (linear Doppler effect), the spectral resolution of vortex-comb spectroscopy is not limited by the mechanical scan distance of the instrument, but the instrument can be operated continuously without interruptions, leading to fast mode-resolved measurements.

Micro‐motion parameters extraction of rotating target based on analytical solution in vortex electromagnetic wave radar

AbstractThe linear Doppler effect and angular Doppler effect in vortex electromagnetic wave radar echoes can be used to extract comprehensive micro‐motion parameters. However, the analytical solution of micro‐motion parameters for rotating targets in vortex EM wave radar has not been obtained. To solve the above problems, the analytical solution of micro‐motion parameters is derived, and a micro‐motion parameter extraction method is proposed. Firstly, the shape and properties of the angular Doppler curve in various cases are discussed. Subsequently, the properties of three points on the angular Doppler curve are derived. The micro‐motion parameters are obtained based on the three points. The simulations demonstrate that the proposed method can greatly reduce the computational complexity and improve the accuracy of micro‐motion parameter extraction.

Revealing the Incidence-Angle-Independent Frequency Shift in the Acoustic Rotational Doppler Effect.

The Doppler effect is a universal wave phenomenon that has inspired various applications due to the induced frequency shift. In the case of the linear Doppler effect, the frequency shift depends on the incident frequency and angle. Here, we unveil the frequency shift dependence induced by the acoustic rotational Doppler effect in the wave-object scattering process. We experimentally demonstrate that this frequency shift is exclusively determined by the angular speed and rotational symmetry of the spinning scatterer while remaining independent of the incident angular momentum and angle. We derive the analytical relationship between the frequency shift and the scatterer's helicity, presenting a novel approach for helical feature recognition. The angle-independent nature of the frequency shift inherently prevents spectrum broadening and offers a solution for precise motion measurement through the rotational Doppler effect. This work provides a rigorous and comprehensive understanding of the acoustic Doppler effect, enriching its applications in helicity and motion detection.

Rotational Doppler Effect: A Review

AbstractGenerally, the linear motion between the source of a wave and an observer leads to a linear Doppler effect. It is associated with the linear momentum of the wave. For electromagnetic beams having a circular polarization or an azimuthal phase distribution, the rotation between the source and the observer results in a less well‐known rotational Doppler effect. It is associated with the angular momentum of the wave. This is particularly the case for vortex beams. Here, the various physical insights that are given to explain the origin of the rotational Doppler effect is reviewed. The focus is on different cases where such an effect gives information on the rotational nature of the probed systems, and also on cases where the rotational Doppler effect is useless. Still debated issues and possible applications are then presented.

The Rotational Doppler Effect of Twisted Photons in Scattered Fields

AbstractAlong with broad applications of the linear Doppler effect, the rotational Doppler effect (RDE) of a structured light source carrying orbital angular momentum (OAM) has attracted significant attention for applications ranging from optical sensors to Doppler cooling. However, the high‐purity structured source's low energy efficiency and unknown optimal OAM parameters have significantly degraded the RDE's performance in previous work. Here, instead of utilizing an optical vortex source, the Doppler features are analyzed in scattered twisted photons carrying OAM with a common light source, and it is demonstrated that the RDE induced by a typical rotator can be extracted using a spiral phase spatial filter (SPSF) at the receiver. This model reveals that a rotating rough surface scatters abundant twisted photons carrying varied OAM values, and the OAM spectrum distribution is modulated by its angular coherence of spatial signature. Furthermore, common surfaces with different autocorrelation structures on received signals using the SPSF method are analyzed theoretically and experimentally. Such a scheme facilitates rotator detection with a generalized nonvortex simple source and dozen–fold improved efficiency with robustness against noncoaxial problems. These demonstrations open a path for studying and applying scattered twisted photons during light detection.

Fragmental optical vortex for the detection of rotating object based on the rotational Doppler effect.

Rotational Doppler effect (RDE), as a counterpart of the conventional linear Doppler effect in the rotating frame, has attracted increasing attention in recent years on rotational object detection. Many previous works have investigated the RDE based on the whole optical vortex field. In this work, we report on the RDE of the partially obstructed optical vortex and the corresponding rotational speed extraction method. Based on the orbital angular momentum (OAM) mode analysis theory, we establish the relationship between the OAM spectrum and the RDE frequency shift of fragmental optical vortex (FOV). The mechanism of the rotational speed extraction is analysed and validated by the numerical simulation and experiments. Further, a dual Fourier transformation method is proposed to accurately obtain the rotational speed which successfully overcomes the problem of the discrete distribution of the RDE signals. Our work may be useful for practical remote sensing based on the optical RDE metrology.

Scattering by a low-velocity charge with applied magnetic fields in a Laguerre–Gaussian beam

A method to analyze the scattering characteristics of a Laguerre–Gaussian (LG) vortex beam by a low-velocity charge in a steady applied magnetic field is investigated in this paper. Based on the plane wave angular spectrum representation and the electromagnetic radiation theory of a moving charge, the expressions of the scattered field and scattered power per unit solid angle are presented. Considering a low-velocity electron, the distribution of the scattered power per unit solid angle is numerically simulated. The effects of electron motion parameters, beam parameters, and applied magnetic field are discussed in detail. The results show that the longitudinal motion of the electron, which is parallel to the direction of the applied magnetic field, makes the distribution of the scattered power no longer maintain radial consistency but has a concave–convex distribution. Due to the periodicity of the circular motion of the electron in the applied magnetic field, the scattering power distribution pattern consists of many annular lobes. The spectral characteristics of the backscattered field are analyzed by fast Fourier transform. It is confirmed that the scattered field satisfies the rotational and the linear Doppler effects, and the accuracy of the formula provided in this paper is verified. This work lays a foundation for further study of the scattering characteristics of plasma on vortex electromagnetic waves and helps to promote the in-depth development of vortex beams in the field of plasma diagnosis.

Detection of a Spinning Object at Different Beam Sizes Based on the Optical Rotational Doppler Effect

The rotational Doppler effect (RDE), as a counterpart of the conventional well-known linear Doppler effect in the rotating frame, has attracted increasing attention in recent years for rotating object detection. However, the effect of the beam size on the RDE is still an open question. In this article, we investigated the influence of the size of the probe light; i.e., the size of the ring-shaped orbital angular momentum (OAM)-carrying optical vortex (OV), on the RDE. Both the light coaxial and noncoaxial incident conditions were considered in our work. We analyzed the mechanism of the influence on the RDE under the light coaxial, lateral misalignment, and oblique incidence conditions based on the small-scatterer model. A proof-of-concept experiment was performed to verify the theoretical predictions. It was shown that both the signal-to-noise ratio and the frequency spectrum width were related to the OV size. The larger the beam size, the stronger the RDE signal observed in the practical detection. Especially in the lateral misalignment condition, the large OV size effectively reduced the signal spreading and enhanced the signal strength. These findings may be useful for practical application of the optical RDE in remote sensing and metrology.

Rotational Doppler effect on reflection upon an ideal rotating propeller

The rotational Doppler shift is the counterpart of the usual linear Doppler effect for rotating bodies. We study by an experimental approach coupled with theoretical considerations the rotational shift of a fundamental laser light reflected on an ideal rotating propeller. We decompose the reflected light on a Laguerre–Gaussian basis and show that only modes having the same rotational symmetry as the propeller are involved in the decomposition. The latter experience a frequency shift proportional to the rotation frequency of the propeller and the topological charge of the beam. Extensions of this work in the microwave domain are then considered.

Rotational Doppler Effect in Vortex Light and Its Applications for Detection of the Rotational Motion

The linear Doppler effect has been widely used to detect the translational motion of objects. However, it suffers difficulties in measuring the angular motion of a rotating target. In recent years, the rotational Doppler effect based on a vortex beam has been helpful to solve the problem of rotational measurement and has attracted extensive attention in remote sensing. This paper expounds the theoretical and experimental basis of the rotational Doppler effect and briefly summarizes its development for the detection of macro and micro targets. Specifically, the properties and analysis methods of a rotational Doppler shift when the vortex beam is misaligned with the rotation axis are described in detail. In addition, the existing problems and further developments in rotation detection based on the rotational Doppler effect are discussed.

Design and experimental demonstration of Doppler cloak from spatiotemporally modulated metamaterials based on rotational Doppler effect.

Recently, spatiotemporally modulated metamaterial has been theoretically demonstrated for the design of Doppler cloak, a technique used to cloak the motion of moving objects from the observer by compensating for the Doppler shift. Linear Doppler effect has an angular counterpart, i.e., the rotational Doppler effect, which can be observed by the orbital angular momentum (OAM) of light scattered from a spinning object. In this work, we predict that the spatiotemporally modulated metamaterial has its angular equivalent phenomenon. We therefore propose a technique to observe the rotational Doppler effect by cylindrical spatiotemporally modulated metamaterial. Conversely, such a metamaterial is able to cloak the Doppler shift associated with linear motion by generating an opposite rotational Doppler shift. This novel concept is theoretically analyzed, and a conceptual design by spatiotemporally modulating the permittivity of a voltage-controlled OAM ferroelectric reflector is demonstrated by theoretical calculation and numerical simulation. Finally, a Doppler cloak is experimentally demonstrated by a spinning OAM metasurface in radar system, which the spatiotemporal reflection phase are mechanically modulated. Our work presented in this paper may pave the way for new directions of OAM carrying beams and science of cloaking, and also explore the potential applications of tunable materials and metasurfaces.

Influence of lateral misalignment on the optical rotational Doppler effect.

The discovery of the optical rotational Doppler effect associated with orbital angular momentum of light paves a new way to detect the rotational speed of spinning objects. In this paper, we investigate the influence of lateral misalignment, i.e., the distance between the beam axis of a probe light and the rotation axis of a spinning object, on the rotational Doppler effect. First, we analyze the mechanism of the rotational Doppler effect of optical vortices based on the linear Doppler effect. Specifically, we consider the general case where the center of the optical vortex does not coincide with the rotation axis, and deduce the generalized formula of rotational Doppler shift based on a local scattering model. It is found that the bandwidth of the rotational Doppler signal depends proportionally on the amount of lateral misalignment, whereas the value of rotational Doppler shift remains constant. A proof-of-concept experiment is performed, and the measured results agree well with theoretical predictions. These findings may be useful for practical application of the optical rotational Doppler effect in remote sensing and metrology.

Analysis of rotational Doppler effect based on radio waves carrying orbital angular momentum

The electromagnetic beam carrying orbital angular momentum (OAM) has a twisted phase front, which can induce a rotational Doppler frequency shift when it is illuminating on a spinning object. In this paper, the rotational Doppler effect induced by a radio wave carrying OAM is theoretically analyzed and experimentally verified. Compared with an optical vortex beam, the divergence angle of a radio wave carrying OAM is typically larger than that of an optical vortex beam, which results in the radio OAM-based sensing system with short-range detection distance. In this case, the receiver's location and the deflection of the rotating plane are important factors that affect the radio rotational Doppler effect. For an off-axis receiver or a deflected spinning object, a series of extra Doppler frequency shifts (L ± N)Ω/2π are induced when the spinning object is illuminated by a wave carrying OAM with topological charge L, even for L = 0, the plane wave. Hence, the high order OAM wave should be used to distinguish the real rotational frequency shift and improve detection sensitivity of spinning velocity. Combining the rotational Doppler effect with the linear Doppler effect, a vector velocity detecting scheme is discussed.

Sharing a Common Origin Between the Rotational and Linear Doppler Effects (Laser Photonics Rev. 11(6)/2017)

By considering either the motion-induced time-evolving phase or the momentum and energy conservation in light-matter interactions, the authors show the relationship between rotational and linear Doppler shifts, either of which can be derived from the other effect, thereby illustrating their shared origin. (Picture: Liang Fang et al., article number 1700183, in this issue)

Sharing a Common Origin Between the Rotational and Linear Doppler Effects

AbstractThe well‐known linear Doppler effect arises from the linear motion between source and observer, while the less well‐known rotational Doppler effect arises from the rotational motion. Here, we present both theories and experiments illustrating the relationship between the rotational and linear Doppler effects. A spiral phaseplate is used to generate a light beam carrying orbital angular momentum and the frequency shift is measured arising from its rotational and/or linear motion. By considering either the motion‐induced time‐evolving phase or the momentum and energy conservation in light‐matter interactions, we derive the rotational Doppler shift, linear Doppler shift, and overall Doppler shift associated with rotational and linear motions. We demonstrate the relationship between rotational and linear Doppler shifts, either of which can be derived from the other effect, thereby illustrating their shared origin. Moreover, the close relationship between rotational and linear Doppler effects is also deduced for a more general moving rough surface.

Detection of a Spinning Object Using Light’s Orbital Angular Momentum

The linear Doppler shift is widely used to infer the velocity of approaching objects, but this shift does not detect rotation. By analyzing the orbital angular momentum of the light scattered from a spinning object, we observed a frequency shift proportional to product of the rotation frequency of the object and the orbital angular momentum of the light. This rotational frequency shift was still present when the angular momentum vector was parallel to the observation direction. The multiplicative enhancement of the frequency shift may have applications for the remote detection of rotating bodies in both terrestrial and astronomical settings.

Novel control for delay-locked loop in IR-UWB communication systems

Timing synchronization represents a major challenge in carrying out highly efficient ultra-wideband (UWB) communications. The delay-locked loop (DLL) method is widely proposed to maintain the satisfactory synchronization and reduce timing error. In this paper, the structure of DLL is modified by using the internal model control (IMC). This novel approach in the telecommunication systems has a good performance of overcoming disturbance and deviations of model parameters. Then the proposed IMC-DLL structure is developed, and by taking a linear Doppler Effect into account. This development is achieved by using the following two approaches: multi-model approach and moving average filter. Finally, the simulation results confirm that the proposed IMC-DLL system is able to achieve satisfactory and accurate tracking even in the presence of Doppler effect, and they also confirm that the proposed DLL has higher transient response, compared with the classical one.

Optical vortices in rotating weakly guiding ideal optical fibres

The structure of l = 1 modes of a weakly guiding ideal optical fibre rotating around its symmetry axis is studied. It is demonstrated that rotation brings forth a novel mode structure in which two circular optical vortices with coinciding signs of circular polarization and topological charge are the eigenmodes propagating with different phase velocities. Rotation-induced corrections to the propagation constants of these vortices are calculated in the first order in angular velocity. The absence of the rotational Doppler effect for optical vortices in such fibres and the implementation of the linear Doppler effect is demonstrated.

A Useful Form of the Minkowski Diagram

We give a diagrammatic representation of the diagonal form of the special Lorentz transformation. The null coordinates x±ct are plotted along a single set of orthogonal axes. Special Lorentz transformations are then represented only by a change of scale along those orthogonal axes. This diagram, which we call a null coordinate diagram, and the Minkowski diagram are closely connected. To demonstrate the use of the null coordinate diagram, we apply it to the linear Doppler effect, time dilation, and Lorentz contraction.

Special Relativity and Diagonal Transformations

We discuss the form of the special Lorentz transformation, and the corresponding transformation of the electromagnetic field, in which the transformation matrix is diagonal. We derive the diagonal form of the special Lorentz transformation directly, in a simple way, and show that it is sometimes more convenient to apply than the algebraically equivalent conventional form of the transformation. The convenience is especially evident in deriving the linear Doppler effect, and the relativistic addition of more than two parallel velocities. By writing Maxwell's equations in terms of linear combinations of coordinates which have simple transformation properties, we arrive at the transformation equations of the Maxwell fields in a diagonal form, as well as at the plane wave solutions, in a natural manner. The derivations and applications described above should be of use in a course on relativity because of their simplicity and directness.