Rotational Doppler Research Articles

Rotational Doppler Effect With Vortex Beams: Fundamental Mechanism and Technical Progress

Structured light beams such as optical vortices can carry the orbital angular momentum (OAM) with an unbounded quantum number. Recent years have witnessed a growing interest in the rotational Doppler effect with vortex light. Here we present an overview on the technical progress in measuring the rotational Doppler effect associated with OAM. This includes how a high-order OAM light beam is crucial for realizing high-sensitivity remote sensing of rotating objects. The basic physical mechanism of rotational Doppler effect is manifested from both perspectives of the wave property and the conservation law of energy. Besides, we summarize the extension of the rotational Doppler effect from linear optics to nonlinear optics, and to quantum realms. Also, we discuss the main challenges and opportunities of angular remote sensing in a realistic scenario for future applications.

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.

Observation of decay of nonadiabatic molecular unidirectional rotation via time-resolved rotational Doppler spectroscopy

In order to investigate the decay of nonadiabatic molecular unidirectional rotation (UDR) for nitrogen molecules, we measured the time-resolved rotational Doppler spectroscopy in first four revival periods after instantaneous excitation by a polarization shaped femtosecond laser. The results show that the rotational Doppler shifts decrease with increasing order of revival periods for full and half rotational revivals. Moreover, the maximum alignment of the molecular UDR at half rotational revivals was demonstrated to delay with revival periods increasing. This work is helpful to understand the kinetic processes of collisional decay for nonadiabatic molecular UDR, especially in the several revival periods after excitation.

Measurement of Orientation and Distance Change Using Circularly Polarized UWB Signals

The article proposes methodology to use circularly polarized (CP) ultra-wideband (UWB) signals for simultaneous measurement of orientation and distance changes between transmitter and receiver. The proposed technique uses the rotational Doppler effect on CP pulsed communication. The amplitude of a CP signal is immune to polarization misalignment in the presence of rotation; however, the phase is subjected to a frequency-invariant shift proportional to the rotation angle. This significantly distorts the pulse shape in the time domain and can be used for the measurement of the rotated angle. By combining the technique with the well-known localization capability of UWB systems, one can precisely measure not only the distance but also the orientation. This is demonstrated by both numerical and experimental studies presented in this article.

Orbital angular momentum-based dual-comb interferometer for ranging and rotation sensing.

We present a dual-comb interferometer capable of measuring both the range to a target as well as the target's transverse rotation rate. Measurement of the transverse rotation of the target is achieved by preparing the probe comb with orbital angular momentum and measuring the resultant phase shift between interferograms, which arises from the rotational Doppler shift. The distance to the target is measured simultaneously by measuring the time-of-flight delay between the target and reference interferogram centerbursts. With 40 ms of averaging, we measure rotation rates up to 313 Hz with a precision reaching 1 Hz. Distances are measured with an ambiguity range of 75 cm and with a precision of 5.9 µm for rotating targets and 400 nm for a static target. This is the first dual-comb ranging system capable of measuring transverse rotation of a target. This technique has many potential terrestrial and space-based applications for lidar and remote sensing systems.

Detection and Demultiplexing of Cylindrical Vector Beams Enabled by Rotational Doppler Effect

Cylindrical vector beams (CVBs) detection is of vital significance in various kinds of studies such as particle observation and mode-division multiplexing (MDM). Herein, a comprehensive detection of CVBs based on the rotational Doppler effect (RDE) including analysis of topological charge (TC), relative amplitude module, and phase for superimposed mode bases is realized. A mode demultiplexing scheme is constructed through the complex amplitude of the harmonic terms in the beating signal. The method resolves both absolute values and signs of the TC of CVB simultaneously, which cannot be simply realized by existing polarization examination techniques. It may be of big potential in related research since an efficient, quantitative, and complete scheme to detect CVBs is verified starting from this work.

Rotational object detection at noncoaxial light incidence based on the rotational Doppler effect.

The rotational Doppler effect (RDE) of optical vortex which can be used to detect the rotation speed, has become a well-known phenomenon and a hot topic of research in recent years. However, because the beam axis must be coaxial with the rotational axis of the object, it can only be used to detect cooperative targets in practical application. Here, we provide a novel approach for measuring rotational speed under light non-coaxial incidence relative to the rotating axis that uses the adjacent frequency difference of rotational Doppler shift signals. Theoretically, the rotational Doppler shift is proportional to the OAM mode of the incident beam, and the nature of the OAM carried by each photon is a discrete or quantized quantity under off-axis conditions leading to the discrete distribution of the Doppler shift signals. Experimentally, by extracting the difference between two adjacent Doppler shift signals, the rotating speed of the object can be determined. Based on our method, the rotational speed of the object can be measured precisely without the pre-known information about the position of the rotating axis. Our work supplies a significant complement to the conventional RDE theory and we believe it may promote the realistic application of the optical RDE-based metrology.

Locating the center of rotation of a planar object using an optical vortex.

The rotational Doppler effect (RDE) of optical vortex beams provides an efficient way to measure the rotational frequency of objects based on rotational Doppler frequency shifts, while the frequency shift signals display a distinct broadening effect when the vortex beam is laterally misaligned with the center of rotation of a planar object. We use a modal decomposition method to reveal the broadening effect and obtain a linear fitting equation between the quantity of signals and lateral misalignments. In an experiment of RDE, the lateral misalignment is extracted from the quantity of signal peaks. The fitting equation is proved to be precise within the uncertainty of ±0.17mm (±2.8% of the vortex beam radius), and the center of rotation is located with an error less than 3.33% of the beam radius. Our work provides a new approach to locate the center of rotation of noncooperative objects, which may be valuable in mechanical manufacturing and optical noncontact metrology.

Detection of a spinning object with circular procession using an optical vortex beam.

The rotational Doppler effect (RDE) provides an efficient way to measure rotational frequency using an optical vortex beam. Crucially, most research based on the RDE just involves a spinning object or a spinning object coupled with a longitudinal velocity along the beam propagation. We analyze the interaction mechanism between optical orbital angular momentum and a spinning object with circular procession and experimentally demonstrate simultaneous measurements of two rotational frequencies. This technique broadens application of the RDE in optical metrology and remote detection of targets with micro-motions.

Fluid vortex mapping using the rotational Doppler effect

The light from a twisted laser beam, scattered at an air/water interface, experiences a rotational Doppler shift. We use a superposition of two beams with different topological charges to measure the beat frequency of the scattered light by a Rankine type vortex at different positions from its center. We show that the angular velocity decreases with the distance in total agreement with a Rankine vortex model. Several extensions are then considered, including the detection of turbulences generated in the wake of airplanes.

Towards the development of new generation spin-orbit photonic techniques

Spin–orbit interaction deals with the interaction and coupling of spin and orbital angular momentum degrees of freedom of spinning particles, which manifests in diverse fields of physics, ranging from atomic, condensed matter to optical systems. In classical light beams, this has led to a number of non-trivial optical phenomena like spin and orbital Hall effect of light, optical Rashba effect, photonic Aharonov–Bohm effect, rotational Doppler effect, transverse spin, Belinfante’s spin-momentum and spin-momentum locking etc. These have been observed in diverse micro- and nano-scale optical systems. These have generated a new area in photonics, namely, spin-orbit photonics that not only deals with fundamental light–matter interaction effects but also opened up the feasibility of a new generation of miniaturized and on-chip integrable multifunctional photonic devices based on the angular momentum and geometrical phase of light. This paper will introduce the emerging field of spin-orbit photonics and will cover the representative spin-orbit photonic effects in a variety of light-matter interactions with examples. In this regard, we also present proof-of-concept demonstrations of two interesting techniques based on the geometrical phase of light, namely, geometrical phase polarimeter and weak value polarimeter.

Experimental and numerical study of the rotational Doppler shift in acoustic waves using static microphones

The rotational Doppler shift in acoustic waves carrying orbital angular momentum (OAM) has been applied in experiments to demonstrate the Zel'dovich amplification, which is analogously linked with the black hole radiance. However, rotating microphones used in the published experiments are difficult to assemble and intrinsically weak in the frequency response at frequencies around 0 Hz. To circumvent the limitations, this paper proposes an experimental method to study the rotational Doppler shift in acoustic OAM waves using static microphones. The Doppler shifted signals viewed by a rotating observer were extracted from the original acoustic signals at frequencies around 100 Hz, where the microphones had flat frequency response. The measured results not only demonstrated the extreme Doppler shift to a negative frequency but also showed that the acoustic amplitudes were very low when the Doppler shifted frequency was 0 Hz. This phenomenon was explained by showing in a time-domain numerical simulation that the wave was co-rotating with the observer. In addition, the characteristics of the simulated pressure contours of the rotating wave have been discussed. The proposed methods can further be used to study the physics related to the wave carrying OAM, such as the acoustic super-radiance.

Rotation of the polarization of light as a tool for investigating the collisional transfer of angular momentum from rotating molecules to macroscopic gas flows

We present a detailed theoretical and experimental study of the rotation of the plane of polarization of light traveling through a gas of fast-spinning molecules. This effect is similar to the polarization drag phenomenon predicted by Fermi a century ago and it is a mechanical analog of the Faraday effect. In our experiments, molecules were spun up by an optical centrifuge and brought to the super-rotor state that retains its rotation for a relatively long time. Polarizability properties of fast-rotating molecules were analyzed considering the rotational Doppler effect and Coriolis forces. We used molecular dynamics simulations to account for intermolecular collisions. We found, both experimentally and theoretically, a nontrivial nonmonotonic time dependence of the polarization rotation angle. This time dependence reflects transfer of the angular momentum from rotating molecules to the macroscopic gas flow, which may lead to the birth of gas vortices. Moreover, we show that the long-term behavior of the polarization rotation is sensitive to the details of the intermolecular potential. Thus, the polarization drag effect appears as a novel diagnostic tool for the characterization of intermolecular interaction potentials and studies of collisional processes in gases.

Direction-discriminated rotational Doppler velocimetry with circularly polarized vortex beams.

The rotational Doppler effect can be exploited in laser rotational Doppler velocimetry to detect the angular velocity of a moving object. Recently, its vectorial counterpart was revealed, which uses vectorial polarization fields and shows the potential to retrieve the full vectorial motion information of a moving object. Here, we further develop the general model for direction-discriminated rotational Doppler velocimetry by considering two optical degrees of freedom (DoFs), i.e., the orbital angular momentum (OAM) and polarization. Analyses indicate that the two optical DoFs of light play different roles in rotational velocity measurement. On the one hand, the OAM DoF enables the detection of the magnitude of rotational velocity; on the other hand, the circular polarization DoF facilitates the determination of the rotation direction by analyzing the relative phase difference between two intensity signals of the superposed light field after two polarizers. We demonstrate an interferometric scheme with two orthogonally circularly polarized beams of opposite OAM for detecting a rotating small object. These demonstrations may provide abundant alternatives for achieving robust Doppler velocimetry in more complicated sensing and metrology applications.

Optical Magnus radiation force and torque on a dielectric layered cylinder with a spinning absorptive dielectric core.

A dielectric cylindrical shell material with an inner stationary absorptive core (or, equivalently, a concentric layered cylinder) illuminated by an axisymmetric wave field (in 2D) with arbitrary polarization will experience a time-averaged radiation force along the direction of wave propagation, whereas the transverse component vanishes as required by symmetry. Counterintuitively, the present analysis shows that when the inner absorptive core material rotates with an initial angular velocity Ω0 around its main geometrical axis, a transverse radiation force component arises (in addition to a longitudinal force) as well as an axial radiation torque component in plane waves. This phenomenon is the analog of the classical hydrodynamic Magnus effect. In this analysis, the instantaneous rest-frame theory and the modal series expansion method in cylindrical coordinates are utilized to formulate the EM/optical scattering from a cylindrical shell with arbitrary thickness, and to compute the optical radiation force and torque vector components. Particular emphases are given on the size parameter of the cylindrical shell, the layer thickness, the angular rotation of the inner absorptive core, and the polarization (TM or TE) of the incident plane waves. Numerical computations illustrate the analysis and explicate the behaviors of the longitudinal, transverse, and axial radiation force and torque components. Related applications for the optical Magnus effect in radiation force and torque investigations can benefit from the results of the present analysis in spin-optics, rotational Doppler shift for optical waves, optical tweezers, optical manipulation of elongated spinning objects, and particle rotation.

Observation of the Rotational Doppler Effect With Structured Beams in Atomic Vapor

A vector beam with the spatial variation polarization has attracted keen interest and is progressively applied in quantum information, quantum communication, precision measurement, and so on. In this letter, the spectrum observation of the rotational Doppler effect based on the coherent interaction between atoms and structured light in an atomic vapor is realized. The geometric phase and polarization of the structured beam are generated and manipulated by using a flexible and efficacious combination optical elements, converting an initial linearly polarized Gaussian beam into a phase vortex beam or an asymmetric or symmetric vector beam. These three representative types of structured beam independently interact with atoms under a longitudinal magnetic field to explore the rotational Doppler shift associated with the topological charge. We find that the rotational Doppler broadening increases obviously with the topological charge of the asymmetric and symmetric vector beam. There is no rotational Doppler broadening observed from the spectrum of the phase vortex beam, although the topological charge, and spatial profile of the beam change. This study can be applied to estimate the rotational velocity of the atom-level or molecule-level objects, measure the intensity of magnetic fields and study the quantum coherence in atomic ensembles.

Rotational Doppler shift of the light transmitted behind a rotating object with rotational symmetries: rotational Doppler shift of the transmitted light

Rotational Doppler shift of the light transmitted behind a rotating object with rotational symmetries: rotational Doppler shift of the transmitted light

Symmetry detection of rotating patterns based on rotational Doppler effect of light

Symmetry detection of rotating patterns based on rotational Doppler effect of light

Remote Measurement of the Angular Velocity Vector Based on Vectorial Doppler Effect Using Air-Core Optical Fiber.

Rotational Doppler effect has made tremendous development in both theoretical and applied research over the last decade. Different from the inertial thinking of focusing on the scalar field dominated by helical phase light, we have revealed a vectorial Doppler effect in our previous work, which is based on the spatially variant polarized light fields to simultaneously acquire the speed and direction of a target. Here, further, we propose a method to construct a flexible and robust velocimeter based on that novel effect by employing an air-core fiber with kilometer-length scale for remotely measuring the vectorial information of angular velocity in situ. In addition, we experimentally substantiate that the measurement system still has commendable accuracy in determining the direction of movement even when the air-core fiber is interfered by the external environment. The demonstrations prove the potential of vectorial Doppler effect in practical scenarios and remote measurements.