The function to measure orbital angular momentum (OAM) distribution of vortex light is essential for OAM applications. Although there are lots of works to measure OAM modes, it is difficult to measure the power distribution of different OAM modes quantitatively and instantaneously, let alone measure the phase distribution among them. In this work, we demonstrate an OAM complex spectrum analyzer, which enables to measure the power and phase distribution of OAM modes simultaneously by employing rotational Doppler Effect. The original OAM mode distribution is mapped to electrical spectrum of beating signals with a photodetector. The power distribution and phase distribution of superimposed OAM beams are successfully retrieved by analyzing the electrical spectrum. We also extend the measurement to other spatial modes, such as linear polarization modes. These results represent a new landmark of spatial mode analysis and show great potentials in optical communication and OAM quantum state tomography.
The 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…
We theoretically investigate the optical rotational Doppler Effect using modal expansion method. We find that the frequency shift content is only determined by the surface of spinning object and the reduced Doppler shift is linear to the change of mode index. The theoretical model makes us better understand the physical processes of rotational Doppler Effect. It can provide theoretical guidance for many related applications, such as detection of rotating bodies, detection of OAM and frequency shift.
Doppler cooling is a widely used technique to laser cool atoms and nanoparticles exploiting the Doppler shift involved in translational transformations. The rotational Doppler effect arising from rotational coordinate transformations should similarly enable optical manipulations of the rotational degrees of freedom in rotating nanosystems. Here, we show that rotational Doppler cooling and heating (RDC and RDH) effects embody rich and unexplored physics, such as a strong dependence on particle morphology. For geometrically confined particles, such as a nanorod that can represent diatomic molecu…
A monochromatic linear source of light is rotated with certain angular frequency and when such light is analysed after reflection then a change of frequency or wavelength may be observed depending on the location of the observer. This change of frequency or wavelength is different from the classical Doppler effect [1] or relativistic Doppler effect [2]. The reason behind this shift in wavelength is that a certain time interval observed by an observer in the rotating frame is different from that of a stationary observer.
We present a theoretical model to sufficiently investigate the optical rotational Doppler effect based on modal expansion method. We find that the frequency shift content is only determined by the surface of spinning object and the reduced Doppler shift is linear to the difference of mode index between input and output orbital angular momentum (OAM) light, and linear to the rotating speed of spinning object as well. An experiment is carried out to verify the theoretical model. We explicitly suggest that the spatial spiral phase distribution of spinning object determines the frequency content. …
We propose and substantiate experimentally the cascaded rotational Doppler effect for interactions of spinning objects with light carrying angular momentum. Based on the law of parity conservation for electromagnetic interactions, we reveal that the frequency shift can be doubled through cascading two rotational Doppler processes which are mirror-imaged to each other. This effect is further experimentally verified with a rotating half-wave plate, and the mirror-imaging process is achieved by reflecting the frequency-shifted circularly polarized wave upon a mirror with a quarter-wave plate in f…
We explain the rotational Doppler effect associated with light beams carrying with orbital angular momentum in left-handed materials (LHMs). We demonstrate that the rotational Doppler effect in LHMs is unreversed, which is significantly different from the linear Doppler effect. The physics underlying this intriguing effect is the combined contributions of negative phase velocity and inverse screw of wave-front. In the normal dispersion region, the rotational Doppler effect induces a upstream energy flow but a downstream momentum flow. In the anomalous dispersion region, however, the rotational…
Cylindrical vector beams (CVBs) detection is of vital significance in kinds of studies such as particle observation, mode-division multiplexing. Here we realize a comprehensive detection of cylindrical vector beams based on the rotational Doppler effect including analysis of topological charges, amplitudes, and phases for mode bases. We construct a mode demultiplexing scheme to obtain the amplitudes, phases in beating signal of collected scattering light by Fourier transformation. The method resolves both absolute values and signs of topological charges ofCVB simultaneously, which can not be s…
When circularly polarized light is scattered from a rotating target, a rotational Doppler shift (RDS) emerges from an exchange of angular momentum between the spinning object and the electromagnetic field. Here, we used coherently spinning molecules to generate a shift of the frequency of a circularly polarized probe propagating through a gaseous sample. We used a linearly polarized laser pulse to align the molecules, followed by a second delayed pulse polarized at 45° to achieve unidirectional molecular rotation. The measured RDS is orders of magnitude greater than previously observed by othe…
The frequency shift of a helical light beam experiencing the rotation near the axis deferring from its own axis (conical evolution) is studied theoretically. Both the energy and the kinematic approaches lead to a paradoxical conclusion that after a whole cycle of the system rotation the beam does not return to its initial state. Another paradox is manifested in the peculiar behavior of the beam transverse pattern rotation at different geometric parameters of the evolving system. A fundamental role of the detecting system motion is substantiated. The special "natural" observer's motion is found…
We compute the shift in the frequency of the spin resonance in a solid that rotates in the field of a circularly polarized electromagnetic wave. Electron spin resonance, nuclear magnetic resonance, and ferromagnetic resonance are considered. We show that contrary to the case of the rotating LC circuit, the shift in the frequency of the spin resonance has strong dependence on the symmetry of the receiver. The shift due to rotation occurs only when rotational symmetry is broken by the anisotropy of the gyromagnetic tensor, by the shape of the body, or by magnetocrystalline anisotropy. General ex…
The rotational Doppler shift of a photon with orbital angular momentum $\pm \ell \hbar$ is shown to be an even multiple of the angular frequency $Ω$ of the reference frame rotation when photon is reflected from the phase-conjugating mirror. We consider the one-arm phase-conjugating interferometer which contains $N$ Dove prisms or other angular momentum altering elements rotating in opposite directions. When such interferometer is placed in the rotating vehicle the $δω=4 (N+1/2) \ell \cdot Ω$ rotational Doppler shift appears and rotation of the helical interference pattern with angular frequenc…
Technological advances in femtosecond laser sources call for the development of increasingly refined characterization tools implying to enrich the existing panel of operable nonlinear interactions. The present paper describes a novel characterization method based on spectral-shearing interferometry which exploits the non-standard rotational Doppler effect for producing the frequency shear. This original approach, called DEER "Doppler Effect for Electric field Reconstruction", provides a spectral-shearing in the absence of frequency conversion and features multiple benefits as for instance the …
Optical interferometry has made tremendous development in fundamentals and applications of light. Traditional optical interferometry using simplex plane phase light just allows one dimensional measurement, but incapable of retrieving multidimensional movement. Here, we present new structured light interferometry to achieve simultaneous determination of rotational and translational dimensionalities (magnitudes and directions) of moving objects by fully exploiting multiple degree of freedoms of structured light. Such multidimensional detectability benefits from multiple amplitude and sign distin…
The rotational Doppler effect associated with light's orbital angular momentum (OAM) has been found as a powerful tool to detect rotating bodies. However, this method was only demonstrated experimentally on the laboratory scale under well controlled conditions so far. And its real potential lies at the practical applications in the field of remote sensing. We have established a 120-meter long free-space link between the rooftops of two buildings and show that both the rotation speed and the rotational symmetry of objects can be identified from the detected rotational Doppler frequency shift si…
We report on the direct measurements of fluid flow vorticity using a spatially shaped beam with a superposition of Laguerre-Gaussian modes that reports on the rotational Doppler shift from microparticles intersecting the beam focus. Experiments are carried out on fluid flows with well-characterized vorticity and the experimental results are found to be in excellent agreement with the expected values even for 200 ms integration times. This method allows for localized real-time determination of vorticity in a fluid flow.
Fundamental and applied concepts concerning the ability of light beams to carry a certain mechanical angular momentum with respect to the propagation axis are reviewed and discussed. Following issues are included: Historical reference; Angular momentum of a paraxial beam and its constituents; Spin angular momentum and paradoxes associated with it; Orbital angular momentum; Circularly-spiral beams: examples and methods of generation; Orbital angular momentum and the intensity moments; Symmetry breakdown and decomposition of the orbital angular momentum; Mechanical models of the vortex light bea…
The interaction of light with rotating media has attracted recent interest for both fundamental and applied studies including rotational Doppler shift measurements. It is also possible to obtain amplification through the scattering of light with orbital angular momentum from a rotating and absorbing cylinder, as proposed by Zel'dovich more than 40 years ago. This amplification mechanism has never been observed experimentally yet has connections to other fields such as Penrose superradiance in rotating black holes. Here we propose a nonlinear optics system whereby incident light carrying orbita…
The visible part ($\approx 550 ÷696$ nm) of the multiline electronic-vibro-rotational emission spectrum of the $D_2$ molecule was recorded with moderate resolution (line widths $\approx 0.013$ nm). The resolution was limited by Doppler broadening of spectral lines. After numerical deconvolution of the recorded intensity distributions and proper calibration of the spectrometer the new set of wavenumber values was obtained. The results are reported in the form of an atlas divided into 43 sections covering about 1.5 nm, containing pictures of images in the focal plane of the spectrometer, intensi…
