The Doppler effect of light was implemented by interference with a reference wave to infer linear velocities in early manifestations, and more recently lateral and angular velocities with scalar phase structured light. A consequence of the scalar wave approach is that it is impossible to deduce the motion direction and position of moving targets directly. Here we overcome this limitation with vectorially structured light, exhibiting spatially variant polarization, allowing both the position and velocity of a particle to be robustly determined by a new vectorial Doppler effect. We use this to successfully implement real time monitoring of instantaneous angular position and velocity of a complicated moving particle, and interpret its physical mechanism as evidence of time reversal symmetry breaking in classically entangled light fields. Our demonstration can easily be extended with arbitrary vector structured fields for complete motion tracking of nontrivial trajectories, offering new vectorial Doppler metrology for universal motion vectors.
We show that majorization provides a powerful approach to the coherence conveyed by partially polarized transversal electromagnetic waves. Here we present the formalism, provide some examples and compare with standard measures of polarization and coherence of vectorial waves.
We experimentally demonstrate the emergence of a purely azimuthally polarized vectorial vortex beam with a phase singularity upon Brewster reflection of focused circularly polarized light from a dielectric substrate. The effect originates from the polarizing properties of the Fresnel reflection coefficients described in Brewster's law. An astonishing consequence of this effect is that the reflected field's Cartesian components acquire local phase singularities at Brewster's angle. Our observations are crucial for polarization microscopy and open new avenues for the generation of exotic states …
A representation of partially spatially coherent and partially polarized stationary electromagnetic fields is given in terms of mutually uncorrelated, transversely shifted, fully coherent and polarized elementary electric-field modes. This representation allows one to propagate non-paraxial partially coherent vector fields using techniques for spatially fully coherent fields, which are numerically far more efficient than methods for propagating correlation functions. A procedure is given to determine the elementary modes from the radiant intensity and the far-zone polarization properties of th…
This study investigated the nonlinear frequency conversions between the six polarization modes of a two-mode birefringent fiber. The aim was to demonstrate that the selective excitation of different combinations of linearly polarized spatial modes at the pump wavelength initiates distinct intermodal vector four-wave mixing processes. In particular, this study shows that exciting two orthogonally polarized LP01 and LP11 modes can result in simultaneous generation of up to three pairs of different spatial modes of orthogonal polarizations at different wavelengths. The role of the phase birefring…
Reconfigurable Momentum-space vectorial lasing enabled by Quasi-BIC
Key Laboratory of Multiscale Spin Physics (Ministry of Education), Applied Optics Beijing Area Major Laboratory, School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院，多尺度自旋物理教育部重点实验室，应用光学北京地区重大实验室）
We study numerically and experimentally the impact of temporal randomness on the formation of analogue optical blast-waves in nonlinear fiber optics. The principle-of-operation is based on a two-components nonlinear interaction occurring between a partially coherent probe wave co-propagating in a normally dispersive optical fiber together with an orthogonally polarized intense short pulse. The cross-polarized interaction induces a dual phase-singularity in the probe profile which leads to the formation of two sharp fronts of opposite velocities. An optical blast-wave is then generated and lead…
Spin-orbit interaction (SOI) have provided a new viable roadmap for the development of spin-based photonics devices. However, existing strategies to control the SOI focus commonly on tailoring the spatial dimension of light fields yet neglecting the inherent temporal one. Herein, we first present ultrafast temporal effects on both spin-to-orbit and orbit-to-local-spin conversions based on the time-assistant vectorial diffractive theory and the fast Fourier transformation. Such interconversions depend upon whether the incident hybridly vectorial light pulse carries vortex phase or not in a sing…
We derive expressions for the energy, linear momentum, and angular momentum content of circularly polarized Laguerre-Gaussian wave-packets propagating in free space. The vectorial nature of the electromagnetic field is taken into account, and the various consequences of paraxial approximation, which is typically invoked in theoretical treatments of the Laguerre-Gaussian beams, are examined.
Position measurement of a levitated particle with vectorial light
Pontifical Catholic University of Rio de Janeiro（里约热内卢天主教大学）；Universidade Federal do Rio de Janeiro（里约热内卢联邦大学）；Tecnológico de Monterrey（蒙特雷理工学院）；University of Southampton（南安普顿大学）
In chiral sum frequency generation (C-SFG), the chiral nature of $χ^{(2)}$ requires the three involved electric fields to be pairwise non-parallel, leading to the traditional non-collinear configuration which is a hindrance for achieving diffraction limited resolution while utilizing it as a label-free imaging contrast mechanism . Here we propose a collinear C-SFG (CC-SFG) microscopy modality by using longitudinal z-polarized vectorial field. Label-free chiral imaging with enhanced spatial resolution (~1.4 times improvement in one lateral and the longitudinal directions over the traditional no…
Seeing full vectorial structures of light fields with a single-shot holographic multiplexed detector
School of Optoelectronic Engineering, Xidian University（西安电子科技大学光电工程学院）；Key Laboratory of Light Field Manipulation and System Integration Applications in Fujian Province, School of Physics and Information Engineering, Minnan Normal University（闽南师范大学物理与信息工程学院福建省光场调控与系统集成应用重点实验室）；School of physics, Xidian University（西安电子科技大学物理学院）；State Key Laboratory of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University（吉林大学电子科学与工程学院集成光学国家重点实验室）
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…
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…
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…
The scattering of a linear wave on an optical event horizon, induced by a cross polarized soliton, is experimentally and numerically investigated in integrated structures. The experiments are performed in a dispersion-engineered birefringent silicon nanophotonic waveguide. In stark contrast with co-polarized waves, the large difference between the group velocity of the two cross-polarized waves enables a frequency conversion almost independent on the soliton wavelength. It is shown that the generated idler is only shifted by 10 nm around 1550 nm over a pump tuning range of 350 nm. Simulations …
Highly confined vectorial electromagnetic field distributions represent an excellent tool for detailed studies in nano-optics and high resolution microscopy, such as nonlinear microscopy, advanced fluorescence imaging or nanoplasmonics. Such field distributions can be generated, for instance, by tight focussing of polarized light beams. To guarantee high quality and resolution in the investigation of objects with sub-wavelength dimensions, the precise knowledge of the spatial distribution of the exciting vectorial field is of utmost importance. Full-field reconstruction methods presented so fa…
The propagation of a Bessel beam (or Bessel-X wave) is analyzed on the basis of a vectorial treatment. The electric and magnetic fields are obtained by considering a realistic situation able to generate that kind of scalar field. Specifically, we analyze the field due to a ring-shaped aperture over a metallic screen on which a linearly polarized plane wave impinges. On this basis, and in the far field approximation, we can obtain information about the propagation of energy flux and the velocity of the energy.
The formula for the frequency shift of a plane-polarized light wave reflected from a uniformly moving mirror is derived directly from the constant light speed postulate and the basic principles of wave optics. Unlike the original derivation by Einstein, our derivation does not involve Lorentz transformations. As such, it lies within the scope of a first course in special relativity.
We experimentally demonstrate for the first time that a linearly polarized beam is focussed to an asymmetric spot when using a high-numerical aperture focussing system. This asymmetry was predicted by Richards and Wolf [Proc.R.Soc.London A, 253, 358 (1959)] and can only be measured when a polarization insensitive sensor is placed in the focal region. We used a specially modified photodiode in a knife edge type set up to obtain highly resolved images of the total electric energy density distribution at the focus. The results are in good agreement with the predictions of a vectorial focussing th…
We employ structured light for the second-harmonic generation from subwavelength AlGaAs nanoparticles that support both electric and magnetic multipolar Mie resonances. The vectorial structure of the pump beam allows addressing selectively Mie-resonant modes and control the strength of the generated nonlinear fields. We observe experimentally the enhancement of the second-harmonic generation for the azimuthally polarized vector beams near magnetic dipole resonance, and match our observations with the numerical decomposion of the Mie-type multipoles for the fundamental and generated second-harm…
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…
We report the first use of an extremely thin vapor cell (thickness ~ 400 nm) to study the magnetic-field dependence of laser-induced-fluorescence excitation spectra of alkali atoms. This thin cell allows for sub-Doppler resolution without the complexity of atomic beam or laser cooling techniques. This technique is used to study the laser-induced-fluorescence excitation spectra of Rb in a 50 G magnetic field. At this field strength the electronic angular momentum J and nuclear angular momentum I are only partially decoupled. As a result of the mixing of wavefunctions of different hyperfine stat…
Skyrmion Generation through the Chirality Interplay of Light and Magnetism
School of Physics and Materials Science, Guangzhou University（广州大学物理与材料科学学院）；School of Physical Sciences, Great Bay University（大湾区大学物理科学与技术学院）；Great Bay Institute for Advanced Study（大湾区高等研究院）
A representation theory of finite electromagnetic beams in free space is formulated by factorizing the field vector of the plane-wave component into a $3 \times 2$ mapping matrix and a 2-component Jones-like vector. The mapping matrix has one degree of freedom that can be described by the azimuthal angle of a fixed unit vector with respect to the wave vector. This degree of freedom allows us to find out such a beam solution in which every plane-wave component is specified by the same fixed unit vector $\mathbf{I}$ and has the same normalized Jones-like vector. The angle $θ_I$ between the fixed…
High-harmonic generation (HHG) in solids has been touted as a way to probe ultrafast dynamics and crystal symmetries in condensed matter systems. Here, we investigate the polarization properties of high-order harmonics generated in monolayer MoS$_2$, as a function of crystal orientation relative to the mid-infrared laser field polarization. At several different laser wavelengths we experimentally observe a prominent angular shift of the parallel-polarized odd harmonics for energies above approximately 3.5 eV, and our calculations indicate that this shift originates in subtle differences in the…
We report on the observation of a Zeeman shift (order of 100 MHz) of the Doppler-broadened D2 transition of both 85Rb and 87Rb isotopes via transmission through a tapered optical nanofiber in the presence of a DC magnetic field. Linearly-polarized light propagating in the nanofiber is analyzed as a superposition of two orthogonally circularly-polarized orientations, σ+ and σ-. In the absence of the magnetic field, the absorption of these polarizations by the atomic vapor, via the evanescent field at the waist of the nanofiber, is degenerate. When a weak magnetic field is applied parallel to th…
