Momentum Transformation Research Articles

Chaotic photon spheres in non-Euclidean billiard

Abstract With the advancement in understanding of the physics inside chaotic systems, chaos has been harnessed from a nuisance to a beneficial factor in optical devices. Light–matter interaction in chaotic systems has been utilised for improving broadband energy harvesting and momentum transformations, achieving light localization beyond diffraction limit and even stabilizing the dynamics of high power laser. While extensive study about wave chaos has been made in deformed microcavities, investigation of how chaos dynamics evolves in curved space manifold remains elusive. Here, we study the non-Euclidean billiard of a torus-like manifold, which is a closed 2D cavity system with effective periodic boundaries. The ray chaotic behaviours on the deformed toroidal surface are explored using the geodesic equation. By tuning the deformation parameter of the torus, we observe the transition of the billiard from the ordered phase state to mixed phase states and then complete ray chaos. The photon sphere of the torus is identified as the transition position from ordered states to chaotic states. Compared with other chaotic behaviours resulted from the random scattering inside deformed cavities, we demonstrate chaotic dynamics purely on a curved surface, which may shed light on the better understanding of chaos in optics.

On-chip trans-dimensional plasmonic router

Abstract Plasmons, as emerging optical diffraction-unlimited information carriers, promise the high-capacity, high-speed, and integrated photonic chips. The on-chip precise manipulations of plasmon in an arbitrary platform, whether two-dimensional (2D) or one-dimensional (1D), appears demanding but non-trivial. Here, we proposed a meta-wall, consisting of specifically designed meta-atoms, that allows the high-efficiency transformation of propagating plasmon polaritons from 2D platforms to 1D plasmonic waveguides, forming the trans-dimensional plasmonic routers. The mechanism to compensate the momentum transformation in the router can be traced via a local dynamic phase gradient of the meta-atom and reciprocal lattice vector. To demonstrate such a scheme, a directional router based on phase-gradient meta-wall is designed to couple 2D SPP to a 1D plasmonic waveguide, while a unidirectional router based on grating metawall is designed to route 2D SPP to the arbitrarily desired direction along the 1D plasmonic waveguide by changing the incident angle of 2D SPP. The on-chip routers of trans-dimensional SPP demonstrated here provide a flexible tool to manipulate propagation of surface plasmon polaritons (SPPs) and may pave the way for designing integrated plasmonic network and devices.

Conversion and storage of modes with orbital angular momentum in a quantum memory scheme

The paper studies the Raman quantum memory protocol as applied to quantum light with orbital angular momentum. The memory protocol is implemented on an ensemble of three-level cold atoms with the $\Lambda$- configuration of energy levels. The possibility of storing quantum statistics of light with an orbital momentum is analysed in the case when the driving field could be treated as a plane wave. The efficiency analysis shows that examined storage/retrieval processes do not cause the efficiency decreasing compared with the spatial multimode memory protocol considered in [Golubeva et al. 2012]]. We also present an effective transformation of the orbital angular momentum of a quantum field on a memory cell using the driving field with orbital angular momentum.

High-energy 2 µm pulsed vortex beam excitation from a Q-switched Tm:LuYAG laser.

We report on the first, to the best of our knowledge, direct generation of pulsed vortex beams at 2 µm from a ${ Q}$Q-switched Tm:LuYAG laser. High-energy Laguerre-Gaussian (${{\rm LG}_{0,l}}$LG0,l) pulsed laser beams with well-defined handedness are selectively excited through spatially matched pump gain distribution and asymmetric cavity loss without using any intracavity handedness-selective optical elements. Pulse energies of 1.48 mJ for the ${{\rm LG}_{0, + 1}}$LG0,+1 mode and 1.51 mJ for the ${{\rm LG}_{0, - 1}}$LG0,-1 mode, respectively, are achieved at a repetition rate of 500 Hz. The pulsed laser beams with helical wavefronts are potentially useful for studying orbital angular momentum transformation dynamics, generation of mid-IR vortex beams, and nanostructuring of organic materials.

A study of the scaling relation $M_{\bullet }\propto R_{e}\sigma ^{3}$ for supermassive black holes and an update of the corresponding theoretical model

In this paper we want to compare the theoretical predictions of a law proposed by Feoli and Mancini, with the most recent experimental data about galaxies and Supermassive black holes. The physical principle behind this law is the transformation of the angular momentum of the interstellar material, which falls into the black hole, into the angular momentum of the radiation emitted in this process. Despite the simplicity of the model, this law shows an excellent agreement with the experimental data for early-type galaxies while a new approach is proposed for spirals.

Chiral Coupling of Valley Excitons and Light through Photonic Spin–Orbit Interactions

AbstractSpintronics employs the spin of electrons to encode information. Akin to spintronics, valleytronics exploits the valley as pseudospin‐carrying controllable binary information. 2D transition metal dichalcogenides (TMDCs) have asymmetric +K and −K valleys. The valley pseudospins of these materials can be manipulated by selective pumping, giving rise to valley‐dependent circularly polarized photoluminescence. The photonic spin–orbit interactions (SOIs) in nanophotonic systems allow the transformation or coupling of optical spin angular momentum to orbital angular momentum of light. Hybridizing 2D TMDC electronic systems with nanophotonic systems can open up an avenue for merging TMDC valley polarization and photonic SOIs to uncover new mechanisms of on‐chip optical information processing and transport. This review focuses on the fundamentals and implications of TMDC valley polarization, photonic SOI effects, and their chiral coupling in hybrid TMDCs–nanophotonic systems. First, the deterministic valley‐dependent optical properties of TMDCs and recent efforts in achieving large valley polarization contrast are reviewed. Then, various SOI effects in nanophotonic systems and their physical mechanisms are summarized. At the end, recent demonstrations of chiral coupling between TMDC valley excitons and light through spin‐direction locking at hybrid interfaces are highlighted.

Orbital angular momentum transformation of optical vortex with aluminum metasurfaces

The orbital angular momentum (OAM) transformation of optical vortex is realized upon using aluminum metasurfaces with phase distributions derived from the caustic theory. The generated OAM transformation beam has the well-defined Bessel-like patterns with multiple designed topological charges from −1 to +2.5 including both the integer-order and fractional-order optical vortices along the propagation. The detailed OAM transformation process is observed in terms of the variations of both beam intensity and phase profiles. The dynamic distributions of OAM mode density in the transformation are further analyzed to illustrate the conservation of the total OAM. The demonstration of transforming OAM states arbitrarily for optical vortex beams will lead to many new applications in optical manipulation, quantum optics, and optical communication.

Mechanical work-canceling strategy modulates initial push-off force depending on vertical jump height

In this study, we examined how jumping strategy changes with increasing vertical jump height from the viewpoint of mechanical work performed on center of mass (CoM) by individual sources (e.g., ground reaction force and gravity) during the countermovement period; we expected that intensity of the countermovement action would change with increasing jump height in a certain manner (e.g., linear relationship), which could be reflected in the changes of the outcome force and/or the work done by each of the individual sources through the countermovement. Six healthy young subjects were instructed to stand upright with both hands on their hips (akimbo posture) and to jump straight up to five different height levels, guided by black markers attached on a ceiling pole. The lowest and highest markers were located at 191 cm and 221 cm from the ground level, respectively. Kinematic and kinetic data obtained from the regular trials were used to estimate mechanical power and work, which were then analyzed to understand the change of the countermovement jump strategy with increasing vertical jump height. We found that 1) mechanical work-canceling strategy modulates initial push-off force depending on the vertical jump height, 2) the initial push-off force was directly determined by asymmetric momentum transformation, and 3) the momentum transformation may be conducted under consideration of accommodating biomechanical constraints.

Quantum gravity modifications of the relativistic ideal gas thermodynamics

In the frame work of the generalized uncertainty principle, we study the theoretical modifications induced by the quantum gravity on the thermodynamics of the relativistic ideal gas. The merit of this work is that we have applied two different research methods while the results of both methods point to a complete consistency between them. These approaches emerge from different viewpoints of the incorporation of the underlying theory. Here, we call them as the modified Hamiltonian method and the modified density of states method. In the first method, we have an active viewpoint and suppose that the Hamiltonian is modified via the momentum transformation induced by the theory. However, in the second method, we adopted rather a passive interpretation and consider a transformation of the coordinates as a result of the theory. In order to have a time invariant volume element of phase space, this method leads to a redefinition of the density of states. We show that these approaches expectedly lead to the same partition functions and hence are equivalent. Since, there are two models of the generalized uncertainty principle, with quadratic and linear momentum terms, we show these equivalencies are established for both models. We obtain the modifications of the thermodynamics of the relativistic ideal gas induced by the quadratic model and estimate the consequences for the limiting case the nonrelativistic domains. All the results are in agreement with the previous issues. Also the results for the extreme relativistic and asymptotic ultrarelativistic domains are obtained which shows novel properties. In addition, we indicate that the black body energy spectrum will be changed, due to the quantum gravity corrections, but this effect can be seen at high temperature limits.

Topological transformation of fractional optical vortex beams using computer generated holograms

Optical vortex beams with fractional topological charges (TCs) are generated by the diffraction of a Gaussian beam using computer generated holograms embedded with mixed screw-edge dislocations. When the input Gaussian beam has a finite wave-front curvature, the generated fractional vortex beams show distinct topological transformations in comparison to the integer charge optical vortices. The topological transformations at different fractional TCs are investigated through the birth and evolution of the points of phase singularity, the azimuthal momentum transformation, occurrence of critical points in the transverse momentum and the vorticity around the singular points. This study is helpful to achieve better control in optical micro-manipulation applications.

Physical process of tidal synchronization and orbital circularization in rotating binaries

The tide is a very important physical factor which can significantly affect the structure and evolution of stars. The physical factors which can affect tidal synchronization and orbital circularization are explored in this paper. For stars with radiative envelopes, radiative damping mechanism is required to explain the observed synchronization and circularization of close binaries. A star can experience a range of oscillations that arise from, and are driven by, the tidal field:the dynamical tides. The dynamical tide is the dynamical response to the tidal force exerted by the companion; it takes into account the elastic properties of the star, and the possibilities of resonances with its free modes of oscillation. The dissipation mechanism acting on this kind of tide is the deviation from adiabaticity of the forced oscillation, due to the radiative damping. Several physical factors can have an influence on the process of radiative damping which is scaled with thermal timescale. These physical factors include stellar mass, initial velocity, orbital period, metallicity, overshooting, etc. According to the equations for angular momentum transfer and chemical elements diffusion, we can obtain how these physical factors affect the evolution of rotating binaries and the mixing of chemical elements in two rotating components. The results indicates that the binaries with massive stars, smaller initial spin velocities, smaller overshooting parameters, and shorter orbital periods can attain the equilibrium speed and orbital circularization early. At synchronous states, the tidal torque is zero and stellar winds continue to brake the star. Therefore, two components cannot keep the synchronous state for a long time. At the equilibrium state, the tidal torque is counteracted by wind torques. Therefore, the equilibrium speed is less than the synchronous one. The system with smaller initial spin velocities reaches the equilibrium speed and orbital circularization early because angular momentum transformation between spin and the orbit can shorten the orbital distance and increase the tidal torques. Nitrogen enrichment in binaries is weaker than the one in single stars due to tidal braking. The results reveal that the system with massive components, higher metallicities, larger overshooting parameters, and shorter orbital periods can display high nitrogen enrichment. Stellar radius is small in the star with lower mass, lower metallicities, slower spin speeds and larger overshooting parameters whereas the star with lower metallicities have higher surface effective temperature. Rapid rotating stars evolve towards low temperature and luminosity in the HR diagram.

Trajectory tracking passivity-based control for marine vehicles subject to disturbances

In this paper we present a dynamic model of marine vehicles in both body-fixed and inertial momentum coordinates using port-Hamiltonian framework. The dynamics in body-fixed coordinates have a particular structure of the mass matrix that allows the application of passivity-based control design developed for robust energy shaping stabilisation of mechanical systems described in terms of generalised coordinates. As an example of application, we follow this methodology to design a passivity-based controller with integral action for fully actuated vehicles in six degrees of freedom that tracks time-varying references and rejects disturbances. We illustrate the performance of this controller in a simulation example of an open-frame unmanned underwater vehicle subject to both constant and time-varying disturbances. We also describe a momentum transformation that allows an alternative model representation of marine craft dynamics that resembles general port-Hamiltonian mechanical systems with a coordinate dependent mass matrix.

An integrated model coupling open-channel flow, turbidity current and flow exchanges between main river and tributaries in Xiaolangdi Reservoir, China

The ever growing importance of sustainable management of reservoir sedimentation has promoted the development and applications of turbidity current models. However, there are few effective and practical models in literature for turbidity currents in a reservoir where the impounded area involves both the main river and its many tributaries. An integrated numerical model coupling open-channel flow, turbidity current and flow exchanges between main river and tributaries is proposed, which can simulate the complex flow and sediment transport in a reservoir where these three physical processes coexist. The model consists of two sets of governing equations for the open-channel flow and turbidity current, which are based on the modified St. Venant equations by taking into account the effect of lateral flow exchanges. These two sets of equations are solved in the finite volume method framework and the solutions are executed in an alternating calculation mode. Different methods are respectively proposed to calculate the discharge of flow exchange caused by free surface gradient and turbidity current intrusion. For the surface-gradient driven flow exchange, a storage cell method, which re-defines the relationship between water level and representative cross-sectional area, is used to update the water level at confluence. For the turbidity current intrusion, a discharge formula is proposed based on the analysis of the energy and momentum transformation in the intruding turbid water body. This formula differs from previous ones in that the effect of tributary bed slope is considered. Two events of water-sediment regulation conducted in the Xiaolangdi Reservoir in 2004 and 2006 were simulated to test the ability of this model. The predicted reservoir drawdown process, the turbidity current evolution and the sediment venting efficiency were in close agreement with the measurements. The necessity to couple the flow exchanges was demonstrated by comparing the performance of the proposed model with different intrusion discharge formulas and the common one-dimensional model neglecting the main river and tributary interaction.

Dynamic consequences of optical spin–orbit interaction

When circularly polarized wave scatters off a sphere, the scattered field forms a vortex with spiraling energy flow. This is due to the transformation of spin angular momentum into orbital one. Here we demonstrate that during this scattering an anomalous force can be induced that acts in a direction perpendicular to the propagation of incident wave. The appearance of this lateral force is made possible by the presence of an interface in the vicinity of scattering object. Besides radiation pressure and tractor-beam pulling forces, this lateral force is another type of non-conservative force that can be produced with unstructured light beams.

From Fock’s transformation to de Sitter space

As with Deformed Special Relativity, we showed recently that the Fock coordinate transformation can be derived from a new deformed Poisson brackets. This approach allowed us to establish the corresponding momentum transformation that keeps invariant the four-dimensional contraction pμxμ. From the resulting deformed algebra, we construct the corresponding first Casimir. After first quantization, we show by using the Klein–Gordon equation that the space-time of the Fock transformation is the de Sitter one. As we will see, the invariant length representing the universe radius in the space-time of Fock’s transformation is exactly the radius of the embedded hypersurface representing the de Sitter space-time.

Wind waves as an element of a hydrodynamic coupled ocean-atmosphere model

A new approach to the coupled simulation of the ocean, atmosphere, and sea waves based on a detailed simulation of ocean-surface processes is described. The role of surface waves and the chain of energy and momentum transformation are briefly described: energy and momentum are transferred by wind to waves, turbulence, and surface currents through the field of surface pressure and tangential stress. Both energy and momentum accumulated in waves are transferred (with a lag) also to currents and turbulence within the ocean surface layer. The possibility of coupling atmosphere, ocean, and sea-wave models is considered.

Nonuniversal relativistic kinematics

We present a systematic derivation of the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) momentum composition law, dispersion relation, and momentum transformation laws, at first order in a power expansion of an ultraviolet energy scale. This work generalizes previous results to the case of particle-dependent relativistic kinematics, which can have interesting phenomenological applications that we explore in the second part of the manuscript.

Ultra-thin optical vortex phase plate based on the metasurface and the angular momentum transformation

The ultra-thin optical vortex phase plate (VPP) has been designed and investigated based on the metasurface of the metal rectangular split-ring resonators (MRSRRs) array. The circularly polarized incident light can convert into corresponding cross-polarization transmission light, and the phase and the amplitude of cross-polarization transmission light can be simultaneously governed by modulating two arms of the MRSRR. The MRSRR has been arranged in a special order for forming an ultra-thin optical VPP that can covert a plane wave into a vortex beam with a variety of the topological charges, and the transformation between spin angular momentum (SAM) and orbital angular momentum (OAM) has been discussed in detail. The multi-spectral characteristics of the VPP have also been investigated, and the operating bandwidth of the designed VPP is 190 nm (in the range of 710–900 nm), which enable a potential implication for integrated optics and vortex optics.

Passivity-based Trajectory-tracking for Marine Craft with Disturbance Rejection

This paper presents a Hamiltonian model of marine vehicle dynamics in six degrees of freedom in both body-fixed and inertial momentum coordinates. The model in body-fixed coordinates presents a particular structure of the mass matrix that allows the adaptation and application of passivity-based control interconnection and damping assignment design methodologies developed for robust stabilisation of mechanical systems in terms of generalised coordinates. As an example of application, we follow this methodology to design a passivity-based tracking controller with integral action for fully actuated vehicles in six degrees of freedom. We also describe a momentum transformation that allows an alternative model representation that resembles general port-Hamiltonian mechanical systems with a coordinate dependent mass matrix. This can be seen as an enabling step towards the adaptation of the theory of control of port-Hamiltonian systems developed in robotic manipulators and multi-body mechanical systems to the case of marine craft dynamics.

Time-dependent coupled harmonic oscillators: Classical and quantum solutions

In this work we present the classical and quantum solutions for an arbitrary system of time-dependent coupled harmonic oscillators, where the masses (m), frequencies (ω) and coupling parameter (k) are functions of time. To obtain the classical solutions, we use a coordinate and momentum transformations along with a canonical transformation to write the original Hamiltonian as the sum of two Hamiltonians of uncoupled harmonic oscillators with modified time-dependent frequencies and unitary masses. To obtain the exact quantum solutions we use a unitary transformation and the Lewis and Riesenfeld (LR) invariant method. The exact wave functions are obtained by solving the respective Milne–Pinney (MP) equation for each system. We obtain the solutions for the system with m1 = m2 = m0eγt, ω1 = ω01e-γt/2, ω2 = ω02e-γt/2 and k = k0.