Frozen Waves Research Articles

Optical trapping with higher-order frozen waves

In this work, we optically trap micro-particles with higher-order frozen waves using holographic optical tweezers. Frozen waves are diffraction-resistant optical beams obtained by superposing co-propagating Bessel beams with the same frequency and order, obtaining efficient modeling of its shape. Based on this, we developed a holographic optical tweezers system for the generation of frozen waves, and with this, it was possible to create traps in a stable way for the trapping and guiding of micro-particles in the transverse plane. The experimental results show that it is possible to obtain an excellent stability condition for optical trapping using higher-order frozen waves. These results indicate that frozen waves are promising for optical trapping and guiding of particles, which may be useful in various applications such as biological research, atomic physics, and optical manipulations using structured light with orbital angular momentum.

Transmission characteristics of vortex frozen waves in different obstacle channels.

The obstacle in a channel is a typical scenario for free-space optical (FSO) communications, however, it will destroy the information in channels, especially for the orbital angular momentum (OAM) multiplexing systems and cause performance degradation. Motivated by the feature of predefining intensity profile, here we propose to use frozen wave (FW) carrying OAM for the FSO communications to mitigate the influence of obstacles on the beam propagation. The key idea is to design the longitudinal intensity profile of FW to distribute the beam energy of the location where the obstacle exists over a large region and focus again on the central region after the obstacle for propagation. By analyzing the cases under different sizes, positions, and shapes of the obstacles with on-axis and off-axis scenarios, it has been demonstrated that the detection probability of OAM mode carried by FW can be improved by 0.35 and 0.15 in short-distance and long-distance transmission scenarios, respectively, when compared to that carried by Bessel-Gaussian beam. It demonstrates the FWs have great potential in the OAM-based FSO communications, especially for the obstacle channels.

Rotating structured light based on perfect vortex

In this letter, we experimentally demonstrated a simplified rotating structured light consisting of two overlapping perfect vortices that are generated by focusing two coaxial Bessel beams with different longitudinal wavenumbers. Named perfect rotating wave (PRW), this beam inherits the characteristic of perfect vortex whose radius is controllable and frozen wave whose transverse intensity profile rotates along transmission direction. The no-sidelobes intensity distribution of PRW facilitates the orientation measurement. Because of the linear responds to the Bessel beams’ propagation distance, the orientation of PRW could be applied in remote sensing to measure optical path, temperature, refractive index and so on.

Probability of orbital angular momentum modes carried by a finite energy frozen wave in turbulent seawater

By developing the spatial coherence radius of a collimated Gaussian beam, we derive the normalized received probability of orbital angular momentum (OAM) modes of the random finite energy frozen wave (FW) in anisotropic weak seawater turbulence based on Rytov theory. We investigate the influences of seawater turbulence and beam parameters on the normalized received probability of OAM modes. This study concludes that the normalized received probability of signal OAM modes increases as the anisotropic factor of the seawater turbulence increases. The rate of dissipation of kinetic energy per unit mass of fluid and the inner scale of turbulence but the normalized received probability of signal OAM modes decreases as the increase of temperature-salinity contribution ratio and the dissipation rate of the mean-squared temperature. For the smaller received diameter of the receiver, larger transverse size and longer signal wavelength, the signal OAM modes achieve the higher normalized received probability. The normalized received probability of signal OAM modes is independent of the quantum number of OAM modes in weak seawater turbulence. The security of signal transmission can be enhanced by designing the position and interval of signals that can be detected along the optical path.

Experimental optical trapping with frozen waves

We report, to the best of our knowledge, the first optical trapping experimental demonstration of microparticles with frozen waves. Frozen waves are an efficient method to model longitudinally the intensity of nondiffracting beams obtained by superposing copropagating Bessel beams with the same frequency and order. Based on this, we investigate the optical force distribution acting on microparticles of two types of frozen waves. The experimental setup of holographic optical tweezers using a spatial light modulator has been assembled and optimized. The results show that it is possible to obtain greater stability for optical trapping using frozen waves. The significant enhancement in trapping geometry from this approach shows promising applications for optical tweezers micromanipulations over a broad range.

Transmittance of finite-energy frozen beams in oceanic turbulence

Frozen waves have the good characteristic for resisting the diffraction and absorption in absorbing medium, which can solve the low transmittance of light waves in seawater. By the turbulence spectrum of seawater and the theory of frozen waves, we develop a frozen wave theory for random field and establish a transmittance model for finite energy frozen beams and analyze the diffracting- and absorption-resistance of finite energy frozen waves from the beam transmission wavelength, beam waist, beam orbital angular momentum quantum number, inner scale of turbulence, outer scale of turbulence, the “temperature structure” constant and the ratio of temperature and salinity. The transmittance of for finite energy frozen waves decreases as the propagation distance increases, and by designing longitudinal profile we can compensate the attenuation loss of the transmittance. We derive that the frozen wave has an optimal wavelength window in “seawater transmission window”. Our results theoretically provide a feasible basis for the establishment of underwater multipoint base station optical communication network.

Frozen waves in turbulent mixing layers

The horizontal vibrations of an interface between miscible fluids trigger a parametric instability, leading to frozen wave patterns. Theory and numerical simulations reveal that the mixing layer size varies as the square of the forcing amplitude in the turbulent regime.

Vibrational convection in a heterogeneous binary mixture. Part 2. Frozen waves

The action of high-frequency vibrations on a heterogeneous binary mixture that fills in a closed container is numerically modelled to validate the theoretical model obtained in the first part of the work, and to investigate the role of interfacial stresses in the evolution of miscible boundaries. Only weightlessness conditions are considered. A recent experimental study reports the threshold ignition of the frozen waves at a miscible interface even under weightlessness conditions, which cannot be explained on the basis of the classical approach that represents a binary mixture as a single-phase fluid with an impurity. This effect, however, can be well explained on the basis of the phase-field equations that were derived in the first part of our work. In particular, we found that when the vibrational forcing is sufficiently strong (the vibrational forcing is primarily determined by the amplitude of the vibrational velocity), above a certain threshold value, then the interface becomes shaped into a ‘frozen’ (time independent to the naked eye) structure of several pillars (the frozen waves) with axes perpendicular to the directions of the vibrations. The threshold level of the vibrations is determined by the interfacial stresses that need to be associated with miscible interfaces. The time needed for setting up the frozen pattern is relatively small, determined by hydrodynamic processes, however this time grows exponentially near the threshold. The frozen pattern remains stable either indefinitely long (if liquids are partially miscible) or until the interface becomes invisible due to diffusive smearing (if liquids are miscible in all proportions). A further increase of the vibrational forcing alters the number of the pillars, which happens discretely when the intensity of the vibrations surpasses a sequence of further critical levels. Correlation of the results with the previous experimental and theoretical studies validates the new approach making it a useful tool for tracing thermo- and hydrodynamic changes in heterogeneous mixtures.

Discrete vector frozen waves in generalized Lorenz-Mie theory: linear, azimuthal, and radial polarizations.

This work aims to provide additional theoretical investigation of a promising class of nondiffracting vector beams-the discrete vector frozen waves (FWs)-in the generalized Lorenz-Mie theory. The exact beam shape coefficients for unsymmetrized FWs with linear, azimuth, and radial polarizations are given in analytic form, thus extending previous derivations based on circularly symmetric Davis or aplanatic Bessel beams. Owing to their unique properties, it is believed that FWs will become important wave fields in optical tweezers, optical system alignment, remote sensing, optical bistouries, atom guiding, and so on. The present analysis is therefore fully justified.

Arbitrary Control of Polarization and Intensity Profiles of Diffraction-Attenuation-Resistant Beams along the Propagation Direction

We report on the theory and experimental generation of a class of diffraction-attenuation-resistant beams with state of polarization (SoP) and intensity that can be controlled on demand along the propagation direction. This is achieved by a suitable superposition of Bessel beams, whose parameters are systematically chosen based on closed-form analytic expressions provided by the Frozen Waves (FWs) method. Using an amplitude-only spatial light modulator, we experimentally demonstrate three scenarios. In the first, the SoP of a horizontally polarized beam evolves to radial polarization and is then changed to vertical polarization, with the beam intensity held constant. In the second, we simultaneously control the SoP and the longitudinal intensity profile, which was chosen such that the beam's central ring can be switched-off over predefined space regions, thus generating multiple foci with different SoP and at different intensity levels along the propagation. Finally, the ability to control the SoP while overcoming attenuation inside lossy fluids is shown experimentally for the first time in the literature (to the best of our knowledge). Therefore, we envision our proposed method to be of great interest for many applications, such as optical tweezers, atom guiding, material processing, microscopy, and optical communications.

The interaction of thermocapillary and vibrational instabilities in a two-layer system subjected to the tangential vibrations

The paper deals with the investigation of interaction of thermocapillary, parametric and frozen wave instability mechanisms in a two-layer system of immiscible incompressible viscous fluids of different densities (more dense fluid is located below). External boundaries are rigid. They are maintained at constant different temperatures. The system is subjected to the gravity force and horizontal vibrations of finite frequency and amplitude. The study is performed taking into account the interface deformations. The thermal expansion of fluids is neglected. It is found that vibrations make strong destabilizing effect on the longwave instability mode related to the interface deformations and stabilizing effect on Pearson instability mode.

Frozen Waves following arbitrary spiral and snake-like trajectories in air

We present, in theory and experiment, a class of non-diffracting and self-healing optical beams whose central spot can be designed to follow off-axis curved trajectories. The intensity of the generated waveform can traverse a spiral path with the possibility of reversing its handedness and changing its longitudinal intensity pattern with propagation, on demand. The central spot can also be designed to evolve from a straight to a curved snake-like trajectory and vice versa. Such flexible level of control can be useful for many applications in atomic guiding, optical trapping, and material processing.

Electromagnetic frozen waves with radial, azimuthal, linear, circular, and elliptical polarizations

Frozen waves (FWs) are a class of diffraction- and attenuation-resistant beams whose intensity pattern along the direction of propagation can be chosen arbitrarily, thus making them relevant for engineering the spatial configuration of optical fields. To date, analyses of such beams have been done essentially for the scalar case, with the vectorial nature of the electromagnetic fields often neglected. Although it is expected that the field components keep the fundamental properties of the scalar FWs, a deeper understanding of their electromagnetic counterparts is mandatory in order to exploit their different possible polarization states. The purpose of this paper is to study the properties of electromagnetic FWs with radial, azimuthal, linear, circular, and elliptical polarizations under paraxial and nonparaxial regimes in nonabsorbing media. An intensity pattern is chosen for a scalar FW, and the vectorial solutions are built after it via the use of Maxwell's equations. The results show that the field components and the longitudinal component of the time-averaged Poynting vector closely follow the pattern chosen even under highly nonparaxial conditions, showing the robustness of the FW structure to parameters variations.

Controlling the topological charge of twisted light beams with propagation

Light beams with azimuthal phase dependence [$exp(i \ell\phi)$] carry orbital angular momentum (OAM) which differs fundamentally from spin angular momentum (SAM) associated with polarization. Striking difference between the two momenta is manifested in the allowable values: where SAM is limited to $\hbar k_0$ per photon, the OAM has unbounded value of $\ell\hbar$ per photon ($\ell$ is integer), thus dramatically exceeding the value of SAM \cite{Ref1,Ref2, Ref3}. OAM has thus been utilized in optical trapping \cite{Ref4}, imaging\cite{Ref2}, and material processing \cite{Ref5}. Furthermore, the unbounded degrees-of-freedom in OAM states have been deployed in data communications \cite{Ref6}. Here, we report an \textit{exceptional} behavior for a class of light beams---known as Frozen Waves (FWs)---whose intensity and azimuthal phase profiles can be controlled along the propagation direction, at will. Accordingly, we generate rotating light patterns that can change their sense of rotation and order of phase twist with propagation. Manipulating OAM along the beam axis can open new directions in optical science and its applications.

Production of dynamic frozen waves: controlling shape, location (and speed) of diffraction-resistant beams.

In recent times, we experimentally realized quite an efficient modeling of the shape of diffraction-resistant optical beams, thus generating for the first time the so-called frozen waves (FW), whose longitudinal intensity pattern can be arbitrarily chosen within a prefixed space interval of the propagation axis. In this Letter, we extend our theory of FWs, which led to beams endowed with a static envelope, through a dynamic modeling of the FWs whose shape is now allowed to evolve in time in a predetermined way. Further, we experimentally create such dynamic FWs (DFWs) in optics via a computational holographic technique and a spatial light modulator. Experimental results are presented here for two cases of DFWs, one of zeroth order and the other of higher order, the latter being the most interesting exhibiting a cylindrical surface of light whose geometry changes in space and time.

Time-average forces over Rayleigh particles by superposition of equal-frequency arbitrary-order Bessel beams

We investigate optical forces exerted by suitable superpositions of equal-frequency Bessel beams—frozen waves—over dielectric, magnetodielectric, and negative-index Rayleigh particles. Frozen waves are capable of providing virtually any desired longitudinal intensity pattern by adequately superposing arbitrary-order Bessel beams, serving as potential beams in optical trapping, atom guiding, optical bistouries, and so on. Analytical expressions for gradient and scattering forces experienced by very small particles are deduced, and our numerical examples reveal that both low- and high-index dielectric and magnetodielectric particles can be efficiently trapped and manipulated. Our results indicate that such wave fields could actually provide three-dimensional traps in multiple transverse planes.

Analytical approach of ordinary frozen waves for optical trapping and micromanipulation.

The optical properties of frozen waves (FWs) are theoretically and numerically investigated using the generalized Lorenz-Mie theory (GLMT) together with integral localized approximation. These waves are constructed from a suitable superposition of equal-frequency ordinary Bessel beams and are capable of providing almost any desired longitudinal intensity profile along their optical axis, thus being of potential interest in applications in which intensity localization may be used advantageously, such as in optical trapping and micromanipulation systems. In addition, because FWs are composed of nondiffracting beams, they are also capable of overcoming the diffraction effects for longer distances when compared to conventional (ordinary) beams, e.g., Gaussian beams. Expressions for the beam-shape coefficients of FWs are provided, and the GLMT is used to reconstruct their intensity profiles and to predict their optical properties for possible biomedical optics purposes.

Producing acoustic ‘Frozen Waves’: Simulated experiments with diffraction/attenuation resistant beams in lossy media

The so-called Localized Waves (LW), and the “Frozen Waves” (FW), have raised significant attention in the areas of Optics and Ultrasound, because of their surprising energy localization properties. The LWs resist the effects of diffraction for large distances, and possess an interesting self-reconstruction —self-healing— property (after obstacles with size smaller than the antenna’s); while the FWs, a sub-class of LWs, offer the possibility of arbitrarily modeling the longitudinal field intensity pattern inside a prefixed interval, for instance 0⩽z⩽L, of the wave propagation axis. More specifically, the FWs are localized fields “at rest”, that is, with a static envelope (within which only the carrier wave propagates), and can be endowed moreover with a high transverse localization.In this paper we investigate, by simulated experiments, various cases of generation of ultrasonic FW fields, with the frequency of f0=1MHz in a water-like medium, taking account of the effects of attenuation. We present results of FWs for distances up to L=80mm, in attenuating media with absorption coefficient α in the range 70⩽α⩽170dB/m.Such simulated FW fields are constructed by using a procedure developed by us, via appropriate finite superpositions of monochromatic ultrasonic Bessel beams.We pay due attention to the selection of the FW parameters, constrained by the rather tight restrictions imposed by experimental Acoustics, as well as to some practical implications of the transducer design.The energy localization properties of the Frozen Waves can find application even in many medical apparatus, such as bistouries or acoustic tweezers, as well as for treatment of diseased tissues (in particular, for the destruction of tumor cells, without affecting the surrounding tissues; also for kidney stone shuttering, etc.).

Producing acoustic frozen waves: simulated experiments

In this paper, we show how appropriate superpositions of Bessel beams can be successfully used to obtain arbitrary longitudinal intensity patterns of nondiffracting ultrasonic wave fields with very high transverse localization. More precisely, the method here described allows generation of longitudinal acoustic pressure fields whose longitudinal intensity patterns can assume, in principle, any desired shape within a freely chosen interval 0 ≤ z ≤ L of the propagation axis, and that can be endowed in particular with a static envelope (within which only the carrier wave propagates). Indeed, it is here demonstrated by computer evaluations that these very special beams of nonattenuated ultrasonic field can be generated in water-like media by means of annular transducers. Such fields at rest have been called by us acoustic frozen waves (FWs). The paper presents various cases of FWs in water, and investigates their aperture characteristics, such as minimum required size and ring dimensioning, as well as the influence they have on the proper generation of the desired FW patterns. The FWs are particular localized solutions to the wave equation that can be used in many applications, such as new kinds of devices, e.g., acoustic tweezers or scalpels, and especially in various ultrasound medical apparatus.

Frozen waves: experimental generation

Frozen waves (FWs) are very interesting particular cases of nondiffracting beams whose envelopes are static and whose longitudinal intensity patterns can be chosen a priori. We present here for the first time (that we know of) the experimental generation of FWs. The experimental realization of these FWs was obtained using a holographic setup for the optical reconstruction of computer generated holograms (CGH), based on a 4-f Fourier filtering system and a nematic liquid crystal spatial light modulator (LC-SLM), where FW CGHs were first computationally implemented, and later electronically implemented, on the LC-SLM for optical reconstruction. The experimental results are in agreement with the corresponding theoretical analytical solutions and hold excellent prospects for implementation in scientific and technological applications.