Counterpropagating Plane Waves Research Articles

Controlling the counterintuitive optical repulsive thrust of nano dimers with counter propagating type waves and background medium.

This work focuses on the utilization of counter-propagating plane waves for optical manipulation, which provides a unique approach to control the behavior of Rayleigh and Dipolar nanoparticles immersed in a homogeneous or heterogeneous medium. Our study presents an interesting finding of a repulsive force between plasmonic-chiral heterodimers where the particles move away from each other in both near and far field regions. Interestingly, this repulsive thrust supports the wave like nature of light for the case of homogeneous background but particle type nature of light for heterogenous background. At first, we have investigated the theory underlying the optical trapping of the chiral particle and the impact of this phenomenon on the overall repulsive behavior of the heterodimers placed in air (homogeneous) background. After that, our proposed set-up has further been investigated putting in air-water interface (heterogenous background) and by varying light angle only a little bit. Our observation for this interface case is suggesting the transfer of Minkowski momentum of photon to each optically pulled Rayleigh or dipolar particle of the dimer set, which ultimately causes a broad-band giant repulsive thrust of the dimers. However, in absence of the other particle in the cluster, a single half-immersed particle does not experience the pulling force for the broad-band spectrum. The 'common' reason of the observed repulsive thrust of the dimers for both the aforementioned cases has been attributed to "modified" longitudinal Optical Binding Force (OBF). Technically, this work may open a new way to control the repulsion and attraction between the nanoparticles both in near and far field regions by utilizing the background and the counter-propagating waves. We also believe that this work manifests a possible simple set-up, which will support to observe a background dependent wave 'or' particle nature of light experimentally.

Optomechanical effects caused by non-zero field quantities in multiple evanescent waves.

Evanescent waves, with their high energy density, intricate local momentum, and spatial distribution of spins, have been the subject of extensive recent study. These waves offer promising applications in near-field particle manipulation. Consequently, it becomes imperative to gain a deeper understanding of the impacts of scattering and gradient forces on particles in evanescent waves to enhance and refine the manipulation capabilities. In this study, we employ the multipole expansion theory to present analytical expressions for the scattering and gradient forces exerted on an isotropic sphere of any size and composition in multiple evanescent waves. The investigation of these forces reveals several unusual optomechanical phenomena. It is well known that the scattering force does not exist in counter-propagating homogeneous plane waves. Surprisingly, in multiple pairs of counter-propagating evanescent waves, the scattering force can arise due to the nonzero orbital momentum (OM) density and/or the curl part of the imaginary Poynting momentum (IPM) density. More importantly, it is found that the optical scattering force can be switched on and off by simply tuning the polarization. Furthermore, optical forces typically vary with spatial position in an interference field. However, in the interference field generated by evanescent waves, the gradient force becomes a spatial constant in the propagating plane as the particle's radius increases. This is attributed to the decisive role of the non-interference term of the electromagnetic energy density gradient. Our study establishes a comprehensive and rigorous theoretical foundation, propelling the advancement and optimization of optical manipulation techniques harnessed through multiple evanescent waves. Specifically, these insights hold promise in elevating trapping efficiency through precise control and manipulation of optical scattering and gradient forces, stimulating further explorations.

A charged particle must be treated relativistically in classical theory

A charged particle which is allowed to accelerate must have relativistic behavior because it is coupled to electromagnetic radiation which propagates at the speed of light. We treat the simple steady-state situation of a charged particle moving in a circular orbit with counter-propagating plane waves providing the power which balances the energy radiated away by the accelerating charge. It is emphasized that only an electromagnetic arrangement, such as a Coulomb potential or a constant magnetic field, can provide the relativistic central force for the particle motion.

Generation of Huygens' dipoles for any spherical nanoparticle excited by counter-propagating plane waves: study of scattered helicity.

Helicity and directionality control of scattered light by nanoparticles is an important task in different photonic fields. In this paper, we theoretically demonstrate that scattered light of lossy spherical nanoparticles excited by using two counter-propagating dephased plane waves with opposite helicity ±1 and the adequate selection of dephase and intensity shows a well defined helicity and a controllable scattering directivity. Numerical examples of Si nanospheres are studied showing their potential application to directional nanoantennas with a well defined helicity. The proposed method is valid for any type of nanoparticle, not only lossy ones.

Optical forces and directionality in one-dimensional PT -symmetric photonics

We discuss the optical forces exerted on parity-time $(\mathcal{PT})$ symmetric heterostructures under normal incidence of a single and two counterpropagating plane waves. The underlying strategy is through generalized parametric space, stemming from consideration of the $\mathcal{PT}$-symmetry condition and Lorentz reciprocity theorem. In such a generalized parametric space, we are able to not only exhaustively indicate various $\mathcal{PT}$ phases and extraordinary wave phenomena but also deduce the directionality and magnitudes of optical forces. We find that when the system is illuminated by a normally incident wave, it can exhibit the symmetric pushing effect in the exact symmetry phase, unidirectional null, and bidirectional null forces (BNF) at the exceptional point, and pulling-pushing flipped forces in the broken symmetry phase, with BNF found at the pushing-pulling turning point. In two counterpropagating plane wave interferences, the magnitudes as well as the directionality of the resultant optical force can be tuned by a relative phase of incident waves. More interestingly, we observe that a null force independent of the relative phase occurred in a specific region of the broken symmetry phase and exceptional point. In addition, we offer several $\mathcal{PT}$-symmetric heterostructures to support our findings. Our results may benefit applications in $\mathcal{PT}$ optomechanics and force rectifiers.

Inkjet assisted patterning of Bragg grating towards multiple color imaging

Despite the rapid progress in various holographical technologies, development and miniaturization, the fabrication of individual design holographic images is still a complicated, costly, time- and labor-consuming process. This research proposes a novel inkjet printing method for obtaining multiple color holographic images based on applying a physical impact on a volume Bragg grating recorded by the interference of counterpropagating plane waves in a commercially available photopolymer material. Inkjet printing technique allows cost-effective, rapid, and reproducible fabrication of high-resolution (≥ 600 dpi) holographic patterns. A specific printable ink composition consisting of monomers in combination with the photoinitiators penetrates the polymer matrix and leads to the swelling of the material. This causes an increase in the period of the recorded grating and visually observed color change of the resulting hologram. Precise control over the ink dosage allows exact shifting of wavelength (∼30 nm for single layer at drop spacing of 50 μm). The printing parameters can be adjusted towards the optimal conditions for obtaining the final image with high quality.

Self-Trapped Nanoparticle Binding via Waveguide Mode

In this paper, we study a stable optomechanical system based on a nanoparticle chain coupled to a waveguide mode. Under the plane wave excitation the nanoparticles form a stable self-organized periodic chain array along the direction of the waveguide through the transverse binding effect. We show that owing to the long-range interaction between the nanoparticles the trapping potential for each nanoparticle in the chain increases linearly with the system size making the formation of long chains more favourable. We propose that this effect can be observed with an optical nanofiber which is a versatile platform for achieving optical binding of atoms and nanoparticles. Our calculations show that binding energy for two nanoparticles is in the range of $9\div13~kT$ reaching the value of 100 $kT$ when the size of the chain is increased to 20 nanoparticles that makes the potential experimental observation of the effect possible. We also suggest the geometry of the two counter-propagating plane waves excitation, which will allow trapping the nanoparticles close to the optical nanofiber providing efficient interaction between the nanoparticles and the nanofiber.

Efficient retrieval of phase information from real-valued electromagnetic field data

While analytic calculations may give access to complex-valued electromagnetic field data which allow trivial access to envelope and phase information, the majority of numeric codes uses a real-valued representation. This typically increases the performance and reduces the memory footprint, albeit at a price: In the real-valued case it is much more difficult to extract envelope and phase information, even more so if counter propagating waves are spatially superposed. A novel method for the analysis of real-valued electromagnetic field data is presented in this paper. We show that, by combining the real-valued electric and magnetic field at a single point in time, we can directly reconstruct the full information of the electromagnetic fields in the form of complex-valued spectral coefficients (k→-space) at a low computational cost of only three Fourier transforms. The method allows for counter propagating plane waves to be accurately distinguished as well as their complex spectral coefficients, i.e. spectral amplitudes and spectral phase to be calculated. From these amplitudes, the complex-valued electromagnetic fields and also the complex-valued vector potential can be calculated from which information about spatiotemporal phase and amplitude is readily available. Additionally, the complex fields allow for efficient vacuum propagation allowing to calculate far field data or boundary input data from near field data. An implementation of the new method is available as part of PostPic1, a data analysis toolkit written in the Python programming language.

Tunable nonlinear coherent perfect absorption with epsilon-near-zero plasmonic waveguides.

We propose a scheme to realize nonlinear coherent perfect absorption (CPA) at the nanoscale using epsilon-near-zero (ENZ) plasmonic waveguides. The general conditions to achieve CPA in a linear ENZ plasmonic waveguide are analyzed and presented. The proposed ENZ waveguides support an effective ENZ response at their cutoff frequency, where the CPA effect occurs under the illumination of two counterpropagating plane waves with equal amplitudes and appropriate phase distributions. In addition, the strong and uniform field enhancement inside the nanochannels of the waveguides at the ENZ resonance can efficiently boost Kerr nonlinearities, resulting in a new all-optical switching intensity-dependent CPA phenomenon that can be tunable with ultrafast speed. The proposed free-standing ENZ structures combine third-order nonlinear functionality with standing wave CPA interference effects in a nanoscale plasmonic configuration, thus leading to a novel degree of tunable light-matter interactions achieved in subwavelength regions. Our findings provide a new platform to efficiently excite nonlinear phenomena at the nanoscale and design tunable coherent perfect absorbers.

Ponderomotive beatwave ion acceleration using twisted light

An all-optical mechanism of ion acceleration in vacuum with two counter-propagating plane waves has been proposed by F. Peano et al., IEEE Trans Plasma Sci. 36, 1857 (2008). A suitable frequency chirping of lasers drives a beat wave with variable phase velocity that traps particles and accelerates them longitudinally. In this paper, direct ion acceleration by two counter-propagating focused laser beams with variable frequencies is considered, and the multi-dimensional effects associated with the finite transverse dimension of lasers are investigated. It is shown that the Gaussian laser beams provide a defocusing transverse force that stops the acceleration process as ions propagate towards regions of smaller laser fields. On the other hand, the Laguerre-Gaussian laser beams with identical orbital angular momentum can confine the off-axis ions radially as they accelerate to high energies. It is shown that the orbital angular momentum of the Laguerre-Gaussian lasers can be used to control the angular momentum of the accelerated ion beam.

Correlation between light-flux fluctuations of two counter-propagating waves in weak atmospheric turbulence.

Expressions for the correlation coefficient between light-flux fluctuations of two waves counter-propagating along a common path in weak turbulence are developed. Only the aperture and inner-scale Fresnel parameters are needed for evaluation of the correlation coefficient if the turbulence spectrum has no path dependence, and of the path weighting functions for the cross-covariance and variances of normalized light-flux fluctuations if the turbulence spectrum is dependent on path locations. Under the condition that atmospheric turbulence is statistically homogeneous over a path, although good correlation between light-flux fluctuations of two counter-propagating spherical waves may be achieved for a relatively small aperture Fresnel parameter or relatively large inner-scale Fresnel parameter, the correlation coefficient between light-flux fluctuations of two counter-propagating plane waves is always lower than 1 obviously. When the aperture Fresnel parameter becomes larger than the inner-scale Fresnel parameter, the inner scale of turbulence tends to play an unimportant role in determining the correlation coefficient.

Classical and quantum dynamics of a charged scalar particle in a background of two counterpropagating plane waves

We consider a scalar particle in a background formed by two counterpropagating plane waves. Two cases are studied: (i) dynamics at a magnetic node and (ii) zero initial transverse canonical momentum. The Lorentz and Klein-Gordon equations are solved for these cases and approximations analyzed. For the magnetic-node solution (homogeneous, time-dependent electric field), the modified Volkov wave function which arises from a high-energy approximation is found to be inaccurate for all energies and the solution itself unstable when the photon emission (nonlinear Compton scattering) is included. For the zero initial transverse canonical momentum case, in both quantum and classical cases, forbidden parameter regimes, absent in the plane-wave model, are identified.

Ground state and the spin precession of the Dirac electron in counterpropagating plane electromagnetic waves

The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal phase planes and the same frequency. Each standing wave consists of two eigenwaves with different complex amplitudes and opposite directions of propagation. The fundamental solution is obtained in the form of the projection operator defining the subspace of solutions to the Dirac equation. It is illustrated by the analysis of the ground state and the spin precession of the Dirac electron in the field of two counterpropagating plane waves with left and right circular polarizations. Interrelations between the fundamental solution and approximate partial solutions is discussed and a criterion for evaluating accuracy of approximate solutions is suggested.

Relativistic Two-Boson System in Presence of Electromagnetic Plane Wave

The relativistic two-body problem is considered for spinless particles subject to an external macroscopic electromagnetic field. When this field is made of the monochromatic superposition of two counter-propagating plane waves (and provided the mutual interaction between particles is known), it is possible to write down explicitly a pair of coupled wave equations (corresponding to a pair of mass-shell constraints) which takes into account also the field contribution. These equations are manifestly covariant; constants of the motion are exhibited, so one ends up with a reduced problem involving five degrees of freedom.

A parity-time symmetric coherent plasmonic absorber-amplifier

Non-Hermitian parity-time (PT)-symmetric optical potentials have led to a new class of unidirectional photonic components based on the spatially symmetric and balanced inclusion of loss and gain. While most proposed and implemented PT-symmetric optical devices have wavelength-scale dimensions, no physical constraints preclude development of subwavelength PT-symmetric components. We theoretically demonstrate a nanoscale PT-symmetric, all-optical plasmonic modulator capable of phase-controlled amplification and directional absorption. The modulator consists of two deeply subwavelength channels composed of either gain or loss dielectric material, embedded in a metallic cladding. When illuminating on-resonance by two counter-propagating plane waves, the aperture's total output can be modulated by changing the phase offset between the two waves. Modulation depths are greater than 10 dB, with output power varying from less than one half of the incident power to more than six times amplification. Off-resonance, the aperture possesses strong phase-controlled directionality with the output from one side varying from perfect absorption to strong scattering and transmission. The device design provides a platform for nanoscale all-optical modulators with gain while potentially enabling coherent perfect absorption and lasing in a single, compact structure.

Nonreciprocal electromagnetic wave propagation in one-dimensional ternary magnetized plasma photonic crystals

In this paper, we propose a one-dimensional ternary photonic crystal based on magnetized plasma to obtain nonreciprocal propagation. By employing the transfer matrix method, the transmission spectra of the counterpropagating plane waves incident from air upon either end of the periodic structure are calculated. Our results reveal that there is a significant contrast between the transmittance of the waves propagated in opposite directions. This means that the structure shows nonreciprocal effects. It is shown that the bandwidth at which nonreciprocity is observed depends on the external magnetic field. The effects of the incident angle and the number of elementary cells on the nonreciprocal behaviors are studied. We demonstrate that nonreciprocity disappears in very small angles of incidence. The designed structure shows nonreciprocal response even in the case of a small number of layers. It is also demonstrated that nonreciprocal effects become stronger when increasing the plasma density and the wavelength of the incident wave.

Metallic nanoparticles in a standing wave: Optical force and heating

We have investigated the absorbed power in a single gold or silver metallic nanoparticle together with the optical force acting upon it if the particle is illuminated by two counter-propagating plane waves forming a standing wave. We have used the Generalized Lorenz–Mie theory (GLMT) and considered the incident wavelengths 250nm≤λvac≤1250nm and particles size parameter 0.1≤d/λvac≤4. Similarly as in the case of dielectric particle we have found that the optical force is equal to zero for all particle positions in the standing wave for certain wavelengths and particle sizes. However, in the case of a metallic object this phenomenon occurs for considerably smaller particles and the conditions change considerably with the illuminating wavelength especially near the localized surface plasmon resonances. Similarly, we have found that the absorbed heat does not change with the position of the particle in the standing wave for certain wavelengths and particle sizes. These sizes generally differ from those giving zero optical force and, therefore, the particle can be trapped at the intensity maximum or minimum and in both cases its heating is maximal or minimal depending on the particle size.

Spontaneous emission of atoms via collisions of Bose-Einstein condensates

The widely used Gross-Pitaevskii equation treats only coherent aspects of the evolution of a Bose-Einstein condensate. However, inevitably some atoms scatter out of the condensate. We have developed a method, based on the field theory formulation, describing the dynamics of incoherent processes which are due to elastic collisions. We can therefore treat processes of spontaneous emission of atoms into the empty modes, as opposed to stimulated processes, which require non-zero initial occupation. In this article we study two counter-propagating plane waves of atoms, calculating the full dynamics of mode occupation, as well as the statistics of scattered atoms. The more realistic case of Gaussian wavepackets is also analyzed.

Local dynamics of laser cooling in an optical lattice

Using the basis of Wannier states, we study the local dynamics of polarization gradient cooling for an atom driven on a Jg52!Je53 transition by a one-dimensional optical lattice. This analysis allows us to formulate a physical picture of the cooling mechanism, analogous to Sisyphus cooling for a J g51/2!Je53/2 atom, which depends strongly on coherences in the Zeeman sublevels of the ground state. In addition, we are able to explain the steady-state properties of the laser-cooled atoms in a regime where the standard semiclassical analysis breaks down. @S1050-2947~97!50309-X# PACS number~s!: 32.80.Pj, 71.23.An The paradigm for sub-Doppler laser cooling is the Sisyphus effect as formulated by Dalibard and Cohen-Tannoudji @1#. The beauty of this model is that it gives a simple physical picture of the cooling mechanism. An atom driven on a Jg51/2!J e53/2 transition moves in a one-dimensional ~1D! light field formed by two counterpropagating plane waves with orthogonal linear polarizations—the 1D lin ’lin configuration. Cooling occurs as atoms are preferentially optically pumped from the peaks of the light shift potential associated with one ground state to the valleys of the other. Indeed, the simplicity of this model led to the realization of this 1D model in the laboratory, signifying a shift away from the image of atoms moving in a disordered ‘‘optical molasses’’ to that of an ordered ‘‘optical lattice’’ @2#. These experiments showed that in the steady state most of the atoms are trapped in the microscopic potential wells of the lattice, oscillating many periods before inelastic photon scattering occurs, and localized to a small fraction of the optical wavelength ~the ‘‘oscillating regime’’ !@ 3 # . Despite the considerable success of the simple Sisyphus model in explaining the basic steady-state properties of the laser-cooled atoms, there has been little detailed study of the dynamics. Recent experiments have shown some discrepancies with the dynamical model proposed in the simple Sisyphus picture @4#. The goal of this article is to develop a physical picture of the cooling mechanism applicable to the experiments: atoms with larger angular momentum trapped in the oscillating regime. Consider, for example, an atom with a ground-state angular momentum Jg52 and excited state Je53, moving in a 1D lin’lin lattice. In this more complex system there is a set of optical potentials associated with the five ground states, coupled by stimulated Raman transitions. For such an atom, two possible semiclassical pictures of the cooling mechanism arise. In one @Fig. 1~a!#, cooling occurs locally at a given lattice site as atoms preferentially climb steep potentials and descend shallow ones. Because of the difference in curvature between these two potentials, atoms expend more of their kinetic energy climbing wells than they regain on the descent, the difference being dissipated in optical pumping. Alternatively, atoms may cool when hopping between lattice sites by making nonadiabatic transitions between the coupled set of optical potentials and preferentially pumping to the potential with the largest light shift @Fig. 1~b!#. The difference between these mechanisms has implications for the diffusion of atoms within the lattice, as studied in recent experiments @5#, and theories @6#. Though fully quantum-mechanical numerical simulations for large-angular-momentum atoms in optical lattices @7,8# have yielded fantastic agreement with experiments, it is difficult to extract the local cooling mechanism. In these simulations the center-of-mass motion was expanded in a basis of free-particle plane waves or Bloch states of the periodic potential @9#, which were delocalized over the entire lattice. In order to gain physical insight into the local cooling dynamics, we reanalyze the system using the basis of Wannier states for the periodic potential. These represent a complete orthonormal set of functions localized at a particular lattice site @10#. As discussed in @2,7#, after identifying the complete set of symmetries of the Hamiltonian, the energy eigenstates are Bloch spinors,

Collection of fluorescence from single molecules in microspheres: effects of illumination geometry

The collection of fluorescence from a molecule inside a sphere illuminated with single or counterpropagating plane waves is modeled. The results are applicable to microdroplet-based single molecule detection techniques and to some microparticle characterization techniques using inelastic emission. The large position-dependent variations in the fluorescence collection rate are primarily attributable to variations in the excitation intensity. With plane-wave illumination the collection from shadow regions is low because the incident energy is refracted by the droplet surface away from these regions. The average collection rate from molecules in shadow regions can be increased by illuminating with counterpropagating beams.