Dark Notch Research Articles

Tailoring nondiffracting fields with a non-Markovian phase imprint.

We experimentally generate nondiffracting speckles that carry non-Markovian properties by encoding the wavefront of a monochromatic laser beam with ring-shaped non-Markovian phases. The resulting non-Markovian nondiffracting fields present a ring-shaped pattern and central dark notches, which are analyzed with an expression of the orbital angular momentum spectra of the wavefront possessing ring-shaped non-Markovian phases. Furthermore, we demonstrate that the intensity profiles of these non-Markovian nondiffracting fields exhibit stability over multiple Rayleigh ranges, and their statistical properties could be controlled with the non-Markovianity of the input phase masks. This work presents an approach for simultaneously tailoring the diffracting property and non-Markovianity of optical fields and provides a deeper understanding of non-Markovian processes.

Conical diffraction in atomic vapor: Mathematical models and numerical calculations

This study investigated the conical diffraction characteristics in the honeycomb lattice of a Λ-type three-level energy system for rubidium atomic configuration. Its band structure incorporates Dirac cones in accordance with the plane wave expansion method. We determined that the rotation angle θ of the three vectors strongly impacted the cone diffraction profile. For θ=0° and 60°, in the reciprocal lattice space, the Dirac cone states were excited, and symmetric cone diffraction was supported. When 0<θ<60°, an asymmetric cone diffraction with a dark notch appeared on the outer edge of the conical ring. The results indicate that the frequency detuning of the coupling field and high-order nonlinear susceptibilities in the medium are effective and concise approaches to manipulate the occurrence of cone diffraction. The findings of this study enhance the understanding of the cone diffraction phenomena and broaden the practical applicability of atomic configuration.

Controllable Self‐Focusing Circular Vortex Pearcey Gaussian Beam with Low Spatial Coherence

AbstractA new type of controllable self‐focusing circular vortex Pearcey Gaussian beam, which can create an optical potential well with adjustable depth and width at the center of the beam by adjusting the coherent width and the number of topological charges, is introduced. As the coherent width increases, the intensity becomes lower in the dark notch caused by the topological charges, which are consistent with the experimental results. In addition, the self‐focusing location and the strength of the circular vortex Pearcey Gaussian beam can be controlled by the spatial coherence in the simulation.

Partially coherent radially polarized circular Airy beam.

We propose and demonstrate a new, to the best of our knowledge, kind of partially coherent vector beam called the partially coherent radially polarized circular Airy beam (PCRPCAB). The PCRPCAB inherits the autofocusing ability of the radially polarized circular Airy beam (RPCAB) and can create an optical potential well at the center of the beam, whose depth can be adjusted by changing the coherent width. We find that, as coherent width decreases, the intensity becomes higher in the dark notch caused by the polarization singularity, and the singularity of the degree of polarization (DOP) remains along propagation, with its waist controllable by the coherent width. Our results make the PCRPCAB a good candidate for optical micromanipulation, disordered optical lattices, etc.

Conical diffraction modulation in honeycomb lattices

We investigate the generation and destruction of asymmetric conical diffraction in honeycomb lattices by adjusting rotation angle θ of the three vectors and considering nonlinearities. For θ = 0° and 60°, the modes of the Dirac cone of the honeycomb lattice are excited, symmetric conical diffraction are obtained. When 0 < θ < 60°, asymmetric conical diffraction with a dark notch appears and the dark notch moves clockwise or anti-clockwise around the outer edge of the bright ring. In addition, it is also demonstrated that both Kerr and saturation nonlinearities can cause triangular deformation of conical diffraction pattern. Under the same nonlinearity, two identical wave centered around different Dirac points can evolve to identical triangular rings pointing in opposite directions. The dark notch at a point of triangular appears and moves in a clockwise or anti-clockwise way for self-focusing and self-defocusing nonlinearity, respectively.

Steady state multiple dark spatial solitons in the biased photorefractive-photovoltaic crystals

We theoretically study the evolution of dark solitons in the biased photorefractive-photovoltaic crystal by using beam propagation method (BPM). We find that when the absolute value of the extra bias field is less than the photovoltaic field, the dark screening-photovoltaic (SP) solitons can be observed. The initial width of the dark notch at the entrance face of the crystal is a key parameter for generating an sequence of dark coherent solitons. If the initial width of the dark notch is small, only a fundamental soliton or Y-junction soliton pair is generated. When the initial width of the dark notch is increased, the dark notch tends to split into an odd (or even) number of multiple dark solitons, which realizes a progressive transition from the low-order solitons to a sequence of higher-order solitons.

The nonlinear Dirac equation in Bose–Einstein condensates: II. Relativistic soliton stability analysis

The nonlinear Dirac equation for Bose–Einstein condensates (BECs) in honeycomb optical lattices gives rise to relativistic multi-component bright and dark soliton solutions. Using the relativistic linear stability equations, the relativistic generalization of the Boguliubov-de Gennes equations, we compute soliton lifetimes against quantum fluctuations and classify the different excitation types. For a BEC of atoms, we find that our soliton solutions are stable on time scales relevant to experiments. Excitations in the bulk region far from the core of a soliton and bound states in the core are classified as either spin waves or as a Nambu–Goldstone mode. Thus, solitons are topologically distinct pseudospin- domain walls between polarized regions of . Numerical analysis in the presence of a harmonic trap potential reveals a discrete spectrum reflecting the number of bright soliton peaks or dark soliton notches in the condensate background. For each quantized mode the chemical potential versus nonlinearity exhibits two distinct power law regimes corresponding to the free-particle (weakly nonlinear) and soliton (strongly nonlinear) limits.

Diffraction-induced instability of coupled dark solitary waves.

We report on a novel instability arising from the propagation of coupled dark solitary beams governed by coupled defocusing nonlinear Schrödinger equations. Considering dark notches on backgrounds with different wavelengths, hence different diffraction coefficients, we find that the vector dark soliton solution is unstable to radiation modes. Using perturbation theory and numerical integration, we demonstrate that the component undergoing stronger diffraction radiates away, leaving a single dark soliton in the other mode/wavelength.

Dark spatial solitons splitting in logarithmically saturable nonlinear media

We numerically simulate the evolution of the dark-notch-bearing optical beam in the logarithmically saturable nonlinear media based on beam propagation method (BPM). The simulation results indicate that the multiple dark spatial solitons are deep, possible in this type of nonlinear media. The number of multiple dark spatial solitons depends on the width of the dark notch, the initial conditions and the peak intensity of the initial input beam. Under the odd and even initial conditions, the odd and even number sequence of multiple dark spatial solitons can be obtained, respectively. For an input beam with fixed optical intensity, the number of dark solitons increases with the width of the initial input dark notch. The behavior of the multiple dark solitons in this type of media is similar to that in a photorefractive nonlinear crystal.

Steady-state multiple dark spatial solitons in closed-circuit photovoltaic media

We theoretically study the formation of the steady state multiple dark photovoltaic solitons in the closed-circuit photovoltaic photorefractive crystal. The results indicate that the formation of the multiple dark photovoltaic solitons in the closed-circuit photovoltaic crystal is dependent on the initial width of the dark notch at the entrance face of the crystal. The number of the solitons generated increases with the initial width of the dark notch. If the initial width of the dark notch is small, only a fundamental soliton or Y-junction soliton pair is generated. As the initial width of the dark notch is increased, the dark notch tends to split into an odd (or even) number of multiple dark photovoltaic solitons sequence, which realizes a progressive transition from a lower-order soliton to a higher-order solitons sequence. When the multiple solitons are generated, the separations between adjacent dark solitons become slightly smaller. The soliton pairs far away from the center have bigger width and less visibility and they move away from each other as they propagate in the photorefractive nonlinear crystal.

Steady-state multiple dark photovoltaic spatial solitons

We theoretically study the formation of the steady state multiple dark photovoltaic spatial solitons in the photovoltaic photorefractive crystal under open-circuit conditions. The results indicate that the initial dark notch width at the entrance face of the crystal is a key parameter for generating an even (or odd) number sequence of multiple dark photovoltaic solitons. The dark notch is generated from a phase or amplitude discontinuity in the center of the input beam. If the initial width of the dark notch is small, only a fundamental soliton or a Y-junction soliton is generated. As the initial width of the dark notch is increased, the dark notch tends to split into an odd (or even) number of multiple dark photovoltaic solitons, realizing a progressive transition from a lower-order soliton to the higher-order multiple solitons. When the multiple dark photovoltaic solitons are generated, the separations between adjacent dark solitons become smaller. Solitons pairs become progressively wider and less visible as their transverse distance from the central dark soliton increases and they move away from each other as they propagate in the photorefractive nonlinear crystal.

Formation of multiple dark photovoltaic spatial solitons

We theoretically study the formation of multiple dark photovoltaic soliton splitting in the quasi-steady-state and steady-state regimes under open-circuit conditions. We find that the initial width of the dark notch at the entrance face of the crystal is a key parameter for generating an even (or odd) number sequence of dark coherent photovoltaic solitons. If the initial width of the dark notch is small, only a fundamental soliton or Y-junction soliton pair is generated. As the initial width of the dark notch is increased, the dark notch tends to split into an odd (or even) number of multiple dark photovoltaic solitons, which realizes a progressive transition from a low-order soliton to a sequence of higher-order solitons. The soliton pairs far away from the centre have bigger width and less visibility. In addition, when the distance from the centre of the dark notch increases, the separations between adjacent dark stripes become slightly smaller.

Surface dark screening solitons

We report on the existence of surface dark screening solitons at the interface between a dielectric medium (air) and a self-defocusing nonlinear material, taking advantage of photorefractive diffusion and drift nonlinearities. It is very interesting that a surface dark soliton is just like half of a dark soliton in bulk, but not a whole dark soliton propagating along surface. The excitation, propagation, and stability of this type of soliton are studied by using the beam-propagation method. Another interesting thing is that this type of dark soliton can be excited by a planar light beam without a necessary dark notch.

Momentum-space interferometry with trapped ultracold atoms

Quantum interferometers are generally set so that phase differences between paths in coordinate space combine constructively or destructively. Indeed, the interfering paths can also meet in momentum space leading to momentum-space fringes. We propose and analyze a method to produce interference in momentum space by phase imprinting part of a trapped atomic cloud with a detuned laser. For one-particle wave functions analytical expressions are found for the fringe width and shift versus the phase imprinted. The effects of unsharpness or displacement of the phase jump are also studied, as well as many-body effects, to determine the potential applicability of momentum-space interferometry. For a broad range of parameters and conditions it is found that a ``dark notch'' in the momentum distribution depends linearly on the phase imprinted, with maximal sensitivity for noninteracting atoms in the ground state of tight traps.

Single-particle density matrix and the momentum distribution of dark “solitons” in a Tonks-Girardeau gas

We study the reduced single-particle density matrix (RSPDM), the momentum distribution, and natural orbitals and their occupancies of dark ``soliton'' (DS) states in a Tonks-Girardeau gas. DS states are specially tailored excited many-body eigenstates, which have a dark solitonic notch in their single-particle density. The momentum distribution of DS states has a characteristic shape with two sharp spikes. We find that the two spikes arise due to the high degree of correlation observed within the RSPDM between the mirror points ($x$ and $\ensuremath{-}x$) with respect to the dark notch at $x=0$; the correlations oscillate rather than decay as the points $x$ and $\ensuremath{-}x$ are being separated.

Spatiotemporal coherence of white light beam trapped within dark spatial soliton

We study experimentally and theoretically temporal and spatial coherence of white light beam through its interaction with a coherent dark spatial soliton in LiNbO3:Fe noninstantaneous nonlinear self-defocusing crystal. Experimental observations show that during this process a portion of the white light beam is trapped within the dark notch of the dark spatial soliton, thus forming a sharp intensity spike. Moreover, numerical simulations show that in this region the coherence length of white light beam increases from ∼11 to 1200μm after 6mm of propagation for almost all frequencies. We find that the intensity spike of each frequency of white light increases with the increase of frequency. While the spatial coherence length of each frequency of white light decreases with the increase of frequency.

Dark spatial solitons in bulk azo-dye-doped polymer using photoinduced molecular reorientation

We report the generation of dark spatial solitons in bulk Disperse Red 1 doped poly(methyl methacrylate) using photoinduced reorientation of azo-dye molecules. Planar solitions are formed when illuminated with a continuous-wave laser at intensities of the order of hundreds of miliwatts per square centimeter. The width of the soliton saturates to a minimum value at high intensity; and when the width of the initial dark notch is reduced, the equilibrium minimum width is unchanged.

Observation of dark spatial photovoltaic solitons in planar waveguides in lithium niobate

We have obtained photovoltaic lenses and dark spatial solitons in planar optical waveguides in lithium niobate doped with iron and copper. For TE modes of lower indices the photovoltaic nonlinearity only partly decreased the width of a dark notch within the outcoupled image of the recording light beam. The corresponding time to reach a steady state of this light-induced change ranged from about 0.1 to 30 s depending on the waveguide sample. For higher modes we observed a full compensation of the divergence of the dark notch on a time scale of some minutes. In some cases this was followed by an extinction of the dark solitons because the light was over-defocused in the highest modes.

Coherence enhancement of spatially incoherent light beams through soliton interactions

We show that the spatial coherence of a partially incoherent light beam can be greatly enhanced through an energy-conserving interaction with an incoherent or a coherent dark spatial soliton. Computer simulations show that during this process a portion of the incoherent beam is trapped within the dark notch of the dark soliton, thus forming a sharp intensity spike. In this region the correlation length dramatically increases by at least 2 orders of magnitude.

(1+1)-Dimensional and (2+1)-dimensional waveguides induced by self-focused dark notches and crosses in LiNbO_3:Fe crystal

We demonstrate that (1+1)-dimensional and (2+1)-dimensional waveguides can be induced by self-focused dark notches and crosses and stored in LiNbO(3):Fe crystals. This is very valuable for information processing and integrated optics. The self-focused dark notches and crosses may be related to the formation of (1+1)-dimensional and (2+1)-dimensional photovoltaic dark spatial solitons in LiNbO(3):Fe crystals.