Optical Knots Research Articles

Effects of aberrations on 3D optical topologies

Optical knots and links are nontrivial three-dimensional topologies consisting of trajectories of phase or polarisation singularities. They are theoretically predicted and experimentally observed in paraxial and nonparaxial regimes and in random and speckle fields. The topological nature of optical knots suggests that environmental disturbances should not alter their topology, hence becoming a resilient vector of information. However, the robustness of optical knots under typical disturbances encountered in optical experiments has not been investigated. Here, we provide the experimental analysis of the effects of optical phase aberrations on optical knots and links. We demonstrate that Hopf links, trefoil and cinquefoil knots are robust to misalignment and phase aberrations. The observed knots are obliterated for high aberration strengths and defining apertures close to the characteristic optical beam size. Our observations indicate these photonic topological structures as viable alternatives for both classical and quantum information processing noisy channels, where optical modes are not applicable.

HST-1 as a window into the energetics of the jet spine of M 87

We present a new interpretation of the optical knot, HST-1, in the jet of M 87. High-sensitivity 22 GHz Very Large Array images have located HST-1 to within 6 mas of the jet axis immediately upstream. Based on 1.7 GHz Very Long Baseline Array images of a bright flare in 2005, we see that preponderance of emission in the early stages originates from an elongated region that is tilted 12.5° from the jet axis. The superluminal motion, shape, location, and the large jet-aligned optical/UV polarization suggest an identification with the putative relativistic spine of the jet. As such, energy flux estimates for HST-1, ∼870 mas from the nucleus, published in 2006, indicate that the central engine injected, Qspine ≈ 2.5 × 1041 ergs s−1, into the base of the spine about 200 yr earlier. Furthermore, previous studies have revealed a tubular protonic jet on sub-mas scales that envelopes a low luminosity core, presumably the faint spine base. It was estimated that the central engine injected, Qtubular jet ≈ 6.1 × 1041 ergs s−1, about 1.5 yr earlier. If one component of the jet is inherently more powerful, a firm constraint on total jet power in the recent past would then exist. If the emitted jet is inherently dominated by the spine (tubular jet), then the total bilaterally symmetric jet power emitted from the central engine was < 4Qspine ≈ 1.0 × 1042 ergs s−1 (< 4Qtubular jet ≈ 2.4 × 1042 ergs s−1) ∼200 (∼1.5) yr earlier. Assuming a nearly constant central engine injected jet power for ∼200 yr indicates a total jet power of ≲2 × 1042 ergs s−1 in epochs of modern observation or ≲3.5% jet production efficiency for an accretion rate of 0.001 M⊙ yr−1. Seemingly, the focus of Event Horizon Telescope Collaboration (EHTC) numerical models should be biased toward jet powers of ≲2 × 1042 ergs s−1, as opposed to larger estimates from ejections many centuries or millennia earlier.

Topological Holography and Storage with Optical Knots and Links

AbstractAfter more than 70 years of development, holography has become an essential tool of modern optics in many applications. In fact, for various applications of different kinds of holographic techniques, stability and antijamming ability are very important. Here, optical topological structures are introduced into holographic technology, and an entirely new concept of optical topological holography is demonstrated to solve stability and antijamming problems. Based on the optical knots and links, the topological holography is not only developed in theory, but also demonstrated experimentally. In addition, a new topological holographic coding is established by regarding each knotted/linked topological structure as an information carrier. Due to the variety of knotted and linked structures and their characteristics of topological protection, such coding can have high capacity as well as robust properties. Furthermore, with writing the hologram into the liquid crystal, robust information storage of 3D topological holography is realized.

Optimization of Light Field for Generation of Vortex Knot

The theory of knots and links focuses on the embedding mode of one or several closed curves in three-dimensional Euclidean space. In an electromagnetic field system, all-optical knots or links composed of phase or polarization singularities have been verified theoretically and experimentally. Recent studies have shown that robust topological all-optical coding can be achieved by using optical knots and links. However, in the current design of optical knots and links based on phase or polarization singularities, the amplitude of light between adjacent singularities is relatively weak. This brings great pressure to detection of optical knots and links and limits their applications. Here, we propose a new optimization method in theory. Compared with the existing design methods, our design method improves the relative intensity distribution of light between adjacent singularities. We verify the feasibility of our design results in experiments. Our study reduces the detection difficulty of optical knots and links, and has a positive significance for promotion of applications of optical knots and links.

High capacity topological coding based on nested vortex knots and links

Optical knots and links have attracted great attention because of their exotic topological characteristics. Recent investigations have shown that the information encoding based on optical knots could possess robust features against external perturbations. However, as a superior coding scheme, it is also necessary to achieve a high capacity, which is hard to be fulfilled by existing knot-carriers owing to the limit number of associated topological invariants. Thus, how to realize the knot-based information coding with a high capacity is a key problem to be solved. Here, we create a type of nested vortex knot, and show that it can be used to fulfill the robust information coding with a high capacity assisted by a large number of intrinsic topological invariants. In experiments, we design and fabricate metasurface holograms to generate light fields sustaining different kinds of nested vortex links. Furthermore, we verify the feasibility of the high-capacity coding scheme based on those topological optical knots. Our work opens another way to realize the robust and high-capacity optical coding, which may have useful impacts on the field of information transfer and storage.

Polychromatic electric field knots

The polarization of a monochromatic optical beam lies in a plane, and in general, is described by an ellipse, known as the polarization ellipse. The polarization ellipse in the tight focusing (non-paraxial) regime forms non-trivial three-dimensional topologies, such as M\"obius and ribbon strips, as well as knots. The latter is formed when the dynamics of specific polarization states, e.g., circular polarization states, are studied upon propagation. However, there is an alternative method to generate optical knots: the electric field's tip can be made to evolve along a knot trajectory in time locally. We propose an intuitive technique to generate and engineer the path traced by the electric field vector of polychromatic beams to form different knots. In particular, we show examples of how tightly focused beams with at least three frequency components and different spatial modes can cause the tip of the electric field vector to follow, locally, a knotted trajectory. Furthermore, we characterize the generated knots and explore different knot densities upon free-space propagation in the focal volume. Our study may provide insight for designing current densities when structured polychromatic electromagnetic fields interact with materials.

Multifrequency study of HH 137 and HH 138: discovering new knots and molecular outflows with Gemini and APEX

ABSTRACT We present a multiwavelength study of two Herbig–Haro (HH) objects (137 and 138) that may be associated. We use Gemini H2 (2.12 μm) and K (2.2 μm) images, as well as Atacama Pathfinder EXperiment molecular line observations and Spitzer image archives. Several H2 knots, linked to the optical chain of knots of HH 137, are identified in the Gemini and Spitzer 4.5 μm images. New shock excited regions related to the optical knots delineating HH 138 are also reported. In addition, a bright 4.5 μm 0.09 pc-long arc-shaped structure, roughly located mid-way between HH 137 and HH 138, is found to be associated with two Spitzer Class I/II objects, which are likely to be the exciting stars. These sources are almost coincident with a high-density molecular clump detected in 12CO(3 − 2), 13CO(3 − 2), C18O(3 − 2), HCO+(3 − 2), and HCN(3 − 2) molecular lines with an local thermodynamic equilibrium (LTE) mass of 36 M⊙. The 12CO(3 − 2) emission distribution over the observed region reveals molecular material underlying three molecular outflows. Two of them (outflows 1 and 2) are linked to all optical knots of HH 137 and HH 138 and to the H2 and 4.5 μm shock emission knots. In fact, the outflow 2 shows an elongated 12CO blue lobe that coincides with all the H2 knots of HH 137, which end at a terminal H2 bow shock. We propose a simple scenario that connects the outflows to the dust clumps detected in the region. A third possible outflow is located to the north-east projected towards a secondary weak and cold dust clump.

Confirming the nature of the knot near the pulsar B1951+32

The energetic and fast-moving radio and γ-ray pulsar B1951+32 is associated with the supernova remnant CTB 80. It powers a complex pulsar wind nebula detected in the radio, Hα and X-rays (Moon et al 2004 ApJ 610 L33). A puzzling optical knot was detected about 0″.5 from the pulsar in the optical and near-IR (Moon et al 2004 ApJ 610 L33; Hester 2000 Bulletin of the AAS 32 1542). It is reminiscent of the unique “inner optical knot” located 0″.6 from the Crab pulsar. Until now there has been no evidence that B1951+32 knot is indeed associated with the pulsar.We observed the pulsar field with the Gemini-North telescope in 2016 to check the association. We performed first near-IR high spatial resolution imaging in the Ks band using the NIRI+Altair instrument and deep optical imaging in the gr bands using the GMOS instrument. Our observations showed that the current knot position is shifted by ≈ 0″.6 from the position measured with the HST in 1997. This is consistent with the known pulsar proper motion and is direct evidence of the pulsar–knot connection. We compared the spectral energy distribution of the knot emission with that of the Crab knot. Possible implications of the results are discussed.

Relative Humidity Sensor Based on a Few-Mode Microfiber Knot Resonator by Mitigating the Group Index Difference of a Few-Mode Microfiber

A highly sensitive relative humidity sensor based on a few-mode microfiber knot resonator (FM-MKR) incorporating a polyvinyl alcohol overlay is investigated. The sensitivity of the proposed FM-MKR to the relative humidity is successfully enhanced by mitigating the difference in effective refractive group indices between the HE11 and HE12 modes. The proposed FM-MKR is structurally composed of two sensing probes, such as an FM-microfiber modal interferometer and an FM-MKR. In the FM-microfiber modal interferometer, two modes (HE11 and HE12) are excited and interfered in a nonadiabatically up-tapered region of the FM-microfiber, resulting in an inline modal interferometer. After making a tie with the FM-microfiber, the FM-MKR is fabricated and two modes must be circulated within the optical knot and cross-coupled independently with a phase delay. By optimizing the diameter of the microfiber (∼4 μm), the difference in effective refractive group indices between HE 11 and HE12 is suppressed, resulting in an improved relative humidity sensitivity of the proposed FM-MKR. By using the fast Fourier transform algorithm, optical transmission spectra of the FM-MKR are converted to spatial frequency spectra to precisely measure the concentration of relative humidity. The absorption of relative humidity in the proposed FM-MKR-based sensing probe effectively changes the resonant wavelength of the FM-microfiber modal interferometer and the spatial frequencies of the FM-MKR depending on the radial mode number ( m ) and the mode order ( k ).

Optical knots and contact geometry II. From Ranada dyons to transverse and cosmetic knots

Some time ago Ranada (1989) obtained new nontrivial solutions of the Maxwellian gauge fields without sources. These were reinterpreted in Kholodenko (2015) [10] (part I) as particle-like (monopoles, dyons, etc.). They were obtained by the method of Abelian reduction of the non-Abelian Yang–Mills functional. The developed method uses instanton-type calculations normally employed for the non-Abelian gauge fields. By invoking the electric–magnetic duality it then becomes possible to replace all known charges/masses by the particle-like solutions of the source-free Abelian gauge fields. To employ these results in high energy physics, it is essential to extend Ranada’s results by carefully analyzing and classifying all dynamically generated knotted/linked structures in gauge fields, including those discovered by Ranada. This task is completed in this work. The study is facilitated by the recent progress made in solving the Moffatt conjecture. Its essence is stated as follows: in steady incompressible Euler-type fluids the streamlines could have knots/links of all types. By employing the correspondence between the ideal hydrodynamics and electrodynamics discussed in part I and by superimposing it with the already mentioned method of Abelian reduction, it is demonstrated that in the absence of boundaries only the iterated torus knots and links could be dynamically generated. Obtained results allow to develop further particle-knot/link correspondence studied in Kholodenko (2015) [13].

Optical knots and contact geometry I. From Arnol’d inequality to Ranada’s dyons

Recently there had been a great deal of activity associated with various schemes of designing both analytic and experimental methods describing knotted structures in electrodynamics and in hydrodynamics. The majority of works in electrodynamics were inspired by the influential paper by Ranada (Lett Math Phys 18:97–106, 1989) and its subsequent refinements. In this work and in its companion we analyze Ranada’s results using methods of contact geometry and topology. Not only our analysis allows us to reproduce his major results but in addition, it provides opportunities for considerably extending the catalog of the known/obtained knot types. In addition, it allows to reinterpret both the electric and magnetic charges purely geometrically thus opening the possibility of treatment of masses and charges in Yang–Mills and gravitational fields purely geometrically.

X-RAY EMISSION FROM STELLAR JETS BY COLLISION AGAINST HIGH-DENSITY MOLECULAR CLOUDS: AN APPLICATION TO HH 248

We investigate the plausibility of detecting X-ray emission from a stellar jet that impacts against a dense molecular cloud. This scenario may be usual for classical T Tauri stars with jets in dense star-forming complexes. We first model the impact of a jet against a dense cloud by 2D axisymmetric hydrodynamic simulations, exploring different configurations of the ambient environment. Then, we compare our results with XMM-Newton observations of the Herbig-Haro object HH 248, where extended X-ray emission aligned with the optical knots is detected at the edge of the nearby IC 434 cloud. Our simulations show that a jet can produce plasma with temperatures up to 10 MK, consistent with production of X-ray emission, after impacting a dense cloud. We find that jets denser than the ambient medium but less dense than the cloud produce detectable X-ray emission only at the impact onto the cloud. From the exploration of the model parameter space, we constrain the physical conditions (jet density and velocity, cloud density) that reproduce well the intrinsic luminosity and emission measure of the X-ray source possibly associated with HH 248. Thus, we suggest that the extended X-ray source close to HH 248 corresponds to the jet impacting on a dense cloud.

Model simulation for periodic double-peaked outbursts in blazar OJ 287: binary black hole plus lighthouse effect

The mechanism of formation for double-peaked optical outbursts observed in blazar OJ 287 is studied. It is shown that they could be explained in terms of a lighthouse effect for superluminal optical knots ejected from the center of the galaxy that move along helical magnetic fields. It is assumed that the orbital motion of the secondary black hole in the supermassive binary black hole system induces the 12-year quasi-periodicity in major optical outbursts by the interaction with the disk around the primary black hole. This interaction between the secondary black hole and the disk of the primary black hole (e.g. tidal effects or magnetic coupling) excites or injects plasmons (or relativistic plasmas plus magnetic field) into the jet which form superluminal knots. These knots are assumed to move along helical magnetic field lines to produce the optical double-peaked outbursts by the lighthouse effect. The four double-peaked outbursts observed in 1972, 1983, 1995 and 2005 are simulated using this model. It is shown that such lighthouse models are quite plausible and feasible for fitting the double-flaring behavior of the outbursts. The main requirement may be that in OJ 287 there exists a rather long (~40–60 pc) highly collimated zone, where the lighthouse effect occurs.

Optical to Mid-Infrared Analysis for the Galaxy Group RSCG 44

We present the detailed Optical to Mid Infrared (MIR) analysis on the compact group of galaxies RSCG44. The optical analysis comprehends both photometric andspectroscopic studies for six galaxies in this group. The overall Optical to MIR data provide maps, spectra, profiles and images to analyse galaxy properties (structure, line-strength features, etc.) of each member searching for signatures of star formation and nucleus activity. In the photometric analysis, we study $BVR$ surface brightness and colors calculated for regions such as galaxy centers, possible bridges, tails and optical knots. Optical direct image also presents residual images (after subtracting isophotal models) and unsharp masked images in order to uncover any hidden structure in the system. The inclusion of maps, profiles and images from the Spitzer Space Telescope (SST) was made in order to provide a complementary outlook for the optical colors and the environment in which the group evolves, hence, a better explanation of the photospheric component and possible photdissociation regimes in polycyclic aromatic hydrocarbon (PAH) emission at 5.8 and 8 μm have provide a disentangled view of dust properties in the interstellar medium (ISM) at MIR. Optical spectra for the group are also provided to establish a more fond comparison between optical to mid infrared properties. The color gradients were compared with the optical spectra of both galaxies, showing in general similar trends for star formation. Globally, color maps, color tables and optical spectra indicate predominant stellar populations from classes I, III and V corresponding to spectral types of K-M stars with ages of at least in theorder of 10 Gyr for models using metallicity ranges with solar and non solar abundances. These results lead us to the conclusion of a moderate star formation rate and a tranquil evolving state of the system.

INVESTIGATION OF THE THERMAL PROPERTIES OF OPTICAL MICROFIBER KNOT RESONATORS

The dependence of optical microfiber knot resonators (MKRs) thermal properties on the geometry parameters is theoretically and experimentally investigated in this article. According to the simulated and experimental results, the thermal properties of MKRs are synthetically determined by the microfiber diameter, refractive index, and thermo-optic coefficients of the external medium. Also, the rules for reinforcing or suppressing the thermal effects of MKRs and MKR-based devices by selecting matched configuration parameters are presented. A good agreement between the simulated and experimental results is obtained. The conclusions derived from our work would provide helpful guidelines in designing MKR-based devices with desired thermal properties to satisfy different requirements in applications.

Generation and interferometric analysis of high charge optical vortices

We report on the generation of optical vortex beams using spatial phase modulation with spiral phase mirrors. The spiral phase mirrors are manufactured by direct machining with an ultra-precision single point diamond turning lathe. The imperfection of the machined phase mirrors and its impact on the generated vortex beams are analyzed with interferometric measurements. Our phase mirror has a surface roughness of 3 nm and a maximum peak–valley deviation of λ/30. The vortex charges of our light beams are directly verified by counting the fringes of their corresponding interferograms. We directly observed the successful generation of an optical vortex beam with a charge as high as 5050. We study the Fourier images of the vortex beams to characterize the quality of the beams. We obtained a conversion efficiency of 92.8% from a TEM00 beam to a vortex beam with charge 1020. This technique of generating optical singularities can potentially be used to produce more complex optical wavefronts, such as optical knots.

INVESTIGATION OF DUAL ACTIVE NUCLEI, OUTFLOWS, SHOCK-HEATED GAS, AND YOUNG STAR CLUSTERS IN MARKARIAN 266

Results of observations with the Spitzer, Hubble, GALEX, Chandra, and XMM-Newton space telescopes are presented for the Luminous Infrared Galaxy (LIRG) merger Mrk 266. The SW (Seyfert 2) and NE (LINER) nuclei reside in galaxies with Hubble types SBb (pec) and S0/a (pec), respectively. Both galaxies have L > L*, and they are inferred to each contain a ~2.5x10^8 M_sun black hole. Mrk 266 SW is likely the primary source of a bright Fe K-alpha line detected from the system, consistent with the reflection-dominated X-ray spectrum of a heavily obscured AGN. Optical knots embedded in an arc with aligned radio continuum radiation, combined with luminous H_2 line emission, provide evidence for a radiative bow shock in an AGN-driven outflow surrounding the NE nucleus. Soft X-ray emission modeled as shock-heated plasma is co-spatial with radio continuum emission between the galaxies. Mid-IR diagnostics indicate roughly equal contributions of AGN and starburst radiation powering the bolometric luminosity. Approximately 120 star clusters have been detected, with most having estimated ages < 50 Myr. Detection of 24 micron emission extending ~34 arcsec (20 kpc) north of the galaxies is interpreted as ~2x10^7 M_sun of dust entrained in an outflowing superwind; at optical wavelengths this region is resolved into a fragmented morphology indicative of Rayleigh-Taylor instabilities in an expanding shell of ionized gas. Mrk 266 demonstrates that the dust "blow-out" phase can begin in a LIRG well before the galaxies fully coalesce during a subsequent ULIRG phase, and rapid gas consumption in luminous dual AGNs (kpc scale separations) early in the merger process may explain the paucity of detected binary QSOs (sub-pc scale orbits) in large surveys. An evolutionary sequence is proposed representing a progression from dual to binary AGNs, accompanied by an increase in observed L_x/L_ir ratios by 10^4 or more.

A MULTI-WAVELENGTH STUDY OF THE JET, LOBES, AND CORE OF THE QUASAR PKS 2101–490

We present a detailed study of the X-ray, optical and radio emission from the jet, lobes and core of the quasar PKS 2101-490 as revealed by new Chandra, HST and ATCA images. We extract the radio to X-ray spectral energy distributions from seven regions of the 13 arcsecond jet, and model the jet X-ray emission in terms of Doppler beamed inverse Compton scattering of the cosmic microwave background (IC/CMB) for a jet in a state of equipartition between particle and magnetic field energy densities. This model implies that the jet remains highly relativistic hundreds of kpc from the nucleus, with a bulk Lorentz factor Gamma ~ 6 and magnetic field of order 30 microGauss. We detect an apparent radiative cooling break in the synchrotron spectrum of one of the jet knots, and are able to interpret this in terms of a standard one-zone continuous injection model, based on jet parameters derived from the IC/CMB model. However, we note apparent substructure in the bright optical knot in one of the HST bands. We confront the IC/CMB model with independent estimates of the jet power, and find that the IC/CMB model jet power is consistent with the independent estimates, provided that the minimum electron Lorentz factor gamma_min > 50, and the knots are significantly longer than the jet width, as implied by de-projection of the observed knot lengths.

SpitzerIMAGING AND SPECTRAL MAPPING OF THE OXYGEN-RICH SUPERNOVA REMNANT G292.0+1.8

We present mid-infrared continuum and emission line images of the Galactic oxygen-rich supernova remnant (SNR) G292.0+1.8, acquired using the MIPS and IRS instruments on the Spitzer Space Telescope. The MIPS 24 micron and 70 micron images of G292.0+1.8 are dominated by continuum emission from a network of filaments encircling the SNR. The morphology of the SNR, as seen in the mid-infrared, resembles that seen in X-rays with the Chandra X-ray Observatory. Most of the mid-infrared emission in the MIPS images is produced by circumstellar dust heated in the non-radiative shocks around G292.0+1.8, confirming the results of earlier mid-IR observations with AKARI. In addition to emission from hot dust, we have also mapped atomic line emission between 14 micron and 36 micron using IRS spectral maps. The line emission is primarily associated with the bright oxygen-rich optical knots, but is also detected from fast-moving knots of ejecta. We confirm our earlier detection of 15-25 micron emission characteristic of magnesium silicate dust in spectra of the radiatively shocked ejecta. We do not detect silicon line emission from any of the radiatively shocked ejecta in the southeast of the SNR, possibly because that the reverse shock has not yet penetrated most of the Si-rich ejecta in that region. This may indicate that G292.0+1.8 is less evolved in the southeast than the rest of the SNR, and may be further evidence in favor of an asymmetric SN explosion as proposed in recent X-ray studies of G292.0+1.8.

Dust in historical Galactic Type Ia supernova remnants with Herschel★

The origin of interstellar dust in galaxies is poorly understood, particularly the relative contributions from supernovae and the cool stellar winds of low-intermediate mass stars. Here, we present Herschel PACS and SPIRE photometry at 70-500um of the historical young supernova remnants: Kepler and Tycho; both thought to be the remnants of Type Ia explosion events. We detect a warm dust component in Kepler's remnant with T = 82K and mass 0.0031Msun; this is spatially coincident with thermal X-ray emission optical knots and filaments, consistent with the warm dust originating in the circumstellar material swept up by the primary blast wave of the remnant. Similarly for Tycho's remnant, we detect warm dust at 90K with mass 0.0086Msun. Comparing the spatial distribution of the warm dust with X-rays from the ejecta and swept-up medium, and Ha emission arising from the post-shock edge, we show that the warm dust is swept up interstellar material. We find no evidence of a cool (25-50 K) component of dust with mass >0.07Msun as observed in core-collapse remnants of massive stars. Neither the warm or cold dust components detected here are spatially coincident with supernova ejecta material. We compare the lack of observed supernova dust with a theoretical model of dust formation in Type Ia remnants which predicts dust masses of 0.088(0.017)Msun for ejecta expanding into surrounding densities of 1(5)cm-3. The model predicts that silicon- and carbon-rich dust grains will encounter the interior edge of the observed dust emission at 400 years confirming that the majority of the warm dust originates from swept up circumstellar or interstellar grains (for Kepler and Tycho respectively). The lack of cold dust grains in the ejecta suggests that Type Ia remnants do not produce substantial quantities of iron-rich dust grains and has important consequences for the 'missing' iron mass observed in ejecta.