Spatial Coherence Parameter Research Articles

A Hanbury Brown and Twiss renascence: measurement of photon correlations yields spatio-temporal coherence

Investigations of photon correlations similar to the Hanbury Brown and Twiss experiment are since the advent of quantum optics in the center of both fundamental and application-oriented research. We derive a factorial moment-generating function of the probability distribution of electromagnetic radiation emitted by a source and absorbed by a photodetector from which we calculate an analytical expression for the second-order correlation coefficient g^{(2)} which reflects spatial coherence properties of the emitted light. The measurement of g^{(2)} thus allows to retrieve the spatial coherence parameter of the light source in terms of the combination of source area, source-detector distance, wavelength and detector area. The validity of the concept is proven by investigating g^{(2)} of true thermal light from a Xenon arc lamp and from the sun for various detector areas, in excellent agreement with the theory. Finally, we suggest a novel scheme for determining light source diameters by exploiting the spatially dependent statistics and confirm its validity by exemplary calculations. These results based on radiation thermodynamics and photon statistics give fresh insight into quantum optical properties of classical light sources, photon correlations and photodetection with promising applications perspectives, more than 68 years after the original Hanbury Brown and Twiss experiment.

Thermal blooming effect and the scaling laws of partial spatially coherent beam array propagating through the atmosphere

The thermal blooming effect and the scaling laws of partially coherent beam (PCB) array propagating in the atmosphere are studied. The four-dimensional (4D) computer code of time-dependent propagation to simulate PCB array through the turbulent atmosphere is designed. Based on numerical simulation, the propagation properties of PCB array are investigated in detail. It is shown that, as the spatial coherence parameter β decreases, the relative beam width increases and the thermal blooming effect becomes more severe. However, the change of the energy Strehl ratio (SRE) versus spatial coherence parameter β is not monotonic because the energy is concentrated on the main lobe for fully coherent beam array. Besides, the scaling laws to estimate the thermal blooming effects of PCB array are investigated. The modified expression of the distortion parameter Nd of a focused PCB array is derived, which is efficient to evaluate the strength of the thermal blooming effects.

Graphene Quantum Dot Crystal Serving as a Multi‐Qubit Circuit Operating at High Temperatures

AbstractLocalized states (LS) of electrons are studied in clusters and in periodic arrays of graphene quantum dots (GQD) formed using narrow graphene stripes with either armchair or zigzag shape of atomic edges. Basic electronic parameters of the system such as the LS energies , inter‐level splitting , wavefunction coherence, and the inter‐dot coupling are controlled by applying the electric potentials to the electrodes. The electron density of states of the periodic quantum dot array regarded as 1D crystal (GC) represents a sequence of very sharp peaks corresponding to LS levels. The spatial coherence parameter (d is the GC period and κ is the electron wave vector) is estimated as , suggesting that the electron coherence involves large clusters of GQD by spreading over 5–20 periods in the artificial crystal. Furthermore, the coherence time τc, which is determined by inelastic electron–phonon collisions is remarkably long, ns even at temperatures K. The above properties of GC open new opportunities for building of the all‐electrically controllable multi‐qubit circuits operating at high temperatures.

Intensity distribution and spectral degree of coherence for array beams in non-Kolmogorov atmospheric turbulence

The propagation expressions of the intensity distribution and the spectral degree of coherence for radial array Gaussian Schell-model beams in non-Kolmogorov atmospheric turbulence have been derived. There exists a maximum of the on-axis intensity for radial array beams on propagation. The optimal propagation distance where the maximum appears has been analyzed in detail. The influence of the generalized structure constant and the initial spatial coherence parameter for the correlated superposition beam is different from the uncorrelated one. In particular, the on-axis intensity maximum exhibits a minimum when the generalized exponent α = 3.1. The spectral degree of coherence for the correlated superposition beam is larger than the uncorrelated one, and the difference between the two superposition styles becomes larger when the spatial coherence parameter becomes larger and the turbulence becomes weaker. Moreover, when α = 3.1 the spectral degree of coherence exhibits a minimum.

Changes in the Beam Parameters of Partially Coherent Sinh-Gaussian Beams after Passage through an Astigmatic Lens

Based on the propagation law of partially coherent beams, the analytical expression of the beam width, waist positions and the far-field divergence angle of partially coherent sinh-Gaussian (ShG) beams through an astigmatic lens were derived. The effect of astigmatism and spatial coherence parameter on the beam parameters was mainly analyzed. It is found that the beam width depends on the astigmatic coefficient, spatial coherence parameter, decentered parameter, fresnel number and propagation distance in general. The astigmatism results in a difference between the beam widths, waist positions and far-field divergence angles in thexandydirections.

CIRCULARITY OF THEINTERSTELLAR BOUNDARY EXPLORERRIBBON OF ENHANCED ENERGETIC NEUTRAL ATOM (ENA) FLUX

As a sharp feature in the sky, the ribbon of enhanced energetic neutral atom (ENA) flux observed by the Interstellar Boundary Explorer (IBEX) mission is a key signature for understanding the interaction of the heliosphere and the interstellar medium through which we are moving. Over five nominal IBEX energy passbands (0.7, 1.1, 1.7, 2.7, and 4.3 keV), the ribbon is extraordinarily circular, with a peak location centered at ecliptic (λRC, βRC) = (219.°2 ± 1.°3, 39.°9 ± 2.°3) and a half cone angle of C = 74.°5 ± 2.°0. A slight elongation of the ribbon, generally perpendicular to the ribbon center-heliospheric nose vector and with eccentricity ~0.3, is observed over all energies. At 4.3 keV, the ribbon is slightly larger and displaced relative to lower energies. For all ENA energies, a slice of the ribbon flux peak perpendicular to the circular arc is asymmetric and systematically skewed toward the ribbon center. We derive a spatial coherence parameter δC ≤ 0.014 that characterizes the spatial uniformity of the ribbon over its extent in the sky and is a key constraint for understanding the underlying processes and structure governing the ribbon ENA emission.

Coherence vortex properties of partially coherent flat-topped vortex beams

The analytical propagation expression of partially coherent flat-topped vortex beams through a paraxial optical ABCD system is derived, and it then is used to investigate the coherence vortex properties of partially coherent flat-topped vortex beams in the Fourier transform and fractional Fourier transform systems. It is shown that in the Fourier transform system the coherence vortex depends on the flat-topped beam order N, spatial coherence parameter α and position (x1,y1) of the reference point, whereas in the fractional Fourier transform system the flat-topped beam order N does not affect the spectral degree of coherence. Furthermore, in both transform systems, depending on the choice of the reference point, the zero value point of the spectral degree of coherence may be present or absent. In particular, if x1=y1=0 is selected, the phase at the zero value point of the spectral degree of coherence may be determinate; thus the coherence vortex does not exist.

Effects of atmosphere on spectrum of modified partially coherent flat-topped beams

The analytical formulas for the spectrum of modified partially coherent flat-topped (MPCFT) beams propagating in a turbulent atmosphere have been derived under strong fluctuation condition of turbulence. The spectral properties of MPCFT beams propagating in a strong turbulence have been investigated, and the changes of on-axis and off-axis spectral distributions have been analyzed quantitatively. The results show that the on-axis relative spectral shift of the modified partially coherent flat-topped beam exhibits spectral switch for the beam order M > 1, and with the increasing propagation distance the blue-shift gradually decreases in atmospheric turbulence. A rapid transition for the off-axis spectrum appears at one critical position in turbulence, and the position decreases with the increasing beam order for the lower beam order and the nearer propagation distance. The spectral properties and the spectral shifts of MPCFT beams also depend on the inner scale, the spatial coherence parameter.

Coherence vortex properties of partially coherent vortex beams

The analytical expression for the propagation of partially coherent flat-topped vortex beams through a paraxial optical ABCD system is derived and used to study the coherence vortex properties of partially coherent vortex beams in the focal region and free space. It is shown that the coherence vortex depends on the beam order N，spatial coherence parameter α and position (x1，y1) of the reference point. Depending on the choice of the reference point，the zero point of the spectral degree of coherence may be present or absent. In particular，if x1=y1=0 is chosen，the phase at the zero point of the spectral degree of coherence may be determinate，thus the coherence vortex does not exist.

Spectral shift of partially coherent flattened multi-Gaussian beams with a hole passing through ABCD optical systems

Based on flattened multi-Gaussian beam model and partially coherent theory, the expression for cross-spectral density of partially coherent flattened multi-Gaussian beam with a hole was given. The analytical expression for on-axis spectrum of partially coherent flattened multi-Gaussian beam with a hole passing through a paraxial ABCD optical system was derived. The spectral shifts of the partially coherent flattened multi-Gaussian beam with a hole propagating in free space and passing through the lens have been analyzed. The effects of the beam profile, spatial coherence parameter and the system parameters on the relative spectral shift have been discussed. Our results show that the inner radius of flattened multi-Gaussian beam with a hole determines its relative spectral shift in near field and its outer radius determines that in far field. For the flattened multi-Gaussian beam with a hole passing through a lens, the on-axis relative spectral shift changes sharply near the focal plane with the increase in Fresnel number and the spatial coherence parameter.

Transformation and spatial shaping of partially coherent cosh-Gaussian beams through an astigmatic lens

Based on the propagation law of partially coherent beams, the closed-form propagation expression for partially coherent cosh-Gaussian (ChG) beams through an astigmatic lens is derived. The transformation and spatial shaping of partially coherent ChG beams through the astigmatic lens are studied and illustrated by numerical examples. It is shown that a suitable choice of the spatial coherence parameter and/or astigmatic coefficient, different beam profiles, such as Gaussian-like, flat-topped and bottle beam profiles, and beam profile with a central dip, at the geometric focal plane and at a certain plane are realizable.

Spectral intensity characteristics of partially coherent flattened multi-Gaussian beams with an axial shadow passing though paraxial ABCD optical systems

Based on the beam model for the flattened multi-Gaussian beams (FMGBs) with an axial shadow and partially coherent theory, the expression for cross-spectral density of partially coherent FMGBs with an axial shadow has been given, and the analytical expression for the spectral intensity of partially coherent FMGBs with an axial shadow passing through paraxial ABCD optical systems has been derived. The spectral shift of partially coherent FMGBs with an axial shadow focused by a thin lens has been analyzed quantitatively. The effects of the beam profile, spatial coherence parameter and the system parameters on the relative spectral shift have been discussed in detail. Our results show that the spectral intensity and the spectral shift of partially coherent FMGBs with an axial shadow passing through paraxial ABCD optical systems depend on the source spectral density, the generalized Fresnel number of the system, the transverse coordinate, the spatially coherence parameter, as well as the beam orders.

Changes in the spectrum of partially coherent flat-top light beam propagating in dispersive or gain media

Based on the flat-top beams model proposed by Li and the propagation theory of partially coherent light, the analytical expression for the spectrum of partially coherent flat-top beam propagating in dispersive or gain media is derived, and the spectral properties are studied quantitatively. The on-axis spectrums in near- and far-fields are analyzed. The effects of dispersive and gain properties of the media as well as the light source parameters such as central frequency, spectrum width and spatial coherence parameter on the spectral shift have been discussed in detail. Our results show that the refractive index of dispersive media and the light source parameters affect the spectral shift, and the profile of flat-top beam determines the spectral changes of blue-shift alternating with red-shift in near-field whereas blue-shift in far-field, which would be useful for the experiments.

The spectral properties of partially coherent flat-topped light beams propagating in linear gain or loss media

Based on the flat-topped beams model proposed by Li and the propagation theory of partially coherent light, the spectrum analytical expression of partially coherent flat-topped beams propagating in the linear gain or loss media was derived and the spectral properties were studied quantitatively by numerical calculation. The variation characteristics of the on-axis spectrum in near- and far-field regions have been discussed in details. The effects of the property of the linear gain or loss media and some parameters of the light source, such as the central frequency, spectrum width and spatial coherence parameter on the spectral shift have also been discussed. It can be shown that the light source parameters have greater effects on the value of the frequency shift than on the total changing trend of the spectrum along the propagation distance, whereas the latter is determined by the beam order of flat-topped beam.