Coherent Gaussian Research Articles

Insensitivity of partially coherent Gaussian -Schell model beams to the impact of dynamic Kolmogorov type turbulence

ABSTRACT The effect of dynamic Kolmogorov kind of turbulence on Gaussian- Schell model beams in different coherence regimes have been explored in detail. The propagation characteristics of such turbulence impacted beams are quantitatively verified at the laboratory level by calculating beam wandering, scintillation index, and Zernike polynomials. It has been experimentally verified that Gaussian Schell model beams are more resilient to the impact of turbulence compared to their fully coherent counterparts under different turbulence strengths. These results find applications in free-space optical communications.

INFLUENCE OF ANISOTROPIC TURBULENT PLASMA ON THE PARTIALLY COHERENT FOUR-PETAL GAUSSIAN VORTEX BEAMS

Based on the extended Huygens-Fresnel principle, the analytical expressions for partially coherent four-petal Gaussian (FPG) vortex beams propagating in turbulent plasma are obtained, the influence of the turbulent plasma parameters on beam profile and coherence of the beams is discussed in detail using numerical examples. It is found that a four-petal Gaussian-shaped intensity distribution will eventually transform into a Gaussian distribution after propagating in turbulent plasma. Meanwhile, turbulent plasma parameters will also influence the coherence characterizations of the beams.

Propagation of Bessel-correlated specular and antispecular beams.

We address the specular properties of Bessel-correlated fields, generated by illuminating a tilted rotating plane-parallel glass plate with a coherent Gaussian beam and passing the output beam though a mirror-based wavefront folding interferometer. This device allows us to produce beams whose specular properties are preserved in propagation. In the far zone, the specular nature of these partially coherent fields is shown to produce intensity-profile oscillations in the sub-diffraction-limit scale. The analytical results at various propagation distances are verified experimentally by using another wavefront-folding interferometer for coherence measurements.

Propagation of partially coherent hyperbolic sinusoidal Gaussian beam in biological tissue

This paper presents intensity evolution of partially coherent hyperbolic sinusoidal Gaussian beam in mouse liver tissue and human upper dermis. Received field is obtained solving Huygens-Fresnel integral. In addition, beam size analysis is carried out. We reach that beam has elliptic Gaussian beams at close distance and these beams are placed circularly. Then, they come together and generate concentric circular rings. Moreover, larger beams can be obtained if coherence length decreases at close distance. We expect that these results will be used at optical medical device designs.

Boosting Entanglement Generation in Down-Conversion with Incoherent Illumination

Entangled photons produced by spontaneous parametric down-conversion have been of paramount importance for our current understanding of quantum mechanics and advances in quantum information. In this process, the quantum correlations of the down-converted photons are governed by the optical properties of the pump beam illuminating the nonlinear crystal. Extensively, the pump beam has been modeled by either coherent beams or by the well-known Gaussian-Schell model, which leads to the natural conclusion that a high degree of optical coherence is required for the generation of highly entangled states. Here, we show that when a novel class of partially coherent Gaussian pump beams is considered, a distinct type of quantum state can be generated for which the amount of entanglement increases inversely with the degree of coherence of the pump beam. This leads to highly incoherent yet highly entangled multiphoton states, which should have interesting consequences for photonic quantum information science.

Approximating the Partially Coherent Additive White Gaussian Noise Channel in Polar Coordinates

We consider the partially coherent additive white Gaussian noise channel (PCAWGN) in optical communications and review the derivation of the exact channel conditional probability model in a closed-form solution in polar coordinates. In addition, we derive a reduced-complexity approximation by replacing the Rician and Tikhonov distributions describing amplitude and phase components, respectively, with their Gaussian approximation under certain assumptions of high SNR and low phase noise or jitter . Our proposal significantly reduces the hardware complexity by removing the modified Bessel functions involved in the exact solution. Furthermore, we compare the proposed approximation with a different metric previously found in the literature and observe that for maximum-likelihood hard symbol decision, both models are in perfect agreement with the optimal detector. However, our model not only reduces the required number of multiplications from 12 to 8 and additions from 9 to 3 (per computed symbol) but also reduces the information loss by at least one and up to several orders of magnitude with respect to the previously published metric when used to compute the channel achievable information rate (AIR). In all the simulation cases, we use QAM constellations of orders 4, 8, 16, and 32 as test input symbol sets.

Coupling characteristics and kurtosis parameter of partially coherent beams in turbulent atmosphere

ABSTRACTCoupling properties and kurtosis parameter (K parameter) of arbitrary beams propagating through atmospheric turbulence are investigated. A correlation factor (C4-factor) is introduced to describe the influence of turbulence on coupling characteristics. The general analytical expression for C4-factor of arbitrary beams in atmospheric turbulence is derived. It is shown that C4-factor of arbitrary beams in the turbulent atmosphere depends on the initial second-order moments and fourth-order moments and turbulence quantities. Taking the partially coherent anomalous elliptical hollow Gaussian (PCAEHG) beam as an example, we can obtain that C4-factor decreases as structure constant of the refractive index fluctuations and inner scale increase, and waist width and transverse coherence length decrease when z > 5 km. Moreover, K parameter of PCAEHG beam in turbulent atmosphere converges to 2 when propagation distance is large enough. It indicates that the profile of PCAEHG beams in turbulent atmosphere finally evolves into fundamental Gaussian distribution.

Tight focusing properties of a circular partially coherent Gaussian beam.

Tight focusing properties of a circular partially coherent Gaussian (CPCG) beam with linear polarization have been studied based on vectorial Debye theory. Expressions for the intensity distribution and degree of coherence near the focus are derived. Numerical calculations are performed to show the intensity distribution and degree of coherence of the CPCG beam in the focal region. It is interesting to find that after focusing the CPCG beam through a high numerical-aperture objective we can obtain a super-length optical needle (>12λ) with homogeneous intensity along the propagation axis and wavelength beam size (∼λ). Moreover, the numerical calculations of coherence illustrate that, in the range of full width at half-maximum of the optical needle, for any two of the parallel electric field components of the optical needle the coherence is close to 1, but for any two of orthometric electric field components the value of coherence is between 0.4 and 0.9. Such a non-diffracting optical needle may have potential applications in atom optical experiments, such as in atom traps and atom switches.

Propagation of partially coherent four-petal elliptic Gaussian vortex beams in atmospheric turbulence.

The beam spreading and evolution behavior of the intensity profile and coherent vortices of partially coherent, four-petal elliptic Gaussian vortex beams propagating in atmospheric turbulence are studied. The analytical expressions for cross-spectral density function, as well as root mean square (rms) beam width, are derived based on the extended Huygens-Fresnel principle. Results showed that, unlike the partially coherent four-petal Gaussian vortex beams, the partially coherent four-petal elliptic Gaussian vortex beam could change its petal number into six. The dependencies of occurrence, appearance, and transition speed from four- to six-petal profile on the topological charge, the beam order, and the ellipticity factor are illustrated. The far field behaviors of partially coherent four-petal elliptic Gaussian vortex beams propagating in atmospheric turbulence and are compared in free space. Beams with larger topological charge, smaller beam order, and larger ellipticity factor were found to be less influenced by atmospheric turbulence. Further, the ellipticity factor can be used as an additional degree of freedom in controlling the conservation distance of coherence vortices' topological charge.

Characterization of nonclassicality of Gaussian states initially generated in optical spontaneous parametric processes by means of induced stimulated emission

In a recent paper [I.I. Arkhipov, Phys. Rev. A 98, 021803 (2018)], it was shown that one can completely identify the nonclassicality of single- and two-mode Gaussian states by means of certain nonclassicality witnesses which are based on intensity moments up to the third order of optical fields, provided that an appropriate coherent displacement is applied to a given Gaussian state. Here, we utilize a mathematical equivalence between the description of the coherent displaced Gaussian states generated in the spontaneous parametric processes and the Gaussian states generated in the corresponding stimulated parametric processes. Resorting to that equivalence, we study and compare the power of those nonclassicality witnesses in the detection of the nonclassicality of the two-mode Gaussian states generated in both the spontaneous and stimulated second subharmonic and down-conversion processes and which are subsequently subject to a beam splitter. We demonstrate that by means of an appropriate induced stimulated emission one can completely identify the nonclassicality of the considered Gaussian states in comparison to the case of the spontaneous emission. This is important from the experimental point of view, as the stimulated emission can be easily implemented in running optical experiments, and such method can exploit just simple linear detectors.

Paraxial propagation of a class of Bessel-correlated fields.

The propagation of a novel class of paraxial spatially partially coherent beams exhibiting Bessel-type correlations is studied in free space and in paraxial optical systems. We show that, under certain conditions, such beams can have functionally identical forms of the absolute value of the complex degree of spatial coherence not only at the source plane and in the far zone, but also at all finite propagation distances. Under these conditions the degree of spatial coherence properties of the field is a shape-invariant quantity, but the spatial intensity distribution is only approximately shape-invariant. The main properties of this class of model beams are demonstrated experimentally by passing a coherent Gaussian beam through a rotating wedge and measuring the coherence of the ensuing beams with a Young-type interferometer realized with a digital micromirror device.

Shaping the intensity and degree of coherence of a partially coherent beam by a 4f optical system with an amplitude filter

It is known that a 4f optical system with an amplitude filter can be adopted to shape the intensity of a coherent Gaussian beam. In this paper, we investigate the propagation of a typical kind of partially coherent beam called a Gaussian Schell-model (GSM) beam through a 4f optical system with an amplitude filter in the frequency plane. It is demonstrated both numerically and experimentally that the 4f optical system with an amplitude filter can be used to shape the intensity and degree of coherence of a GSM beam simultaneously. The shaped beam displays interesting properties and forms controllable far-field intensity lattices, which may be useful for particle trapping and information transfer.

A numerical approach to optimal coherent quantum LQG controller design using gradient descent

This paper is concerned with coherent quantum linear quadratic Gaussian (CQLQG) control. The problem is to find a stabilizing measurement-free quantum controller for a quantum plant so as to minimize a mean square cost for the fully quantum closed-loop system. The plant and controller are open quantum systems interconnected through bosonic quantum fields. In comparison with the observation–actuation structure of classical controllers, coherent quantum feedback is less invasive to the quantum dynamics. The plant and controller variables satisfy the canonical commutation relations (CCRs) of a quantum harmonic oscillator and are governed by linear quantum stochastic differential equations (QSDEs). In order to correspond to such oscillators, these QSDEs must satisfy physical realizability (PR) conditions in the form of quadratic constraints on the state-space matrices, reflecting the CCR preservation in time. The symmetry of the problem is taken into account by introducing equivalence classes of coherent quantum controllers generated by symplectic similarity transformations. We discuss a modified gradient flow, which is concerned with norm-balanced realizations of controllers. A line-search gradient descent algorithm with adaptive stepsize selection is proposed for the numerical solution of the CQLQG control problem. The algorithm finds a local minimum of the LQG cost over the parameters of the Hamiltonian and coupling operators of a stabilizing coherent quantum controller, thus taking the PR constraints into account. A convergence analysis of the algorithm is presented. Numerical examples of designing locally optimal CQLQG controllers are provided in order to demonstrate the algorithm performance.

Nonparaxial propagation of a partially coherent four-petal Gaussian beam in free space

Based on the generalized Rayleigh-Sommerfeld diffraction integral, the equations of nonparaxial propagation, far field propagation and paraxial propagation of a partially coherent four-petal Gaussian beam in free space are obtained. The results show that the far field propagation and paraxial propagation can be regarded as special cases of nonparaxial propagation. The normalized intensity and degree of coherence of a nonparaxial partially coherent four-petal Gaussian beam are illustrated and analyzed using numerical example.

An efficient simplified analysis model of a partially coherent Gaussian vortex beam

Based on the Gaussian–Schell model, analytical expression of the axial light intensity of a partially coherent Gaussian vortex beam (PCGVB) is deduced. The transformation law of axial light intensity is analyzed and a comparison to a partially coherent fundamental-mode Gaussian beam is made. The results show that for a low coherent Gaussian vortex beam, the light intensity distribution can be expressed as a common Gaussian beam with the same coherence length instead. The substitution result is more accurate, especially when the coherence is lower or the value of topological charge is smaller. Moreover, based on axial light intensity, a convenient analytical model of the light intensity distribution of a PCGVB is presented.

Propagation characters of multi-Gaussian beam with large eccentric displacement in collisionless plasma: Higher order paraxial theory

The multiple coherent identical Gaussian beams with symmetry distribution are abbreviated as multi-Gaussian beam, of which the propagation characters in collisionless plasma are studied with the WKB method and higher order paraxial theory. The initial beam profile presents the flat top like or hollow like distribution when the eccentric displacement is large enough. Based on the derived nonlinear propagation equations, the initial condition analyses are performed, and the impact of eccentric displacement on the free propagation effect and ponderomotive nonlinearity is thoroughly discussed. The propagation characters of dimensionless beam width parameter, spot intensity, and spatial distribution of plasma electron density are presented. Results show that the initial spot intensity is expanding outwards along the propagation and the ring structure of electron evacuation in plasmas is generated.

Propagation of partially coherent Laguerre Gaussian beams through inhomogeneous turbulent atmosphere.

Analytical formulas for the root-mean-square (rms) spatial width, the rms angular width, and the M2-factor of partially coherent standard Laguerre Gaussian beams (PC-SLGBs) and partially coherent elegant Laguerre Gaussian beams (PC-ELGBs) in inhomogeneous turbulent atmosphere have been derived. The propagation properties of PC-SLGBs and PC-ELGBs in inhomogeneous atmospheric turbulence are studied numerically and comparatively. It can be found that the propagation of laser beams in inhomogeneous turbulence is different from that in homogeneous turbulence. It is also shown that relative rms spatial widths and M2-factors of PC-ELGBs are more affected by inhomogeneous turbulence than those of PC-SLGBs. Moreover, the relative rms spatial widths and M2-factors of PC-SLGBs and PC-ELGBs in inhomogeneous turbulent atmosphere are closely related with waist widths, coherence widths, zenith angles, inner scales, and beam orders. Furthermore, the saturation propagation distance of the relative M2-factor and rms angular width with zenith angles of π/6 are 20 km and 0.5 km, respectively.

Evolution properties of partially coherent four-petal Gaussian beams in oceanic turbulence

Based on the extended Huygens–Fresnel integral formula, the analytical expressions for partially coherent four-petal Gaussian beam propagating in oceanic turbulence are derived, and the influences of coherence length, beam order N and the parameters of oceanic turbulence (the rate of dissipation of turbulent kinetic energy per unit mass of fluid, the rate of dissipation of mean square temperature and the relative strength of temperature and salinity fluctuations) on average intensity properties are investigated using numerical examples in detail. The results show that the beam with the higher beam order N or coherence length will lose its initial four-petal profiles slower. It is also indicated that the beam will evolve into a Gauss-like beam more rapidly with increasing oceanic turbulence strength. The results have the potential application in underwater laser communication using a partially coherent four-petal Gaussian beam.

部分相干反常椭圆空心高斯光束在非Kolmogorov湍流中的光束漂移

部分相干反常椭圆空心高斯光束在非Kolmogorov湍流中的光束漂移

Complex degree of coherence measurement for classical statistical fields.

We propose a new method for measuring real and imaginary parts of the complex degree of coherence of a classical field obeying Gaussian statistics. Our method is based on mixing incoherently a coherent Gaussian beam, a local oscillator, and the statistical field. We stress that our approach is especially beneficial for revealing the complex degree of coherence of inhomogeneous two-dimensional fields. As an illustration, we report the complex degree of the coherence measurement of a complex Gaussian-correlated beam. Our method can find applications in image transmission and recovery.