Spectral Degree Of Coherence Research Articles

Propagation Properties of Gaussian Schell-Model Beam Array in the Jet Engine Exhaust Induced Turbulence

The effects of the jet engine turbulence on a Gaussian Schell-Model (GSM) beam array propagating in a jet engine plume are studied theoretically. The analytical expressions of the cross-spectral density (CSD) function, the spectral degree of coherence (DOC) and the mean-squared beam width for a GSM beam array propagating through a jet engine plume region are derived based on the extended Huyens-Fresnel integral. It is found that the profile of spectral density and the DOC of a GSM beam array gradually transfer to an elliptical shape as the propagation distance increases, and the elliptical degree becomes greater with increasing source coherence length. Besides, as the source coherence length decreases, the effect of the jet engine turbulence on the beam broadening is smaller and the profile of the DOC appears sidelobes at short distance. It is also found that the values of effective coherence width nearly remain the same for different values of source coherence length after propagating a certain distance. Furthermore, the effects of the number of beamlets on the beam width and effective coherence width are investigated in detail.

Self-reconstruction of twisted Laguerre-Gaussian Schell-model beams partially blocked by an opaque obstacle.

Twisted Laguerre-Gaussian Schell model (TLGSM) beams are a novel type of partially coherent beams, which carry the twist phase and the vortex phase simultaneously. In this paper, the self-reconstruction (SR) of the TLGSM beam partially blocked by an opaque obstacle and propagating through a thin lens focusing system is studied in detail. Implementing the pseudo-mode expansion method, we represent the TLGSM beam as a superposition of spatially coherent modes, which is applicable for calculating the cross spectral density (CSD) and spectral degree of coherence (SDOC) of such a beam using the Fourier transform. The numerical results reveal that the twist parameter, a measure of the strength of a twist phase, determines the characteristics of the SR. In the case of the topological charge of the vortex is positive, the SR capability of spectral density is significantly improved with the increase of the twist parameter. The physical mechanism behind these phenomena is analyzed in detail from the point view of mode expansion. Further, the dependence of the side ring intensity and SR capability of the SDOC on the twist parameter are also investigated. It is found that the SR capability and side ring intensity of the SDOC are simultaneously enhanced for a large twist parameter, providing an efficient way to determine the number of topological charge. Our study results may find application in communication and information recovery applications.

Propagation characteristics of a partially coherent self-shifting beam in random media.

In a recent publication [Opt. Lett.43, 4727 (2018)OPLEDP0146-959210.1364/OL.43.004727], a novel class of partially coherent sources with complex degrees of coherence was introduced. In this paper, we obtain the expression of the cross-spectral density function of the self-shifting beam generated from a light source propagating in random media. Then we calculated and simulated the behaviors of the spectral density and the spectral degree of coherence in the propagation. The results show that there will be a phenomenon of self-shifting in propagation, and the coherence of the beam is Gaussian when it is far enough from the light source. The light intensity is weakened with an increase in turbulence, while the wander of the center of the spectral density remains unchanged in different media.

Propagation of Gaussian Schell-model beams through a jet engine exhaust.

Theoretical predictions of light beam interactions with jet engine exhaust are of importance for optimization of various optical systems, including LIDARs, imagers and communication links operating in the vicinity of aircrafts and marine vessels. Here we extend the analysis previously carried out for coherent laser beams propagating in jet engine exhaust, to the broad class of Gaussian Schell-Model (GSM) beams, being capable of treating any degree of coherence in addition to size and radius of curvature. The analytical formulas for the spectral density (SD) and the spectral degree of coherence (DOC) of the GSM beam are obtained and analyzed on passage through a typical jet engine exhaust region. It is shown that for sources with high coherence, the transverse profiles of the SD and the DOC of the GSM beams gradually transition from initially circular to elliptical shape upon propagation at very short ranges. However, such transition is suppressed for sources with lower coherence and disappears in the incoherent source limit, implying that the GSM source with low source coherence is an excellent tool for mitigation of the jet engine exhaust-induced anisotropy of turbulence. The physical interpretation and the illustration are included.

Twisted rectangular Laguerre–Gaussian correlated sources in anisotropic turbulent atmosphere

The ability to impress twist phase on random sources has led to new insights into coherence theory as well as important applications in optical tweezers and optical communications. In the paper, a new class of twisted sources named rectangular Laguerre–Gaussian correlated (TRLGC) fields is introduced based on a superposition of a mutually incoherent, tilted and displaced partially coherent beams. The analytical expressions for the cross-spectral density and the second-order moments of a TRLGC beam propagating through anisotropic non-Kolmogorov turbulent atmosphere are derived. The evolution characteristics of a TRLGC beam such as the spectral intensity, the spectral degree of coherence, and the beam quality are investigated in detail. It is shown that higher values of twist factor can significantly suppress the anisotropic beam spreading induced by the anisotropy of turbulence. Moreover, owing to the twist phase and higher-order coherence parameter, the anti-turbulence capability of partially coherent beams is further enhanced. For anticipated atmospheric communication channel conditions, a comprehensive selection of initial beam parameters, receiver aperture size and receiver capability, etc., is very important. Our work is helpful for exploring new forms of twistable sources and enriches potential applications of novel partially coherent beams in free space optical communications.

The spectral properties of a partially coherent Lommel-Gaussian beam in turbulent atmosphere

Based on the extended Huygens–Fresnel principle, the analytical propagation equations of a partially coherent Lommel-Gaussian (PCLG) beam propagating in atmospheric turbulence have been introduced. The spectral properties of the PCLG beam in turbulent atmosphere are explored. It is found by numerical simulations that after propagating in turbulent atmosphere, the intensity distribution and spectral degree of coherence (SDOC) of the PCLG beam vary on propagation. The intensity distribution of the PCLG beam depends closely on the strength of atmospheric turbulence and the parameters of the source beam, and will eventually transform into a Gaussian profile at the receiver plane. In addition, with smaller OAM quantum number and structure constant or bigger wavelength, the SDOC of the PCLG beam spreads more rapidly. The results are expected to be useful for understanding the properties of the Lommel-Gaussian beam in turbulence.

Spatial coherence mapping of structured sources: a flexible instrument for solar studies.

We conceptually describe and design, to first order, an instrument to locally map the spatial coherence of extended and structured sources, such as fiber bundles or the Sun, considered as a mosaic of individual solar cells, which is our main motivation. Our solar coherence instrument (SCI) is an instrument for an afocal solar space telescope; the light from its exit pupil dynamically selects one individual solar cell at a time and performs a series of Young-like experiments with different baselines in order to measure the spectral degree of coherence and therefore the effective correlation length that can be assigned for that solar cell. SCI needs flexibility in terms of selective imaging and Young experiments, which is provided by two digital micromirror devices (DMDs), a technology currently under space qualification. SCI is a compact instrument based on retroreflections, and it generates all data required to image the source, to select the cells, and to implement sequentially a series of Young apertures on a re-imaged pupil. It was designed using the (already launched) Hinode solar optical telescope as a baseline, and the first estimation of the SNR, using commercial DMDs and array sensors, while measuring the modulation of Young interference fringes validates our first-order design.

Field Correlations in Surface Plasmon Speckle

In this work fluctuations in the electric field of surface plasmon polaritons undergoing random scattering on a rough metallic surface are considered. A rigorous closed form analytic expression is derived describing second order correlations in the resulting plasmon speckle pattern assuming statistically stationary and isotropic roughness. Partially coherent planar Schell-model source fields can also be described within the developed framework. Behaviour of the three-dimensional degree of cross polarisation and spectral degree of coherence is also discussed. Expressions derived take full account of dissipation in the metal with non-universal behaviour exhibited within the correlation length of the surface and source fields.

Phase detection of coherence singularities and determination of the topological charge of a partially coherent vortex beam

In the theory of partial coherence, coherence singularities can occur in the spectral degree of coherence (SDOC): in case the fields at two different points are completely uncorrelated, the phase of the SDOC is undefined. For a partially coherent vortex beam, the detection of coherence singularities is linked to the measurement of topological charge, whose magnitude equals the number of ring dislocations in its far field amplitude. However, the phase distribution of coherence singularities is rarely mentioned in the literature and the amplitude distribution can hardly reflect the sign of topological charge. In this letter, we present a phase-analysis method for measuring the coherence singularities by introducing a movable perturbation at a certain point in an illumination window of a finite size. Using the proposed method, we measure experimentally the coherence singularities of a partially coherent vortex beam in the focal plane. From the results, the magnitude and sign of the topological charge can be determined simultaneously from the phase distribution of the coherence singularities. Our results can find application in information transmission.

Nonparaxial Propagation Properties of Specially Correlated Radially Polarized Beams in Free Space

A specially correlated radially polarized (SCRP) beam with unusual physical properties on propagation in the paraxial regime was introduced and generated recently. In this paper, we extend the paraxial propagation of an SCRP beam to the nonparaxial regime. The closed-form 3 × 3 cross-spectral density matrix of a nonparaxial SCRP beam propagating in free space is derived with the aid of the generalized Rayleigh–Sommerfeld diffraction integral. The statistical properties, such as average intensity, degree of polarization, and spectral degree of coherence, are studied comparatively for the nonparaxial SCRP beam and the partially coherent radially polarized (PCRP) beam with a conventional Gaussian–Schell-model correlation function. It is found that the nonparaxial properties of an SCRP beam are strikingly different from those of a PCRP beam. These nonparaxial properties are closely related to the correlation functions and the beam waist width. Our results may find potential applications in beam shaping and optical trapping in nonparaxial systems.

Generation of an Adjustable Optical Cage through Focusing an Apertured Bessel-Gaussian Correlated Schell-Model Beam

An adjustable optical cage generated by focusing a partially coherent beam with nonconventional correlation function named the Bessel–Gaussian correlated Schell-model (BGCSM) beam is investigated in detail. With the help of the generalized Huygens–Fresnel integral and complex Gaussian function expansion, the analytical formula of the BGCSM beam passing through an apertured ABCD optical system was derived. Our numerical results show that the generated optical cage can be moderately adjusted by the aperture radius, the spatial coherence width, and the parameter β of the BGCSM beam. Furthermore, the effect of these parameters on the effective beam size and the spectral degree of coherence were also analyzed. The optical cage with adjustable size can be applied for particle trapping and material thermal processing.

Twisted Laguerre-Gaussian Schell-model beam and its orbital angular moment.

It is well known that a light beam with vortex phase or twist phase carries orbital angular momentum (OAM), while twist phase only exists in a partially coherent beam. In this paper, we introduce a new partially coherent beam, named twisted Laguerre-Gaussian Schell-model (TLGSM) beam. This TLGSM beam carries both vortex phase and twist phase. Further, the evolutional properties of the spectral density and spectral degree of coherence (SDOC)] of the TLGSM beam passing through a paraxial ABCD optical system are explored in detail. Our results reveal that the vortex and twist phases' handedness significantly affects the evolution properties. When the twist phase's handedness is the same as that of the vortex phase, the beam profile maintains a dark hollow shape during propagation and the side rings in SDOC are suppressed; however, when the handedness of two phases is opposite, then the beam shape evolves into a Gaussian shape and the side rings in SDOC are enhanced. Furthermore, we obtain the analytical expression for the OAM of the TLGSM beam. It is found that the vortex phase's and twist phase's contributions to the OAM are interrelated, which greatly increases the amount of OAM. In addition, the OAM variation of the TLGSM beam passing through an anisotropic optical system is also explored in detail. Our results will be useful for information transfer and optical manipulations.

Evolution properties of the radially polarized multi-Gaussian Schell-model beam in uniaxial crystals.

The evolution properties of the normalized intensity distribution, the spectral degree of coherence (SDOC), and the spectral degree of polarization (SDOP) of the radially polarized multi-Gaussian Schell-model (MGSM) beam in uniaxial crystals are illustrated. Numerical results show that the intensity distribution of the radially polarized MGSM beam gradually evolves from a doughnut shape into an elliptical symmetric flattop shape and retains its elliptical flattop shape on further propagation in anisotropic crystals. The evolution behavior of the SDOC and SDOP for the radially polarized MGSM beam is quite different from that of the linearly polarized one. In addition, the influences of the spatial coherence length δ0, beam index M, and the ratio of the extraordinary refractive index to the ordinary refractive index ne/no of the uniaxial crystals on the evolution properties of the normalized intensity distribution, the SDOC, and the SDOP of the radially polarized MGSM beam are discussed in detail.

Evolution properties of a Gaussian Schell-model Array beam in a uniaxial crystal orthogonal to the optical axis

The analytical formulas of the Gaussian Schell-model Array (GSMA) beams propagating in a uniaxial crystal orthogonal to the optical axis are derived. The evolution properties of the spectral density, the spectral degree of coherence (SDOC), and the effective beam width of the GSMA beams in a uniaxial crystal are investigated in detail. It is shown that a GSMA beam exhibits splitting property inside a uniaxial crystal, and the propagation properties are closely related with parameters of the uniaxial crystal and beam parameters. The results provide a way for the modulation of the GSMA beam.

Propagation properties of rectangular Laguerre–Gaussian-correlated Schell-model beams in atmospheric turbulence

ABSTRACTBased on the extended Huygens–Fresnel principle and the second-order moments of the Wigner distribution function (WDF), the analytical expressions for the cross-spectral density (CSD) and the propagation factor of a rectangular Laguerre–Gaussian-correlated Schell-model (LGCSM) beam propagating in atmospheric turbulence are derived. The statistical properties, such as the average intensity, the spectral degree of coherence (SDOC) and the propagation factor, of a rectangular LGCSM beam in free space and atmospheric turbulence are comparatively analysed. It is illustrated that a rectangular LGCSM beam exhibits self-splitting and combing properties on propagation in atmospheric turbulence, and the self-splitting properties of such beam are closely related to its beam orders m and n, which is quite different from other self-splitting beams. In addition, the rectangular LGCSM beam has an advantage for reducing the turbulence-induced degradation compared with the conventional partially coherent beams.

Propagation Characteristics of a Twisted Cosine-Gaussian Correlated Radially Polarized Beam

Recently, partially coherent beams with twist phases have attracted growing interest due to their nontrivial dynamic characteristics. In this work, the propagation characteristics of a twisted cosine-Gaussian correlated radially polarized beam such as the spectral intensity, the spectral degree of coherence, the degree of polarization, the state of polarization, and the spectral change are investigated in detail. Due to the presence of the twisted phase, the beam spot, the degree of coherence, and the state of polarization experience rotation during transmission, but the degree of polarization is not twisted. Meanwhile, although their rotation speeds closely depend on the value of the twist factor, they all undergo a rotation of π / 2 when they reach the focal plane. Furthermore, the effect of the twist phase on the spectral change is similar to the coherence, which is achieved by modulating the spectral density distribution during transmission. The twist phase opens up a useful guideline for manipulation of novel vector structure beams and enriches potential applications in the field of beam shaping, optical tweezers, optical imaging, and free space optical communications.

Coherence properties of a random electromagnetic vortex beam propagating in biological tissues

ABSTRACTBased on the extended Huygens-Fresnel principle and the unified theory of polarization and coherence, the coherence properties of random electromagnetic Gaussian Schell model (GSM) vortex beams propagating through biological tissues were investigated. It was shown that with an increasing propagation distance, the change in the spectral degree of coherence |μ(ρ, −ρ, z)| is more complex than that of μ(0, ρ, z). If the change in |μ(ρ, −ρ, z)| is divided into the preceding and latter stages, then the change in μ(0, ρ, z) is similar to that of |μ(ρ, −ρ, z)| at the latter stage. The wavelength of the far-infrared beam (λ = 10.6 µm) is similar to that emitted by the biological tissues, and a resonance with water molecules occurs in the biological tissues. At the initial plane, the larger ρx corresponds to a smaller value of |μ(ρ, −ρ, z)|, and during the propagation process, the spatial coherent interval is wider for |μ(ρ, −ρ, z)| than for μ(0, ρ, z). The fluctuation change depth of |μ(ρ, −ρ, z)| in the biological tissues is somewhat shallower than that of μ(0, ρ, z) under the same conditions, such as the same biological tissue, the same wavelength, or the same interval between two field points. In addition, the spatial self-correlation length σyy has an effect on |μ(ρ, −ρ, z)| and on μ(0, ρ, z) to a different extent, while the changes in these two quantities are independent of the spatial mutual-correlation length σxy of the random electromagnetic GSM vortex beam.

Polarization properties of stochastic electromagnetic beams modulated by a wavefront-folding interferometer.

We consider the field generated by a wavefront-folding interferometer which is illuminated by a stochastic electromagnetic beam. The specular property and anti-specular property are discussed in the vector case. Take electromagnetic Gaussian Schell-model beam as an example, we investigate the spectral density, the spectral degree of coherence, the spectral degree of polarization as well as the state of polarization of the polarized portion of the field on propagation. Results show that the polarization properties including the degree of polarization, the orientation angle and the degree of ellipse can be adjusted by the phase difference of the interferometer and the phase retardation introduced by the prism. The results may be applied in free-space optical communication.

Experimental Bell violations with classical, non-entangled optical fields

We report experiments in which the Bell parameter S that enters the Clauser–Horne–Shimony–Holt inequality: , attains values . In our experiments, we used two spatially separated optical beams, the electric fields of which were correlated to one another. The amount of correlation was quantified by the spectral degree of coherence . This quantity measures the correlation between fields that exist at two distant locations and whose respective polarizations are given in terms of angles α and β, which can be set independently from one another. Such a correlation qualifies for the construction of the Bell parameter S. By changing the amount of field correlation, we could cover a range that goes from to . Our experimental findings should provide useful material for the ongoing, theoretical discussions about the quantum–classical border.

Evolution properties of a radial phased-locked partially coherent Lorentz-Gauss array beam in oceanic turbulence

The concept of a radial phased-locked partially coherent Lorentz-Gauss array (PCLGA) beam generated by a Schell-model source has been introduced. Based on the Huygens-Fresnel principle, the analytical expressions for the cross-spectral density function of a radial phased-locked PCLGA beam propagation in oceanic turbulence has been derived. The average intensity and coherence properties of a radial phased-locked PCLGA beam propagating in oceanic turbulence are illustrated using numerical examples. The influences of coherence length and oceanic turbulence on the evolution properties and spectral degree of coherence are analyzed in details. The results show that radial phased-locked PCLGA beam propagation in stronger oceanic turbulence will evolve into Gaussian-like beam more rapidly as the propagation distance increases.