Twisted Gaussian Schell-model Beams Research Articles

Propagation of the COAM matrix of a twisted Gaussian Schell-model beam

The Coherence-Orbital Angular Momentum (COAM) matrix elements of an optical beam describe its mode-to-mode radial correlations. An analytic expression for the COAM matrix of a Twisted Gaussian Schell-Model (TGSM) beam propagating in a vacuum is derived and analyzed in detail, with the help of the Huygens–Fresnel integral. Additionally, we show how to recover the cross-spectral density of the TGSM beam from its COAM matrix, expressing the result in an elegant symmetric form. Due to the unique properties of the TGSM beam, the analysis of its individual OAM correlations will deliver further insight for their applications to imaging, laser communication, optical tweezers, and other modalities.

Coherence-OAM matrix properties of a twisted Gaussian Schell model beam.

Based on the cross-spectral density (CSD) function, the coherence-orbital angular momentum (COAM) matrix of twisted Gaussian Schell-model (TGSM) beam is proposed, and the COAM matrix is used to describe the correlation between OAM modes in TGSM optical field. The COAM matrix characteristics of TGSM beam are analyzed by numerical simulation. The results show that the COAM matrix characteristics of TGSM beam depend on the initial parameters of the beam. In addition, a method of generating TGSM beam by superposition of COAM matrix element modes is described, and the influence of different initial parameters on the superposition characteristics is studied. The results reveal the internal relationship between the coherent structure of the optical field, the twist phase and the OAM modes. Our work helps to explore new expressions of partially coherent beams and promote the practical application of optimizing partially coherent beams.

Twisted Gaussian Schell-model breathers and solitons in strongly nonlocal nonlinear media.

Based on the Snyder-Mitchell linear model and the cross-spectral density (CSD) function, the analytical propagation formula of twisted Gaussian Schell-model (TGSM) beams in strongly nonlocal nonlinear medium (SNNM) is derived. Then the propagation characteristics of TGSM beam are studied. It is found that the soliton radius is jointly determined by the initial power, coherence length, and twist factor; the degree of spatial coherence is adjusted by changing the twist factor without affecting the soliton intensity. In the case of non-soliton properties, there is a threshold of coherence length which makes partially coherent beams have the same evolution law as completely coherent beams. Furthermore, increasing the twist factor, decreasing the coherence length and initial power can improve the beam quality of the beam propagating in SNNM.

Experimental synthesis of partially coherent beam with controllable twist phase and measuring its orbital angular momentum

Abstract Twist phase is a nontrivial second-order phase that only exists in a partially coherent beam. Such twist phase endows the partially coherent beam with orbital angular momentum (OAM) and has unique applications such as in super-resolution imaging. However, the manipulation and the detection of the twist phase are still far from easy tasks in experiment. In this work, we present a flexible approach to generate a famous class of twisted Gaussian Schell-model (TGSM) beam with controllable twist phase by the superposition of the complex field realizations using a single phase-only spatial light modulator. The precise control of the amplitude and phase of the field realizations allows one to manipulate the strength of the twist phase easily. In addition, we show that the twist factor, a key factor that determines the strength of twist phase and the amount of OAM, can be measured by extracting the real part of the complex degree of coherence of the TGSM beam. The experiment is carried out with the help of the generalized Hanbury Brown and Twiss experiment as the generated TGSM beam obeys Gaussian statistics. The flexible control and detection of the twist phase are expected to find applications in coherence and OAM-based ghost imaging.

Influence of Kerr nonlinearity on propagation characteristics of twisted Gaussian Schell-model beams.

The analytical propagation formulae of twisted Gaussian Schell-model (TGSM) beams through nonlinear Kerr media are derived. It is found that a TGSM beam is less sensitive to Kerr nonlinearity than a Gaussian Schell-model (GSM) beam. Furthermore, the propagation characteristics of TGSM beams with stronger twist and worse spatial coherence are less affected by Kerr nonlinearity. The self-focusing effect enhances the beam twist, but degrades the beam spatial coherence. In the atmosphere (one kind of self-focusing media), a TGSM beam has greater resistance to self-focusing effects and atmospheric turbulence effects than a GSM beam or an ideal Gaussian beam.

Evolution properties of the orbital angular momentum spectrum of twisted Gaussian Schell-model beams in turbulent atmosphere.

We derive the analytical formula of the energy weight of each orbital angular momentum (OAM) mode of twisted Gaussian Schell-model (TGSM) beams propagating in weak turbulent atmosphere. The evolution of its OAM spectrum is studied by numerical calculation. Our results show that the OAM spectrum of a TGSM beam changes with the beam propagating in turbulent atmosphere, which is completely different from that of the TGSM beam propagating in free space. Furthermore, influences of the source parameters and the turbulence parameters on the OAM spectrum of a TGSM beam in turbulent atmosphere are analyzed. It is found that the source parameters and turbulence parameters, such as twist factor, coherence length, beam waist size, and structure constant, have a significant influence on the OAM spectrum, but the value of the wavelength and inner scale have little influence. Increasing the beam waist size or decreasing the coherence length would lead to the OAM spectrum broadened in the source plane, but would be robust for the OAM modes of the TGSM beam in the turbulent atmosphere. It is clear that the bigger the value of the twist factor, the more asymmetric the OAM mode of the TGSM beam is, and the better mode distribution can be maintained when it propagates in turbulent atmosphere. Our results have potential applications in reducing the error rate of free-space optical communication and detecting the atmospheric parameters.

Ghost Imaging with a Partially Coherent Beam Carrying Twist Phase in a Turbulent Ocean: A Numerical Approach

Ghost imaging (GI) is an indirect imaging approach that can retrieve an object’s image even in a harsh environment through measuring the fourth-order correlation function (FOCF) between the signal and idle optical paths. In this paper, we study lensless GI with a partially coherent beam carrying twist phase, i.e., twisted Gaussian Schell-model (TGSM) beam, in the presence of oceanic turbulence. Explicit expression of the FOCF is derived based on the optical coherence theory and Rytov approximation, and the effects of the twist phase and the oceanic turbulence on the quality and visibility of image are investigated in detail through numerical examples. Our results show that the simulated oceanic turbulence strongly affects the GI. The quality of image decreases monotonously with an increase of the strength of turbulence whereas the visibility increases. When the illumination light carries a twist phase, the visibility of the image is improved while the quality of the image is reduced in contrast to those without a twist phase. By properly selecting the strength of the twist phase, the image can still be maintained at an acceptable level of quality with high visibility. Furthermore, it is found that the quality and visibility of the ghost image are less affected by the oceanic turbulence using a TGSM beam with larger twist factor. Our findings will be useful for the application of GI in an oceanic turbulent environment.

Generating bona fide twisted Gaussian Schell-model beams.

We experimentally realize bona fide twisted Gaussian Schell-model (TGSM) beams by converting an anisotropic GSM beam into a TGSM beam with a set of just three cylindrical lenses. In contrast to the previously reported experimental technique for generating TGSM beams, we are able to explicitly generate anisotropic GSM beams with simultaneously controlled beam widths and transverse coherence lengths along two mutually orthogonal directions, prior to converting them to genuine TGSM beams.

Second-order moments of a twisted Gaussian Schell-model beam in anisotropic turbulence

Analytical formulas for the Wigner distribution functions and the second-order moments (SOMs) of a twisted Gaussian Schell-model (TGSM) beam propagating through anisotropic turbulence have been derived by means of a tensor method. It is found that the propagation law for the SOMs of a TGSM beam spreading in turbulence can be described as a first-order optical systems propagation law with an additional turbulence-induced effect. Based on the SOMs, second-order statistics in terms of the effective beam width, the M2-factor, the orbital angular momentum flux, and the effective radius curvature are analyzed in detail. One finds that the anisotropic turbulence leads to an anisotropic spreading of light beams, and a TGSM beam is less affected by turbulence than a Gaussian Schell-model beam without the twist phase. For short distance propagation, the light beam is more sensitive to the initial beam parameters than turbulence parameters, while for sufficiently long transmission distance, the beam characteristics are determined at most by turbulence statistics. The method can be extended to study the propagation characteristics of various coherent and partially coherent complex Gaussian beams, such as flat-topped beams, dark hollow beams, and array beams in turbulence, and promotes important supports in free-space optical communications and remote sensing.

Entanglement and Complete Positivity: Relevance and Manifestations in Classical Scalar Wave Optics

AbstractEntanglement of states and Complete Positivity of maps are concepts that have achieved physical importance with the recent growth of quantum information science. They are however mathematically relevant whenever tensor products of complex linear (Hilbert) spaces are involved. We present such situations in classical scalar paraxial wave optics where these concepts play a role: propagation characteristics of coherent and partially coherent Gaussian beams; and the definition and separability of the family of Twisted Gaussian Schell Model (TGSM) beams. In the former, the evolution of the width of a projected one‐dimensional beam is shown to be a signature of entanglement in a two‐dimensional amplitude. In the latter, the partial transpose operation is seen to explain key properties of TGSM beams.

Statistical properties of a radially polarized twisted Gaussian Schell-model beam in an underwater turbulent medium.

Average intensity and the normalized powers of the completely polarized and the completely unpolarized portions of a radially polarized twisted Gaussian Schell-model (TGSM) beam propagating in underwater turbulence are examined. In our formulation, our previously obtained atmospheric turbulence solution for the same radially polarized TGSM beam using the extended Huygens-Fresnel principle is utilized, with the inclusion of our recently derived expression for the atmospheric turbulence structure constant in terms of underwater turbulence parameters. Effects of the rate of dissipation of mean-squared temperature, rate of dissipation of kinetic energy per unit mass of fluid, kinematic viscosity, and the contribution of the temperature-to-salinity ratio to the refractive index spectrum on the average intensity, and the normalized powers of the completely polarized and completely unpolarized portions of a radially polarized TGSM beam propagating in underwater turbulence are presented.

Propagation of a radially polarized twisted Gaussian Schell-model beam in turbulent atmosphere

Propagation properties of a scalar twisted Gaussian Schell-model (TGSM) beam in turbulent atmosphere has been studied in detail. In this paper, we explore the propagation properties of a radially polarized TGSM beam in turbulent atmosphere. Analytical formulae for the elements of the cross-spectral density matrix of a radially polarized TGSM beam propagating in turbulent atmosphere are derived based on the extended Huygens–Fresnel integral. We find that the atmospheric turbulence induces degeneration of the intensity distribution and depolarization of a radially polarized TGSM beam on propagation, while the twist phase plays a role in anti-degradation and anti-depolarization. Furthermore, we also find that the twist phase induces not only the rotation of the beam spot but also changes of the state of polarization on propagation, which are caused by the fact that the twist phase imposes orbital angular momentum on the beam. Thus, the twist phase can be used to control the propagation properties of radially polarized partially coherent beam. Our results will be useful in some applications, such as optical trapping and free-space optical communications.

Twisted Gaussian Schell-model beams as series of partially coherent modified Bessel-Gauss beams.

We show that twisted Gaussian Schell-model (TGSM) beams can be represented through an incoherent superposition of partially coherent beams carrying optical vortices and whose cross-spectral densities are expressed in terms of modified Bessel functions. Moreover, starting from this result, we show that the modal expansion of the cross-spectral density of a TGSM source can be directly obtained through simple mathematics.

Evolution properties of a twisted Gaussian Schell-model beam in a uniaxial crystal

Paraxial propagation of a linearly polarised twisted Gaussian Schell-model (TGSM) beam in a uniaxial crystal is investigated. With the help of a tensor method, an analytical formula for the cross-spectral density (CSD) of a TGSM beam propagating in a uniaxial crystal orthogonal to the optical axis is derived. The evolution properties of the intensity distribution, the coherence widths and the twist factor of a TGSM beam in a uniaxial crystal are illustrated numerically. It is shown that the TGSM beam becomes an anisotropic TGSM beam in a uniaxial crystal and its evolution properties are closely related with its initial coherence, twist factor and the parameters of the crystal. The uniaxial crystal provides an effective way for modulating the properties of a TGSM beam, which will be useful in some applications, such as free-space optical communications and nonlinear optics, where a partially coherent beam with controlled beam profile and twist factor is required.

Second-order statistics of a twisted Gaussian Schell-model beam in turbulent atmosphere

We present a detailed investigation of the second-order statistics of a twisted gaussian Schell-model (TGSM) beam propagating in turbulent atmosphere. Based on the extended Huygens-Fresnel integral, analytical expressions for the second-order moments of the Wigner distribution function of a TGSM beam in turbulent atmosphere are derived. Evolution properties of the second-order statistics, such as the propagation factor, the effective radius of curvature (ERC) and the Rayleigh range, of a TGSM beam in turbulent atmosphere are explored in detail. Our results show that a TGSM beam is less affected by the turbulence than a GSM beam without twist phase. In turbulent atmosphere the Rayleigh range doesn't equal to the distance where the ERC takes a minimum value, which is much different from the result in free space. The second-order statistics are closely determined by the parameters of the turbulent atmosphere and the initial beam parameters. Our results will be useful in long-distance free-space optical communications.

Radiation force of scalar and electromagnetic twisted Gaussian Schell-model beams

Radiation force of a focused scalar twisted Gaussian Schell-model (TGSM) beam on a Rayleigh dielectric sphere is investigated. It is found that the twist phase affects the radiation force and by raising the absolute value of the twist factor it is possible to increase both transverse and longitudinal trapping ranges at the real focus where the maximum on-axis intensity is located. Numerical calculations of radiation forces induced by a focused electromagnetic TGSM beam on a Rayleigh dielectric sphere are carried out. It is found that radiation force is closely related to the twist phase, degree of polarization and correlation factors of the initial beam. The trapping stability is also discussed.

Ghost imaging with twisted Gaussian Schell-model beam

Based on the classical optical coherence theory, ghost imaging with twisted Gaussian Schell-model (GSM) beams is analyzed. It is found that the twist phase of the GSM beam has strong influence on ghost imaging. As the absolute value of the twist factor increases, the ghost image disappears gradually, but its visibility increases. This phenomenon is caused by the fact that the twist phase enhances the transverse spatial coherence of the twisted GSM beam on propagation.

衍射扭曲高斯谢尔模型光束在远场的光谱移动和光谱开关

衍射扭曲高斯谢尔模型光束在远场的光谱移动和光谱开关

Focusing properties of twisted Gaussian Schell-model beams passing through a system: The aperture lens or the aperture and lens separated

Starting from the propagation law of partially coherent light, the focusing properties of twisted Gaussian Schell-model (TGSM) beams passing through an optical system consisting of an aperture lens or through a system consisting of a separated aperture and lens are studied. The propagation expressions for focused TGSM beams have been derived. Our main attention is focused on the effect of the coherence of partially coherent light, the twist parameter and the distance between the aperture and lens on the focusing properties of TGSM beams. Numerical calculation results are given to illustrate how the coherence of partially coherent light, the twist parameter and the distance between the aperture and lens affect the axial irradiance in the focused field.

Spectral shifts and spectral switches of twisted Gaussian Schell-model beams passing through an aperture

Starting from the propagation law of partially coherent light, the spectrum of twisted Gaussian Schell-model (TGSM) beams passing through an aperture is studied. Detailed numerical calculation results are presented, and illustrated. It is shown that the spectral shifts and switches can also take place for TGSM beams, and as compared with the aberration-free Gaussian Schell-model (GSM) beams case, the twist factor affects the spectral shifts and spectral switches. Numerical calculation results are given to illustrate how the twist factor affects the spectral behavior.