Self-imaging of partially coherent light in graded-index media

Measuring the orbital angular momentum of generalized higher-order twisted partially coherent beams

Recently a new family of partially coherent fields incorporating generalized inseparable cross-coupled phases named generalized higher-order twisted partially coherent beams (GHTPCBs) have been introduced. The twist factor u is a key parameter that not only quantifies the strength of the generalized cross-coupled phase for a given order, but also determines the amount of the concomitant orbital angular momentum (OAM). In this paper, we propose a simple and reliable method to measure the factor u using a two-pinhole mask. Without need of complicated optical system, it only requires to capture the far-field diffraction intensity distribution of the GHTPCB passing through the mask. By analyzing the Fourier spectrum of the intensity distribution, the value of twist factor can be derived nearly in real time. The influence of the separation distance between two pinholes and the pinholes' diameter and position on the measurement accuracy are thoroughly studied both in theory and experiment. The experimental results agree well with the theoretical results. Our methodology can also be extended to measure the sole factor of similar position dependent phases such as the topological charge of a vortex phase.

Fast measurement of coherence-orbital angular momentum matrices of random light beams using off-axis holography and coordinate transformation

We propose an effective protocol to measure the coherence-orbital angular momentum (COAM) matrix of an arbitrary partially coherent beam. The method is based on an off-axis holography scheme and the Cartesian-polar coordinate transformation, which enables to simultaneously deal with all the COAM matrix elements of interest. The working principle is presented and discussed in detail. A proof-of-principle experiment is carried out to reconstruct the COAM matrices of partially coherent beams with spatially uniform and non-uniform coherence states. We find an excellent agreement between the experimental results and the theoretical predictions. In addition, we show that the OAM spectrum of a partially coherent beam can also be directly acquired from the measured COAM matrix.

Sharp focusing of partially coherent Bessel-correlated beams by a graded-index lens

The nonparaxial focusing of partially coherent Bessel-correlated beams carrying vortices by a graded-index lens is investigated using the decomposition of the incident field into coherent modes and the quantum mechanical operator method. The influence of the coherence state and the incident beam aperture on tight focusing is analyzed. Our results show that a partially coherent Bessel-correlated beam can be focused into a spot of smaller size than coherent light.

Focusing of partially coherent light by a graded-index lens

We use coherence theory to study how the focusing of an optical beam by a graded-index (GRIN) lens is affected when the incoming beam is only partially coherent. The Gaussian-Schell model is used to show that the intensity of a partially coherent beam exhibits self-imaging and evolves in a periodic fashion in a GRIN medium with a parabolic index profile. Spatial coherence of the beam affects a single parameter that governs how much the beam is compressed at the focal point. Our results show that the focal spot size depends on the fraction of the beam's diameter over which coherence persists. Focusing ceases to occur, and the beam may even expand at the focal point of a GRIN lens, when this fraction is below 10%.

Propagation of Gaussian Schell-model beams in modulated graded-index media

The evolution of partially coherent beams in longitudinally modulated graded-index media is studied. The special cases of Gaussian Schell-model beams and parametric modulation, when the modulation period is half the fiber self-imaging period, are examined in detail. We show that the widths of the intensity and coherence of Gaussian Schell-model beams undergo amplification in parametrically modulated parabolic graded-index media. The process is an analog of quantum mechanical parametric amplification and generation of squeezed states. Our work may find application in spatial and temporal imaging of partially coherent beams in fiber-based imaging systems.

Vortex preserving statistical optical beams

We establish a general form of the cross-spectral density of statistical sources that generate vortex preserving partially coherent beams on propagation through any linear ABCD optical system. We illustrate our results by introducing a class of partially coherent vortex beams with a closed form cross-spectral density at the source and demonstrating the beam vortex structure preservation on free space propagation and imaging by a thin lens. We also show the capacity of such vortex preserving beams of any state of spatial coherence to trap nanoparticles with the refractive index smaller than that of a surrounding medium.

Change in phase singularities of a partially coherent Gaussian vortex beam propagating in a GRIN fiber

In this paper, we have derived the analytical formulae for the cross-spectral densities of partially coherent Gaussian vortex beams propagating in a gradient-index (GRIN) fiber. In numerical analysis, the variations of the intensity and the phase distributions are demonstrated to illustrate the change in singularities within a GRIN fiber. It turns out that the beam intensity and phase distribution change periodically in the propagation process. The partially coherent Gaussian vortex beams do not typically possess the center intensity zero in the focal plane, which usually called 'hidden' singularities in intensities detection. We demonstrated the phase singularities more clearly by the phase distribution, one finds that the phase vortex of a partially coherent beam will crack near the focus, and opposite topological charge will be generated, we attribute to the wave-front decomposition and reconstruction of the vortex beams by the GRIN fiber. Our results show that the change in phase singularities not only affected by the GRIN fiber, but also by the initial coherence of the beam source, and high initial coherence will be more conducive to maintaining the phase singularities in the propagation. Our results may find applications in singular optics, wave-front reconstruction and optical fiber communications.

Three-dimensional localized Airy-Gaussian wave packets in a gradient-index medium

By solving the Schrödinger equation in spatial and temporal coordinates, the exact solution of the chirped Airy-Gaussian (CAiG) wave packets in a gradient-index medium is obtained. Based on that, we conduct a theoretical analysis about the properties of CAiG wave packets and discover that the chirp factor, the distribution factor, the initial velocity, as well as the propagation distance have an effect on the wave packets in both the propagation process and the spatiotemporal profiles. Among these, the Gaussian distribution factor, which is first added to the initial pulses, also alters the peculiarities of the Airy-Gaussian beams in the temporal domain and spatial domain. In addition, the investigation about the radiation force illuminates certain evolution properties of the CAiG wave packets well.

Self-steering partially coherent vector beams

We introduce a class of self-steering partially coherent vector optical beams with the aid of a generalized complex Gaussian representation. We show that such partially coherent vector beams have mobile guiding centers of their intensity and polarization state distributions on the beam free space propagation that could be employed to generate far-field polarization arrays. Further, we introduce theoretically and realize experimentally a class of vector beams with inhomogeneous statistical and nontrivial far-field angular distributions, which we term cylindrically correlated partially coherent (CCPC) vector beams. We find that such novel beams possess, in general, cylindrically polarized, far-field patterns of an adjustable degree of polarization. The steering control of the intensity and polarization of the self-steering CCPC vector beam is also demonstrated in experiment. Our findings can find important applications, such as trapping of neutral microparticles and excitation of novel surface waves.

Transmission of a polychromatic electromagnetic multi-Gaussian Schell-model beam in an inhomogeneous gradient-index fiber

We derive analytical expressions for the cross-spectral density matrix of polychromatic electromagnetic multi-Gaussian Schell-model (EMGSM) beam transmission through a gradient-index fiber. The space-spectrum evolution properties for the spectral density, spectral shift, degree of polarization, and electromagnetic coherence state of a polychromatic EMGSM beam with Lorentzian line type spectrum and central wavelength λ₀=1550  nm propagation in a silica-clad germania core inhomogeneous graded-index fiber are studied in detail. We show that these statistical properties exhibit periodicity in the fiber, caused by the focusing property of square-law media, which can be reminiscent of the self-imaging effect of optical fields. The effects of the nonconventional correlation functions of the polychromatic EMGSM beam on the transmission properties are also investigated.

Efficient tensor approach for simulating paraxial propagation of arbitrary partially coherent beams

Complicated partially coherent beams (PCBs) are useful in many applications, such as free-space optical communications, particle trapping and optical imaging, while usually it is hard to derive analytical propagation formulae for such beams, and one has to fall back on numerical methods. The conventional numerical methods have some intrinsic drawbacks. In this paper, we introduce an efficient tensor approach (ETA) for simulating paraxial propagation of arbitrary PCBs. The ETA is a direct reconstruction of the propagated PCB without aliasing and rippling problems, and the algorithm is simple and robust with a tensor/matrix multiplication as the main calculation. The validity of ETA is verified through comparing simulation results with analytical results, numerical integration results and experimental results, respectively. The ETA provides a fast and reliable way for simulating paraxial propagation of arbitrary PCBs.

Complex Gaussian representations of partially coherent beams with nonconventional degrees of coherence

We adopt the recently introduced complex Gaussian function to expand the partially coherent beams with nonconventional degrees of coherence, and derive detailed representations of Hermite-Gaussian correlated Schell-model beam, elliptical Laguerre-Gaussian correlated Schell-model beam, and multi-Gaussian correlated Schell-model beam. Complex Gaussian representation of a partially coherent beam provides a convenient way for treating its propagation. As an application example, we explore the self-splitting properties of a Hermite-Gaussian correlated Schell-model beam propagating in a uniaxial crystal with the help of the complex Gaussian representation, and it is found that the uniaxial crystal can be used to control the splitting properties.

Self-steering partially coherent beams

We introduce a class of shape-invariant partially coherent beams with a moving guiding center which we term self-steering partially coherent beams. The guiding center of each such beam evolves along a straight line trajectory which can be engineered to make any angle with the x-axis. We show that the straight line trajectory of the guiding center is the only option in free space due to the linear momentum conservation. We experimentally generate a particular subclass of new beams, self-steering Gaussian Schell beams and argue that they can find applications for mobile target tracing and trapped micro- and/or nanoparticle transport.

Self-reconstruction of partially coherent light beams scattered by opaque obstacles

Self-reconstruction refers to an ability of certain fully coherent optical beams to recover their spatial profiles after scattering by obstacles. In this communication, we extend the self-reconstruction concept to partially coherent beams. We show theoretically and verify experimentally that any partially coherent beam can self-reconstruct its intensity profile and state of polarization upon scattering from an opaque obstacle provided the beam coherence area is reduced well below the obstacle area. We stress that our self-reconstruction technique is independent of the obstacle shape and it is scalable to the case of multiple obstacles or even of inhomogeneous media as long as a characteristic obstacle area or a medium inhomogeneity scale is well in excess of the beam coherence area or length, respectively. We anticipate the technique to be instrumental in applications ranging from beam shaping to image transfer and trapped particle manipulation in turbid media.

Propagation of optical coherence lattices in the turbulent atmosphere

We explore the propagation of recently introduced optical coherence lattices (OCLs) in the turbulent atmosphere. We show that the lattice intensity profile and the spatial degree of coherence will display periodicity reciprocity over long propagation distances even though the lattices are affected by the turbulence. The lattice periodicity reciprocity has been previously conjectured to be advantageous for free-space information transfer and optical communications. We then show how one can increase the distance over which the lattice periodicity reciprocity is preserved in the turbulent atmosphere by engineering input lattice beam parameters. We also show that the OCLs have scintillation indices lower than those of Gaussian beams.

Fluctuating pulse propagation in resonant nonlinear media: self-induced transparency random phase soliton formation

We numerically investigate partially coherent short pulse propagation in nonlinear media near optical resonance. We examine how the pulse state of coherence at the source affects the evolution of the ensemble averaged intensity, mutual coherence function, and temporal degree of coherence of the pulse ensemble. We report evidence of self-induced transparency random phase soliton formation for the relatively coherent incident pulses with sufficiently large average areas. We also show that random pulses lose their coherence on propagation in resonant media and we explain this phenomenon in qualitative terms.