Information encryption with optical technologies has become increasingly important due to remarkable multidimensional capabilities of light fields However, the optical encryption protocols proposed to date have been primarily based on the first-order field characteristics, which are strongly affected by interference effects and make the systems become quite unstable during light-matter interaction Here, we introduce an alternative optical encryption protocol whereby the information is encoded into the second-order spatial coherence distribution of a structured random light beam via a generalized van Cittert-Zernike theorem We show that the proposed approach has two key advantages over its conventional counterparts First, the complexity of measuring the spatial coherence distribution of light enhances the encryption protocol security Second, the relative insensitivity of the second-order statistical characteristics of light to environmental noise makes the protocol robust against the environmental fluctuations, eg, the atmospheric turbulence We carry out experiments to demonstrate the feasibility of the coherence-based encryption method with the aid of a fractional Fourier transform Our results open up a promising avenue for further research into optical encryption in complex environments

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Optical coherence encryption with structured random light.

Polarization singularities are superpositions of orbital angular momentum (OAM) states in orthogonal circular polarization basis. The intrinsic OAM of light beams arises due to the helical wavefronts of phase singularities. In phase singularities, circulating phase gradients and, in polarization singularities, circulating Stokes phase gradients are present. At the phase and polarization singularities, undefined quantities are the phase and Stokes phase, respectively. Conversion of circulating phase gradient into circulating Stokes phase gradient reveals the connection between phase (scalar) and polarization (vector) singularities. We demonstrate this by theoretically and experimentally generating polarization singularities using phase singularities. Furthermore, the relation between scalar fields and Stokes fields and the singularities in each of them is discussed. This paper is written as a tutorial-cum-review-type article keeping in mind the beginners and researchers in other areas, yet many of the concepts are given novel explanations by adopting different approaches from the available literature on this subject.

Phase Singularities to Polarization Singularities

The ability to overcome the adverse effect induced by the obstacles within the transmission link is a central challenge in long-distance optical image transmission and is significantly crucial in free-space optical communication. In this work, we introduce an efficient protocol to realize the robust far-field optical image-signal transmission by modulating the spatial-coherence structure of a partially coherent random light source. The image information encoded in the spatial-coherence structure can be stably transmitted to the far field and can resist the influence of obstructions within the communication link. This is due to the self-reconstruction property of the spatial-coherence structure embedded with the cross phase in the far field. We demonstrate experimentally that the image information can be recovered well by measuring the second-order spatial-coherence structure of the obstructed random light in the far field. Our findings open a door for robust optical signal transmission through the complex environment and may find application in optical communication through a turbulent atmosphere. 

Robust Far-Field Optical Image Transmission with Structured Random Light Beams

The generation of a perfect optical vortex (POV) has been an important area of research since the concept was introduced by Ostrovsky et al. [Opt. Lett. 38, 534 (2013)]. In this Letter, we provide the details of the experimental demonstration of a POV using perfect Laguerre–Gaussian beams via a phase-only spatial light modulator. The perfect beam properties, including radius, beam width, and ring thickness, are investigated in detail. We verify the vortex nature of the proposed perfect Laguerre–Gaussian beams including their topological charge value and sign. Finally, in addition to the scalar beams, we propose the vector perfect Laguerre–Gaussian beams both theoretically and experimentally and evaluate their perfect characteristics. The derived results clearly illustrate the perfect characteristics of such beams independent of the polarization state. The findings reported here can find significant applications in various fields including optical tweezers, optical imaging, and high capacity optical communications.

Experimental realization of scalar and vector perfect Laguerre–Gaussian beams

We propose and demonstrate a new, to the best of our knowledge, kind of partially coherent vector beam called the partially coherent radially polarized circular Airy beam (PCRPCAB). The PCRPCAB inherits the autofocusing ability of the radially polarized circular Airy beam (RPCAB) and can create an optical potential well at the center of the beam, whose depth can be adjusted by changing the coherent width. We find that, as coherent width decreases, the intensity becomes higher in the dark notch caused by the polarization singularity, and the singularity of the degree of polarization (DOP) remains along propagation, with its waist controllable by the coherent width. Our results make the PCRPCAB a good candidate for optical micromanipulation, disordered optical lattices, etc.

Partially coherent radially polarized circular Airy beam.

We suggest tailoring of the illumination’s complex degree of coherence for imaging specific two- and three-point objects with resolution far exceeding the Rayleigh limit. We first derive a formula for the image intensity via the pseudo-mode decomposition and the fast Fourier transform valid for any partially coherent illumination (Schell-like, non-uniformly correlated, twisted) and then show how it can be used for numerical image manipulations. Further, for Schell-model sources, we show the improvement of the two- and three-point resolution to 20% and 40% of the classic Rayleigh distance, respectively.

Optimizing illumination’s complex coherence state for overcoming Rayleigh’s resolution limit

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.

Vortex preserving statistical optical beams

The degree of coherence function of a light beam could be used for optical encryption, robust optical imaging, and other purposes. However, recent works demonstrated that it has a puny self-reconstruction ability that gets worse as the obstacle is further away from the source. In this manuscript, we propose a method by which, with the help of only the introduction of a cross-phase structure in the degree of coherence function, the self-reconstruction ability of the degree of coherence function could be significantly enhanced. The performance of the method is independent of the location of the obstacle. The results, achieved in this manuscript, will shed new light on optical imaging, optical encryption, and optical communication in a complex environment.

Enhancing the self-reconstruction ability of the degree of coherence of a light beam via manipulating the cross-phase structure

We propose theoretically and numerically, for the first time, the generation of novel partially coherent truncated Airy beams (NPCTABs) with Airy-like distributions for both intensity and degree of coherence via Fourier phase processing. We demonstrate a clear link between the magnitude and frequency of intensity and degree of coherence distributions oscillations of generated beams, and the source coherence and the phase screen parameter. Thus, the source coherence and phase can serve as convenient parameters to control the intensity and degree of the coherence of NPCTABs. Furthermore, we discover that NPCTABs are more stable than the fully coherent truncated Airy beams (FCTABs) during their propagation in free space and can maintain their Airy-like profile for an extended propagation distance. The interesting and tunable characteristics of these novel beams may find applications in particle trapping, phase retrieval, and optical imaging.

Xin Liu

Papers

Experimental realization of scalar and vector perfect Laguerre–Gaussian beams

Optimizing illumination’s complex coherence state for overcoming Rayleigh’s resolution limit

Vortex preserving statistical optical beams

Enhancing the self-reconstruction ability of the degree of coherence of a light beam via manipulating the cross-phase structure

Generation of novel partially coherent truncated Airy beams via Fourier phase processing