The orbital angular momentum of light is distinct from the angular momentum associated with the spin or polarisation state of the light. Thus linearly polarised modes can carry angular momentum. Laguerre-Gaussian laser modes have been identified as a class of modes that can possess such orbital angular momentum. Hermite-Gaussian modes may be converted to Laguerre-Gaussian modes, characterised by two integer indices l and p, by the use of a mode converter. The l index occurs in the azimuthal phase factor eil ϕ in the field distribution of Laguerre-Gaussian beams which possess an orbital angular momentum equivalent to lħ per photon 1.

Second Harmonic Generation and the Orbital Angular Momentum of 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

This paper proposes a new color image encryption system based on compressed sensing and multi-image cross pixel scrambling approach. In the encryption process, firstly, the color image is decomposed into three sub-images according to tricolor theory; then the three decomposed images are sparsely processed by the discrete wavelet transform; finally, the different Gaussian random matrices are used to observe them. In order to enhance the security of the system, the multi-image cross pixel scrambling approach is used in the encryption process. The system can achieve accurate recovery of original information from a small amount of observations, which saves transmission bandwidth and storage space of information. During the decryption process, the images are processed by a modified regularization adaptive matching pursuit algorithm according to the corresponding Gaussian random matrix to recover the three grayscale sub-images. Theoretical analysis and simulation results prove the feasibility and safety of the encryption system.

An encryption system for color image based on compressive sensing

Self-referenced interference of laterally displaced vortex beams for topological charge determination

In this paper, a noise-resistant image encryption scheme is proposed. We have used a cubic-logistic map, Discrete Wavelet Transform (DWT), and bit-plane extraction method to encrypt the medical images at the bit-level rather than pixel-level. The proposed work is divided into three sections; In the first and the last section, the image is encrypted in the spatial domain. While the middle section of the proposed algorithm is devoted to the frequency domain encryption in which DWT is incorporated. As the frequency domain encryption section is a sandwich between the two spatial domain encryption sections, we called it a ”sandwich encryption.” The proposed algorithm is lossless because it can decrypt the exact pixel values of an image. Along with this, we have also gauge the proposed scheme’s performance using statistical analysis such as entropy, correlation, and contrast. The entropy values of the cipher images generated from the proposed encryption scheme are more remarkable than 7.99, while correlation values are very close to zero. Furthermore, the number of pixel change rate (NPCR) and unified average change intensity (UACI) for the proposed encryption scheme is higher than 99.4% and 33, respectively. We have also tested the proposed algorithm by performing attacks such as cropping and noise attacks on enciphered images, and we found that the proposed algorithm can decrypt the plaintext image with little loss of information, but the content of the original image is visible.

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Noise-Resistant Image Encryption Scheme for Medical Images in the Chaos and Wavelet Domain

This study demonstrates a self-referenced interferometric method to estimate the magnitude and sign of a high-order topological charge (TC) carried by incoming optical vortex beams. The proposed method uses a right-angle prism in a Mach-Zehnder interferometer setup with controlled lateral shift and tilt between the wavefronts of interfering beams. The in-line interference with its conjugate results in a petal-shaped fringe pattern, where the number of petals reveals the magnitude of the TC. When the direction of one of the interfering beams is laterally displaced and rotated to emerge at a small angle for off-axis interference such that the vortices overlap at the output plane, then a fork-like interference pattern with better visibility is obtained, which can be used for estimating the magnitude as well as the sign of the TC. Through numerical simulation and optical experiment, it is shown that the technique is capable of estimating the TC of Laguerre-Gaussian beams even with a nonzero radial index.

Modified Mach-Zehnder interferometer for determining the high-order topological charge of Laguerre-Gaussian vortex beams

For practical application of any optical cryptographic technique, good quality decryption is necessary. Exclusive-OR (XOR) operation is a well-known technique for image encryption but faces the problem of quality degradation, while optically implemented. One of the reasons for quality degradation is the presence of laser speckles. The other reason is the noise that induces around image pixels. In this study, we demonstrate an image encryption using XOR operation based on light-emitting diode (LED) and quick response code, which not only reduces the damage caused by speckles but also overcomes the noise problem. The results with green and white LEDs and laser sources have been compared. Overall, the proposed optical cryptosystem is simple, compact, and cost-effective.

Enhanced exclusive-OR and quick response code-based image encryption through incoherent illumination.

Interference of a vortex beam with a reference beam can specify the amount of orbital angular momentum carried by the beam. In this study, we demonstrate that the vortex beam produces spiral-shaped interference fringes when interfered with its converging and laterally displaced copy. The analysis will help determine the topological charge, especially its sign. Theoretical description, including intensity and phase profile, has been presented. It is expected that the demonstrated technique would find application in diverse areas, such as in the fields of optical communication and spiral interferometry.

Self-referenced spiral interferogram using modified lateral shearing Mach–Zehnder interferometer

In this paper, we present a simple and flexible non-interferometric method to generate various polarization singularity lattice fields. The proposed method is based on a double modulation technique that uses a single reflective spatial light modulator to generate different lattice structures consisting of V-point and C-point polarization singularities. The present technique is compact with respect to previous experimental realization techniques. Different structures having star and lemon fields are generated without altering the experimental setup. In addition, the same setup can be used to obtain different types of inhomogeneous fields embedded with isolated polarization singularities even of higher orders. The Stokes polarimetry method has been used to obtain the polarization distributions of generated fields, which are in good agreement with simulated results.

Praveen Kumar

Papers

Modified Mach-Zehnder interferometer for determining the high-order topological charge of Laguerre-Gaussian vortex beams

Self-referenced interference of laterally displaced vortex beams for topological charge determination

Enhanced exclusive-OR and quick response code-based image encryption through incoherent illumination.

Self-referenced spiral interferogram using modified lateral shearing Mach–Zehnder interferometer

Non-interferometric technique to realize vector beams embedded with polarization singularities