COVID-19 (SARS-CoV-2) is rapidly spreading in South Asian countries, especially in India. India is the fourth most COVID-19 affected country at present i.e., until July 10, 2020. With limited medical facilities and high transmission rate, the study of COVID-19 progression and its subsequent trajectory needs to be analyzed in India. Epidemiologic mathematical models have the potential to predict the epidemic peak of COVID-19 under different scenarios. Lockdown is one of the most effective mitigation policies adopted worldwide to control the transmission rate of COVID-19 cases. In this study, we use an improvised five compartment mathematical model, i.e., Susceptible (S)-Exposed (E)-Infected (I)-Recovered (R)-Death (D) (SEIRD) to investigate the progression of COVID-19 and predict the epidemic peak under the impact of lockdown in India. The aim of this study is to provide a more precise prediction of epidemic peak and to evaluate the impact of lockdown on epidemic peak shift in India. For this purpose, we examine the most recent data (from January 30, 2020 to July 10, 2020 i.e., 160 days) to enhance the accuracy of outcomes obtained from the proposed model. The model predicts that the total number of COVID-19 active cases would be around 5.8 × 10⁵ on August 15, 2020 under current circumstances. In addition, our study indicates the existence of under-reported cases i.e., 10⁵ during the post-lockdown period in India. Consequently, this study suggests that a nationwide public lockdown would lead to epidemic peak suppression in India. It is expected that the obtained results would be beneficial for determining further COVID-19 mitigation policies not only in India but globally as well.

Perfect optical vortices (POVs) are annular beams designed such that their radii are, in principle, independent of topological charge, making them attractive for structured illumination and optical manipulation. We present a systematic experimental and numerical study of POVs generated using a phase-only spatial light modulator and investigate how controlled angular anisotropy reshapes their structure across a wide range of charges. Three distinct regimes are identified. In the absence of anisotropy, charge-invariant annuli persist only for moderate charges, while higher charges exhibit multi-ring, Bessel-like structure accompanied by a gradual increase in effective radius. At moderate anisotropy, these multi-ring profiles consolidate into single opened annuli with tunable azimuthal asymmetry. In this regime, speckle cross-correlation remains structured even for widely separated charges that exhibit weak correlations under isotropic encoding. At extreme anisotropy, annular intensity profiles converge across all charges, forming pseudo-POVs that remain annular in intensity but exhibit pronounced redistribution of OAM-dependent signatures and a collapse of charge-dependent cross-correlation signatures within the sensitivity of intensity-only measurements. Non-interferometric speckle analysis supports these findings. Autocorrelation rules out trivial ellipticity as the origin of radius convergence, while cross-correlation reveals sensitivity to charge ordering at low anisotropy and an effective loss of charge distinguishability within intensity-only diagnostics at extreme anisotropy. Together, these results clarify the robustness limits of POVs under angular deformation and establish angular anisotropy as a practical control parameter for engineering and diagnosing annular vortex beams.

Introduction: We present a polarization-coded binary phase mask based on spherical aberration (BPM-SA), which is numerically investigated to extend the depth of focus. Methods: First, we generate the baseline binary phase mask by binarizing the fourth-order spherical-aberration phase function into concentric 0- and π-phase zones. To improve axial beam shaping, we introduce polarization coding using Jones retarders in the binary zones, and combine the resulting fields through a linear analyzer. Results: The depth of focus (DOF) was evaluated using a 90% axial intensity criterion. Compared with a BPM-SA, the proposed polarization-coded BPM-SA suppresses the central intensity dip caused by destructive interference. Discussion: Polarization coding synthesizes a continuous, uniform axial intensity profile over an extended depth of focus (EDOF) without significantly degrading transverse resolution.