Evolution of C-point singularities and polarization coverage of Poincaré-Bessel beam in self-healing process.

As a vector version of scalar Bessel beams, Poincaré-Bessel beams (PBBs) have attracted a great deal of attention due to their non-diffracting and self-healing properties as well as the presence of polarization singularities. Previous studies of PBBs have focused on cases that consist of a superposition of Bessel beams in orthogonal circular polarization states; here, we present a theoretical and experimental study of PBBs for which the polarization states are taken to be linear, which we call a linear PBB. Using a mode transformation of a full Poincaré beam constructed from linear polarization states, we observe the linear PBB as providing an in-principle infinite number of covers of the Poincaré sphere in the transverse plane and with an infinite number of C-points with positive and negative topological indices. We also study the dynamics of C-point singularities in a linear PBB in the process of self-healing after being obstructed by an obstacle, providing insight into "Hilbert Hotel" style evolution of singularities in light beams. The present study can be useful for imaging in the presence of depolarizing surroundings, studying turbulent atmospheric channels, and exploring the rich mathematical concepts of transfinite numbers.

Harnessing nonlinear frequency upconversion of Talbot effect with flexible Talbot lengths.

We report on a simple experimental scheme demonstrating nonlinear frequency upconversion of the Talbot effect with controllable Talbot lengths at high conversion efficiency. Using a microlens array (MLA) as an array illuminator at 1064 nm onto a 1.2-mm-thick BiBO crystal, we have observed the second harmonic Talbot effect in green at 532 nm with a Talbot length twice that of the pump Talbot length. However, the Talbot length is constant for fixed parameters of the periodic object and the laser wavelength. With the formulation of a suitable theoretical framework, we have implemented a generic experimental scheme based on the Fourier transformation technique to independently control the Talbot lengths of the MLA in both the pump and the second harmonic, overcoming the stringent dependence of MLA parameters on the self-images. Deploying the current technique, we have been able to tune the Talbot lengths from zT = 26 cm to zT = 62.4 cm in the pump and zT = 12.4 cm to zT = 30.8 cm in the second harmonic, respectively. The single pass conversion efficiency of the Talbot images is 2.91% W-1, an enhancement of a factor of 106 as compared to the previous reports. This generic experimental scheme can be used to generate long-range self-images of periodic structures and also to program desired Talbot planes at required positions at both pump and upconverted frequency to avoid any mechanical constraints of experiments.

Tunable, high-power, high-order optical vortex beam generation in the mid-infrared.

We report the generation of tunable high-order optical vortices in the mid-infrared (mid-IR) using a picosecond optical parametric oscillator (OPO). The OPO is based on MgO:PPLN as the nonlinear gain medium and synchronously pumped by a mode-locked Yb-fiber laser at 1064 nm. Using a singly-resonant oscillator configuration for the OPO, we have achieved direct transfer of pump optical vortices to the non-resonant idler beam, with the resonant signal in the Gaussian cavity mode. We demonstrate the successful transfer of pump optical vortices of order, lp = 1 to 5, to the idler beam of the same order across the mid-IR, with an output power of 630 mW to 130 mW across 2538 nm to 4035 nm for the highest idler vortex order, li = 5. To the best of our knowledge, this is the first report of an OPO pumped by a vortex beam of order as high as lp = 5 and generating idler vortices of high order in the mid-IR.

Tunable vortex beam generation using an optical parametric oscillator with an antiresonant-ring interferometer.

We report a high-average-power picosecond optical vortex source tunable in the near-infrared, using an antiresonant-ring (ARR) interferometer internal to an optical parametric oscillator (OPO) in combination with an external cylindrical lens for astigmatic mode conversion. The ARR OPO is tunable in the signal across 1457-1647 nm with a vortex intensity profile and up to 1 W of average power at 1602 nm. The corresponding idler is tunable over 3006-3945 nm in a Gaussian intensity profile with as much as 1.6 W at 3168 nm. The vortex signal and the Gaussian idler exhibit passive power stability better than 1.7% rms and 1.3% rms, respectively, over >1h. The signal pulses have a Gaussian duration of <19ps with a time-bandwidth product of ΔτΔν<3.6 across the tuning range.

Nonlinear frequency conversion of 3D optical bottle beams generated using a single axicon.

We demonstrate a novel experimental scheme to generate and study the nonlinear frequency conversion of a three-dimensional (3D) optical Bessel bottle beam (BBB). Using a single axicon and standard optical components and controlling the spot size and divergence of the input Gaussian beam to the axicon, we have generated stable micron-size, high-power optical BBB with tunable spatial characteristics. The BBB has a series of low-intensity regions surrounded by high intensity with diameters of ∼30µm and 17 µm, respectively, at a variable period of 2.3 to 6.4 mm along with the beam propagation. Using the single-pass second harmonic generation (SHG) of femtosecond BBB at 1064 nm in a bismuth triborate nonlinear crystal, we have generated BBB at 532 nm with output power as high as 75 mW and single-pass SHG efficiency of 1.9%. We also observed the self-healing of the BBB at both pump and SHG wavelengths. It is interesting to note that the pump beam truncation shows self-healing in the SHG beam. Such observation proves the direct transfer of the pump's spatial characteristics to the SHG beam in the nonlinear process, potentially useful for imaging even in the turbid medium in biology. This generic scheme can be used at different wavelengths and timescales (continuous-wave to ultrafast).

Modelling the role of optimal social distancing on disease prevalence of COVID-19 epidemic.

COVID-19 first spread from Wuhan, China in December 2019 but it has already created one of the greatest pandemic situations ever witnessed. According to the current reports, a situation has arisen when people need to understand the importance of social distancing and take enough precautionary measures more seriously. Maintaining social distancing and proper hygiene, staying at isolation or adopting the self-quarantine strategy are some common habits which people should adopt to avoid from being infected. And the growing information regarding COVID-19, its symptoms and prevention strategies help the people to take proper precautions. In this present study, we have considered a SAIRS epidemiological model on COVID-19 transmission where people in the susceptible environment move into asymptotically exposed class after coming contact with asymptotically exposed, symptomatically infected and even hospitalised people. The numerical study indicates that if more people from asymptotically exposed class move into quarantine class to prevent further virus transmission, then the infected population decreases significantly. The disease outbreak can be controlled only if a large proportion of individuals become immune, either by natural immunity or by a proper vaccine. But for COVID-19, we have to wait until a proper vaccine is developed and hence natural immunity and taking proper precautionary measures is very important to avoid from being infected. In the latter part, a corresponding optimal control problem has been set up by implementing control strategies to reduce the cost and count of overall infected individuals. Numerical figures show that the control strategy, which denotes the social distancing to reduce disease transmission, works with a higher intensity almost after one month of implementation and then decreases in the last few days. Further, the control strategy denoting the awareness of susceptible population regarding precautionary measures first increases up to one month after implementation and then slowly decreases with time. Therefore, implementing control policies may help to reduce the disease transmission at this current pandemic situation as these controls reduce the overall infected population and increase the recovered population.

Watt-level, ultrafast, tunable yellow source based on single-pass, fourth-harmonic generation of Cr2+:ZnS laser at 2360 nm.

We report a compact source of high power, tunable, ultrafast yellow radiation using fourth-harmonic generation of a mid-IR laser in two-stage frequency-doubling processes. Using Cr2+:ZnS laser at 2360 nm frequency-doubled in a multi-grating MgO:PPLN crystal, we have generated near-IR radiation tunable across 1137-1200 nm with average output power as high as 2.4 W and pulse width of ∼60fs. Subsequently, the near-IR radiation is frequency-doubled using a bismuth triborate (BIBO) crystal to produce coherent yellow radiation tunable across 570-596 nm with a maximum average power of ∼1W. The source has a maximum mid-IR to yellow (near-IR to yellow) single-pass conversion efficiency as high as ∼29.4% (∼47%). Without any pulse compression, the yellow source has output pulses at a repetition rate of 80 MHz with a pulse width of ∼130fs in Gaussian-shaped and a spectral width of ∼4nm corresponding to a time-bandwidth product of 0.45. The generated output beam has a Gaussian transverse beam profile with measured M2 values of Mx2∼1.07 andMy2∼1.01.

Epidemic model of COVID-19 outbreak by inducing behavioural response in population.

COVID-19 has spread around the world since December 2019, creating one of the greatest pandemics ever witnessed. According to the current reports, this is a situation when people need to be more careful and take the precaution measures more seriously, unless the condition may become even worse. Maintaining social distances and proper hygiene, staying at isolation or adopting the self-quarantine method are some of the common practices that people should use to avoid the infection. And the growing information regarding COVID-19 and its symptoms help the people to take proper precautions. In this present study, we consider an SEIRS epidemiological model on COVID-19 transmission which accounts for the effect of an individual's behavioural response due to the information regarding proper precautions. Our results indicate that if people respond to the growing information regarding awareness at a higher rate and start to take the protective measures, then the infected population decreases significantly. The disease fatality can be controlled only if a large proportion of individuals become immune, either by natural immunity or by a proper vaccine. In order to apply the latter option, we need to wait until a safe and proper vaccine is developed and it is a time-taking process. Hence, in the latter part of the work, an optimal control problem is considered by implementing control strategies to reduce the disease burden. Numerical figures show that the control denoting behavioural response works with higher intensity immediately after implementation and then gradually decreases with time. Further, the control policy denoting hospitalisation of infected individuals works with its maximum intensity for quite a long time period following a sudden decrease. As, the implementation of the control strategies reduce the infected population and increase the recovered population, so, it may help to reduce the disease transmission at this current epidemic situation.

Multi-structured-beam optical parametric oscillator.

Structured beams, conventionally generated through the spatial mode conversion of the Gaussian laser beams, have attracted great interest in recent years. Optical parametric oscillators (OPOs) have demonstrated the potential for the generation of tunable structured beams directly from an input pump source. However, to date, a particular OPO design has been shown to produce such beams only in a specific configuration and different spatial structured beams require different system architectures. Here, we report the generation of multiple-structured beams from a single OPO device. Using a vortex-beam-pumped ultrafast OPO in singly-resonant oscillator design and through the control of the mode structure of the resonant beam using a simple intracavity aperture, we generate vortex, Airy, vortex Airy, and Gaussian signal beams over a tunable wavelength range across 1457-1680 nm, simultaneous with vortex beam in the non-resonant idler across 2902-3945 nm, from different ports of the device. The signal and idler vortices have output power in excess of 1 W and maximum vortex order of li=2, while the Airy beam and vortex Airy beam have output power of more than 200 mW. The generic experimental design can be used to provide multi-structured spatial beams with broad tunability across different spectral regions by proper selection of pump laser and nonlinear material and in all times-scales from continuous-wave to ultrafast femtosecond domain.

Tunable ultraviolet vortex source based on a continuous-wave optical parametric oscillator.

We report a continuous-wave (cw) optical parametric oscillator (OPO) generating optical vortices tunable in the ultraviolet (UV). Based on MgO:sPPLT as the nonlinear crystal, the singly resonant OPO is pumped by a cw vortex beam in the green, and deploying intracavity sum-frequency generation (SFG) between the undepleted pump and the Gaussian resonant signal in the crystal of BiB3O6, it can generate optical vortices of order, luv=1 and 2, tunable across 332-344 nm in the UV with a maximum power of 12 mW. Due to conservation of orbital angular momentum in the parametric process, the OPO also produces a non-resonant idler output beam in a vortex spatial profile of order li=1 and 2, identical to the pump vortex, with the signal beam in Gaussian distribution. The idler vortex is tunable across 1172-1338 nm with maximum output power of 1.3 W.

Controlled generation of array beams of higher order orbital angular momentum and study of their frequency-doubling characteristics.

We report on a simple and compact experimental scheme to generate high-power, ultrafast, higher-order vortex-array beams. Simply by using a dielectric microlens-array (MLA) and a plano-convex lens, we have generated array-beams carrying the spatial property of the input beam. Considering the MLA as a 2D sinusoidal phase-grating, we have numerically calculated the intensity pattern of the array-beams in close agreement with the experimental results. Using vortex beams of order as high as l = 6, we have generated vortex array-beam with individual vortices of orders up to l = 6. We have also theoretically derived the parameters controlling the intensity pattern, size, and the array-pitch and verified experimentally. The single-pass frequency-doubling of vortex-array at 1064 nm in a 1.2 mm long BiBO crystal produced green vortex-array of order, lsh = 12, twice the order of pump beam. Using lenses of different focal lengths, we have observed the vortex-arrays of all orders to follow a focusing dependent conversion similar to the Gaussian beam. The maximum power of the green vortex-array is measured to be 138 mW at a single-pass efficiency as high as ~3.65%. This generic experimental scheme can be used to generate the array beams of desired spatial intensity profile across a wide wavelength range by simply changing the spatial profile of the input beam.

Tunable vector-vortex beam optical parametric oscillator.

Vector-vortex beams, having both phase and polarization singularities, are of great interest for a variety of applications. Generally, such beams are produced through systematic control of phase and polarization of the laser beam, typically external to the source. However, efforts have been made to generate vector-vortex beams directly from the laser source. Given the operation of the laser at discrete wavelengths, vector-vortices are generated with limited or no wavelength tunability. Here, we report an experimental scheme for the direct generation of vector-vortex beams. Exploiting the orbital angular momentum conservation and the broad wavelength versatility of an optical parametric oscillator, we systematically control the polarization of the resonant beam using a pair of intracavity quarter-wave plates to generate coherent vector-vortex beam tunable across 964-990 nm, with output states represented on the higher-order Poincaré sphere. The generic experimental scheme paves the way for new sources of structured beams in any wavelength range across the optical spectrum and in all time-scales from continuous-wave to ultrafast regime.

Single-pass, second-harmonic generation of high-power, ultrafast mid-IR Cr2+:ZnS laser at 2360 nm.

We report on a compact and simple ultrafast source producing tunable radiation in the near-IR wavelength range. Based on single-pass frequency doubling of an ultrafast Cr2+:ZnS laser at 2360 nm with pulse width of 43 fs at a repetition rate of 80 MHz in MgO:PPLN crystal, the source produces maximum average output power of ∼2.43 W tunable across 1137-1200 nm with a maximum single-pass conversion efficiency as high as 65%. Without use of any pulse compression technique, the source produces output pulses in Gaussian shape with measured pulse width of ∼60 fs and spectral width of 39 nm centered at 1180 nm corresponding to a time-bandwidth product of 0.5. The output beam has a Gaussian spatial profile with measured M2<1.32 and a peak-to-peak power fluctuation of 3% over 2 h. Using MgO:PPLN crystal of two different lengths, 1 mm and 2 mm, we have observed that the optimum second-harmonic generation efficiency of an ultrafast pulse laser, even in the presence of temporal walk-off, appears in the low pump focusing condition.

Controlled generation of vortex and vortex dipole from a Gaussian pumped optical parametric oscillator.

We report on direct generation of optical vortices from a continuous-wave (cw), Gaussian beam pumped doubly resonating optical parametric oscillator (DRO). Using a 30-mm long MgO doped periodically poled lithium tantalate (MgO:sPPLT) crystal based DRO, pumped in the green by a frequency-doubled Yb-fiber laser in Gaussian spatial profile we have generated signal and idler beams in vortex mode of order, l = 1, tunable across 970-1178 nm. Controlling the overlap between the Gaussian pump beam with the fundamental cavity mode of the resonant signal and idler beams of the DRO through the tilt of the pump beam and/or the cavity mirror in transverse plane, we have generated both signal and idler beams in vortex and vortex dipole spatial profiles. Using the theoretical formalism for the vortex beam generation through the superposition of two Gaussian beams we have numerically calculated the spatial profile of the generated beam in close agreement with our experiment results. The generic experimental scheme can be used to generate optical vortex across the electromagnetic spectrum and in all time scales (cw to ultrafast) using suitable OPO.

Simultaneous generation of high-power, ultrafast 1D and 2D Airy beams and their frequency-doubling characteristics.

We report on a simple experimental scheme based on a pair of cylindrical lenses (convex and concave) of the same focal length and common optical elements, producing high power optical beams in 1D and/or 2D Airy intensity profiles with laser polarization as the control parameter. Using an ultrafast Yb-fiber laser at 1064 nm of average power of 5 W in a Gaussian spatial profile and pulse width of ∼180 fs, we have generated 1D and 2D Airy beams at an efficiency of 80% and 70%, respectively, and a pulse width of ∼188 and ∼190 fs, respectively. We have measured the transverse deflection rate of 1D and 2D beams to be ∼5.0×10-5 1/mm and ∼2.0×10-5 1/mm, respectively. Simply rotating the polarization state of the 1D cubic phase modulated beam in the experiment, we can produce 1D and 2D Airy beams on demand. Using a 5 mm long bismuth borate (BiB3O6), we have also studied frequency-doubling characteristics of both 1D and 2D Airy beams. Like the 2D Airy beam, the 1D Airy beam also produces a frequency-doubled 1D Airy and an additional 1D spatial cubic structure. Like the Gaussian beams, we have observed the focusing dependence of conversion efficiency for both 1D and 2D Airy beams, producing green 1D and 2D Airy beams of output powers in excess of 110 and 150 mW for 3.4 and 2.8 W of fundamental power, respectively.

Orbital angular momentum exchange in a picosecond optical parametric oscillator.

We report on the orbital angular momentum (OAM) exchange among the interacting beams in an ultrafast optical parametric oscillator (OPO). The singly-resonant OPO is synchronously pumped by a picosecond vortex beam from a frequency-doubled Yb-fiber laser at 532 nm in the green. We demonstrate successful transfer of the pump OAM mode to the non-resonant idler beam tunable across 1109-1209 nm, with OAM as high as lp=3. Controlling the cavity loss and spatial overlap between the resonant signal and the pump beam in the nonlinear crystal, we have generated signal and idler OAM mode combinations, (ls,li) of (0,2) and (1,1), and (0,3) and (1,2) for pump OAM mode lp=2 and 3, respectively. Using a pump power of 1 W, we have generated idler OAM mode of orders, li=1, 2, and 3, with maximum output powers of 202, 113, and 57 mW, respectively. To the best of our knowledge, this is the first report on controlled generation of OAM modes from an ultrafast OPO.

On-axis intensity modulation-free, segmented, zero-order Bessel beams with tunable ranges.

We propose and experimentally demonstrate a novel experimental scheme to generate high on-axis peak intensity, segmented, smooth, zero-order quasi-Bessel beams with tunable ranges. Illuminating the axicon with hollow Gaussian beams (HGBs) of different orders, we have generated Bessel beams of varying ranges at different positions away from the axicon. The presence of a dark core at the center of the HGBs removes the effect of imperfection in the axicon tip. As a result, the entire power of the input beam is transformed into a zero-order Bessel beam without any on-axis intensity modulation. We observe the decrease in range and increase in on-axis peak intensity of the zero-order Bessel beam with the order of HGBs. Controlling the superposition of the HGBs of different orders to the axicon, we have demonstrated the increase in the range of the Bessel beam. The current technique can also produce Bessel beams of different intensity distributions, including single-peak or multiple-peak Bessel beams. Using single-pass second-harmonic generation in nonlinear crystals of different lengths, we have further verified the increase of on-axis peak intensity of the Bessel beam with the order of the HGBs and the increase in the range of the Bessel beam due to the superposed HGBs.

High-power, continuous-wave, tunable mid-IR, higher-order vortex beam optical parametric oscillator.

We report on a novel experimental scheme to generate continuous-wave (cw), high-power, and higher-order optical vortices tunable across a mid-IR wavelength range. Using a cw, two-crystal, singly resonant optical parametric oscillator (T-SRO) and pumping one of the crystals with a Gaussian beam and the other crystal with optical vortices of orders lp=1-6, we have directly transferred the vortices at near-IR to the mid-IR wavelength range. The idler vortices of orders li=1-6 are tunable across 2276-3576 nm with a maximum output power of 6.8 W at an order of li=1 for the pump power of 25 W, corresponding to a near-IR vortex to mid-IR vortex conversion efficiency as high as 27.2%. Unlike the SROs generating optical vortices restricted to lower orders (≤2) due to the elevated operation threshold of SROs with higher-order pump vortices, here the coherent energy coupling between the resonant signals of two crystals of T-SRO facilitates the transfer of pump vortex of any order to the idler wavelength without a stringent operation threshold condition. The generic experimental scheme can be used in any wavelength range across the electromagnetic spectrum and in all timescales, from cw to ultrafast regimes.

Robust, high brightness, degenerate entangled photon source at room temperature.

We report on a compact, simple and robust high brightness entangled photon source at room temperature. Based on a 30-mm-long periodically-poled potassium titanyl phosphate crystal, the source produces non-collinear, type-0, phase-matched, degenerate photons at 810 nm with spectral brightness as high as ~0.41 ± 0.02 (~0.025 ± 0.02) MHz/mW/nm for multi (single) mode fiber coupling. So far, this is the highest number of degenerate photons generated using a continuous-wave laser pumped bulk crystal and detected using multimode fiber. We have studied the dependence of pump focusing on the brightness of the generated photons collected using both multimode, and single mode fibers. For a fixed pump power and crystal parameters, the SPDC source has an optimum pump waist radius producing maximum number of paired photons. Combining the crystal in a novel system architecture comprised with Sagnac interferometer and polarizing optical elements, the source produces polarization entangled photon states with high spectral brightness. Even in the absence of any phase compensation, the entangled photon states detected using single mode fiber have a Bell's parameter, S = 2.63 ± 0.02, violating the Bell's inequality by nearly 32 standard deviations and fidelity of 0.975. The compact footprint, robust design, and room temperature operation, make our source ideal for various quantum communication experiments.

High power, high repetition rate, tunable broadband mid-IR source based on single-pass optical parametric generation of a femtosecond laser.

We report on single-pass optical parametric generation for high power, high repetition rate (RR), ultrafast broadband optical radiation in the mid-IR. Taking advantage of broad phase-matching bandwidth (BW) of the crystals for the interacting waves having zero group velocity mismatch, we have used a 50 mm long MgO-doped periodically poled LiNbO3 crystal to develop a single-pass, parametric source producing femtosecond output pulses at a RR of 78 MHz. Pumping with a femtosecond Yb-fiber laser at 1064 nm, the source produces signal and idler radiation tunable across 1422-1561 nm and 4229-3342 nm, respectively. The signal radiation has a pulse and spectral BW of 296 fs and 9.2 nm centered at 1492 nm, respectively, with a time-BW product ∼0.37, close to the transform limit. The idler radiation has spectral BW as high as 123 nm centered at 3709 nm. The source produces a signal (idler) beam of power of 2.07 W (0.54 W) at 1492 nm (3709 nm) in a Gaussian spatial profile with peak-to-peak passive power fluctuation better than 5% (4%) over 4 h at a single-pass conversion efficiency as high as ∼55%.