Divide and structure: generating and interswitching orthogonal eigenstates of complementary petal beams using a π-shifted Sagnac interferometer.

One of the many facets of structured light are Ferris wheel/petal beams that can be generated by the addition/superposition of two beams with opposite vorticity/orbital angular momentum (OAM). We demonstrate a simple scheme employing a π-shifted Sagnac interferometer (SI) containing a spiral phase plate (SPP) that divides and structures an incoming beam into two azimuthally complementary petal beams representing orthogonal eigenstates. The half-wave plate in the SI can interswitch/route these intensity patterns between the two outputs of the interferometer. The results are interpreted as a double symmetry breaking--that of helicity due to SPP and handedness due to HWP--experienced by counterpropagating beams in the π-shifted SI. In general, for a Laguerre-Gaussian (LG) incoming mode, the SI produces two orthogonal output states, each consisting of a sum or difference of distinct SPP-modified LG modes and resulting in complementary petal beams convoluted with the incoming mode. We also introduce a three-mirror π-shifted SI that can switch on and switch off opposite sign vortices into different SI arms. The scheme can find applications in particle trapping, information transmission/development of communications protocols, and signal processing (i.e., multiplexing/demultiplexing when using beams with high vorticity/OAM).

Divide and focus: generating novel focal polarization modalities by symmetry-based phase tailoring in one dimension.

Symmetry-based tailoring of photonic systems recently heralded the advent of novel concepts, such as photonic topological insulators and bound states in the continuum. In optical microscopy systems, similar tailoring was shown to result in tighter focusing, spawning the field of phase- and polarization-tailored light. Here, we show that even in the fundamental case of 1D focusing using a cylindrical lens, symmetry-based phase tailoring of the input field can result in novel features. Dividing the beam or utilizing a π phase shift for half the input light along the non-invariant focusing direction, these features include a transverse dark focal line and a longitudinally polarized on-axis sheet. While the former can be used in dark-field light-sheet microscopy, the latter, similar to the case of a radially polarized beam focused by a spherical lens, results in a z polarized sheet with reduced lateral size when compared with the thickness of a transversely polarized sheet produced by focusing a non-tailored beam. Moreover, the switching between these two modalities is achieved by a direct 90° rotation of the incoming linear polarization. We interpret these findings in terms of the requirement to adapt the symmetry of the incoming polarization state to match the symmetry of the focusing element. The proposed scheme may find application in microscopy, probing anisotropic media, laser machining, particle manipulation, and novel sensor concepts.

Vectorial spin Hall effect of light upon tight focusing.

The spin Hall effect of light is a manifestation of angular momentum conservation in the process of spin-orbit interaction of light. This optical Hall effect is exhibited in tight focusing of a circularly polarized asymmetric input beam as a shift of the center of gravity of the focal spot in the transverse plane, perpendicular to the direction/axis of symmetry breaking. It is commonly established that the direction of this shift depends on the sign of the spin. Here we show, for the first time, to the best of our knowledge, both analytically and by numerical simulation, that different Cartesian components of an asymmetric circularly polarized focused beam shift in opposite directions by different amounts. Moreover, these shifts depend on the type and degree of the asymmetry and thus can be tuned/controlled. We show how these field components' shifts are related to spin and orbital angular momentum shifts. These findings shed new light on the spin optical Hall effect, facilitate new/simpler ways to measure it, and may broaden the gamut of its applications in manipulation and trapping of particles by light and precision metrology.

Enlightening Arago-Poisson spot using structured light.

We show that structured light can amplify the intensity of an Arago-Poisson bright spot, the cornerstone proof of the wave nature of light, by several orders of magnitude. Specifically, we use a thin annular beam produced by either an axicon-lens combination or two axicons to illuminate an opaque circular obstacle. Experimental results confirm the numerical calculations. By judiciously choosing our scheme's parameters, the bright spot intensity can be higher than that of the original beam, meaning that structured light facilitates "focusing" of light behind an obstacle. This amplification, in addition to didactic elucidation of this classical effect, can find use in optical alignment/metrology, lithography, aberration measurements, as well as in basic science studies of the Arago-Poisson spot in matter waves.

Breaking the symmetry to structure light.

We show that by breaking the symmetry of a beam subjected to tight focusing, namely by obscuring half of it or, equivalently, shifting the beam away from the lens axis, it is possible to obtain novel light properties in the focal spot which, to the best of our knowledge, have not been observed before. For example, a linearly polarized beam half-obstructed or shifted from the axis generates longitudinal and transverse electrical field components, both of which peak on-axis. The ratio of the intensities of these two components can be tuned by changing the shift distance, the size, and the azimuthal location of the displaced incoming beam. Moreover, such symmetry breaking of a linearly polarized beam acts as a catalyst for producing distributions of circular polarization/longitudinal spin angular momentum, as well as orbital angular momentum, in the focal plane. The simple method for generating co-incident longitudinal and transverse components with a controllable ratio may find applications in laser machining, particle manipulation, etc.

Tuning the resolution and depth of field of a lens using an adjustable ring beam illumination.

A pair of axicons with an adjustable separation between them is used to generate a variable diameter ring beam with high efficiency. This beam illuminates a lens to produce quasi-diffraction-free beams with a tunable spot size and depth of field. We studied the generated beam characteristics while changing either the ring diameter or its thickness. Such a scheme has applications in adjustable imaging, including nondiffracting beam microscopy, material processing with an irradiance above a certain threshold value, and particle trapping/manipulation.

Comparison of different schemes for stimulated Brillouin scattering enhancement.

A comparison of different schemes to enhance stimulated Brillouin Scattering (SBS) in single-mode optical fiber is performed. Specifically, we evaluated SBS generation efficiency in a 3 km length fiber with and without power recycling versus the same fiber placed in a ring resonator and in a ring resonator in a recycling configuration. For the latter case, a large number of both odd and even higher-order Stokes and anti-Stokes harmonics is generated. We show that the choice of the scheme is dictated by specific application. In addition, when incorporating a ring resonator in a Sagnac loop, a flat optical frequency comb is generated.

Extension of the span and optimization of the optical "magic carpet": generation of a wide quasi-nondiffracting light sheet.

Light sheet illumination is the basis in developing light sheet microscopy (LSM), a technique with significant advantages compared with other classical techniques. Most proposed optical systems to generate light sheets for LSM use many optical elements, which require extensive adjustments and are costly; moreover, they generate a nonuniform or semiuniform light sheet or have a short depth of field (DOF). A simple scheme using a pair of double slits and a cylindrical lens for generating a quasi-nondiffracting 2D light sheet was reported in Opt. Lett.40, 5121 (2015)OPLEDP0146-959210.1364/OL.40.005121. In the present investigation, we elaborate on the optimization of the mask used. As the separation between the two slits increases, the light sheet becomes thinner and the DOF smaller and vice versa. The slits' width does not affect the light sheet thickness, but it does affect the intensity of the side lobes. For convergence angles of the inner slits from 0.75° to 8°, an optimum ratio of the slits' separation/width of 2.182 is recommended. The obtained light sheet is quasi-diffraction-free, namely, while its DOF is comparable with that of a Gaussian beam, its diffraction broadening is substantially smaller. We also add to the previously developed configuration a Powell lens in order to expand the beam in the spanwise direction while keeping nearly constant intensity in this dimension. We perform scalar diffraction theory calculations and conduct measurements showing the nearly constant intensity in the significantly broadened span of the light sheet. Potential applications for the augmented width include imaging of certain large embryos, laser micromachining, and microparticle image velocimetry.

Tighter focus for ultrashort pulse vector light beams: change of the relative contribution of different field components to the focal spot upon pulse shortening.

We investigate the focusing of Poisson-spectrum few cycle pulsed light beams for linear, circular, azimuthal, and radial input polarizations with and without a first-order vortex. It is shown that, for all the considered cases, the focal spot is tighter when compared to long pulses due to the increased blue frequency content in the ultrashort pulses spectrum. More significantly, we show, for what we believe is the first time, that upon pulse shortening different focused beam vector components associated with different Bessel functions J0 and J1 undergo a change in the relative weight of their respective contribution to the focal spot size. This effect is caused by the different spectral dependencies of J0 and J1 near the focus. This newly discovered property of broadband ultrashort pulses could be exploited in light-matter interactions advantageously.

Separating the Siamese twins: using a π-shifted Sagnac interferometer to control the relative weight/influence of circular and linear birefringence on the loop transmission facilitating their measurement.

We demonstrate a novel method to measure circular birefringence (CB) and linear birefringence (LB) present simultaneously in the device under study. By using a π-shifted Sagnac interferometer, the scheme eliminates the dependence on incoming polarization and on the orientation angle of the linear birefringence. Moreover, due to different handedness symmetry/response of CB and LB to counter-propagating waves, the technique allows us to control the relative influence of the two birefringences leading to a requirement of only two measurements to determine both of them. Thus, comparing to Stokes polarimeters and other methods, our scheme has advantages when characterizing media containing both birefringences. Our findings are experimentally confirmed.

Time behavior of focused vector beams.

We elucidate the pecularities of time behavior of focused vector optical fields. In particular, for linear or radial incident polarizations, we demonstrate explicitly the π/2 phase delay between transverse and longitudinal components of the field generated at the focus, i.e., their appearance and reaching the peak at different instances of the optical period. For clockwise circular polarization with -1 order vortex the longitudinal component is in phase with the transverse one. For clockwise circular polarization, the same circular polarization with a +1 order vortex and for radial polarization with +1 order vortex the longitudinal field component has a constant, azimuthally rotating in time shape and it coexists with one or simultaneously with both x and y field components. In addition, we show that the recently studied ultrafast rotating dipole produced by focusing an azimuthally polarized vortex beam [Opt. Lett.41, 1605 (2016)OPLEDP0146-959210.1364/OL.41.001605] differs significantly from a pattern obtained by focusing circularly polarized light. The numerically calculated field component distributions are verified by simplifying the system with an application of a narrow ring aperture allowing precise analytical expressions to be obtained confirming the phase relations between different field components. These findings will have to be taken into account or can be taken advantage of when using vector beams in studying light-matter interactions (particle manipulation and acceleration) and especially ultrafast optical phenomena.

Ultrafast rotating dipole or propeller-shaped patterns: subwavelength shaping of a beam of light on a femtosecond time scale.

We report on a remarkable property of azimuthally (radially) polarized light beams containing a vortex or an orbital angular momentum: upon tight focusing of a first-order vortex beam, the subwavelength spot has a shape of an electric (magnetic) dipole rotating at an optical frequency. For beams with a vortex of order m, the generated pattern is propeller-shaped and rotates at a 1/m fraction of the optical frequency. The applications include petahertz control of electrical or optical conductance between two electrodes or waveguides of two-terminal junctions.

Toward the optical "magic carpet": reducing the divergence of a light sheet below the diffraction limit.

In 3D, diffraction-free or Bessel beams are well known and have found applications in diverse fields. An analog in 2D, or pseudonondiffracting (PND) beams, is a nontrivial problem, and existing methods suffer from deficiencies. For example, Airy beams are not highly localized, some PND beams have significant side lobes, and a cosine beam has to be truncated by a very narrow aperture thus discarding most of the energy. We show, both theoretically and experimentally, that it is possible to generate a quasi-nondiffracting 2D light beam in a simple and efficient fashion. This is achieved by placing a mask consisting of a pair of double slits on a cylindrical lens. The applications include light sheet microscopy/optical sectioning and particle manipulation.

Creating order with the help of randomness: generating transversely random, longitudinally invariant vector optical fields.

We show that it is possible to generate transversely random, diffraction-free/longitudinally invariant vector optical fields. The randomness in transverse polarization distribution complements a previously studied one in intensity of scalar Bessel-type beams, adding another degree of freedom to control these beams. Moreover, we show that the relative transversely random phase distribution is also conserved along the optical axis. Thus, intensity, phase, and polarization of Bessel-type beams can be transversely random/arbitrary while invariant upon propagation. Such fields may find applications in encryption/secure communications, optical trapping, etc.

Development of spot size and lateral intensity distribution generated by exponential, logarithmic, and linear axicons.

Axicons are known to produce a nearly Bessel beam transverse intensity distribution. It has been previously recognized that linear axicons and logarithmic axicons with a predefined distant depth of field (DOF) and no blocking present a development region characterized by an enlarged central spot size. In this paper, we aim to obtain a better insight on the formation of lateral light distribution in this development region. We also examine the spot size and transverse intensity distribution of the recently developed exponential axicon. We present experiments and detailed nonparaxial numerical simulations for a plane wave passing through these optical elements and show that the lateral intensity distribution they generate differs from that of a Bessel beam for a significant part of their DOF. This anomaly/irregularity in the formation of nondiffracting Bessel beams has to be taken into account in applications of these axicons, such as imaging or optical trapping.

Engineering the smallest 3D symmetrical bright and dark focal spots.

A simple roadmap is established for the construction of the smallest three-dimensional (3D) isotropic focal spots. It is achieved in a 4Pi configuration by imposing a restriction/condition of equal transverse and longitudinal spot sizes to determine the position of an annular aperture and then optimize its size. The calculations were performed for cylindrically symmetric radial, azimuthal, and circular polarizations for the cases of in-phase and out-of-phase counter-propagating beams as well as when a vortex was added to the beams. A diffraction-limited bright 3D isotropic spot containing solely longitudinal or transverse electric field components is obtained, while the 3D dark spot can be formed from one of two complementary combinations, each containing both transverse and longitudinal field components.

Righting the handedness' dichotomy: schemes of Sagnac interferometer containing chiral elements for suppression of dependence on circular birefringence and circular dichroism.

We present two configurations (one with and another without a half-wave plate) of a Sagnac interferometer (SI) containing chiral optical elements where either the Sagnac loop mirror's (SLM) reflectance is circular birefringence (CB) independent or polarization dependence/circular dichroism (CD) is canceled in both reflection and transmission. These schemes allow use of chiral components as feedback elements/filters in SLM of a laser and in switches/modulators and sensors requiring compensation of chiral media CD, as well as allowing calibration of CD measurements. We also compare/show the differences between SI containing devices with either CB or linear birefringence (LB).

Imaging properties of three refractive axicons.

The imaging properties of three types of refractive axicons are examined by using them in an imaging system. A linear axicon, a logarithmic axicon, and a Fresnel axicon are characterized by determining their point spread functions (PSFs) experimentally and by numerical simulation. The PSFs, which vary along the depth of field for the cases considered in the present investigation, are used in digital filters to denoise the images. A comparison of the imaging performance of these three optical elements is presented.

Removing left-right asymmetry in a Sagnac interferometer applied to cancel its reflectance dependence on birefringence.

We present a left-right symmetry restoring method, which removes the detrimental birefringence in the single-mode fiber Sagnac interferometer, achieved with the aid of a half waveplate oriented at a specific angle. We show theoretically and demonstrate experimentally that adding a π-shift between clockwise and counterclockwise propagating, horizontally (in fiber loop plane) polarized field components, the Sagnac loop mirror's reflection becomes independent on birefringence of an element placed in the loop.

Characterization of a refractive linear axicon with distant depth of field and no central blocking.

We report the manufacturing and characterization of a refractive linear axicon producing a linearly increasing axial intensity Bessel-type beam over a predetermined range starting away from the axicon and without central blocking when illuminated by a plane wave. This is in contrast to a classical axicon that generates a diffraction-free beam starting from the axicon tip and extending to a range limited by the input beam aperture. The measured characteristics of the beam produced by the linear axicon, including its intensity distribution and spot size, are in good agreement with the theoretical predictions. Together with logarithmic axicon and exicon, this is another element of the axicon family that can generate a prescribed intensity distribution over a chosen range/depth of field.