Rotating light fields of an azimuthally polarized light beam generated by two-belt spiral phase modulation

The tightly focused light fields of an azimuthally polarized light beam through a two-belt spiral phase plate were investigated. The focused light fields are presented in accordance with vectorial diffraction theory. The results show that a rotating light field with different intensity patterns can be produced by altering the azimuthal polarization state and modulating the two-belt spiral phase. A concurrent change in spiral handedness in the two-belt phase plate causes the rotation to occur along the direction of propagation, and the relative angular offset in the two-belt spiral phase plate can be exploited to rotate the light fields. The proposed method is useful for engineering the intensity distribution near the focal plane and related applications.     

Dielectric tensor measurement from a single Mueller matrix image

A technique for measuring dielectric tensors in anisotropic layered structures, such as thin films of biaxial materials, is demonstrated. The ellipsometric data are collected in a quasi-monochromatic Mueller matrix image acquired over a large range of incident and azimuthal angles by illuminating a very small area on the sample with a focused beam from a modulating polarization state generator. After the beam interacts with the sample, the reflected and/or transmitted light is collected using an imaging polarization state analyzer. An image of the exit pupil of a collection objective lens is formed across a CCD such that each pixel collects light from a different angle incident on the sample, thus acquiring ellipsometric data at numerous incident angles simultaneously. The large range of angles and orientations is necessary to accurately determine dielectric tensors. The small but significant polarization aberrations of the low-polarization objective lenses used to create and collect the focused beams provide a significant challenge to accurate measurement. Measurements are presented of a thin-film E-type polarizer and a stretched plastic biaxial film.     

Singularities in cylindrical vector beams

Cylindrical vector beams with azimuthal and radial polarization distributions are studied for singularities. It is shown experimentally that these beams have screw dislocation as well as edge dislocation at the same time. The relation between phase and polarization of light beam is the key to understand this fact. We envisage that this has potential application in phase synthesis using polarization engineering. Further, the polarization singularities in these inhomogeneously polarized beams are examined by measuring Stokes parameters across the cross-section of these beams.     

Tight focusing properties of hybridly polarized vector beams

We theoretically investigate the tight focusing properties of hybridly polarized vector beams. Some numerical results are obtained to illustrate the intensity, phase, and polarization of tightly focused hybridly polarized vector beams. It is shown that the shape of the focal pattern may change from an elliptical beam to a ring focus with increasing radial index. The phase distribution around the tightly focused ring is shown to be the helical phase profile, indicating that the radial-variant spin angular momentum of hybridly polarized vector beams can be converted into the radial-variant orbital angular momentum.     

Polarization pattern of vector vortex beams generated by q-plates with different topological charges

We describe the polarization topology of the vector beams emerging from a patterned birefringent liquid crystal plate with a topological charge q at its center (q-plate). The polarization topological structures for different q-plates and different input polarization states have been studied experimentally by measuring the Stokes parameters point-by-point in the beam transverse plane. Furthermore, we used a tuned q=1/2-plate to generate cylindrical vector beams with radial or azimuthal polarizations, with the possibility of switching dynamically between these two cases by simply changing the linear polarization of the input beam.     

Dark-field imaging with cylindrical-vector beams

Dark-field illumination provides an imaging mode that rejects specular light, thereby highlighting edge features. We analyze dark-field imaging by using cylindrical vector beam illumination with a confocal microscope equipped with a microstructure fiber mode filter. A numerical model based on rigorous coupled-wave analysis has been used to analyze the method. We acquired images of separated edges features to investigate the edge separation resolution of the method. A through-focus comparison of azimuthal and radial polarization shows a measurable dependence of edge separation on polarization.     

Depth-minimized, large period half-wave corrugation for linear to radial and azimuthal polarization transformation by grating-mode phase management

The transformation of the polarization distribution of a laser beam from linear to radial and azimuthal by means of a subwavelength binary corrugation etched in a high-index substrate faces fabrication difficulties and an inherent contradiction preventing the achievement of both conditions of 100% transmission and of π phase difference between polarization components. The contradiction is solved by resorting to an easily fabricable high-index corrugation on a low-index substrate where a larger period gives rise to grating-mode reflection/transmission phases that permit the fulfillment of both conditions with a depth-minimized corrugation. From the principle of the solution, a targeted numerical search gives the complete set of the corresponding shallow structures, achieving polarization rotation in a fitting analytical form versus normalized variables.     

Enlightening darkness to diffraction limit and beyond: comparison and optimization of different polarizations for dark spot generation

We compare generation of a dark spot using focusing of beams with azimuthal polarizion, radial polarization with a vortex, and a circular polarization with either a first or second order vortex. By optimization of the amplitude-phase pupil, it is ascertained that azimuthal polarization is the most suitable one to obtain the diffraction bounded dark spot per se whose scalar approximation limit has FWHM=0.29λ. Consequently, for dark spot generation, this polarization plays the role of the radial polarization in creation of the diffraction-limited bright spot. Using azimuthal polarization, it is shown that an amplitude-phase filter allows generation of a subdiffractive dark spot in a prescribed finite area.     

A New Method for Spectral Performance Evaluation of a Chromatic and Achromatic Quarter-Wave Retarder

When a polarized polychromatic beam passes through a quarter-wave retarder, the constituent spectral components suffer different changes in the state of polarization. As a result, when the beam passes through an analyzer, the intensity of the resultant beam changes, depending on the orientation of the analyzer, state of polarization of the input beam, spectral and spatial intensity distribution of the source and the wavelength-dependent retardance of the quarter-wave retarder. The intensity variation of the resulting beam is theoretically and experimentally observed, with the variation of the azimuthal angle of the analyzer for film-type chromatic and prism-type achromatic quarter-wave retarders. The spectral performances of achromatic retarders are generally evaluated by measuring retardances at discrete wavelengths by using a monochromatic beam of light over the wavelength range of interest. In this study, a simple method is used for computing the fractional nonlinear polarization (FNLP) from theoretically and experimentally obtained intensity variations for evaluating the spectral performance of both achromatic and chromatic quarter-wave retarders operating over a broad spectral range in the visible region using a polychromatic beam of light. FNLP variation is also shown for a film-type chromatic quarter-wave retarder using a monochromatic source of light. The experimentally obtained values are compared with theoretical values and a good agreement is observed. The applications of the method for the performance evaluation of quarter-wave retarders are discussed.     

Phase compensation of azimuthally polarized j(1) bessel-gaussian laser beams

As other semiconductor lasers, concentric-circle-grating, surface-emitting lasers are compact, light, and efficient. However, unlike other semiconductor lasers, they emit high-power, low-divergence azimuthally polarized J(1) Bessel-Gaussian beams. Because of their azimuthal polarization, they have a null at the center of the beam that makes them undesirable for certain applications. Binary phase compensation, a lossless technique previously used to improve the far-field profile of linearly polarized Hermite-Gaussian beams, is adapted to these azimuthally polarized beams to rid them of their axial nulls and improve their beam profile.     

Optical response of a single spherical particle in a tightly focused light beam: application to the spatial modulation spectroscopy technique

We develop a new and numerically efficient formalism to describe the general problem of the scattering and absorption of light by a spherical metal or dielectric particle illuminated by a tightly focused beam. The theory is based on (i) the generalized Mie theory equations, (ii) the plane-wave decomposition of the converging light beam, and (iii) the expansion of a plane wave in terms of vector spherical harmonics. The predictions of the model are illustrated in the case of silver nanoparticles. The results are compared with the Mie theory in the local approximation. Finally, some effects related to the convergence of the beam are analyzed in the context of experiments based on the spatial modulation spectroscopy technique.     

Focal shift of a focused partially coherent Laguerre-Gaussian beam of all orders

Abstract

We explore the focusing properties of a partially coherent Laguerre–Gaussian (LG) beam of all orders, particularly the focal shift (i.e. the shift of the actual focal plane away from the geometrical focal plane). We derive the analytical expressions for the average intensity and the effective beam width of a focused partially coherent LG beam, and we adopt the minimum effective beam width instead of the conventional maximum on-axis intensity to determine the actual focal plane. It is found that the focused beam shape, minimum effective beam width and the focal shift of a focused partially coherent LG beam are determined by its initial coherence width, radial mode order and azimuthal mode order (i.e. topological charge) together. Our results may be useful for optical trapping and micro-fabrication, where precise focal position and prescribed beam shape are required.     

Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. I. Localized model description of an on-axis tightly focused laser beam with spherical aberration

Calculation of the radiation trapping force in laser tweezers by use of generalized Lorenz-Mie theory requires knowledge of the shape coefficients of the incident laser beam. The localized version of these coefficients has been developed and justified only for a moderately focused Gaussian beam polarized in the x direction and traveling in the positive z direction. Here the localized model is extended to a beam tightly focused and truncated by a high-numerical-aperture lens, aberrated by its transmission through the wall of the sample cell, and incident upon a spherical particle whose center is on the beam axis. We also consider polarization of the beam in the y direction and propagation in the negative z direction to be able to describe circularly polarized beams and reflected beams.     

Changes of intensity distribution of a tightly focused plane-wave pulse induced by lens dispersion

The tightly focusing properties of a linearly polarized plane-wave pulse through a high numerical aperture (NA) lens with dispersion are formulated. The effects of lens dispersion on the tightly focused intensity distribution in the focal region are studied in detail. It is found that, because of the lens dispersion, the intensity of the side lobe of the focused light spot strengthens in the transverse direction and the size of the main lobe of the focused light spot increases in the longitudinal direction as the pulse duration decreases. In addition, we compare the effects of dispersion of lens made by different types of glass on tightly focusing properties of a pulse beam. The results will be helpful to choose suitable high NA objective lens in experiment.     

Symmetrically coated pellicle beam splitters for dual quarter-wave retardation in reflection and transmission

A trilayer pellicle that consists of a high-index center layer that is symmetrically coated on both sides by a low-index film can be designed to produce differential reflection and transmission phase shifts of +/- 90 degrees at oblique incidence and equal throughput for the p and the s polarizations. Such a device splits a beam of incident linearly polarized light into two orthogonal circularly polarized components that travel in well-separated angular directions. Examples of infrared dual quarter-wave retarders that use a symmetrically coated Ge pellicle at 77 degrees angle of incidence are presented. A 50-50% splitter requires a symmetric pellicle with at least five layers. Error analysis shows that the thicknesses of the high-index layers must be tightly controlled. These circular polarization beam splitters are intended for operation with a well-collimated light source and can be used as the basis of a novel circular polarization Michelson interferometer.     

Measurement of the surface profile of an axicon lens with a polarization phase-shifting shearing interferometer

We present a Twyman-Green interferometer (TGI)-based polarization phase-shifting shearing interferometric technique for testing the conical surface of an axicon (AX) lens. In this technique, the annular beam generated due to the passing of an expanded collimated laser beam traveling along the axis of revolution of the transparent glass AX element is split up into its reflected and transmitted components, having the plane of polarization in the orthogonal planes, by the polarization beam splitter (PBS) cube of the TGI-based optical setup. The split-up components are made to travel unequal paths along the two arms of the TGI and are recombined by the PBS. Because of the difference in path lengths traveled by the annular conical beams, a linear shear is introduced along the radial direction between the interfering components. Thus, the resulting interference pattern gives a map of the optical path difference (OPD) between two successive close points along a radial direction on the conical surface of the AX lens. The OPD map along radial directions, and hence the slopes/profiles of the conical surface, are obtained by applying polarization phase-shifting interferometry. Results obtained for an AX lens are presented.     

Smallest flattop focus by polarization engineering

Spatial engineering of polarization as a new method of beam shaping is analyzed by using scalar diffraction theory. For the one-dimensional case, it is shown that the smallest flattop far-field distribution can be obtained by adopting a linear polarization that changes direction as a linear function of location in the pupil plane. The resulting light field is functionally equivalent to a cosinusoidal function modulation of the wavefront but maintains high efficiency. This polarization beam shaping technique proves to be highly useful in applications where diffraction effects need to be taken into account. The extension of this technique to two-dimensional beam shaping is also demonstrated.     

Electromagnetic field for a tightly focused beam incident upon ordinary and layered plane surfaces

A solution procedure is developed for the determination of the electromagnetic field that results from the interaction of a tightly focused beam with a plane surface with and without a layer. The effects of angle of incidence, relative index of refraction, polarization, layer thickness, and incident beam profile on the resulting electromagnetic field distribution are demonstrated.     

Scattering of a tightly focused beam by an optically trapped particle

Near-forward scattering of an optically trapped 5-mum-radius polystyrene latex sphere by the trapping beam was examined both theoretically and experimentally. Since the trapping beam is tightly focused, the beam fields superpose and interfere with the scattered fields in the forward hemisphere. The observed light intensity consists of a series of concentric bright and dark fringes centered about the forward-scattering direction. Both the number of fringes and their contrast depend on the position of the trapping beam focal waist with respect to the sphere. The fringes are caused by diffraction that is due to the truncation of the tail of the trapping beam as the beam is transmitted through the sphere.     

Spectral Filtering of Light Possessing Non-gaussian Statistics

Abstract

We have used a heterodyne detection technique to observe the intensity fluctuations and statistics of non-Gaussian scattered light, formed by illuminating a rotating ground-glass screen with a tightly focused laser beam. This type of light field contains the characteristic ‘glints’ commonly observed with laser radar systems. It is demonstrated both theoretically and experimentally that the statistics of the fluctuating intensity are significantly altered by spectral filtering of the light. In the limit, when the filter bandwidth becomes much narrower than the overall spectral linewidth of the scattered light, the distribution of intensities tends to that expected for complex Gaussian field statistics (i.e. a negative exponential). We compare this behaviour with that obtained by other workers for spectral filtering within the linewidth of light from a single-mode laser.