Longitudinal field modes probed by single molecules

Nonparaxial and paraxial focusing of azimuthal-variant vector beams

Based on the vectorial Rayleigh-Sommerfeld formulas under the weak nonparaxial approximation, we investigate the propagation behavior of a lowest-order Laguerre-Gaussian beam with azimuthal-variant states of polarization. We present the analytical expressions for the radial, azimuthal, and longitudinal components of the electric field with an arbitrary integer topological charge m focused by a nonaperturing thin lens. We illustrate the three-dimensional optical intensities, energy flux distributions, beam waists, and focal shifts of the focused azimuthal-variant vector beams under the nonparaxial and paraxial approximations.

Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent

Optical beams exhibiting a long depth of focus and a minimum spot size can be obtained with the tight focusing of a narrow annulus of radially polarized light, leading to a needle of longitudinally polarized light. Such beams are of increasing interest for their applications, for example in optical data storage, particle acceleration, and biomedical imaging. Hence one needs to characterize the needles of longitudinally polarized light obtained with different focusing optics and incident beams. In this paper, we present analytical expressions for the electric field of such a nearly nondiffracting, subwavelength beam obtained with a parabolic mirror or an aplanatic lens. Based on these results, we give expressions of the transverse and longitudinal full widths at half maximum of the focal lines as a function of the width of the incident annular beam and we compare the performances of the two focusing systems. Then, we propose a practical solution to produce a needle of longitudinally polarized light with a tunable axial extent and a transverse width reaching the theoretical limit of 0.36λ.

Axial separation of orthogonally polarized focal field components due to a radially polarized beam

In this paper, we investigate the field distribution in the focal volume of an aberrated radially polarized beam. Using two different forms of the vectorial diffraction theory, we show that the presence of defocus in the beam displaces both the axially and the radially polarized fields parallel to the optical axis of the focusing lens, while the presence of spherical aberration primarily shifts the longitudinally polarized field only. This facilitates axial separation of the two orthogonally polarized field components, resulting in a significant boost to the ratio of the peak longitudinally polarized field to the peak laterally polarized field in the focal plane. We further show that with an appropriate combination of oppositely signed defocus and spherical aberration, the energy density in the focal volume due to the longitudinally polarized field can be caused to peak at the focal plane. The results obtained are expected to be beneficial to the applications requiring a stronger longitudinally polarized focal field relative to the laterally polarized focal field component.

Focusing properties of vector vortex beams emitted by photonic-crystal lasers

We experimentally investigate the focusing properties of first- and second-order vector beams and vector vortex beams generated by photonic-crystal lasers. When the azimuthal indices of the vector beam (l) and the phase dependence (n) match, strong intensity appears at the center of focus. Our theoretical analyses agree well with the experimental results and predict that the central intensity has circular polarization.

Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams

We introduce an imaging technique based on second-harmonic generation with cylindrical vector beams that is extremely sensitive to three-dimensional orientation and nanoscale morphology of metal nano-objects. Our experiments and second-harmonic field calculations based on frequency-domain boundary element method are in very good agreement. The technique provides contrast for structural features that cannot be resolved by linear techniques or conventional states of polarization and shows great potential for simple and cost-effective far-field optical imaging in plasmonics.

Invited review article: combining scanning probe microscopy with optical spectroscopy for applications in biology and materials science

This is a comprehensive review of the combination of scanning probe microscopy (SPM) with various optical spectroscopies, with a particular focus on Raman spectroscopy. Efforts to combine SPM with optical spectroscopy will be described, and the technical difficulties encountered will be examined. These efforts have so far focused mainly on the development of tip-enhanced Raman spectroscopy, a powerful technique to detect and image chemical signatures with single molecule sensitivity, which will be reviewed. Beyond tip-enhanced Raman spectroscopy and/or topography measurements, combinations of SPM with optical spectroscopy have a great potential in the characterization of structure and quantitative measurements of physical properties, such as mechanical, optical, or electrical properties, in delicate biological samples and nanomaterials. The different approaches to improve the spatial resolution, the chemical sensitivity, and the accuracy of physical properties measurements will be discussed. Applications of such combinations for the characterization of structure, defects, and physical properties in biology and materials science will be reviewed. Due to the versatility of SPM probes for the manipulation and characterization of small and/or delicate samples, this review will mainly focus on the apertureless techniques based on SPM probes.

Quantitative scheme for full-field polarization rotating fluorescence microscopy using a liquid crystal variable retarder

We present a quantitative scheme for full-field polarization rotating fluorescence microscopy. A quarter-wave plate, in combination with a liquid crystal variable retarder, provides a tunable method to rotate polarization states of light prior to its being coupled into a fluorescence microscope. A calibration of the polarization properties of the incident light is performed in order to correct for elliptical polarization states. This calibration allows the response of the sample to linear polarization states of light to be recovered. Three known polarization states of light can be used to determine the average fluorescent dipole orientations in the presence of a spatially varying dc offset or background polarization-invariant fluorescence signal. To demonstrate the capabilities of this device, we measured a series of full-field fluorescence polarization images from fluorescent analogs incorporated in the lipid membrane of Burkitts lymphoma CA46 cells. The fluorescent lipid-like analogs used in this study are molecules that are labeled by either a DiI (1,1(')-Dioctadecyl 3,3,3('),3(')-Tetramethylindocarbocyanine) fluorophore in its head group or a Bodipy (4,4-difluoro-4-bora-3a,4a-diaza-s-indacene) molecule in its acyl chain. A spatially varying contrast in the normalized amplitude was observed on the cell surface, where the orientation of the DiI molecules is tangential to the cell membrane. The internally labeled cellular structures showed zero response to changes in linear polarization, and the net linear polarization amplitude for these regions was zero. This instrument provides a low cost calibrated method that may be coupled to existing fluorescence microscopes to perform investigations of cellular processes that involve a change in molecular orientations.

Cross-polarization of linearly polarized Hermite-Gauss laser beams

Evolution of transverse intensity profiles for the dominant and cross-polarization components of linearly polarized Hermite-Gauss laser beams is studied experimentally as the beams propagate away from their waist. Measured intensity profiles and their evolution with propagation are in good agreement with the theoretical predictions.

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.

Near-field probing of slow Bloch modes on photonic crystals with a nanoantenna

We study the near-field probing of the slow Bloch laser mode of a photonic crystal by a bowtie nano-aperture (BNA) positioned at the end of a metal-coated fiber probe. We show that the BNA acts as a polarizing nanoprobe allowing us to extract information about the polarization of the near-field of the slow-light mode, without causing any significant perturbation of the lasing process. Near-field experiments reveal a spatial resolution better than λ/20 and a polarization ratio as strong as 110. We also demonstrate that the collection efficiency is two orders of magnitude larger for the BNA than for a 200 nm large circular aperture opened at the apex of the same metal-coated fiber tip. The BNA allows for overcoming one of the main limitations of SNOM linked to the well-known trade off between resolution and signal-to-noise ratio.

Polarization-dependent ablation of silicon using tightly focused femtosecond laser vortex pulses

We demonstrate experimentally that, in a tight focusing geometry, circularly polarized femtosecond laser vortex pulses ablate material differently depending on the handedness of light. This effect offers an additional degree of freedom to control the shape and size of laser-machined structures on a subwavelength scale.

Cylindrical vector beams for rapid polarization-dependent measurements in atomic systems

We demonstrate the use of cylindrical vector beams - beams with spatially varying polarization - for detecting and preparing the spin of a warm rubidium vapor in a spatially dependent manner. We show that a modified probe vector beam can serve as an atomic spin analyzer for an optically pumped medium, which spatially modulates absorption of the beam. We also demonstrate space-variant atomic spin by optical pumping with the vector beams. The beams are thus beneficial for making single-shot polarization-dependent measurements, as well as for providing a means of preparing samples with position-dependent spin.

Generating inhomogeneously polarized higher-order laser beams by use of diffractive optical elements

We propose an improved version of the earlier developed optical arrangement for generating inhomogeneously polarized laser light modes with the aid of a diffractive optical element (DOE) with carrier frequency. By eliminating lenses from the optical arrangement, we achieve the miniaturization, reduced light losses, a smaller number of parameters being matched, and a simpler system adjustment procedure. Note that all the capabilities of the previous version, namely, the universality and simple readjustment to different polarization types, are fully retained. The numerical modeling of the polarization mode combiner has made it possible to analyze its performance and capabilities. In the experiments, the quality of the resulting beams is shown to be improved. For generating higher-order cylindrical beams, a lower-order mode at the output of the polarization mode combiner is additionally transformed with a DOE that operates in the zero diffraction order, introducing radial phase changes.

Fiber based polarization filter for radially and azimuthally polarized light

We demonstrate a new fiber based concept to filter azimuthally or radially polarized light. This concept is based on the lifting of the modal degeneracy that takes place in high numerical aperture fibers. In such fibers, the radially and azimuthally polarized modes can be spectrally separated using a fiber Bragg grating. As a proof of principle, we filter azimuthally polarized light in a commercially available fiber in which a fiber Bragg grating has been written by a femtosecond pulsed laser.

Generation of radially polarized beams based on thermal analysis of a working cavity

The laser oscillation and polarization behavior of a side-pumped Nd:YAG laser are studied theoretically and experimentally by a thermal model for a working cavity. We use this model along with the Magni method, which gives a new stability diagram, to show important characteristics of the resonator. High-power radially and azimuthally polarized laser beams are obtained with a Nd:YAG module in a plano-plano cavity. Special regions and thermal hysteresis loops are observed in the experiments, which are concordant with the theoretical predictions.

Generation of nondiffracting quasi-circular polarization beams using an amplitude modulated phase hologram

We propose an approach to the generation of nondiffracting quasi-circularly polarized beams by a highly focusing azimuthally polarized beam using an amplitude modulated spiral phase hologram. Numerical verifications are implemented in the calculation of the electromagnetic fields and Poynting vector field near the focus based on the vector diffraction theory, and the polarization of the wavefront near the focal plane is analyzed in detail by calculating the Stokes polarization parameters. It is found that the electric field, magnetic field, and Poynting vector field can simultaneously be uniform and nondiverging over a relatively long axial range of ~7.23λ. In the transverse plane, the ellipticity and azimuthal angle of the local polarization ellipse varies from point to point. No polarization singularity and phase singularity are found at the beam center, which makes the bright spot possible.

Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light

A higher-order Poincaré sphere and Stokes parameter representation of the higher-order states of polarization of vector vortex beams that includes radial and azimuthal polarized cylindrical vector beams is presented. The higher-order Poincaré sphere is constructed by naturally extending the Jones vector basis of plane wave polarization in terms of optical spin angular momentum to the total optical angular momentum that includes higher dimensional orbital angular momentum. The salient properties of this representation are illustrated by its ability to describe the higher-order modes of optical fiber waveguides, more exotic vector beams, and a higher-order Pancharatnam-Berry geometric phase.

Finite-difference time-domain (FDTD) analysis on the interaction between a metal block and a radially polarized focused beam

Radially polarized focused beams have attracted a great deal of attention because of their unique properties characterized by the longitudinal field. Although this longitudinal field is strongly confined to the beam axis, the energy flow, i.e., the Poynting vector, has null intensity on the axis. Hence, the interaction of the focused beam and matter has thus far been unclear. We analyzed the interactions between the focused beam and a subwavelength metal block placed at the center of the focus using three-dimensional finite-difference time-domain (FDTD) calculation. We found that most of the Poynting energy propagates through to the far-field, and that a strong enhancement of the electric field appeared on the metal surface. This enhancement is attributed to the constructive interference of the symmetric electric field and the coupling to the surface plasmon mode.

Efficient excitation of surface plasmons in metal nanorods using large longitudinal component of high index nano fibers

We report theoretical calculations of the mode fields of high index lead silicate and silicon nano fibers, and show that their strong longitudinal component enables efficient excitation of surface plasmons within a silver nanorod placed at the fiber tip. An excitation efficiency 1600 times higher than that of the standard single mode fibers has been achieved using a 350nm diameter silicon fiber at 1.1μm wavelength, while a factor of 640 times higher efficiency is achieved for a 400nm diameter lead silicate F2 glass fiber. The strong localized field emerging from the end of the rod serves as a nano-scale source with adjustable beam width, and such sources offer a new approach to high-resolution microscopy, particle manipulation and sensing.

Influence of the higher-orders of diffraction on the pattern evolution for tightly focused beams

The mechanism of the nonparaxial propagation for tightly focused beams is investigated in the view of the influence of the higher-orders of diffraction (HOD). The HOD induce novel propagation characteristics which are crucially different from those predicted by the traditional paraxial theory. Based on the management of HOD, we propose an approach on controlling the intensity pattern of the focus to satisfy the application requirements.

Light microscopy with doughnut modes: a concept to detect, characterize, and manipulate individual nanoobjects

Higher order laser modes, mainly called doughnut modes (DMs) have use in many different branches of research, such as, bio-imaging, material science, single-molecule microscopy, and spectroscopy. The main reason of their increasing importance is that recently, the techniques to generate well-defined DMs have been refined or rediscovered. Although their potential is still not fully utilized, their specifically polarized field distribution gives rise to a wide field of applications. They are contributing to complete our fundamental knowledge of the optical properties of single emitting species, such as molecules, nanoparticles, or quantum dots, offering insight into the three-dimensional dipole or particle orientation in space. The perfect zero intensity in the focus center qualifies some DMs for stimulated emission depletion (STED) microscopy. For the same reason, they have been suggested for trapping and tweezing applications.

On focused fields with maximum electric field components and images of electric dipoles

We study focused fields which, for a given total power and a given numerical aperture, have maximum electric field amplitude in some direction in the focal point and are linearly polarized along this direction. It is shown that the optimum field is identical to the image of an electric dipole with unit magnification. In particular, the field which is the image of an electric dipole whose dipole vector is parallel to the optical axis, is identical to the field whose longitudinal component is maximum at the image point.

Probing the radiative transition of single molecules with a tunable microresonator

Using a tunable optical microresonator with subwavelength spacing, we demonstrate controlled modulation of the radiative transition rate of a single molecule, which is measured by monitoring its fluorescence lifetime. Variation of the cavity length changes the local mode structure of the electromagnetic field, which modifies the radiative coupling of an emitting molecule to that field. By comparing the experimental data with a theoretical model, we extract both the pure radiative transition rate as well as the quantum yield of individual molecules. We observe a broad scattering of quantum yield values from molecule to molecule, which reflects the strong variation of the local interaction of the observed molecules with their host environment.

Revealing local field structure of focused ultrashort pulses

We utilize the interaction of tightly focused ultrashort pulses with transparent media to imprint their local polarization in the focal region. In particular, we demonstrate that this technique allows for a subwavelength resolution diagnostic of complex polarization states including the presence of the longitudinal component of the electric field. Moreover, we demonstrate the first ever material ablation with the longitudinal electric field of femtosecond pulses.

Excitation isotropy of single CdSe/ZnS nanocrystals

We study the dimensionality of the excitation transition dipole moment for single CdSe/ZnS core-shell nanocrystals using azimuthally and radially polarized laser modes. The comparison of measured and simulated single nanocrystal excitation patterns shows that single CdSe/ZnS quantum dots possess a spherically degenerated excitation transition dipole. We show that the dimensionality of the excitation transition dipole moment distribution is the same for all individual CdSe/ZnS nanocrystals, disregarding the difference in core size and irrespective of variations in the local environment. In contrast to the emission transition dipole moment, which is oriented in one plane, the excitation transition dipole moment of a single CdSe/ZnS quantum dots possesses an isotropy in three dimensions.

Passively mode-locked radially polarized laser based on ceramic Nd:YAG rod

A mode-locked radially polarized laser based on a ceramic Nd:YAG rod that was transversely pumped by LD bars. The maximum output power of 10.6 W was achieved with the frequency of 45 MHz, the average pulse width of 75 ps Abstract: By using a semiconductor saturable absorber mirror, we demonstrated the generation of and the beam quality of M2 = 2.11.

Nonlinear generation of broadband polarisation vortices

Polarisation-vortex beams over a broad wavelength region are generated by nonlinear transformation of a radially-polarized mode in a specially-designed optical fiber. The beams are produced by stimulated Raman scattering from 20-ns 1064-nm laser pulses, and up to the 4th order Stokes shift is observed. Measurements of polarization-selected intensity profiles of individual Stokes components show that the generated light maintains the desired spatial intensity distribution and radial polarization of the pump mode. At the highest pump power, 300 W, the process creates a coherent vortex beam from 1064 nm to 1310 nm, which is a span of nearly 250 nm.

Engineering of high purity ultra-long optical needle field through reversing the electric dipole array radiation

We report a new method to create high purity longitudinally polarized field with extremely long depth of focus in the focal volume of a high numerical aperture (NA) objective lens. Through reversing the radiated field from an electric dipole array situated near the focus of the high-NA lens, the required incident field distribution in the pupil plane for the creation of an ultra-long optical needle field can be found. Numerical examples demonstrate that an optical needle field with a depth of focus up to 8λ is obtainable. Throughout the depth of focus, this engineered focal field maintains a diffraction limited transverse spot size (<0.43λ) with high longitudinal polarization purity. From the calculated pupil plane distribution, a simplified discrete complex pupil filter can be designed and significant improvements over the previously reported complex filters are clearly demonstrated.

Three-dimensional, arbitrary orientation of focal polarization

We demonstrate a simple setup for generating a three-dimensional arbitrary orientation of the polarization vector in a laser focus. The key component is the superposition of a linearly and a radially polarized laser beam, which both can be controlled individually in intensity and relative phase. We exemplify the usefulness of this setup by determining the spatial orientation of a single silver nanorod in three-dimensional space by recording the angle-variable backscattered light intensity.

Studying surface chemistry beyond the diffraction limit: 10 years of TERS

The use of an illuminated scanning probe tip to greatly enhance Raman scattering from the sample underneath the tip is one of the most intriguing developments in optical spectroscopy, and the steeply increasing number of publications per year shows that chemists, physicists and biologists alike recognize the importance and great potential of this technique. With tip-enhanced Raman spectroscopy (TERS), one of the main goals in surface science has been achieved, namely the combination of scanning probe microscopy and optical spectroscopy such as Raman spectroscopy. Important here is the use of the tip as an optical antenna to substantially increase the emitted radiation and to simultaneously improve the optical resolution much beyond the Abbe diffraction limit. This permits the correlation of topographic and chemical information of the same surface region. The synergy of detailed insight in morphology and the chemical nature of the target species facilitates data interpretation significantly and enables characterization of interfaces at the nanometer scale. A wide variety of substrates and sample molecules have been studied with TERS since the first publication of tip-enhanced Raman spectra, and the technique has reached a first level of maturity on its 10th birthday, with TERS applications extending into various research fields from surface chemistry over biology to nanoscale physics.

Bowtie nano-aperture as interface between near-fields and a single-mode fiber

We present the development and study of a single bowtie nano-aperture (BNA) at the end of a monomode optical fiber as an interface between near-fields/nano-optical objects and the fiber mode. To optimize energy conversion between BNA and the single fiber mode, the BNA is opened at the apex of a specially designed polymer fiber tip which acts as an efficient mediator (like a horn optical antenna) between the two systems. As a first application, we propose to use our device as polarizing electric-field nanocollector for scanning near-field optical microscopy (SNOM). However, this BNA-on-fiber probe may also find applications in nanolithography, addressing and telecommunications as well as in situ biological and chemical probing and trapping.

On the experimental investigation of the electric and magnetic response of a single nano-structure

We demonstrate an experimental method to separately test the optical response of a single sub-wavelength nano-structure to tailored electric and magnetic field distributions in the optical domain. For this purpose a highly focused y-polarized TEM10-mode is used which exhibits spatially separated longitudinal magnetic and transverse electric field patterns. By displacing a single sub-wavelength nano-structure, namely a single split-ring resonator (SRR), in the focal plane, different coupling scenarios can be achieved. It is shown experimentally that the single split-ring resonator tested here responds dominantly as an electric dipole. A much smaller but yet statistically significant magnetic dipole contribution is also measured by investigating the interaction of a single SRR with a magnetic field component perpendicular to the SRR plane (which is equivalent to the curl of the electric field) as well as by analyzing the intensity and polarization distribution of the scattered light with high spatial resolution. The developed experimental setup as well as the measurement techniques presented in this paper are a versatile tool to investigate the optical properties of single sub-wavelength nano-structures.

Polarization characterization in the focal volume of high numerical aperture objectives

In this paper the polarization states of linearly and radially polarized plane wave and doughnut beams in the focal volume of high numerical aperture objectives are studied. Through manipulating the incident polarization states of laser beams as well as the apodization of an objective and adjusting the numerical aperture of an objective, focal fields dominantly with either one transverse component or one longitudinal component can be generated. Furthermore, tailored polarization distributions with three polarization components of the same strength are also found.

Vectorial fiber laser using intracavity axial birefringence

In this paper we investigate the polarization properties of a fiber laser with an intracavity c-cut calcite crystal that is capable of producing reconfigurable vectorial output modes. Vectorial modes with radial, azimuthal and generalized cylindrical vector polarizations can be generated by translating one lens within the laser cavity. Detailed studies of the mode polarization evolution show that the modes inside the laser cavity can be spatially homogeneously polarized in one section of the cavity while being spatially inhomogeneously polarized in another section of the cavity, which opens the opportunities for many potential new fiber laser design possibilities and applications. Furthermore, more complicated vectorial vortex output modes are also observed by purposefully introducing angular misalignments.

Effects of scatterers' sizes on near-field coherent anti-Stokes Raman scattering under tightly focused radially and linearly polarized light excitation

We employ the finite-difference time-domain (FDTD) technique as a numerical approach to studying the effects of scatterers' sizes on near-field coherent anti-Stokes Raman scattering (CARS) microscopy under tightly focused radially and linearly polarized light excitations. The FDTD results show that in a uniform medium (water), the full width at half maximum (FWHM) (transverse resolution) of radially polarized near-field CARS (RP-CARS) radiation is approximately 7.7% narrower than that of linearly polarized near-field CARS (LP-CARS) imaging, whereas the depth of focus (DOF) of RP-CARS radiation is 6.5% longer than LP-CARS. However, with the presence of scatterers in the uniform medium, both the FHWM and DOF of near-field RP-CARS radiation become much narrower compared to those of near-field LP-CARS radiation. In addition, the signal to nonresonant background ratio of near-field RP-CARS is significantly improved when the scatterer's size is larger than a half wavelength of the pump light field. This work suggests that near-field CARS radiations are strongly influenced by the scatterers' sizes in the medium; and near-field RP-CARS microscopy is superior to the near-field LP-CARS by providing both higher transverse and axial resolutions for three-dimensional molecular imaging of fine structures in biological systems.

Design of DOE for generating a needle of a strong longitudinally polarized field

A needle of strong longitudinally polarized field with homogeneous intensity along the optical axis, long depth of focus, and subdiffraction beam size can be generated by focusing a radially polarized light with a high-NA lens and a diffractive optical element (DOE) with belts. A method combining the global-search-optimization algorithm and the tight focusing properties of the radially polarized light is proposed to design the DOE. Based on the tight focusing properties, the light incident on the lens is divided into two parts: areas A and B. We discover that the longitudinal field in the focal region is mainly dependent on the number of belts in area B but not the total number of belts in the DOE.

Grating-based optical scheme for the universal generation of inhomogeneously polarized laser beams

We propose and analyze a new optical system to transform linearly polarized laser modes into axially symmetric (radial or azimuthal) modes that show more promise in various applications, as well as generating various inhomogeneously polarized configurations. The system is based on the coherent composition of modal beams with phase diffraction gratings that allow the intermode phase shift to be varied without the need for auxiliary components. What makes the system simple and universal is the use of diffractive optical elements to generate required mode patterns with specific space orientation along with the simultaneous generation of different beams with different transverse mode content, all of which can subsequently be combined.

Full vectorial imaging of electromagnetic light at subwavelength scale

We propose a concept of near-field imaging for the complete experimental description of the structure of light in three dimensions around nanodevices. It is based on a near-field microscope able to simultaneously map the distributions of two orthogonal electric-field components at the sample surface. From a single 2D acquisition of these two components, the complementary electric and magnetic field lines and Poynting vector distributions are reconstructed in a volume beneath the sample using rigorous numerical methods. The experimental analysis of localized electric and magnetic optical effects as well as energy flows at the subwavelength scale becomes possible. This work paves the way toward the development of a complete electromagnetic diagnostic of nano-optical devices and metamaterials.

Sub-wavelength focal spot with long depth of focus generated by radially polarized, narrow-width annular beam

We demonstrate the formation of a sub-wavelength focal spot with a long depth of focus using a radially polarized, narrow-width annular beam. Theoretical analysis predicts that a tighter focal spot (approximately 0.4 lambda) and longer depth of focus (more than 4 lambda) can be formed by a longitudinal electric field when the width of the annular part of the beam is decreased. Experimental measurements using a radially polarized beam from a photonic crystal laser agree well with these predictions. Tight focal spots with long depths of focus have great potential for use in high-tolerance, high-resolution applications in optical systems.

Analytical beam propagation model for clipped focused-Gaussian beams using vector diffraction theory

Vector diffraction theory is applied to the case of focused TEM(00) Gaussian beams passing through a spatially limiting aperture in order to investigate the propagation of these clipped focused-Gaussian beams. Beam distributions at different axial distances show that a traditional M(2) propagation model cannot be used for the propagation of clipped focus-Gaussian beams. Using Luneberg's vector diffraction theory and Fresnel approximations, an analytical model for the on-axis transverse and longitudinal electric fields and intensity distributions is presented including predictions of the maximum obtainable intensity. In addition, an analytical expression is provided for the longitudinal component of the electric field of a TEM(00) mode unperturbed Gaussian beam. Experimental results are also presented and compared to the model's predictions.

Three-dimensional orientation of single molecules in a tunable optical lambda/2 microresonator

A tightly focused radially polarized laser beam forms an unusual bimodal field distribution in an optical lambda/2-microresonator. We use a single-molecule dipole to probe the vector properties of this field distribution by tuning the resonator length with nanometer precision. Comparing calculated and experimental excitation patterns provides the three-dimensional orientation of the single-molecule dipole in the microresonator.

Visualizing the optical interaction tensor of a gold nanoparticle pair

The control of optical fields on the nanometer scale is a central theme of plasmonics and nanophotonics. Methods for characterizing localized optical field distributions are necessary to validate theoretical predictions, to test nanofabrication procedures, and to provide feedback for design improvements. Typical methods of probing near fields (e.g., single molecule fluorescence and near-field microscopy) cannot probe both the complex-valued and vectorial nature of the field distributions. We demonstrate that a nanoparticle probe with isotropic polarizability in combination with polarization control of excitation and detection beams provides access to this information through the interaction tensor. For a sample consisting of a single nanoparticle we show that the recorded images correspond to maps of the local Green's function tensor elements that couple the probe and sample. The tensorial mapping of interacting nanoparticles is of interest for optical sensing, optical antennas, surface-enhanced Raman scattering, nonlinear optics, and molecular rulers.

Azimuthally and radially polarized light with a nematic SLM

We demonstrate a technique for generating azimuthally and radially polarized beams using a nematic liquid crystal spatial light modulator and a pi phase step. The technique is similar in concept to prior techniques that interfere TEM(01) and TEM(10) laser modes, but the presented technique removes the requirement of interferometric stability. We calculate an overlap integral of >0.96 with >70% efficiency from an input Gaussian mode. The technique can easily switch between beams with azimuthal and radial polarization.