Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams

Abstract

Highly confined vectorial electromagnetic field distributions represent an excellent tool for detailed studies in nano-optics and high resolution microscopy, such as nonlinear microscopy 1 , advanced fluorescence imaging 2-4 or nanoplasmonics 5,6 . Such field distributions can be generated, for instance, by tight focussing of polarized light beams [7][8][9][10] . To guarantee high quality and resolution in the investigation of objects with sub-wavelength dimensions, the precise knowledge of the spatial distribution of the exciting vectorial field is of utmost importance. Full-field reconstruction methods presented so far involved, for instance, complex near-field techniques 11,12 . Here, we demonstrate a simple and straight-forward to implement measurement scheme and reconstruction algorithm based on the scattering signal of a single spherical nanoparticle as a field-probe. We are able to reconstruct the amplitudes of the individual focal field components as well as their relative phase distributions with sub-wavelength resolution from a single scan measurement without the need for polarization analysis of the scattered light. This scheme can help to improve modern microscopy and nanoscopy techniques.In the optical analysis of sub-wavelength objects such as cellular structures 13 , plasmonic particles 5,6,14 or single spins 3 , nano-optical tools including highly resolving microscopy techniques are used. Because such methods utilise complex and highly confined vector fields, the exact knowledge of the corresponding spatial field distributions is crucial. In the last decades, several techniques have been proposed to map these focal fields, such as using metal knife edges 15,16 to probe the total electric energy density distribution, fluorescence molecules 17 , tapered fibres 18,19 or tip-based methods 12 to image specific field orientations, or near-field scanning optical microscope (NSOM) techniques to extract amplitude and even phase information 11 . These NSOM-based methods require complex measurement and detection schemes and calibration procedures to allow for amplitude and phase a) Electronic mail: thomas.bauer@mpl.mpg.de mapping of individual field components. As an alternative approach for measuring phase information also a single particle scattering scheme was proposed recently 22 , where the authors show that Mie-scattering can distinguish the topological charge of vortex-beams.We now demonstrate a precise and easily implementable field reconstruction technique for highly confined field distributions created by arbitrary focusing systems, based on, what we call, Mie-scattering nanointerferometry. The basic concept of this reconstruction method for highly confined focal field distributions can be understood as follows. We use a metallic nanosphere on a glass substrate as local field sensor and scan it stepwise through the focal field distribution under investigation. If the particle size is chosen small enough, it will be excited by the local electric field E(r 0 ) only. Its response can be described,...

Influence of the substrate material on the knife-edge based profiling of tightly focused light beams

“…Furthermore the asymmetric shape of the curves caused by a plasmonic excitation of the knife-pad will be shown and discussed within the article (see Chapter 4. by vectorial diffraction theory [21][22][23] (black line). We note that these modifications are not caused by the focusing system, since we can independently characterize our focal spots using an alternative technique [5] but by the interaction of the beam and the knife-edge samples. In all figures the experimental points are compared to our theoretical calculations (continuous lines).…”

“…For such tightly focused and highly confined light beams, several beam reconstruction techniques have been proposed and discussed in literature. Some of these methods even allow for the measurement of amplitudes and phases of individual electric field components in diffraction-limited focal spots [5][6][7][8]. Another technique, which is normally used to determine the electric field intensity distribution in the cross-section of light beams experimentally, is the so-called knife-edge method which we want to discuss here in more detail [9][10][11][12][13][14].…”

Accurate Feeding of Nanoantenna by Singular Optics for Nanoscale Translational and Rotational Displacement Sensing

“…The singularity usually refers to the discontinuity or undefined value in the light field itself. Around these singularities of the fields, rapidly spatially varying field patterns occur, which has led to new applications such as high-precision nanoscale metrology and superresolution imaging [13,[15][16][17][18][19][20][21][22][23].In this Letter, we use two different kinds of singularities: The so-called V-point polarization singularity in an azimuthally polarized beam [24][25][26] and the phase singularity in a Hermite-Gaussian beam to precisely excite one individual element of two identical parallel metallic nanorod antennas separated by a deep subwavelength gap. The precise alignment of the singularity with the two nanorods gives an accurate feeding of them far beyond the diffraction limit.…”

“…The singularity usually refers to the discontinuity or undefined value in the light field itself. Around these singularities of the fields, rapidly spatially varying field patterns occur, which has led to new applications such as high-precision nanoscale metrology and superresolution imaging [13,[15][16][17][18][19][20][21][22][23].…”

Tighter spots of light with superposed orbital-angular-momentum beams

“…Furthermore, a more advanced experimental method as described in Ref. [55] should be used if the full field information (amplitudes and phases of individual field components) of the beams under study need to be measured. In Fig.…”