Sebastian Kosmeier

Optical Eigenmodes; exploiting the quadratic nature of the energy flux and of scattering interactions

We report a mathematically rigorous technique which facilitates the optimization of various optical properties of electromagnetic fields. The technique exploits the linearity of electromagnetic fields along with the quadratic nature of their interaction with matter. In this manner we may decompose the respective fields into optical quadratic measure eigenmodes (QME). Key applications include the optimization of the size of a focused spot, the transmission through photonic devices, and the structured illumination of photonic and plasmonic structures. We verify the validity of the QME approach through a particular experimental realization where the size of a focused optical field is minimized using a superposition of Bessel beams.We report a mathematically rigorous technique which facilitates the optimization of various optical properties of electromagnetic fields in free space and including scattering interactions. The technique exploits the linearity of electromagnetic fields along with the quadratic nature of the intensity to define specific Optical Eigenmodes (OEi) that are pertinent to the interaction considered. Key applications include the optimization of the size of a focused spot, the transmission through sub-wavelength apertures, and of the optical force acting on microparticles. We verify experimentally the OEi approach by minimising the size of a focused optical field using a superposition of Bessel beams.For over a century diffraction theory has been thought to limit the resolution of focusing and imaging in the optical domain. The size of the smallest spot achievable is inversely proportional to the range of spatial wavevectors available. Here, we show that it is possible to locally beat the diffraction limit at the expense of efficiency. The method is based on the linearity of Maxwells equations and that the interaction between light and its surroundings may be considered quadratic in nature with respect to the electromagnetic fields. We represent the intensity and spot size as a quadratic measure with associated eigenmodes. Using a dynamic diffractive optical element, we demonstrate optical focussing to an area 4 times smaller than the diffraction limit. The generic method may be applied to numerous physical phenomena relating to linear and measurable properties of the electromagnetic field that can be expressed in a quadratic form.

Far field subwavelength focusing using optical eigenmodes

We report the focusing of light to generate a subdiffractive, subwavelength focal spot of full width half maximum 222 nm at an operating wavelength of 633 nm using an optical eigenmode approach. Crucially, the spot is created in the focal plane of a microscope objective thus yielding a practical working distance for applications. The optical eigenmode approach is implemented using an optimal superposition of Bessel beams on a spatial light modulator. The effects of partial coherence are also discussed. This far field method is a key advance toward the generation of subdiffractive optical features for imaging and lithographic purposes.

Coherent control of plasmonic nanoantennas using optical eigenmodes

The last decade has seen subwavelength focusing of the electromagnetic field in the proximity of nanoplasmonic structures with various designs. However, a shared issue is the spatial confinement of the field, which is mostly inflexible and limited to fixed locations determined by the geometry of the nanostructures, which hampers many applications. Here, we coherently address numerically and experimentally single and multiple plasmonic nanostructures chosen from a given array, resorting to the principle of optical eigenmodes. By decomposing the light field into optical eigenmodes, specifically tailored to the nanostructure, we create a subwavelength, selective and dynamic control of the incident light. The coherent control of plasmonic nanoantennas using this approach shows an almost zero crosstalk. This approach is applicable even in the presence of large transmission aberrations, such as present in holographic diffusers and multimode fibres. The method presents a paradigm shift for the addressing of plasmonic nanostructures by light.

Enhanced two-point resolution using optical eigenmode optimized pupil functions

Pupil filters have the capability to arbitrarily narrow the central lobe of a focal spot. We decompose the focal field of a confocal-like imaging system into optical eigenmodes to determine optimized pupil functions, that deliver superresolving scanning spots. As a consequence of this process, intensity is redistributed from the central lobe into side lobes restricting the field of view (FOV). The optical eigenmode method offers a powerful way to determine optimized pupil functions. We carry out a comprehensive study to investigate the relationship between the size of the central lobe, its intensity, and the FOV with the use of a dual display spatial light modulator. The experiments show good agreement with theoretical predictions and numerical simulations. Utilizing an optimized sub-diffraction focal spot for confocal-like scanning imaging, we experimentally demonstrate an improvement of the two-point resolution of the imaging system.

Nonredundant Raman imaging using optical eigenmodes

Various forms of imaging schemes have emerged over the last decade that are based on correlating variations in incident illuminating light fields to the outputs of single “bucket” detectors. However, to date, the role of the orthogonality of the illumination fields has largely been overlooked, and, furthermore, the field has not progressed beyond bright field imaging. By exploiting the concept of orthogonal illuminating fields, we demonstrate the application of optical eigenmodes (OEis) to wide-field, scan-free spontaneous Raman imaging, which is notoriously slow in wide-field mode. The OEi approach enables a form of indirect imaging that exploits both phase and amplitude in image reconstruction. The use of orthogonality enables us to nonredundantly illuminate the sample and, in particular, use a subset of illuminating modes to obtain the majority of information from the sample, thus minimizing any photobleaching or damage of the sample. The crucial incorporation of phase, in addition to amplitude, in the imaging process significantly reduces background noise and results in an improved signal-to-noise ratio for the image while reducing the number of illuminations. As an example we can reconstruct images of a surface-enhanced Raman spectroscopy sample with approximately an order of magnitude fewer acquisitions. This generic approach may readily be applied to other imaging modalities such as fluorescence microscopy or nonlinear vibrational microscopy.

Optical eigenmodes for imaging applications

We decompose the light field in the focal plane of an imaging system into a set of optical eigenmodes. Subsequently, the superposition of these eigenmodes is identified, that optimizes certain aspects of the imaging process. In practice, the optical eigenmodes modes are implemented using a liquid crystal spatial light modulator. The optical eigenmodes of a system can be determined fully experimentally, taking aberrations into account. Alternatively, theoretically determined modes can be encoded on an aberration corrected spatial light modulator. Both methods are shown to be feasible for applications. To achieve subdiffractive light focussing, optical eigenmodes are superimposed to minimize the width of the focal spot within a small region of interest. In conjunction with a confocal-like detection process, these spots can be utilized for laser scanning imaging. With optical eigenmode engineered spots we demonstrate enhanced two-point resolution compared to the diffraction limited focus and a Bessel beam. Furthermore, using a first order ghost imaging technique, optical eigenmodes can be used for phase sensitive indirect imaging. Numerically we show the phase sensitivity by projecting optical eigenmodes onto a Laguerre-Gaussian target with a unit vortex charge. Experimentally the method is verified by indirect imaging of a transmissive sample.

Optical Quadratic Measure Eigenmodes

We report a mathematically rigorous technique which facilitates the optimization of various optical properties of electromagnetic fields. The technique exploits the linearity of electromagnetic fields along with the quadratic nature of their interaction with matter. In this manner we may decompose the respective fields into optical quadratic measure eigenmodes (QME). Key applications include the optimization of the size of a focused spot, the transmission through photonic devices, and the structured illumination of photonic and plasmonic structures. We verify the validity of the QME approach through a particular experimental realization where the size of a focused optical field is minimized using a superposition of Bessel beams.We report a mathematically rigorous technique which facilitates the optimization of various optical properties of electromagnetic fields in free space and including scattering interactions. The technique exploits the linearity of electromagnetic fields along with the quadratic nature of the intensity to define specific Optical Eigenmodes (OEi) that are pertinent to the interaction considered. Key applications include the optimization of the size of a focused spot, the transmission through sub-wavelength apertures, and of the optical force acting on microparticles. We verify experimentally the OEi approach by minimising the size of a focused optical field using a superposition of Bessel beams.For over a century diffraction theory has been thought to limit the resolution of focusing and imaging in the optical domain. The size of the smallest spot achievable is inversely proportional to the range of spatial wavevectors available. Here, we show that it is possible to locally beat the diffraction limit at the expense of efficiency. The method is based on the linearity of Maxwells equations and that the interaction between light and its surroundings may be considered quadratic in nature with respect to the electromagnetic fields. We represent the intensity and spot size as a quadratic measure with associated eigenmodes. Using a dynamic diffractive optical element, we demonstrate optical focussing to an area 4 times smaller than the diffraction limit. The generic method may be applied to numerous physical phenomena relating to linear and measurable properties of the electromagnetic field that can be expressed in a quadratic form.