Jörg Baumgartl

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.

Visualization of the birth of an optical vortex using diffraction from a triangular aperture.

The study and application of optical vortices have gained significant prominence over the last two decades. An interesting challenge remains the determination of the azimuthal index (topological charge) ℓ of an optical vortex beam for a range of applications. We explore the diffraction of such beams from a triangular aperture and observe that the form of the resultant diffraction pattern is dependent upon both the magnitude and sign of the azimuthal index and this is valid for both monochromatic and broadband light fields. For the first time we demonstrate that this behavior is related not only to the azimuthal index but crucially the Gouy phase component of the incident beam. In particular, we explore the far field diffraction pattern for incident fields incident upon a triangular aperture possessing non-integer values of the azimuthal index ℓ. Such fields have a complex vortex structure. We are able to infer the birth of a vortex which occurs at half-integer values of ℓ and explore its evolution by observations of the diffraction pattern. These results demonstrate the extended versatility of a triangular aperture for the study of optical vortices.

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.

Automated laser guidance of neuronal growth cones using a spatial light modulator

The growth cone of a developing neuron can be guided using a focused infra-red (IR) laser beam [1]. In previous setups this process has required a significant amount of user intervention to adjust continuously the laser beam to guide the growing neuron. Previously, a system using an acousto-optical deflector (AOD) has been developed to steer the beam [2]. However, to enhance the controllability of this system, here we demonstrate the use of a computer controlled spatial light modulator (SLM) to steer and manipulate the shape of a laser beam for use in guided neuronal growth. This new experimental setup paves the way to enable a comprehensive investigation into beam shaping effects on neuronal growth and we show neuronal growth initiated by a Bessel light mode. This is a robust platform to explore the biochemistry of this novel phenomenon.

Supercontinuum Airy Beams

Airy beams are of great interest as a result of their unusual characteristics, they are non-diffracting and also propagate along a parabolic path due to the presence of a transversal acceleration component. In this paper the generation of a white light Airy beam is presented, an investigation is also carried out to determine how the properties of an Airy beam change with the wavelength and spatial coherence of the source. A supercontinuum source is used in conjunction with a spatial light modulator to produce the Airy beams. The wavelength dependence study of the Airy beam parameters was carried out by inserting interference filters into the supercontinuum beam path to select each wavelength. The parameters investigated are the deflection coefficient of the Airy beam, b0, this quantifies the parabolic path traveled by the beam; the characteristic length, x0, which is related to the lobe spacing, and lastly the aperture coefficient, a0. The deflection coefficient and the characteristic length were both found to be wavelength dependent. The aperture coefficient did not alter as a result of wavelength, however it was found to be dependent on the spatial coherence, and therefore on the M2 value, of the beam. The other parameters, b0 and x0, are unaffected by the spatial coherence of the source.

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.

Advanced Studies of ‘Non-Diffracting’ Light Fields

We explore the propagation and applications in optical trapping and biophotonics of ‘non-diffracting’ light fields. This includes studies using Bessel light modes and Airy light fields that exhibit parabolic trajectories.