• optical microcavity
• microscopy
• k-space imaging
• Fourier transform spectroscopy
• hyperspectral imaging
• master thesis
• pump probe
• semiconductors
• exciton-polariton

Microscopy is one of the most important tools for many scientific investigations. In particular, by projecting the magnified real-space image of a sample on a camera, using the optical elements of a microscope, the micro-morphology of a large variety of samples is revealed, but no or little information about the spectral properties of the collected light can be discerned. Moreover, information about the direction of light coming from an illuminated sample and its angle-dependent spectral properties, collected by each pixel of the camera, within the numerical aperture of the microscope objective, is also lost.
To recover this information an imaging of the reciprocal space, or the space of wavevectors (k-space), is necessary. This kind of distribution provides useful information about light-matter interaction, in general, that cannot be obtained with other methods. There are a lot of samples and phenomena that can be analyzed with this technique, such as single-molecule fluorescence, Raman scattering of 2D materials, photonic crystals, optical antennas, microcavities etc. Specifically, the latter are optical resonators with dimensions comparable to the wavelength of light, made of reflective elements which confine photons in few resonance modes due to constructive interference. Geometry and resonance conditions in such devices create peculiar angular patterns for emitted/incident light.
Historically, to retrieve information at different angles in a microscope setup, a circular aperture was used to select a small solid angle of the propagating light in the optical path. In this way, by changing the lateral position of the aperture, spectra for different collected angles can be recorded but with a poor angular resolution.
To improve the measurement process, k-space imaging has been introduced. To perform such a measurement a Bertrand lens is needed to image the back focal plane of the objective lens on a two-dimensional detector. This kind of setup is not only faster, but can retrieve spectra over larger angular range, compared to previous setups. However, still it can't capture any spectral information from the images.
Hyperspectral imaging, is a powerful tool, which allows to acquire a spectrum for every pixel of the image. It can be done in two ways, through raster scanning (acquisition point-by-point or line-by-line) or in widefield (where the whole scene is acquired at once). The general approach, in both cases, is to use a dispersive spectrometer to acquire the light intensity as a function of the spatial coordinates.
An alternative approach uses Fourier transform spectrometers, instead of the dispersive ones, which are way more advantageous. They acquire the full spectrum of light as a function of the spatial coordinates resulting in a three-dimensional data-set, called hypercube. Among them, the most reliable employ birefringent interferometers, including the TWINS: a common-path ultrastable birefringent interferometer that allows to generate the phase-locked replicas of the optical waveform required for FT spectroscopy.
The main purpose of this work is to present a novel Fourier transform hyperspectral microscope based on the TWINS working in k-space.
In the first chapter of this thesis we are going to focus on Fourier transform spectroscopy: its advantages with respect to spectroscopy made with dispersive materials, the interferometers that can be used to perform measurements with this technique and how it can be applied to hyperspectral imaging.
The second chapter will focus on k-space imaging, particularly describing the working principle and layout of a microscope, and the possible configurations of the Bertrand lens that can be used to image the back focal plane of the objective.
The third chapter will show how the k-space hyperspectral microscope is composed, the optimization process that leads to the final result and even the errors behind its construction.
Finally, the thesis will focus on some measurements performed with this apparatus on different optical microcavities filled with organic semiconductors, that show the power and reliability of this tool, alongside other information on these cavities retrieved from pump-probe measurements in k-space.