Manipulation of Polarized Transverse Spatial Modes to Induce Non-Linear Structures using the Geometric Phase

Drew King-Smith


The purpose of this experiment is to observe non-linear structures visible in the intensity distribution of light that are produced by the interference of a mode of light known as the "hedgehog" mode with another hedgehog mode that has acquired a geometric phase to its electromagnetic field. The hedgehog mode is the combination of two different Hermite-Gaussian modes of light: the HG10x mode and the HG01y mode. In order to produce these modes of light, a Gaussian mode is directed at a Spatial Light Modulator which converts the Gaussian mode into the HG10x mode by means of an interference pattern that acts as a diffraction grating. This HG10x mode is then directed into the first of two interferometers where the first interferometer makes the HG01y mode and the hedgehog mode. The first interferometer consists of two beam splitters, two mirrors, a Dove Prism, linear polarizer, and half-wave plate. The HG10x mode is split into two paths at the first beam splitter, where one path travels through the Dove Prism, linear polarizer and the half-wave plate in order to create the HG01y mode and the other path does not affect the original HG10x mode. These two paths combine at the second beam splitter to form the hedgehog mode and exit the first interferometer. The second interferometer consists of two beam splitters, three mirror and one quarter-wave plate. The first hedgehog mode is sent to the final beam splitter with no other optical elements acting on it, so it remains unchanged. The second hedgehog mode is directed through a quarter-wave plate in order to add phase delay to the electromagnetic field and thus acquire a geometric phase. The hedgehog mode with the acquired geometric phase is then interfered with the unchanged hedgehog mode at the last beam splitter in order to induce the non-linear structures. While no structures have been observed thus far, there are several reasons as to why the structures are not present: intensity distribution issues of the hedgehog modes and the HG01y mode and not enough control of the phase delay on the hedgehog’s electromagnetic field. These issues are discussed along with possible solutions by means of a new Dove Prism and the use of a device known as the Soleil Babinet Compensator. A new Dove Prism may help for better rotating the polarization, thus keeping the full intensity distribution of the HG01y mode when passing through through the linear polarizer. An ideal replacement for the current Dove prism would be an optical rotator, which rotates modes to an arbitrary angle. The Soleil Babinet Compensator would allow greater precision for controlling the phase delay.