Cylindrical vector (CV) beams are a set of transverse spatial modes that exhibit a cylindrically symmetric intensity profile and a variable polarization about the beam axis. They are composed of a non-separable superposition of orbital and spin angular momentum. Critically, CV beams are also the eigenmodes of optical fiber and, as such, are of wide-spread practical importance in photonics and have the potential to increase communications bandwidth through spatial multiplexing. Here, we derive the coupled amplitude equations that describe the four-wave mixing (FWM) of CV beams in optical fibers. These equations allow us to determine the selection rules that govern the interconversion of CV modes in FWM processes. With these selection rules, we show that FWM conserves the total angular momentum, the sum of orbital and spin angular momentum, in the conversion of two input photons to two output photons. When applied to spontaneous four-wave mixing, the selection rules show that photon pairs can be generated in CV modes directly and can be entangled in those modes. Such quantum states of light in CV modes could benefit technologies such as quantum key distribution with satellites.
Although the internally hydrogen-bonded species malonaldehyde (C 3 O 2 H 4 ) is considered an important prototype molecule for intramolecular proton transfer, its far-IR spectrum is not well understood. Using high-resolution spectra obtained from the Canadian Light Source synchrotron in Saskatoon, Saskatchewan, I have made significant progress in understanding its low-energy vibrational structure. A new rotational characterization of the vibrational ground state tunnelling-split pair is presented here, which benefits from these new IR measurements covering a more complete range of rotational parameter space than was reported previously. Full rotational analyses have been performed for three low-energy vibrational states at 241, 390, and 405 cm -1 and these states (as well as states at 273 and 282 cm -1 ) have been conclusively matched to early microwave measurements [W. F. Rowe, Ph.D. Thesis, Harvard University, 1975].Progress has been made toward developing a theoretical treatment of malonaldehyde using the Generalized Semi-Rigid Bender Hamiltonian to describe the large-amplitude tunnelling motion.iii to my parents, for support and encouragement iv Acknowledgements I would like to thank my supervisors, Dr.
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