Optical cavities can support many transverse and longitudinal modes. A paraxial scalar theory predicts that the resonance frequencies of these modes cluster in different orders. A nonparaxial vector theory predicts that the frequency degeneracy within these clusters is lifted, such that each order acquires a spectral fine structure, comparable to the fine structure observed in atomic spectra. In this paper, we calculate this fine structure for microcavities and show how it originates from various nonparaxial effects and is codetermined by mirror aberrations. The presented theory, which applies perturbation theory to Maxwell's equations with boundary conditions, proves to be very powerful. It generalizes the effective one-dimensional description of Fabry-Perot cavities to a three-dimensional multi-transverse-mode description. It thereby provides physical insights into several mode-shaping effects and a detailed prediction of the fine structure in Fabry-Perot spectra.
Coherent optical states consist of a quantum superposition of different photon number (Fock) states, but because they do not form an orthogonal basis, no photon number states can be obtained from it by linear optics. Here we demonstrate the reverse, by manipulating a random continuous single-photon stream using quantum interference in an optical Sagnac loop, we create engineered quantum states of light with tunable photon statistics, including approximate weak coherent states. We demonstrate this experimentally using a true single-photon stream produced by a semiconductor quantum dot in an optical microcavity, and show that we can obtain light with g ð2Þ ð0Þ → 1 in agreement with our theory, which can only be explained by quantum interference of at least 3 photons. The produced artificial light states are, however, much more complex than coherent states, containing quantum entanglement of photons, making them a resource for multiphoton entanglement.
In 1995, Hadley formulated an elegant effective-index model to describe the formation of transverse modes in optical cavities [1]. We apply this model to Fabry-Perot cavities and discuss its limitations, using the well-known paraxial solutions of these cavities as reference. We also introduce a new model, which we call the phase-plate model, that has less limitations and yields the correct first-order correction to the resonance frequencies for longer cavities. The analysis uses scalar optical fields in the paraxial limit.
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