Treatment of the spectrum of squeezing based on the modes of the universe. I. Theory and a physical picture

For a leaky cavity driven by an active medium, we clarify the connection between the concepts of single-quasimode squeezing (for the intracavity field) and spectral squeezing (for the input and output fields). Our analysis is based on a rigorous construction of the Fox-Li quasimodes of an empty cavity by a superposition of the true modes of a perfect, large (infinitely large in the limit) cavity which fully subsumes the leaky cavity. To illustrate the physical importance of spectral squeezing (as defined here and as used by other authors), we consider a novel model of a microscopic system that is sensitive to the generalized quadratures of the field. We obtain a simple picture of the reasons why the quantum-noise reduction is in general different inside and outside the cavity. An important special case of our picture is that if the {ital intracavity} field is perfectly squeezed, then the {ital output} field shows no squeezing at all. Our considerations apply to a wide class of systems, examples of which are discussed in the companion paper.