  We present a comprehensive study of second-order nonlinear difference
frequency generation in triply resonant cavities using a theoretical framework
based on coupled-mode theory. We show that optimal quantum-limited conversion
efficiency can be achieved at any pump power when the powers at the pump and
idler frequencies satisfy a critical relationship. We demonstrate the existence
of a broad parameter range in which all triply-resonant DFG processes exhibit
monostable conversion. We also demonstrate the existence of a
geometry-dependent bistable region.
