Degenerate four-wave mixing in triply resonant Kerr cavities

Journal Article · Tue Mar 15 00:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.033834· OSTI ID:21541391

Ramirez, David M; Joannopoulos, J D; Soljacic, Marin ^[1]; Rodriguez, Alejandro W ^[2]; Hashemi, Hila; Johnson, Steven G ^[2]

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1. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)
2. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)

We demonstrate theoretical conditions for highly efficient degenerate four-wave mixing in triply resonant nonlinear (Kerr) cavities. We employ a general and accurate temporal coupled-mode analysis in which the interaction of light in arbitrary microcavities is expressed in terms of a set of coupling coefficients that we rigorously derive from the full Maxwell equations. Using the coupled-mode theory, we show that light consisting of an input signal of frequency {omega}{sub 0}-{Delta}{omega} can, in the presence of pump light at {omega}{sub 0}, be converted with quantum-limited efficiency into an output shifted signal of frequency {omega}{sub 0}+{Delta}{omega}, and we derive expressions for the critical input powers at which this occurs. We find the critical powers in the order of 10 mW, assuming very conservative cavity parameters (modal volumes {approx}10 cubic wavelengths and quality factors {approx}1000). The standard Manley-Rowe efficiency limits are obtained from the solution of the classical coupled-mode equations, although we also derive them from simple photon-counting 'quantum' arguments. Finally, using a linear stability analysis, we demonstrate that maximal conversion efficiency can be retained even in the presence of self- and cross-phase modulation effects that generally act to disrupt the resonance condition.

• OSTI ID: 21541391
• Journal Information: Physical Review. A, Vol. 83, Issue 3; Other Information: DOI: 10.1103/PhysRevA.83.033834; (c) 2011 American Institute of Physics; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EFFICIENCY
FREQUENCY MIXING
FREQUENCY MODULATION
KERR EFFECT
MATHEMATICAL SOLUTIONS
MAXWELL EQUATIONS
NONLINEAR PROBLEMS
OPTICAL PUMPING
PHOTONS
QUALITY FACTOR
RESONANCE
VISIBLE RADIATION
WAVELENGTHS
BOSONS
DIELECTRIC PROPERTIES
DIFFERENTIAL EQUATIONS
DIMENSIONLESS NUMBERS
ELECTRICAL PROPERTIES
ELECTROMAGNETIC RADIATION
ELEMENTARY PARTICLES
EQUATIONS
MASSLESS PARTICLES
MODULATION
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
PUMPING
RADIATIONS