Nonlinear harmonic generation and devices in doubly resonant Kerr cavities

Hila Hashemi, Alejandro W. Rodriguez, J. D. Joannopoulos, Marin Soljačić, and Steven G. Johnson
Phys. Rev. A 79, 013812 – Published 13 January 2009

Abstract

We describe a theoretical analysis of the nonlinear dynamics of third-harmonic generation (ω3ω) via Kerr (χ(3)) nonlinearities in a resonant cavity with resonances at both ω and 3ω. Such a doubly resonant cavity greatly reduces the required power for efficient harmonic generation, by a factor of VQ2, where V is the modal volume and Q is the lifetime, and can even exhibit 100% harmonic conversion efficiency at a critical input power. However, we show that it also exhibits a rich variety of nonlinear dynamics, such as multistable solutions and long-period limit cycles. We describe how to compensate for self- and cross-phase modulation (which otherwise shifts the cavity frequencies out of resonance), and how to excite the different stable solutions (and especially the high-efficiency solutions) by specially modulated input pulses.

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  • Received 3 August 2008

DOI:https://doi.org/10.1103/PhysRevA.79.013812

©2009 American Physical Society

Authors & Affiliations

Hila Hashemi1, Alejandro W. Rodriguez2, J. D. Joannopoulos2, Marin Soljačić2, and Steven G. Johnson1

  • 1Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 2Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

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Vol. 79, Iss. 1 — January 2009

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