Abstract

We present a self-consistent model of anomalous second-harmonic generation in glass fibers. The model involves the interference of photoionization amplitudes arising from optical fields having frequencies ω and 2ω. The photoelectrons are emitted anisotropically with a dependence on the relative phase of the two optical fields. The simplest case is an interference between one-photon ionization at 2ω and two-photon ionization at ω. Fermi’s Golden Rule gives the rates, ${\dot{\rho }}_{+}$ and ${\dot{\rho }}_{-}$, of electron emission in the positive and negative directions: where g(ω) is a lineshape factor, k and K|µ2|² are the 1- and 2-photon rate constants. The photocurrent generated by the anisotropic ionization develops a space-charge field: where e₀ is 10⁵ - 10⁶ V/cm, depending on material parameters. The space charge field, in conjunction with χ⁽³⁾ for the glass, produces a properly phase-matched χ⁽²⁾. Energy considerations suggest that the interference is between higher order ionization processes; these also lead to a suitable χ⁽²⁾. In the slowly varying envelope approximation the intensity of the second-harmonic field grows as a saturating exponential: The small signal gain G₀ is estimated to be on the order of 10dB/cm-consistent with the experimentally observed 0.1 to 6dB/cm.

© 1990 Optical Society of America