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Conference on Lasers and Electro-Optics

Theory and measurement of degenerate four-wave mixing in a resonant three-level absorber

David E. Watkins, G. R. Phipps

Published Jan 1, 1982• 0 citations
Publisher

Abstract

The study of degenerate four-wave mixing (DFWM) in the doped alkali halide KCI:KReO4 was prompted by the observation that this material behaves like an ideal, homogeneously broadened two-level saturable absorber at CO2 laser wavelengths,1 for which a simple theory of DFWM exists.2
DOI
10.1364/cleo.1982.wc20

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We describe the first reported observation of resonantly enhanced phase conjugation through degenerate four-wave mixing (DFWM) in doped alkali halides. We also describe the first reported quantitative comparison of the resonant DFWM process in the infrared with the theory of Abrams and Lind [Opt. Lett. 2, 94 (1978); 3, 205 (1978)]. The comparison for small values of alpha0L is shown to be excellent. For alpha0L in excess of 3, experiment and theory diverge because of pump attenuation by the resonant medium.
Detailed measurements have been made of degenerate four-wave mixing (DFWM) in a resonant homogeneously broadened gas. The measurements were performed in SF6{\mathrm{F}}_{6}F6​ using a pulsed CO2{\mathrm{O}}_{2}O2​ laser operated on the 10.4-\ensuremath{\mu} m branch. A pulse width of 1.2 nsec was used to reduce effects of collisional relaxation. Data are also presented for pulse widths of 140 nsec. At high-energy fluences (\ensuremath{\sim}0.1 J/cm2{\mathrm{cm}}^{2}cm2) pulse breakup is observed and is believed to arise from multiple-photon effects. The data obtained with the short pulse width are compared to a four-level saturable-absorber model where excellent agreement is obtained when pump absorption is included. The qualitative behavior of DFWM due to dispersion is also demonstrated in the wings of the SF6{\mathrm{F}}_{6}F6​ absorption spectrum. Peak reflectivities of 38% were readily obtained. In addition contributions due to a coherent three-level nonlinearity are presented showing a contribution equal to the measured saturable contribution.
This dissertation presents experimental and theoretical studies of transient degenerate four wave mixing (DFWM) in organic dyes. Chapter 1 is an introduction to DFWM. Chapter 2 describes DFWM experiments that were performed in the gain medium of a dye laser. Chapter 3 presents the theory of DFWM of short pulses in three level saturable media. Chapter 4 presents DFWM experiments of femtosecond pulses in the saturable absorber of a passively modelocked ring dye laser. Chapter 5 presents the theory of DFWM of ultrashort pulses in resonant media.
A calculation of degenerate four-wave mixing in a homogeneously broadened two-level saturable absorber is presented. An analytical formula for the local electric dipole polarization responsible for degenerate four-wave mixing is derived for arbitrary electric-field strengths. The overall efficiency of the medium is calculated by numerically solving the coupled wave equations with the use of the phase-matching electric dipole polarization. Solutions are presented when the laser is tuned on and off resonance for various input laser intensities and linear absorption coefficients. Optimal conditions for maximum efficiency are discussed.
We have investigated degenerate four-wave mixing (DFWM) in a strongly absorbing molecular gas. A theory taking into account saturable absorption of the interacting beams is used to explain the dependence of the DFWM reflectivity on laser intensity and on the molecular number density. These parameters have a great influence on the observed spectra, owing to linear absorption that suppresses the DFWM signal in the line center of the molecular transitions. The great sensitivity of the spectra to the experimental conditions limits the applicability of DFWM for spectroscopic studies in absorbing media.