Sensitive detection of sodium in a flame using parametric four-wave mixing and seeded parametric four-wave mixing Mark J. Ferne ´ e, 1 Peter F. Barker, 2, * Alan E. W. Knight, 1 and Halina Rubinsztein-Dunlop 2 1 Molecular Dynamics Laboratory, Faculty of Science and Technology, Griffith University, Nathan, Queensland 4111, Australia 2 Laser Science Centre, Physics Department, University of Queensland, St. Lucia, Queensland 4072, Australia Received 15 September 1997 Two-photon resonant parametric four-wave mixing and a newly developed variant called seeded parametric four-wave mixing are used to detect trace quantities of sodium in a flame. Both techniques are simple, requiring only a single laser to generate a signal beam at a different wavelength which propagates collinearly with the pump beam, allowing efficient signal recovery. A comparison of the two techniques reveals that seeded parametric four-wave mixing is more than two orders of magnitude more sensitive than parametric four-wave mixing, with an estimated detection sensitivity of 5 10 9 atoms/cm 3 . Seeded parametric four-wave mixing is achieved by cascading two parametric four-wave mixing media such that one of the parametric fields generated in the first high-density medium is then used to ‘‘seed’’ the same four-wave mixing process in a second medium in order to increase the four-wave mixing gain. The behavior of this seeded parametric four-wave mixing is described using semiclassical perturbation theory. A simplified small-signal theory is found to model most of the data satisfactorily. However, an anomalous saturationlike behavior is observed in the large signal regime. The full perturbation treatment, which includes the competition between two different four-wave mixing processes coupled via the signal field, accounts for this apparently anomalous behavior. S1050-29479803903-1 PACS numbers: 42.65.Ky, 32.80.-t I. INTRODUCTION The remote sensing of atoms and molecules is important for a large number of applications where restrictions to ac- cess, environmental hazards, and other factors prevent the use of direct detection methods. Optical techniques offer some of the best possibilities for remote sensing, being largely noninvasive and nonperturbative. However, there is no single optical technique that is suited to all applications, so the development of alternative detection strategies may provide effective solutions for certain applications. Important factors for any potential remote sensing technique are sim- plicity of operation and sensitivity. The use of coherent techniques for remote sensing is par- ticularly advantageous as the detected signal travels in a co- herent beam in a direction determined by the phase matching conditions in the medium. This enables efficient recovery of the signal, even over relatively long distances. Degenerate four-wave mixing DFWM and related coherent nonlinear techniques based on resonance enhancement of the nonlinear refractive index have found increasing application in com- bustion diagnostics and remote sensing applications, provid- ing good spatial resolution and high sensitivity 1. However, these techniques tend to provide such benefits at the expense of simplicity, normally requiring multiple beams to achieve the appropriate phase matching and often requiring multiple colors. Furthermore, these techniques generally involve sig- nificant population transfer due to strong resonance enhance- ment and are therefore susceptible to and limited by satura- tion effects. Currently there appears to be no nonlinear technique that requires only a single undivided pump beam and is suitable for trace species detection. DFWM and its variants form a special class of four-wave mixing FWM that may be interpreted in terms of diffrac- tion from a laser-induced grating formed within the nonlin- ear medium 2. However, in general FWM is a property of the nonlinear response of the polarization of the medium and cannot necessarily be interpreted in terms of a laser-induced grating. Two-photon resonant parametric four-wave mixing PFWM is a member of this more general class. PFWM involves two-photon resonant pumping of the upper state in a three-level system. Both the upper state and ground state are dipole coupled to an intermediate state, through which a transition back to the ground state can occur. This produces two new fields which are nearly resonant with the interme- diate state and which are generated simultaneously, both starting from zero-point fluctuations 3. PFWM in atomic species has been studied extensively for nonlinear frequency conversion in high-density systems where the nonlinear susceptibility can be made sufficiently large 4. PFWM also offers some unique advantages for this class of nonlinear technique, such as only requiring a single laser beam and returning a coherent signal at a frequency different from, but in most circumstances traveling col- linearly with the pump laser. Such a technique would mini- mize the optical access requirement and simplify signal re- trieval and as such be strongly suited to remote sensing if it were sufficiently sensitive. In previous applications the me- dium density could always be increased to a point where efficient FWM is achieved; hence until now, sensitivity has not been an issue of concern. Considering PFWM must si- multaneously generate two different fields using two-photon resonant pumping, with both fields starting from zero-point *Present address: Department of Mechanical and Aerospace En- gineering, Princeton University, Princeton, NJ. PHYSICAL REVIEW A APRIL 1998 VOLUME 57, NUMBER 4 57 1050-2947/98/574/280212/$15.00 2802 © 1998 The American Physical Society