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Constructive interference in four-photon resonantly enhanced six-wave mixing

Nandini Mukherjee

Published May 8, 1994• 0 citations
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Abstract

Enhancement of third-harmonic generation near four-photon resonance showed1 new possibilities for direct upconversion of visible or infrared light into VUV light. However, the observed efficiencies of the four-photon resonant six-wave mixing were low. Our theoretical analysis2 showed that the efficiency is limited because of a destructive interference between the two-photon resonant Raman process E2E3 and the four- photon resonant excitation E 1 4 as shown in Fig. 1(a).

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Enhancement of third-harmonic generation near four-photon resonance showed1 new possibilities for direct upconversion of visible or infrared light into VUV light. However, the observed efficiencies of the four-photon resonant six-wave mixing were low. Our theoretical analysis2 showed that the efficiency is limited because of a destructive interference between the two-photon resonant Raman process E2E3 and the four- photon resonant excitation E 1 4 as shown in Fig. 1(a).
We consider four-photon resonant six-wave mixing and show that the efficiency of harmonic generation is limited due to destructive interference between different optical harmonics. Following the idea of ``induced transparency'' of Harris et al. [Phys. Rev. Lett. 64, 1107 (1990)], it is shown that in the presence of an auxiliary electromagnetic coupling between the four-photon excited level and a third level, the interference between various excitation channels can be made constructive. Depending upon the strength of the auxiliary wave, absorption and dispersion-free propagation of the generated wave lead to high conversion efficiency.
The ability to introduce additional resonances in the nonlinear optical susceptibility of a medium by the injection of an additional radiation field is an attractive possibility from the standpoint of efficient tunable frequency mixing processes in the VUV. The possibility of such processes suggest themselves in previous observations in atomic mercury where an enhancement of several orders of magnitude in the third harmonic generation efficiency has been reported when the input frequency is four-photon resonant with the 6S → 6D transition(1).
Many of the most impressive demonstrations of the efficient generation of vacuum ultraviolet (VUV) light have made use of two‐photon resonantly enhanced four‐wave mixing to generate light at ωVUV =2ωL1±ωL2. The two‐photon resonance state is coupled to the ground state both by two photons from the first laser, or by a photon from the second laser and one from the generated VUV beam. We show here that these two coherent pathways destructively interfere once the second laser is made sufficiently intense, thereby leading to an important limiting effect on the achievable conversion efficiency.
We consider effects which occur when four-wave sum frequency generation and multiphoton ionization are induced by lasers tuned near a three-photon resonance and simultaneously near or at a dipole allowed four-photon resonance. In studies with unfocused laser beams, if the phase mismatch of the generated four-wave-mixing field is large and the related two-photon resonance for the absorption of a four-wave-mixing photon and a laser photon results in strong absorption of the four-wave-mixing field, a coherent cancellation occurs between the pumping of the resonance by two- and four-photon processes. This interference effect occurs when the first laser is tuned on either side of the three-photon resonance and \ensuremath{\Vert}\ensuremath{\Delta}kr{\mathit{k}}_{\mathit{r}}kr​L\ensuremath{\Vert}\ensuremath{\gg}1, where \ensuremath{\Delta}kr{\mathit{k}}_{\mathit{r}}kr​ is the mismatch and L is the length of the path of the laser beams in the gas. With focused laser beams large differences occur between ionization with unidirectional beams and with counterpropagating laser beams when \ensuremath{\Vert}\ensuremath{\Delta}kr{\mathit{k}}_{\mathit{r}}kr​b\ensuremath{\Vert}\ensuremath{\gg}1, where b is the confocal parameter of the focused laser beams. Strong absorption of the four-wave-mixing field is shown not to be necessary for strong destructive interference with focused laser beams when the phase mismatch is large. This work also suggests an explanation for earlier experiments where the presence of a four-photon resonance enabled the generation of third-harmonic light in a positively dispersive wavelength region. We argue that this process can occur when the laser used to achieve the four-photon resonance is focused on the small z (z is the coordinate in the direction of propagation) side of the focal point of the laser responsible for the third-harmonic generation. In this way the absorption of the third-harmonic light on one side of the focal point is made much stronger than on the other side. Correspondingly, contributions to the third-harmonic field from the two sides of the focal point are unequal and cannot undergo complete destructive interference as would otherwise occur in a positively dispersive region.
The interference between two different quantum-mechanical pathways for four-wave mixing in sodium vapor has been observed. The four-wave mixing was enhanced by two-photon resonance with the 5s state, for one pathway, and the 4d state, for the other. The phase of the interference could be varied continuously by varying laser frequencies, and constructive and destructive interference effects were studied. A model based on third-order perturbation theory gives a good description of the features observed.