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Physical Review Letters

Measurements of optical phase variations using interfering multiphoton ionization processes

Ce Chen, Daniel S. Elliott

Published Oct 1, 1990• 174 citations
Publisher

Abstract

We have used interfering multiphoton ionization processes to measure changes in the relative phase between two optical laser beams. In this work, the phase variation is due to the \ensuremath{\pi} phase shift of a focused Gaussian beam as it propagates through the focal region. An array of linear collection electrodes is used to measure the multiphoton ionization rate as a function of the distance from the beam waist when two laser fields are resonant with an atomic transition, one through a linear process, the other through a three-photon process.

DOI
10.1103/physrevlett.65.1737

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Physical Review Letters•Jan 28, 1985•14 citations
We have used interfering multiphoton ionization processes to measure changes in the relative phase between two optical laser beams. In this work, the phase variation is due to the \ensuremath{\pi} phase shift of a focused Gaussian beam as it propagates through the focal region. An array of linear collection electrodes is used to measure the multiphoton ionization rate as a function of the distance from the beam waist when two laser fields are resonant with an atomic transition, one through a linear process, the other through a three-photon process.
This thesis reports an experimental study of an interference phenomenon between one-photon and three-photon 6s$\sp1$S$\sb0$-6p$\sp1$P$\sb1$ transition amplitudes in a vapor of atomic mercury. The interference was observed by monitoring the multiphoton ionization signal. Using a three-cell design we were able to separate the third-harmonic generation process and the interfering absorption processes such that we could externally control the relative phase between the two transition amplitudes and directly study the interference phenomena. We observed that the multiphoton ionization signal, which is a measure of the net transition moment, varied sinusoidally as the relative phase increased. Using an eight-electrode design to collect the electrons ionized at different positions along the beam axis around the focal region, we measured the phase shift of the interference due to the π\piπ phase shift of a focused Gaussian beam propagating through the focal region. The experimental setup and the experimental procedure are discussed in detail. This new method can be used in the study of many phase sensitive processes including potential applications in coherent control of chemical reactions.
We have demonstrated an interference between multiphoton ionization processes that results in a phase-sensitive enhancement or inhibition of the net ionization rate. We focus two laser beams, either of which can induce an atomic transition between the same two states, into a cell containing atomic mercury. One of the fields is at a wavelength of 185 nm and can linearly induce the 6s 1S0 → 6p 1P1 transition in mercury. The other field is at a wavelength precisely three times as long, and it can excite the 6p resonance by a three-photon process. The absorption of two additional visible photons ionizes the mercury. In the presence of both fields, the transition amplitudes interfere, and their relative phases become very important. Their phases can be controlled by controlling the phases of the optical fields inducing the transitions. Coherence between the two fields, vital for the interference, is ensured by generating one field from the other using a nonlinear third-harmonic process. We have also demonstrated the effect of spatial phase variations between the two fields on the local photo-ionization rate.
The non linear interaction between an intense laser radiation and atoms leads to ionization through the absorption of N photons from the laser radiation via laser-induced virtual states. The multiphoton ionization rate varies as a function of the laser intensity I as IN. We discuss the two most important effects which govern multiphoton ionization processes : resonance effects and laser-coherence effects. In a moderate laser intensity range (107 - 109 W cm-2) corresponding to the two, three or four-photon ionization of atoms, resonance effects play a dominant role while the photon statistics of the laser radiation are relatively unimportant. On the contrary, in the very high intensity range (1012 - 1013 W cm-2) required to observe large Nth - order ionization processes, coherence effects play a dominant role through N! enhancement in the N-photon ionization rate, while resonance effects are completely damped due to the high laser intensity. We conclude by reviewing the possible applications of multiphoton absorption processes in other fields.
The phase control of molecular absorption, first proposed by Shapiro, Hepburn, and Brumer was accomplished with CH3I using the technique of Chen, Yin, and Elliott. Red light (λ near 603 nm) was focused in a cell containing CH3I gas at a pressure around 1 Torr. The emerging light, a coherent mixture of the fundamental and the third harmonic (λ near 201 nm), was refocused on a molecular beam of CH3I and multiphoton ionization was detected. Ionization was by two simultaneous processes: a uv photon absorption followed by the absorption of two red photons (1+2 process) and an absorption of three red photons followed by the absorption of two more (3+2 process). Because of the sharp resonant Rydberg transition at 201 nm, the one and three photon matrix elements dominate the transition. Interference between the amplitudes of these two paths was demonstrated by varying the pressure and, hence, the index of refraction of the Ar gas in a tuning cell where the two light beams were refocused by two spherical mirrors. The modulation depth varied with wavelength but had a maximum of 75%, the largest modulation so far observed in this kind of experiment.
Multiphoton ionization in the region near a three-photon resonance is treated for focused, plane-polarized Gaussian beams with diffraction-limited beam divergence. In this situation, a third-harmonic field is generated within the laser beam. At, and very near, three-photon resonance the driving rate for the upper-state probability amplitude due to one-photon absorption of third-harmonic light becomes nearly equal to the corresponding three-photon rate due to the laser field, but these effects are 180\ifmmode^\circ\else\textdegree\fi{} out of phase. As a consequence of this cancellation between two pumping terms, the three-photon resonance line essentially disappears at moderate concentrations and the observed ionization has a line shape that is close to the phase-matching curve for third-harmonic generation. The ionization signal, near but not on the resonance, is due almost entirely to absorption of third-harmonic photons plus other laser photons; three-photon resonantly enhanced multiphoton ionization by the laser is much weaker. This is particularly true on the blue side of the three-photon resonance at detunings where phase matching occurs. The problem is treated quite generally with predictions of the full line shape for nnn-photon ionization and third-harmonic light generation near three-photon resonance, including the rather strong influences of positively dispersive buffer gases. We also show that the cancellation between the one-photon and the three-photon process is partially spoiled in the presence of a counterpropagating beam at the same frequency.
An optimum laser intensity that maximizes the photoionization yield is found in a two-photon resonant, three-photon ionization experiment. At laser intensities higher than this optimum, a negative value is obtained for the exponential index describing this multiphoton process, both at zero detuning and at the detuning for which the signal is maximized. Despite the presence of large (> 1 \AA{}A) optical Stark shifts, Gaussian beam-focusing effects produce an excitation spectrum peaked near zero detuning and reverse the sense of its skewness.