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Journal of the Optical Society of America B

Nonlinear optical balance

James J. Wynne, Robert W. Boyd

Published Feb 1, 1987• 0 citations
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Abstract

Suppression of photoionization, fluorescence, amplified spontaneous emission, and nonlinear optical conversion have all been reported in the presence of resonant multiphoton excitation.1 At first glance, the nonlinear phenomena manifesting this suppression and the order of the nonlinear processes appear to be quite distinct. In some cases, this suppression has been shown to result from a destructive interference (alternatively, a competition) between alternative excitation pathways to the resonant intermediate state.2

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Approach to nonlinear optical balance

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In the presence of resonant multiphoton excitation, experimental observations of photoionization, fluorescence, and amplified spontaneous emission have shown suppression of these effects.1 There is a common mechanism tying these phenomena together. All these processes involve the coherent nonlinear coupling of two or more optical waves via a dissipative nonlinear optical medium. Independent of initial conditions, as these waves propagate through the nonlinear medium, they develop amplitudes and relative phases that minimize the dissipative losses. The condition of minimum loss is one in which the excitation of the nonlinear medium is reduced due to the waves being in a state of nonlinear optical balance. This balance is stabilized by the dissipation. Other combinations of amplitude and phase are more lossy and rapidly damped out.

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When a strong near-resonant laser beam propagates through an atomic vapor, it can simultaneously induce several different nonlinear optical processes. In certain restricted conditions, these processes evolve independently of one another, but in general these processes compete. We have observed competition1 between four-wave mixing2 (FWM) and amplified spontaneous emission3 (ASE) and have presented an explanation for this phenomenon based on the solution of the coupled-amplitude equations of nonlinear optics. We extend our previous work by presenting a more detailed theoretical explanation of this effect and evidence that competition of this sort occurs quite generally in nonlinear optical systems.

Journal of the Optical Society of America B•Jan 1, 1986•0 citations

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Competition has been observed between amplified spontaneous emission (ASE) and four-wave mixing (FWM). Previously, competition between an incoherent and coherent process was observed in the form of suppression of multiphoton ionization by third harmonic generation.1,2 In our experiment, an input laser was tuned precisely to the 3s → 3d two-photon allowed transition in atomic sodium vapor and the emission was observed in both the forward and backward directions. In these conditions, either FWM or ASE can occur. Ignoring the possibility of competition between these two processes, the calculated gain for ASE is much larger than that for FWM. However, we have observed experimentally that FWM and not ASE occur. To determine that it is the presence of efficient FWM that suppresses ASE, we have excited the atomic vapor instead with counterpropagating pump waves of different frequency. In this case, FWM, being a phase-matched process, cannot occur and strong ASE is observed. The nature of this competition is explained by solving the coupled Maxwell and density matrix equations for a three-level system. It is found that the suppression is due to the destructive interference between two different pathways of excitation of the 3d level which results in trapping of the population in the ground state.

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Competition between amplified spontaneous emission and the four-wave-mixing process

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Competition between amplified spontaneous emission (ASE) and the four-wave-mixing (FWM) process has been observed under conditions of two-photon resonant excitation of the sodium 3d level. The nature of the competition is that the FWM process is able to prevent the occurrence of ASE, even though the gain of the ASE process calculated in the absence of competition effects is much larger than that of FWM. The ASE is suppressed because the fields generated by the FWM process create a new excitation pathway connecting the ground and 3d levels, and under quite general conditions this pathway interferes destructively with that due solely to the applied laser field. These effects are modeled theoretically by solving perturbatively the density-matrix equations of the atomic system, thereby determining the population in the upper level and the nonlinear polarization of the medium. The coupling between the various optical fields due to the nonlinear polarization is described by coupled amplitude equations. The solution to these equations predicts that when the wave-vector mismatch is not too large the fields evolve spatially to reach steady-state values, and that the population excited to the 3d level by the total steady-state optical field is much smaller than that due to the incident laser field alone. We have observed experimentally the suppression of ASE by FWM and have observed that this suppression does not occur when the medium is excited with counterpropagating beams that cannot efficiently excite the FWM process. In addition, we have conducted a series of experiments that shows that the degree of suppression of ASE depends on the intensity and focusing characteristics of the incident laser as expected on the basis of our theoretical model.

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In recent years a strong interest has developed in the study of the basic coupling mechanisms governing high order multiphoton processes in atomic systems.1 Such interest has been stimulated by the rapid advances in short pulse generation techniques which allow atomic interactions at an intense field strength of the order of atomic field to be studied. Furthermore, good understanding of the highly nonlinear photon interactions is necessary to evaluate the possibility of using multiphoton processes2 as a means to couple energy into excited states emitting in the x-ray region.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 21, 1986•2 citations
Suppression of photoionization, fluorescence, amplified spontaneous emission, and nonlinear optical conversion have all been reported in the presence of resonant multiphoton excitation.1 At first glance, the nonlinear phenomena manifesting this suppression and the order of the nonlinear processes appear to be quite distinct. In some cases, this suppression has been shown to result from a destructive interference (alternatively, a competition) between alternative excitation pathways to the resonant intermediate state.2
In the presence of resonant multiphoton excitation, experimental observations of photoionization, fluorescence, and amplified spontaneous emission have shown suppression of these effects.1 There is a common mechanism tying these phenomena together. All these processes involve the coherent nonlinear coupling of two or more optical waves via a dissipative nonlinear optical medium. Independent of initial conditions, as these waves propagate through the nonlinear medium, they develop amplitudes and relative phases that minimize the dissipative losses. The condition of minimum loss is one in which the excitation of the nonlinear medium is reduced due to the waves being in a state of nonlinear optical balance. This balance is stabilized by the dissipation. Other combinations of amplitude and phase are more lossy and rapidly damped out.
When a strong near-resonant laser beam propagates through an atomic vapor, it can simultaneously induce several different nonlinear optical processes. In certain restricted conditions, these processes evolve independently of one another, but in general these processes compete. We have observed competition1 between four-wave mixing2 (FWM) and amplified spontaneous emission3 (ASE) and have presented an explanation for this phenomenon based on the solution of the coupled-amplitude equations of nonlinear optics. We extend our previous work by presenting a more detailed theoretical explanation of this effect and evidence that competition of this sort occurs quite generally in nonlinear optical systems.
Competition has been observed between amplified spontaneous emission (ASE) and four-wave mixing (FWM). Previously, competition between an incoherent and coherent process was observed in the form of suppression of multiphoton ionization by third harmonic generation.1,2 In our experiment, an input laser was tuned precisely to the 3s → 3d two-photon allowed transition in atomic sodium vapor and the emission was observed in both the forward and backward directions. In these conditions, either FWM or ASE can occur. Ignoring the possibility of competition between these two processes, the calculated gain for ASE is much larger than that for FWM. However, we have observed experimentally that FWM and not ASE occur. To determine that it is the presence of efficient FWM that suppresses ASE, we have excited the atomic vapor instead with counterpropagating pump waves of different frequency. In this case, FWM, being a phase-matched process, cannot occur and strong ASE is observed. The nature of this competition is explained by solving the coupled Maxwell and density matrix equations for a three-level system. It is found that the suppression is due to the destructive interference between two different pathways of excitation of the 3d level which results in trapping of the population in the ground state.
Competition between amplified spontaneous emission (ASE) and the four-wave-mixing (FWM) process has been observed under conditions of two-photon resonant excitation of the sodium 3d level. The nature of the competition is that the FWM process is able to prevent the occurrence of ASE, even though the gain of the ASE process calculated in the absence of competition effects is much larger than that of FWM. The ASE is suppressed because the fields generated by the FWM process create a new excitation pathway connecting the ground and 3d levels, and under quite general conditions this pathway interferes destructively with that due solely to the applied laser field. These effects are modeled theoretically by solving perturbatively the density-matrix equations of the atomic system, thereby determining the population in the upper level and the nonlinear polarization of the medium. The coupling between the various optical fields due to the nonlinear polarization is described by coupled amplitude equations. The solution to these equations predicts that when the wave-vector mismatch is not too large the fields evolve spatially to reach steady-state values, and that the population excited to the 3d level by the total steady-state optical field is much smaller than that due to the incident laser field alone. We have observed experimentally the suppression of ASE by FWM and have observed that this suppression does not occur when the medium is excited with counterpropagating beams that cannot efficiently excite the FWM process. In addition, we have conducted a series of experiments that shows that the degree of suppression of ASE depends on the intensity and focusing characteristics of the incident laser as expected on the basis of our theoretical model.
In recent years a strong interest has developed in the study of the basic coupling mechanisms governing high order multiphoton processes in atomic systems.1 Such interest has been stimulated by the rapid advances in short pulse generation techniques which allow atomic interactions at an intense field strength of the order of atomic field to be studied. Furthermore, good understanding of the highly nonlinear photon interactions is necessary to evaluate the possibility of using multiphoton processes2 as a means to couple energy into excited states emitting in the x-ray region.