In this study, we measured the temporal correlations in the electromagnetic field radiated by a laser in the threshold region of oscillation, from $\frac{1}{10}$ to 10 times threshold intensity. The experimental results are compared with theoretical predictions based on solutions of a Fokker-Planck equation. We stabilized the intensity of a He-Ne cw gas laser by means of a long-time-constant servo system which controlled the cavity length. Using a fast photomultiplier as detector, we recorded the photoelectron count distribution within a short counting time (3 \ensuremath{\mu}sec) while the photomultiplier was exposed to the laser light. From the photoelectron count distribution measurement, we calculated second, third, and fourth normalized cumulants of the intensity probability density function of the light field. The normalized cumulant is a measure of "pure" correlations among photons because the contributions from lower-order correlations are removed. The statistics of the photoelectron count distribution shows that the intensity fluctuations at about $\frac{1}{10}$ threshold are nearly those of a Gaussian field, and continuously approach those of a constant-amplitude field as the intensity is raised to about 10 times threshold. The normalized second, third, and fourth cumulants of the intensity probability density function of the laser light were also measured at 17 and 42% of threshold intensity as the counting time was increased from 3 to 1000 \ensuremath{\mu}sec. The results agree with predictions computed under the assumption that the dependence of the correlation functions on the time variables is the same as for Gaussian light.In this study, we measured the temporal correlations in the electromagnetic field radiated by a laser in the threshold region of oscillation, from $\frac{1}{10}$ to 10 times threshold intensity. The experimental results are compared with theoretical predictions based on solutions of a Fokker-Planck equation. We stabilized the intensity of a He-Ne cw gas laser by means of a long-time-constant servo system which controlled the cavity length. Using a fast photomultiplier as detector, we recorded the photoelectron count distribution within a short counting time (3 \ensuremath{\mu}sec) while the photomultiplier was exposed to the laser light. From the photoelectron count distribution measurement, we calculated second, third, and fourth normalized cumulants of the intensity probability density function of the light field. The normalized cumulant is a measure of "pure" correlations among photons because the contributions from lower-order correlations are removed. The statistics of the photoelectron count distribution shows that the intensity fluctuations at about $\frac{1}{10}$ threshold are nearly those of a Gaussian field, and continuously approach those of a constant-amplitude field as the intensity is raised to about 10 times threshold. The normalized second, third, and fourth cumulants of the intensity probability density function of the laser light were also measured at 17 and 42% of threshold intensity as the counting time was increased from 3 to 1000 \ensuremath{\mu}sec. The results agree with predictions computed under the assumption that the dependence of the correlation functions on the time variables is the same as for Gaussian light.

Physical ReviewFeb 10, 196979 citations

Third-order intensity correlations in laser light

Mario Corti, Vittorio Degiorgio

Optics CommunicationsMay 1, 197424 citations

Fourth-Order Spatial Correlation of Thermal Light

Feng Wen, Xun Zhang, Xinxin Xue +3 more

We investigate the fourth-order spatial correlation properties of pseudo-thermal light in the photon counting regime, and apply the Klyshko advanced-wave picture to describe the process of four-photon coincidence counting measurement. We deduce the theory of a proof-of-principle four-photon coincidence counting configuration, and find that if the four randomly radiated photons come from the same radiation area and are indistinguishable in principle, the fourth-order correlation of them is 24 times larger than that when four photons come from different radiation areas. In addition, we also show that the higher-order spatial correlation function can be decomposed into multiple lower-order correlation functions, and the contrast and visibility of low-order correlation peaks are less than those of higher orders, while the resolutions all are identical. This study may be useful for better understanding the four-photon interference and multi-channel correlation imaging.We investigate the fourth-order spatial correlation properties of pseudo-thermal light in the photon counting regime, and apply the Klyshko advanced-wave picture to describe the process of four-photon coincidence counting measurement. We deduce the theory of a proof-of-principle four-photon coincidence counting configuration, and find that if the four randomly radiated photons come from the same radiation area and are indistinguishable in principle, the fourth-order correlation of them is 24 times larger than that when four photons come from different radiation areas. In addition, we also show that the higher-order spatial correlation function can be decomposed into multiple lower-order correlation functions, and the contrast and visibility of low-order correlation peaks are less than those of higher orders, while the resolutions all are identical. This study may be useful for better understanding the four-photon interference and multi-channel correlation imaging.

Chinese Physics LettersNov 1, 20144 citations

Third- and Higher-Order Intensity Correlations in Laser Light

Cyrus D. Cantrell, M. Lax, Wallace Arden Smith

Springer eBooksJan 1, 19732 citations

Stimulated radiative corrections in hydrogen in the presence of a strong laser field

Edmond Arnous, J. Bastian, A. Maquet

The stimulated radiative corrections (or ac-Stark shift, or light shift...) of the energy levels of a hydrogenic atom irradiated by an intense, nonresonant, monomode laser field, are evaluated within the framework of the time-dependent perturbation theory, up to and including fourth order. The calculation is performed by using a Sturmian representation of the Coulomb Green's function. Whenever it is possible, comparison is made with other results, and several limiting cases are considered. If the laser frequency $\ensuremath{\omega}\ensuremath{\rightarrow}0$, one recovers the results of the dc-Stark effect. If $2\ensuremath{\omega}$ becomes larger than the ionization energy of the atomic state considered, the fourth-order level shift acquires an imaginary part which may be connected, via an extension of the optical theorem, to the two-photon ionization cross section. We point out also the difficulties encountered, when trying to get sensible estimates from partial summation of the infinite sums entering the perturbative expression of the fourth-order amplitudes. Finally, the order of magnitude of these various corrections is discussed.The stimulated radiative corrections (or ac-Stark shift, or light shift...) of the energy levels of a hydrogenic atom irradiated by an intense, nonresonant, monomode laser field, are evaluated within the framework of the time-dependent perturbation theory, up to and including fourth order. The calculation is performed by using a Sturmian representation of the Coulomb Green's function. Whenever it is possible, comparison is made with other results, and several limiting cases are considered. If the laser frequency $\ensuremath{\omega}\ensuremath{\rightarrow}0$, one recovers the results of the dc-Stark effect. If $2\ensuremath{\omega}$ becomes larger than the ionization energy of the atomic state considered, the fourth-order level shift acquires an imaginary part which may be connected, via an extension of the optical theorem, to the two-photon ionization cross section. We point out also the difficulties encountered, when trying to get sensible estimates from partial summation of the infinite sums entering the perturbative expression of the fourth-order amplitudes. Finally, the order of magnitude of these various corrections is discussed.

Physical Review AFeb 1, 198321 citations

In this study, we measured the temporal correlations in the electromagnetic field radiated by a laser in the threshold region of oscillation, from

\frac{1}{10}

to 10 times threshold intensity. The experimental results are compared with theoretical predictions based on solutions of a Fokker-Planck equation. We stabilized the intensity of a He-Ne cw gas laser by means of a long-time-constant servo system which controlled the cavity length. Using a fast photomultiplier as detector, we recorded the photoelectron count distribution within a short counting time (3 \ensuremath{\mu}sec) while the photomultiplier was exposed to the laser light. From the photoelectron count distribution measurement, we calculated second, third, and fourth normalized cumulants of the intensity probability density function of the light field. The normalized cumulant is a measure of "pure" correlations among photons because the contributions from lower-order correlations are removed. The statistics of the photoelectron count distribution shows that the intensity fluctuations at about

\frac{1}{10}

threshold are nearly those of a Gaussian field, and continuously approach those of a constant-amplitude field as the intensity is raised to about 10 times threshold. The normalized second, third, and fourth cumulants of the intensity probability density function of the laser light were also measured at 17 and 42% of threshold intensity as the counting time was increased from 3 to 1000 \ensuremath{\mu}sec. The results agree with predictions computed under the assumption that the dependence of the correlation functions on the time variables is the same as for Gaussian light.