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Optics

A Triple Correlator of Radiation Intensities of a Multimode Semiconductor Laser

Michael V. Lebedev, A. A. Demenev, A.L. Parakhonsky, O. V. Misochko

Published Dec 11, 2019• 1 citation
Publisher

Abstract

In this work, temporal correlations of radiation intensities of a multimode Fabry-Perot (FP) semiconductor laser are studied. Second- and third-order intensity correlation functions are measured both for the multimode FP laser and a pulsed Ti: Sapphire (TiSp) laser. Triple correlators of the latter demonstrate an ordinary product of double correlators (the classic case). The behavior of the multimode laser is more complex and can indicate the quantum nature of optical field correlations. We follow a specific phenomenological formula for calculation of the triple temporal correlator.

DOI
10.3390/opt1010003

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In this work, temporal correlations of radiation intensities of a multimode Fabry-Perot (FP) semiconductor laser are studied. Second- and third-order intensity correlation functions are measured both for the multimode FP laser and a pulsed Ti: Sapphire (TiSp) laser. Triple correlators of the latter demonstrate an ordinary product of double correlators (the classic case). The behavior of the multimode laser is more complex and can indicate the quantum nature of optical field correlations. We follow a specific phenomenological formula for calculation of the triple temporal correlator.
The purpose of this investigation was to construct the experimental apparatus for measuring second-order intensity correlation functions of the type T2,2 (x,t,x,t+T) = < : I(x,t)I(x,t+T):>. This measurement was applied to the radiation field produced by a two axial mode Helium-Neon gas laser in order to verify the intensity fluctuation correlations due to the beating of the two axial modes of the laser. The axial mode separation was measured for comparison with a scanning Fabry Perot interferometer and also an RF spectrum analyzer. The correlation measurement was also applied to the second harmonic radiation field produced by the. parametric interaction in a LiNb03 crystal pumped with two axial modes. The experimental determination of the correlation <:I(x,t)I(x,t+T):> involves a time-spectroscopy measurement in which one photon is detected at point x, and another at point x, T seconds later, and measuring the probability of two-fold coincident detection as a function of T. The radiation field was split into two beams at a partially transmitting reflector, each of which was directed incident on the photocathode of a photomultiplier tube. The photoelectron pulses from the tubes were amplified and standardized. These standardized pulses were then temporally correlated with the use of a time-to-amplitude converter (TAC) and a multi-channel pulse height analyzer (MA). The time-to-amplitude conversions generated by the TAC were stored in the channels of the PHA, which was a direct measure of the two-fold delayed coincidence detection rate, R(T). The second-order intensity correlation functions <:I(x,t)I(x,t+T):> are determined from measurements of R(T). The fluctuating components of the second-order intensity correlation functions were found to be in agreement with what would be expected on a classical basis. Correspondingly, the capability is demonstrated of the experimental apparatus measuring a quantity relating to the second-order intensity correlation function.
In this study, we measured the temporal correlations in the electromagnetic field radiated by a laser in the threshold region of oscillation, from 110\frac{1}{10}101​ 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 110\frac{1}{10}101​ 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.
The theory of the intensity correlations between photons of different frequencies is re-examined from basic principles and is found to lead to an expression for the correlation function containing operator products which are normally ordered in time. This expression leads to results which are free of certain extra contributions that arise in another version of this theory which contains non-normally ordered products. The analysis presented is based on a description of the frequency-filtering process in terms of Fabry-Perot interferometers. The mirrors of the interferometers are modelled as classical dielectrics. The EM field in the presence of these dielectrics is then quantised and the intensity correlation function defined in terms of these modified field operators. The results are examined in detail for the case of a light field radiated by a two-level atom.
A procedure for the measurement of intensity correlations of the type $〈:\stackrel{^}{I}(\mathrm{x}, t)\stackrel{^}{I}(\mathrm{x}, t+\ensuremath{\tau}):〉$ and $〈:\stackrel{^}{I}(\mathrm{x}, t)\ifmmode\times\else\texttimes\fi{}\stackrel{^}{I}(\mathrm{x}, t+{\ensuremath{\tau}}_{1})\stackrel{^}{I}(\mathrm{x}, t+{\ensuremath{\tau}}_{2}):〉$ with the use of a time-to-amplitude converter is developed. The procedure is used to measure second- and third-order intensity fluctuation correlation functions of the optical field produced by a gas laser operated at various levels near its threshold of oscillation. The results are shown to be in agreement with the predictions of laser theories.