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Journal of Modern Optics

Low-frequency Beats Produced by Interference of Laser Modes

P. Hariharan, Ichiro Fujima, Ninita H. Brown, Barry C. Sanders

Published Aug 1, 1993• 5 citations
Publisher

Abstract

A helium-neon laser operating in three or more axial modes can generate, at a photo detector with a nonlinear response to intensity, beat signals with frequencies corresponding to the second differences between the frequencies of these modes. This paper presents a quantum-field theoretical treatment of the formation of such low-frequency beats, as well as experimental data demonstrating that interference effects corresponding to the production of such beats can be observed even at light levels at which the probability of at least one photon from each of the three modes being present simultaneously in the optical path is negligible.

DOI
10.1080/09500349314551541

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A helium-neon laser operating in three or more axial modes can generate, at a photo detector with a nonlinear response to intensity, beat signals with frequencies corresponding to the second differences between the frequencies of these modes. This paper presents a quantum-field theoretical treatment of the formation of such low-frequency beats, as well as experimental data demonstrating that interference effects corresponding to the production of such beats can be observed even at light levels at which the probability of at least one photon from each of the three modes being present simultaneously in the optical path is negligible.
Heterodyne interferometry uses beats produced by superposing two light waves with different frequencies at a photodetector. The output from the photodetector then contains a component at the beat frequency which can be processed to obtain information on changes in the optical path difference. We present experimental results which show that beats can be observed down to power levels at which the mean time interval between the arrival of photons at the photodetector is much greater than the transit time from the laser source to the detector and also when the mean time interval between photons is greater than the period of the beat. These results show that the beats are not due to the interference of one photon with another, but arise from a succession of single-photon events. It follows that measurements can be made even at extremely low photon fluxes by using homodyne detection and extending the integration time.
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.
We present a theoretical treatment of the coherent three-level beat signals occurring in the transient response of a Doppler-broadened molecular system with coupled closely spaced levels resonating with an intense monochromatic cw laser field. When the degenerate levels of the molecular system are suddenly split by means of an external Stark or Zeeman field, the transmitted laser radiation exhibits decaying beats at frequencies related to the level splitting or Raman frequency. This effect has been the subject of earlier theoretical analyses, but some relevant aspects such as the velocity integration, were not taken into account. A perturbation treatment, complete to third order in laser field strength, is used to calculate the velocity-integrated induced polarization and the corresponding reradiated field. The calculation takes into account both Raman-type processes, which lead to transient oscillations at the Raman frequency ${\ensuremath{\omega}}_{21}$, and population-saturation effects. In particular, population-induced transient oscillations at half the Raman frequency, $\frac{{\ensuremath{\omega}}_{21}}{2}$, are predicted. The relative importance of the various oscillations is analyzed as a function of the laser detuning and other parameters, including velocity-changing collisions. The relationship between the three-level beat signals and the well-known quantum-beat effect studied in fluorescence is explored.
Quantum beats can be produced in fourth-order interference such as in a Hong-Ou-Mandel (HOM) interferometer by using photons with different frequencies. Here we present theoretically the appearance of interference of quantum beats when the HOM interferometer is combined with a Franson-type interferometer. This combination can make the interference effect of photons with different colors take place not only within the coherence time of downconverted fields but also in the region beyond that. We expect that it can provide a new method in quantum metrology, as it can realize the measurement of time intervals in three scales. (C) 2015 Chinese Laser Press