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The Review of Laser Engineering

Two-Photon Correlation of Imperfectly Mode-Locked Pulses.

Yoko Miyamoto, Masahiro Matsuoka

Published Jan 1, 1995• 0 citations
Publisher

Abstract

The Gaussian noise burst model and the domain model for imperfectly mode-locked pulses are examined through comparison with two types of two-photon correlation experiments. These models are known to agree with autocorrelation measurements using nonlinear optical methods. The Gaussian noise burst model does not give correct results for the pulse-cycleaveraged, normalized second-order correlation function at zero time-delay, and the domain model fails to explain the two-component dip in coincidence count rate curves obtained with the interferometer configuration.

DOI
10.2184/lsj.23.1002

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The Gaussian noise burst model and the domain model for imperfectly mode-locked pulses are examined through comparison with two types of two-photon correlation experiments. These models are known to agree with autocorrelation measurements using nonlinear optical methods. The Gaussian noise burst model does not give correct results for the pulse-cycleaveraged, normalized second-order correlation function at zero time-delay, and the domain model fails to explain the two-component dip in coincidence count rate curves obtained with the interferometer configuration.
The excitation of photon echo by noise pulses that are formed by modulation of the carrying frequency with Gauss noise is modeled. The modeling is based on optical Bloch equations the solution of which for noise pulse realizations is constructed by their stepwise approximation. In terms of the formalism of state transfer matrices, the two- and three-pulse excitation modes are analyzed. The complex envelopes of the primary and stimulated echo responses are determined. In the linear (low-level-signal) mode, the shape of the two-pulse echo corresponds to that of the time delayed and inverted noise pulse. The boundary of the linear mode, upon exceeding of which distortions of the shape of the noise pulse become noticeable, is determined. The shape of the stimulated (three-pulse) echo in the linear mode corresponds to that of the autocorrelation function of the noise pulse realization. Upon passage beyond the boundary of the linear mode, the shape of the three-pulse echo corresponds either to the cross-correlation function of distorted noise pulses (with different intensities) or to the autocorrelation function of distorted pulses (with the same intensities). The modeled photon echo excitation modes can be used in photon echo processors to process signals in the light range.
Two-photon fluorescence traces used for picosecond pulse-width measurement are analyzed and described by intensity correlation functions, also known as second-order coherence functions. The correlation functions and the fluorescence traces are discussed for three special types of light emission and calculated in detail for a three-mode laser model in free-running, mode-locking, and FM-like operation. A rigorous calculation for the fluorescence intensity excited by a laser oscillating in a large number of modes with arbitrary amplitudes and phases is also given. The shapes of the fluorescence traces are found to be essentially the same for both, free-running and ideally mode-locked emission, but with different contrast ratios of 1.5 : 1 and 3 : 1, respectively.
We develop a general representation for ensembles of non-stationary random pulses in terms of statistically uncorrelated, time-delayed, frequency-shifted Gaussian pulses which are classical counterparts of coherent states of a quantum harmonic oscillator. We show that the two-time correlation function describing second-order statistics of the pulses can be expanded in terms of the complex Gaussian pulses. We also demonstrate how the novel formalism can be applied to describe recently introduced Gaussian Schell-model pulses and pulse trains generated by typical mode-locked lasers.