Third-order Intensity Correlation Research Articles

Ab initio spatial phase retrieval via intensity triple correlations.

Second-order intensity correlations from incoherent emitters can reveal the Fourier transform modulus of their spatial distribution, but retrieving the phase to enable completely general Fourier inversion to real space remains challenging. Phase retrieval via the third-order intensity correlations has relied on special emitter configurations which simplified an unaddressed sign problem in the computation. Without a complete treatment of this sign problem, the general case of retrieving the Fourier phase from a truly arbitrary configuration of emitters is not possible. In this paper, a general method for ab initio phase retrieval via the intensity triple correlations is described. Simulations demonstrate accurate phase retrieval for clusters of incoherent emitters which could be applied to imaging stars or fluorescent atoms and molecules. With this work, it is now finally tractable to perform Fourier inversion directly and reconstruct images of arbitrary arrays of independent emitters via far-field intensity correlations alone.

A Triple Correlator of Radiation Intensities of a Multimode Semiconductor Laser

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.

Optical nonclassicality test based on third-order intensity correlations

We develop a nonclassicality criterion for the interference of three delayed, but otherwise identical, light fields in a three-mode Bell interferometer. We do so by comparing the prediction of quantum mechanics with those of a classical framework in which independent sources emit electric fields with random phases. In particular, we evaluate third-order correlations among output intensities as a function of the delays, and show how the presence of a correlation revival for small delays cannot be explained by the classical model of light. The observation of a revival is thus a nonclassicality signature, which can be achieved only by sources with a photon-number statistics that is highly sub-Poissonian. Our analysis provides strong evidence for the nonclassicality of the experiment discussed by Menssen et al. [Menssen et al., Phys. Rev. Lett, 118, 153603 (2017)], and shows how a collective "triad" phase affects the interference of any three or more light fields, irrespective of their quantum or classical character.

Temporal response of a random medium from third-order laser speckle frequency correlations.

We demonstrate for the first time that the temporal response of a random medium can be obtained from optical intensity fluctuations. Our method uses third-order intensity correlations of measured speckle patterns from a multiple scattering random medium as a function of optical frequency. In particular, our experimental results for the temporal response extracted from third-order intensity correlations are in good agreement with the predictions of a diffusion model. Our results are valid for waves in random media where the scattered field is described by circular complex Gaussian statistics.

Unbalanced third-order correlations for full characterization of femtosecond pulses

Phase and intensity from correlation and spectrum only (PICASO) is a simple and accurate method for fully characterizing femtosecond pulses. We extend this technique to make use of third-order intensity correlations. Unbalancing the interferometer makes the retrieval algorithm sensitive to the direction of time and improves the retrieval of certain pulse shapes. We investigate the sensitivity of the retrieval to direction of time as a function of the degree of imbalance in the correlator.

Measuring the temporal intensity of ultrashort laser pulses by triple correlation

By measuring the triple correlation of an ultrashort laser pulse, it is possible to determine the temporal envelope of the pulse intensity. No assumptions on the analytic form of the pulse shape and no iterative algorithms are necessary. The method is extremely stable even for noisy data, and is a powerful tool for pulses that have a strong amplitude modulation. A multi-shot and a single-shot arrangement of the triple correlator has been realized. PACS: 42.60.By; 42.65.-k; 42.79.Fm Laser pulses as short as several femtoseconds can now be generated in many laboratories all over the world [1]. Since electronic devices, and even the fastest streak cameras, are too slow to measure the temporal evolution of these pulses, there has been an extensive search for novel measurement techniques over the past few years. All of these techniques rely on autocorrelation or crosscorrelation methods of a pulsed electric field, using various nonlinear effects such as second harmonic generation [2] or the optical Kerr effect [3]. In order to extract the temporal intensity, either an analytic pulse shape has to be assumed or iterative algorithms have to be used [4]. With a new experimental setup that uses a cascaded thirdorder nonlinear effect and introduces two independent delay times, background-free triple correlation of a femtosecond laser pulse has been measured in similar fashion to the technique proposed by Weber and Dandliker [5]. The method is different from the scheme proposed in [6], which relies on a single-step third-order nonlinear effect and on counterpropagating beams. The triple-correlation theory has been successfully applied in astronomy in order to increase the resolution of imaging systems [7, 8] and to measure the temporal correlation properties of lasers operating near their threshold [9]. In the late 1960s, it was shown that the third-order intensity correlation is sufficient to determine the time-dependent intensity of a laser pulse [10]. Following a scheme proposed in the mid-1980s [11], the intensity of a short laser pulse can be extracted without any assumptions about the pulse shape and using a recursive algorithm only. The measurement contains redundant information, and therefore the pulse intensity can be calculated by various paths, leading to the correct pulse shape even for very noisy data. Since the pulse intensity is obtained by a direct mathematical operation, this method is well suited for pulses with strong amplitude modulations. It has been proposed that such tailored pulses can, for example, be used in quantum control experiments [12].

Measurement of ultraviolet subpicosecond pulses based on ultrafast beam deflection

We describe a beam-deflection technique based on the ultrafast electronic Kerr effect for measuring the duration of ultrashort laser pulses in a wide spectral range. Using this method, which provides the third-order intensity correlation function, we have measured subpicosecond KrF laser pulses. The results are in good agreement with the Kerr-shutter autocorrelation measurement.

Single-shot measurement of ultraviolet and visible femtosecond pulses using the optical Kerr effect

We present a method that allows the single-shot measurement of femtosecond pulses in the ultraviolet as well as the visible spectral regions. The method is based on the optical Kerr shutter technique, and it provides the third-order intensity correlation function.

Single-shot measurement of femtosecond pulses using the optical Kerr effect

The authors demonstrate the optical Kerr shutter technique as a simple and powerful tool for single-shot measurements of femtosecond pulses over a wide spectral range. The method provides the third-order intensity correlation function which gives information about pulse asymmetry and pulse structures.

Measurement of ultraviolet femtosecond pulses using the optical kerr effect

We demonstrate the optical Kerr shutter technique as a simple and powerful tool for the measurement of femtosecond pulses in the ultraviolet as well as in the visible spectral region. The method provides the third-order intensity correlation function which gives information about pulse asymmetry and pulse structures.

Phase determination of second-order coherence function

By making use of recent calculations on the third-order intensity correlations, we suggest a method for the numerical computation of the phase of the normalized second-order coherence function. The method is applicable for a laser working well below its threshold of oscillation.

Third-order intensity correlations in laser light

Abstract The third-order intensity correlation function of a single-mode laser beam has been measured with high accuracy near the laser threshold by using a fast digital correlator. The results are in good agreement with recent theoretical computations.

Third-order intensity correlations in laser light

The third-order intensity correlation function of a single-mode laser beam has been measured with high accuracy near the laser threshold by using a fast digital correlator. The results are in good agreement with recent theoretical computations.

Higher-Order Correlation Properties of a Laser Beam

The intrinsic third-order intensity correlation function of a laser beam has been measured by a digital correlation technique, for a He: Ne laser operating near threshold. The results are compared with some recent calculations of Cantrell, Lax, and Smith and are found to be in good agreement.

Calculation of third-order intensity correlations in a laser near threshold

The third-order correlation function of the intensity fluctuation of a laser near threshold is calculated and compared with the experiments of Davidson and Mandel.

Recovery of Laser Intensity from Correlation Data

It is shown that third-order intensity correlations are sufficient to determine the time-dependent intensity of a Q-switched laser. As a consequence, all higher-order correlations are related to the third and an expression for this relation is presented.