Temporal Cross-correlation Function Research Articles

Time-domain Hong-Ou-Mandel interference of quasi-thermal fields and its application in linear optical circuit characterization.

We study temporal correlations of interfering quasi-thermal fields, obtained by scattering laser radiation on a rotating ground glass disk. We show that the Doppler effect causes oscillations in the temporal cross correlation function. Furthermore, we propose how to use Hong-Ou-Mandel interference of quasi-thermal fields in the time domain to characterize linear optical circuits.

Optical anemometry based on the temporal cross-correlation of angle-of-arrival fluctuations obtained from spatially separated light sources

The temporal cross-correlation function of the angle-of-arrival (AOA) fluctuations of two optical waves propagating through atmospheric turbulence carries information regarding the average wind velocity transverse to the propagation path. We present and discuss two estimators for the retrieval of the path-averaged beam-transverse horizontal wind velocity, v(t). Both methods retrieve v(t) from the temporal cross-correlation function of AOA fluctuations obtained from two closely spaced light-emitting diodes (LEDs). The first method relies on the time delay of the peak (TDP) of the cross-correlation function, and the second method exploits its slope at zero lag (SZL). Over a 9 h period during which v(t) varied between -1.3 ms(-1) and 2.0 ms(-1), the maximum rms difference between optically retrieved and in situ measured 10 s estimates of v(t) was found to be 0.18 ms(-1) for the TDP estimator and 0.23 ms(-1) for the SZL estimator. Applicability and limitations of these two optical wind retrieval techniques are discussed.

On the Vortex Dynamic of Airflow Reattachment Forced by a Single Non-thermal Plasma Discharge Actuator

Commercial and military aircrafts or miniature aerial vehicles can suffer from massive flow separation when high angles of attack are required. Single dielectric barrier discharge (DBD) actuators have demonstrated their capability of controlling such a separated flow at low external velocity. However, the processes resulting in the improvement of the flight performances remain unclear. In the present study, the reattachment process along the suction side of a NACA 0015 placed at an angle of attack of 16° is experimentally investigated for an external velocity of 20 m/s (Re = 260,000). A single DBD actuator is mounted at the leading edge of the model. The velocity fields above the suction side of the airfoil are measured by a high-speed acquisition system (3 kHz). The results indicate that the baseline flow presents shed vortices that form at the leading edge and linearly grow along the free shear layer axis. This vortex shedding is organized and exhibits a specific frequency of about 90 Hz. The continuous actuation produces a partial flow reattachment up to 70% of the chord length. Temporal cross-correlation function indicates the presence of a vortex shedding at the trailing edge of the controlled flow. Finally, the temporal analysis demonstrates that the reattachment process requires 50 ms to reach a stabilized attached flow. The time-resolved analysis of the reattachment suggests that the actuation by plasma discharge acts as a catalyser by reinforcing one of the coherent flow structures already existing in the natural flow.

Direct Observation of Hydrodynamic Rotation-Translation Coupling between Two Colloidal Spheres

By combining optical tweezers with polarization microscopy, the hydrodynamic coupling between position and orientation fluctuations in a pair of colloidal spheres has been measured. Imaging of birefringent particles under crossed polarizers allows for the simultaneous determination of the positions and orientations of both particles. The temporal cross-correlation function between random displacements of one particle and orientation fluctuations of its neighbor allows for the quantification of the hydrodynamic rotation-translation coupling between the spheres. Our results are in good agreement with predictions for the hydrodynamic mobility tensors calculated in the creeping-flow limit of the Navier-Stokes equation.

Independent particle size and shape estimation from polarization fluctuation spectroscopy

Polarization fluctuation spectroscopy (PFS) is similar to conventional photon correlation spectroscopy (PCS) but measures the fluctuations in different polarizations of scattered light to obtain shape information in addition to the size information available from the temporal variations. The sample must be such that it forms a suspension sufficiently dilute that no multiple scattering occurs but sufficiently dense that the scattered light should be Gaussian in nature. The PFS technique measures the cross-correlation coefficient of intensities scattered into two polarization states to recover the aspect ratio of the particles. In this paper, it is shown how determination of the complete temporal cross-correlation function enables independent measurement of the size and shape parameters of a mono-disperse sample. The robustness of the technique is demonstrated using experimental data.

Sum frequency beam analysis for the determination of the temporal characteristics of ultrashort light pulses

An extension of the single-shot second harmonic beam method proposed earlier for picosecond pulse duration measurements is presented for the case of two incident pulses of differing frequencies, durations and transverse sizes. The solution of the wave equation for noncollinear sum frequency generation in a nonlinear crystal by two Gaussian, spatially limited ultrashort pulses is given. It is shown that the width (τ 1 2 +τ 2 2 )1/2 of the temporal cross-correlation function of the two pulses can be deduced from the spatial energy distribution of the sum frequency beam. The method can be used e.g. in the case of a relatively weak secondary pulse obtained in some nonlinear processes. Preliminary experimental results demonstrating the possibilities offered by the method are presented.

Speckle field of curved, rotating surfaces of Gaussian roughness illuminated by a laser light spot*

The first- and second-order space-time correlation functions of the optical field and the intensity, respectively, are calculated for the case of a rotating symmetrical curved surface with Gaussian roughness, scattering laser light into the far-field zone from a small illuminated spot. The incident beam is either collimated or spherical. The diameter of the illuminated area is small compared with the radii of curvature. The mean surface is approximated by a torus with two principal radii of curvature. The sphere, the cone, and the flat surface are special cases. Optical phase variations linear and quadratic in the surface coordinates are included in the calculation. The surface is assumed to be very rough. It is found that the correlation function of the intensity depends on the radius of the incident beam, the local surface velocity, and the radii of curvature in the illuminated region. Curvature decreases the decay time of the correlation functions. This is confirmed by experiments carried out with the flat disk, the sphere, and the cone. The temporal cross-correlation function of the outputs of two detectors in the speckle field obtained with an incident spherical wave is very sensitive to normal displacements of the surface.