Source Coherence Time Research Articles

Light-field microscopy with correlated beams for high-resolution volumetric imaging

Light-field microscopy represents a promising solution for microscopic volumetric imaging, thanks to its capability to encode information on multiple planes in a single acquisition. This is achieved through its peculiar simultaneous capture of information on light spatial distribution and propagation direction. However, state-of-the-art light-field microscopes suffer from a detrimental loss of spatial resolution compared to standard microscopes. In this article, we experimentally demonstrate the working principle of a new scheme, called Correlation Light-field Microscopy (CLM), where the correlation between two light beams is exploited to achieve volumetric imaging with a resolution that is only limited by diffraction. In CLM, a correlation image is obtained by measuring intensity correlations between a large number of pairs of ultra-short frames; each pair of frames is illuminated by the two correlated beams, and is exposed for a time comparable with the source coherence time. We experimentally show the capability of CLM to recover the information contained in out-of-focus planes within three-dimensional test targets and biomedical phantoms. In particular, we demonstrate the improvement of the depth of field enabled by CLM with respect to a conventional microscope characterized by the same resolution. Moreover, the multiple perspectives contained in a single correlation image enable reconstructing over 50 distinguishable transverse planes within a 1 mm3 sample.

Numerical research on partially coherent flat-topped beam propagation through atmospheric turbulence along a slant path.

In this paper, we investigate the propagation of partially coherent flat-topped (PCFT) beams through atmospheric turbulence along a slant path. Using wave optics simulation (WOS), we calculated the on-axis intensity of PCFT beams in both vacuum and turbulence links, finding that PCFT beams will self-focus during propagation and that the beam coherence length has a significant impact on this focusing phenomenon. The effects of the zenith angle and the source coherence length on the scintillation index and mean signal-to-noise ratio (SNR) are analyzed. Furthermore, taking into consideration the limitation of available devices, we examined the impacts of source coherence time and detector integration time on the performance of PCFT beams in slant links. WOS results indicate as much as an extra 2 dB SNR gain from PCFT beams in short links in comparison with Gaussian Schell-model beams.

Temporal imaging based on first-order field correlation

Different from second-order temporal ghost imaging usually realized by means of second-order correlation measurement, in this paper, we investigate theoretically temporal imaging with temporally thermal light via first-order field correlation based on a Mach-Zehnder interferometer. The paraxial wave equation describing the diffraction of light and the differential equation characterizing the dispersion of light pulse are given. Based on the similarity between these equations, the duality between the paraxial diffraction of the light in the spatial domain and the dispersion of the temporal narrow-band pulse in the dispersive medium (i.e. the space-time duality) is obtained, and the impulse response functions in the time domain for several optical systems are also presented. Then in terms of the space-time duality, we design the scheme for temporal imaging via first-order thermal field correlation based on a Mach-Zehnder interferometer and obtain the intensity expression for first-order temporal imaging according to the temporal impulse response functions, and discuss the influences of the source pulse width and coherence time on the image visibility and resolution. The result shows that the temporal signal can be reconstructed through temporal first-order temporal imaging. Furthermore, when the source’s coherence time is fixed, the image visibility decreases as the pulse width increases. However, the image resolution increases. When the source’s pulse width is fixed, the image visibility increases as the coherence time increases. And yet the image resolution decreases. Specially, when the source’s pulse width is 100 ps and the coherence time is 0.5 ps, the image quality (taking both the visibility and resolution into account) of a temporally rectangular object is satisfactory. In the simulation, the distance and width of the temporal rectangular object are 20 ps and 8 ps, respectively. It is shown that there is a dilemma between the visibility and resolution of first-order temporal imaging which is similar to the result of second-order ghost imaging. Our result discussed herein could be valuable in the reconstruction and detection of temporal signal via first-order temporal ghost imaging with temporally thermal light.

Propagation of partially coherent beams with convex-shaped spatial coherence modulation in vertical turbulent links.

The convex partially coherent beam (CPCB) is a special type of nonuniformly correlated beam with a convex-shaped complex degree of coherence (DoC) distributions. Previously our research has illustrated the potential of CPCBs with super-Gaussian DoCs in free-space optical communications (FSOC), mainly manifested as self-focusing which can be transferred into extra scintillation reduction and SNR gain. In this study, the effects of the DoC transition slopes are analyzed and more details about the turbulence propagation of CPCBs with super-Gaussian shaped DoC are revealed. By means of wave optics simulation, the longitudinal intensity evolution of the CPCB is explored, showing that the DoC slope has a profound influence on the self-focusing features such as the focusing plane and the peak intensity. Aperture scintillation and mean SNR at the receiver end of some short-range vertical turbulent links are numerically computed. The obtained results show that, with CPCBs, an ~2 dB SNR gain can be achieved as compared to conventional Gaussian Schell-modal (GSM) beams. However, CPCBs are preferred only in shorter links, which is found to be relevant to the power-in-the-bucket of the receiving aperture. Furthermore, the impacts of the ratio of the source coherence time to the detector integration time are investigated, implying that the CPCB is less susceptible than the GSM. We have also examined the off-axis scintillation of the CPCB. Due to its convex-shaped DoC, the CPCB has significantly reduced off-axis scintillation, which can be beneficial in the presence of pointing errors.

Non-Gaussian statistics and optical rogue waves in stimulated Raman scattering

We explore theoretically and numerically optical rogue wave formation in stimulated Raman scattering inside a hydrogen filled hollow core photonic crystal fiber. We assume a weak noisy Stokes pulse input and explicitly construct the input Stokes pulse ensemble using the coherent mode representation of optical coherence theory, thereby providing a link between optical coherence and rogue wave theories. We show that the Stokes pulse peak power probability distribution function (PDF) acquires a long tail in the limit of nearly incoherent input Stokes pulses. We demonstrate a clear link between the PDF tail magnitude and the source coherence time. Thus, the latter can serve as a convenient parameter to control the former. We explain our findings qualitatively using the concepts of statistical granularity and global degree of coherence.

Multipath correlation interference and controlled-NOT gate simulation with a thermal source

We theoretically demonstrate a counter-intuitive phenomenon in optical interferometry with a thermal source: the emergence of second-order interference between two pairs of correlated optical paths even if the time delay imprinted by each path in one pair with respect to each path in the other pair is much larger than the source coherence time. This fundamental effect could be useful for experimental simulations of small-scale quantum circuits and of 100%-visibility correlations typical of entangled states of a large number of qubits, with possible applications in high-precision metrology and imaging. As an example, we demonstrate the polarization-encoded simulation of the operation of the quantum logic gate known as controlled-NOT gate.

Investigation on the Phase Noise and EVM of Digitally Modulated Millimeter Wave Signal in WDM Optical Heterodyning System

In this paper, theoretical model on phase noise in self-heterodyning optical system for mmW generation is proposed. Phase noise is impacted by optical path difference between both optical tones and laser source coherence time, but also by RF generators phase noise. Phase noise measurements of the mmW signal and RF sources have been realized to discuss the validity of the model. Based both on the theoretical approach and on the phase noise characterizations, an error vector magnitude (EVM) model is developed to quantify the impact of the optical self-heterodyning output phase noise on up-converted broadband digital signal (ECMA 387 standard).

Statistics of intensity of backscattered semiconductor laser radiation in single-mode optic fiber

We have studied the statistics of the intensity of backscattered radiation of a semiconductor laser in single-mode optic fiber as a function of the probing laser pulse duration and coherence time. It is shown that, at a given radiation source coherence time, the intensity distribution function varies, depending on the pulse duration, from nearly exponential to nearly Gaussian. The exponential statistics provides a better sensitivity for a coherent reflectometer with direct detection. Using the calculated distribution function, it is possible to qualitatively determine the degree of deterioration of the reflectometer sensitivity with respect to external factors during increasing probing pulse duration or decreasing laser coherence time. These data provide criteria for the optimum choice of a radiation source for the coherent fiber-optic reflectometer.

The influence of the degree of coherence of a semiconductor laser on the statistic of the backscattered intensity in a single-mode optical fiber

The results of the study of the statistical dependence of the backscattered light intensity of a semiconductor laser in a single-mode fiber on the duration of the probing pulse and the source coherence time are presented. It is shown that, for a given light coherence time, the intensity distribution function changes with increasing pulse duration from the function close to the exponential one for the pulse duration approximately equal to the coherence time to the function close to the Gaussian one for the pulse duration exceeding the coherence time. The exponential statistics of scattered light makes it possible to obtain a higher sensitivity for the coherent reflectometer using the direct detection method.

Beat Noise Compensation in OCDMA Systems Using Soft Decoding Based FEC

In this paper we study Forward Error Correction (FEC) under beat noise assumption in the context of incoherent Optical Code Division Multiple Access (OCDMA) systems. Due to the use of unipolar codes, Multiple Access Interference (MAI) amount and thus beatings between different user contributions known as beat noise, constitute important limitations in particular for high data rates. In order to compensate for these two major limitations, we propose a solution using FEC based on a soft decoding algorithm. For this purpose, we analyze the OCDMA received signal distribution and establish a new model, based on a mixture of chi-square distributions, valuable for any OCDMA code parameters and any source coherence time values. From this model, we establish the error probability analytical expression under beat noise assumption and determine the reliability parameters required for the FEC soft decoder initialization. To illustrate the performance, we use Low Density Parity Check (LDPC) codes and show that the LDPC adapted decoder is highly efficient in reducing beat noise and MAI for incoherent OCDMA systems, even when beat noise has a severe impact. In addition, we point out that this solution permits increasing data rates or number of active users.

Performance degradation of source matching in optical CDMA due to source coherence effects

In this paper we study the performance of source matching technique for an optical code division multiple access (OCDMA) system in the presence of source coherence effects and square law detection process. We use a binary-asymmetric channel (BAC) model for an OCDMA system employing an all-optical passive correlator receiver. Source coherence effects lead to relative-intensity-noise (RIN) and phase-induced-intensity-noise (PIIN), which are included in our analysis. Previous studies only considered multiple access interference (MAI) noise, resulting in a Z-channel (where errors only occur for the transmission of data bit zero) model, and neglected RIN and PIIN. The presence of RIN and PIIN leads to errors occurring for both transmitted data bits one and zero, thus a BAC model. We show that source matching gain depends on the normalized source coherence time, defined as the ratio of the optical source coherence time to the bit duration. Our analysis shows that, while MAI limited analysis predicts that increasing the number of users increases the source matching gain, when taking into account RIN and PIIN, source matching gain is both bit rate and source type dependent, and tends to zero for very high numbers of users.

Scintillations of incoherent flat-topped Gaussian source field in turbulence

The intensity fluctuations of incoherent flat-topped Gaussian beams are evaluated when such sources are used in weakly turbulent horizontal atmospheric links. The formulation is developed for a detector having a response time much longer than the source coherence time. The flat-topped Gaussian profile is obtained by superposing many Gaussian beams, then the incoherence is introduced through delta correlation in space. The scintillation index of the incoherent flat-topped Gaussian beams is found to be smaller than the scintillation index of the corresponding incoherent Gaussian beams at the same link length, source size, and wavelength. When compared with the coherent counterparts, the intensity fluctuations of the incoherent flat-topped Gaussian beams are much smaller, yielding the same value only at the spherical wave limit, as expected. Transmitter aperture averaging is a special case of our solution.

Source coherence impairments in a direct detection direct sequence optical code-division multiple-access system

We demonstrate that direct sequence optical code- division multiple-access (DS-OCDMA) encoders and decoders using sampled fiber Bragg gratings (S-FBGs) behave as multipath interferometers. In that case, chip pulses of the prime sequence codes generated by spreading in time-coherent data pulses can result from multiple reflections in the interferometers that can superimpose within a chip time duration. We show that the autocorrelation function has to be considered as the sum of complex amplitudes of the combined chip as the laser source coherence time is much greater than the integration time of the photodetector. To reduce the sensitivity of the DS-OCDMA system to the coherence time of the laser source, we analyze the use of sparse and nonperiodic quadratic congruence and extended quadratic congruence codes.

Biased π-Shifted Low-Coherence Interferometry for Measuring Polarization Mode Dispersion (PMD)

Conventional low-coherence interferometry (LCI) has been employed in the measurement of polarization mode dispersion (PMD) of fiber-optic components and fibers. However, the smallest PMD, which can be measured using this technique, is limited by the coherence length of the source. We propose and study a biased π-shifted Michelson interferometer where a birefringent crystal (biasing crystal) is inserted in front of the interferometer to introduce a bias differential group delay larger than the coherence time of the source. In this way, the limitation imposed by the source coherence time is overcome and PMDs much smaller than the source coherence time, in the order of several femtoseconds, can be measured. A theoretical model of the biased π-shifted LCI is developed based on Jones calculus. Experimental observations have been demonstrated to agree well with the theoretical model. Measurements for the PMD have been shown and compared with those obtained through the Jones matrix eigenanalysis.

Measurement of femtosecond Polarization Mode Dispersion (PMD) using biased p-shifted low-coherence interferometry

Conventional low-coherence interferometry (LCI) can be employed in the measurement of polarization mode dispersion (PMD) of fiber-optic components and fibers. However, the smallest PMD, which can be measured using this technique, is limited by the coherence length of the source. We propose a biased p-shifted Michelson interferometer where a birefringent crystal is inserted in front of the interferometer to introduce a bias differential group delay (DGD) larger than the coherence time of the source. In this way, the limitation imposed by the source coherence time has been overcome and PMDs much smaller than the source coherence time, in the order of several femtoseconds, can be measured. Experimental results for the PMD have been shown and compared with Jones matrix eigen-analysis. The theoretical model confirms the experimental observations.

Optical noise coherence effects in a Mach-Zehnder system

In this paper we present an exact, quantitative theoretical study of coherence effects in the optical noise spectrum of a Mach-Zehnder system coupled to a random-phase source. A simple, analytic formula for the output noise spectrum is derived. This formula is exact and valid for arbitrary source coherence time. We demonstrate two new facts concerning coherence effects: (1) These effects give rise to quasiperiodic features in the noise spectrum with period 1//spl tau/, where /spl tau/ is the time-of-flight difference between the two interferometer arms. (2) When the source coherence time is of the order of magnitude of /spl tau/ or larger, the noise spectrum is sensitive to changes in /spl tau/ on the scale of the optical period. It is suggested that this phenomenon can be used for optical RF interferometry. The characteristics of the noise spectrum are studied analytically, and illustrated by several numerical calculations. The results can be used to estimate the optical noise in any interferometric system in which the main contribution to the output field comes from two optical paths.

Novel and significant results on the non-recirculating delay line with a fiber loop

We show theoretically and experimentally that the behavior of the non-recirculating delay line with a fiber loop (NDLL) cannot be explained by assuming intensity summation over the whole structure even though the fiber delays are much bigger than the source coherence time (incoherent operation regime). These results have important implications in the analysis and design of incoherent fiber-optic filters incorporating loops.

Effect of laser phase noise in Sagnac interferometers

A theoretical analysis of the responsivity and the noise caused by backscattering in a Sagnac interferometer used as a sensor for reciprocal measurands, such as acoustic waves, is presented. Both Rayleigh backscattering and reflections from splices are taken into account. The noise power is found to increase proportionally to the source coherence time, and a noise equivalent phase shift in the range of 0.1*10/sup -6/ rad r.m.s./Hz/sup 1/2/ is predicted for typical fibers and diode lasers. Experimentally, a noise equivalent phase shift of 2.5*10/sup -7/ rad r.m.s./Hz/sup 1/2/ at 10 kHz was observed, with a detector current of 3 mu A. >

Optical fibre ring resonators: analysis off transient response

The paper investigates the temporal response of a passive fibre optic ring resonator illuminated by an amplitude stabilised single mode pulsed laser light source of frequency ω0. The output pulse shape is found to depend on the input pulse shape, the ratio of the source coherence time τc to the resonator delay time τ, and also the ring resonator phase delay ω0τ. Under certain conditions, periodic oscillations in output intensity occur, and the paper provides a simple physical explanation of these in terms of the resonator phase delay.

Creation and dynamics of molecular states prepared with coherent vs partially coherent pulsed light

The mixed state of an isolated molecule, which results from one-photon absorption using a pulsed laser of arbitrary coherence, is obtained using a simple model for a partially coherent laser source. The relative effect of the pulse time τ, source coherence time τcoh, and field correlation time τc on the prepared state and on its subsequent molecular dynamics are described. Numerical computations on several properties are provided and support obtained for the analytical result showing that under certain circumstances the falloff of the survival probability of the created molecular state depends primarily on the pulse time τ.