Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Optics

Partial spectral and temporal coherence of plane-wave pulse trains in second-harmonic generation

Henri Pesonen, Juha-Matti Huusko, Xiaorun Zang, Ari T. Friberg, Jari P. Turunen, Tero Setälä

Published Dec 7, 2021• 1 citation
Publisher

Abstract

Abstract We study the spectral and temporal coherence effects in the passage of a Gaussian Schell-model (GSM) scalar, plane-wave pulse train through a slab of nonlinear optical crystal exhibiting second-harmonic generation. We show that due to the nonlinear interaction the temporal and spectral degrees of coherence of the fundamental (F) and second-harmonic (SH) pulse trains at the exit facet may deviate markedly from the GSM and the global degree of coherence of the SH wave generally decreases with increasing incident F beam intensity. In addition, we find that due to the partial coherence of the incident GSM field the transmitted SH wave may show a double-peaked intensity distribution.

DOI
10.1088/2040-8986/ac3f94

Related papers

Second-harmonic generation of temporally low-coherence light

Xiaohui Zhao, Lailin Ji, Dong Liu +9 more

In this Letter, we study the second-harmonic (SH) generation of temporally low-coherence light using the statistical optics method. By introducing the statistical characteristics of low-coherence light into the nonlinear coupled wave equation, we predict the self-convolution relationship between the power spectral density of the second-harmonic and that of the fundamental wave and demonstrate it in experiments. The effects of phase matching and group velocity matching on the second-harmonic bandwidth and conversion efficiency are analyzed, which is beneficial to improve the efficiency of low-coherent SH light. Combining the statistics optics and nonlinear optics, our research provides a suitable mathematical model for the study of nonlinear frequency conversion processes of temporally low-coherence light. Due to its statistical characteristics and temporal incoherence, low-coherence SH light would have further applications in uniform illumination, quantum optics, metrology, and so on.

APL Photonics•Sep 1, 2020•22 citations

Effect of partial coherence on diffraction intensity of a Gaussian Schell-model beam using two-level atomic grating

Sobia Asghar, Ziauddin Ziauddin, Shahid Qamar +1 more

The role of spatial coherence on diffraction intensity is investigated for a partially coherent incident Gaussian Schell-model beam which is diffracted from a two-level atomic grating. It is shown that the performance of the atomic grating is greatly influenced by the spectral coherence width of the partially coherent fields. It is observed that relatively large intensity of the diffracted light can be obtained via spatial coherence, beam width, interaction length, and mode index of partially coherent incident light. The scheme provides possibilities for the potential applications of atomic grating in lensless imaging using the partially coherent light field.

Journal of the Optical Society of America B•Dec 13, 2016•12 citations

Interaction of high-power laser pulses with atomic media. II. Optical second-harmonic generation

Kenzo Miyazaki, Takuzo Sato, Hiroshi Kashiwagi

It is theoretically and experimentally demonstrated that optical second-harmonic generation (SHG) is possible to be observed in atomic media irradiated with an intense laser pulse. The SHG is induced by a static electric field spontaneously generated in the interaction, and any special condition is not required for the SHG. The experiment to observe the SHG has been made using atomic sodium vapor and a mode-locked Nd-doped yttrium aluminum garnet laser system (pulse duration, 28 psec; output energy \ensuremath{\lesssim}50 mJ). The second harmonic (SH) polarization, spatial beam pattern, and dependences of SH signal on the sodium density and on the fundamental intensity have been examined. The experimental results agree well with the theoretical predictions and numerical results.

Physical Review A•Mar 1, 1981•43 citations

Unveiling Structured Optical Coherence in Nonlinear Optics

Zihao Pang, Ady Arie

Nonlinear optical interactions are typically driven by coherent sources. Recently, however, incoherent sources have also been shown to offer new opportunities in nonlinear optics. Here we study the effects of the source incoherence in second harmonic generation. We derive and experimentally validate an analytic expression for the far-field coherence function at the second harmonic frequency, which is a generalization of the well-known van Cittert-Zernike theorem. Unlike the linear optics case, here the results depend not only on the source spatial distribution, but also on the nonlinear structure of the crystal. We further show, by performing Young's double-slit measurement, that the coherence at the second harmonic increases as the light propagates inside the nonlinear crystal. Our results establish nonlinearity as a degree of freedom for optical coherence, opening a new research area at the interface of statistical optics and nonlinear optics.

arXiv:2607.13296•Jul 14, 2026•0 citations

Two-time coherence of pulse trains and the integrated degree of temporal coherence

Rahul Dutta, Ari T. Friberg, Goëry Genty +1 more

We examine the temporal coherence properties of trains of nonidentical short optical pulses in the framework of the second-order coherence theory of nonstationary light. Considering Michelson's interferometric measurement of temporal coherence, we demonstrate that time-resolved interferograms reveal the full two-time temporal coherence function of the partially coherent pulse train. We also show that the result given by the time-integrated Michelson interferogram equals the true degree of temporal coherence only when the pulse train is quasi-stationary, i.e., the coherence time is a small fraction of the pulse duration. True two-time and integrated coherence functions produced by specific models representing perturbed trains of mode-locked pulses and supercontinuum pulse trains produced in nonlinear fibers are illustrated.

Journal of the Optical Society of America A•Aug 7, 2015•12 citations

Waves in spatio-spectral and -temporal coherence of evolving ultra-intense twin beams

Jan Peřina

Waves in the spatio-spectral and -temporal coherence of evolving ultra-intense twin beams are predicted: Twin beams with low intensities attain maximal coherence in the beam center until certain threshold intensity is reached. Then the area of maximal coherence moves with increasing intensity from the beam center towards its edges leaving the beam center with low coherence (the first coherence wave). For even larger intensities, a new coherence maximum is gradually built in the beam center with the increasing intensity and, later, it again moves towards the beam edges forming the second coherence wave. Rotationally-symmetric twin beams are analyzed within a three-dimensional model that couples spectral and spatial degrees of freedom. Relation between the twin-beam coherence and its local density of modes during the nonlinear evolution is discussed.

Scientific Reports•Mar 12, 2019•6 citations
Abstract We study the spectral and temporal coherence effects in the passage of a Gaussian Schell-model (GSM) scalar, plane-wave pulse train through a slab of nonlinear optical crystal exhibiting second-harmonic generation. We show that due to the nonlinear interaction the temporal and spectral degrees of coherence of the fundamental (F) and second-harmonic (SH) pulse trains at the exit facet may deviate markedly from the GSM and the global degree of coherence of the SH wave generally decreases with increasing incident F beam intensity. In addition, we find that due to the partial coherence of the incident GSM field the transmitted SH wave may show a double-peaked intensity distribution.
In this Letter, we study the second-harmonic (SH) generation of temporally low-coherence light using the statistical optics method. By introducing the statistical characteristics of low-coherence light into the nonlinear coupled wave equation, we predict the self-convolution relationship between the power spectral density of the second-harmonic and that of the fundamental wave and demonstrate it in experiments. The effects of phase matching and group velocity matching on the second-harmonic bandwidth and conversion efficiency are analyzed, which is beneficial to improve the efficiency of low-coherent SH light. Combining the statistics optics and nonlinear optics, our research provides a suitable mathematical model for the study of nonlinear frequency conversion processes of temporally low-coherence light. Due to its statistical characteristics and temporal incoherence, low-coherence SH light would have further applications in uniform illumination, quantum optics, metrology, and so on.
The role of spatial coherence on diffraction intensity is investigated for a partially coherent incident Gaussian Schell-model beam which is diffracted from a two-level atomic grating. It is shown that the performance of the atomic grating is greatly influenced by the spectral coherence width of the partially coherent fields. It is observed that relatively large intensity of the diffracted light can be obtained via spatial coherence, beam width, interaction length, and mode index of partially coherent incident light. The scheme provides possibilities for the potential applications of atomic grating in lensless imaging using the partially coherent light field.
It is theoretically and experimentally demonstrated that optical second-harmonic generation (SHG) is possible to be observed in atomic media irradiated with an intense laser pulse. The SHG is induced by a static electric field spontaneously generated in the interaction, and any special condition is not required for the SHG. The experiment to observe the SHG has been made using atomic sodium vapor and a mode-locked Nd-doped yttrium aluminum garnet laser system (pulse duration, 28 psec; output energy \ensuremath{\lesssim}50 mJ). The second harmonic (SH) polarization, spatial beam pattern, and dependences of SH signal on the sodium density and on the fundamental intensity have been examined. The experimental results agree well with the theoretical predictions and numerical results.
Nonlinear optical interactions are typically driven by coherent sources. Recently, however, incoherent sources have also been shown to offer new opportunities in nonlinear optics. Here we study the effects of the source incoherence in second harmonic generation. We derive and experimentally validate an analytic expression for the far-field coherence function at the second harmonic frequency, which is a generalization of the well-known van Cittert-Zernike theorem. Unlike the linear optics case, here the results depend not only on the source spatial distribution, but also on the nonlinear structure of the crystal. We further show, by performing Young's double-slit measurement, that the coherence at the second harmonic increases as the light propagates inside the nonlinear crystal. Our results establish nonlinearity as a degree of freedom for optical coherence, opening a new research area at the interface of statistical optics and nonlinear optics.
We examine the temporal coherence properties of trains of nonidentical short optical pulses in the framework of the second-order coherence theory of nonstationary light. Considering Michelson's interferometric measurement of temporal coherence, we demonstrate that time-resolved interferograms reveal the full two-time temporal coherence function of the partially coherent pulse train. We also show that the result given by the time-integrated Michelson interferogram equals the true degree of temporal coherence only when the pulse train is quasi-stationary, i.e., the coherence time is a small fraction of the pulse duration. True two-time and integrated coherence functions produced by specific models representing perturbed trains of mode-locked pulses and supercontinuum pulse trains produced in nonlinear fibers are illustrated.
Waves in the spatio-spectral and -temporal coherence of evolving ultra-intense twin beams are predicted: Twin beams with low intensities attain maximal coherence in the beam center until certain threshold intensity is reached. Then the area of maximal coherence moves with increasing intensity from the beam center towards its edges leaving the beam center with low coherence (the first coherence wave). For even larger intensities, a new coherence maximum is gradually built in the beam center with the increasing intensity and, later, it again moves towards the beam edges forming the second coherence wave. Rotationally-symmetric twin beams are analyzed within a three-dimensional model that couples spectral and spatial degrees of freedom. Relation between the twin-beam coherence and its local density of modes during the nonlinear evolution is discussed.