Gaussian Schell-model Pulsed Research Articles

Propagation Properties of Generalized Schell-Model Pulse Sources in Dispersive Media

A model of a generalized pulse source, whose complex degree of temporal coherence is described by a function of the nth power difference of two instants, was constructed. As examples, we consider the generalized Gaussian and multi-Gaussian Schell-model pulse sources and study their propagation in dispersive media. It is indicated that such pulse beams present unique self-focusing, off-axis self-shifting and asymmetric self-splitting characteristics by adjusting the power exponent and phase parameters. Further, we explicitly discuss how the coherence time, summation factor as well as the dispersive coefficient significantly affect the self-focusing and self-shifting behaviors of the pulse beam. The results will benefit some applications involving pulse shaping, optical trapping and remote sensing.

Theoretical analysis of Hanbury Brown and Twiss interferometry at soft-x-ray free-electron lasers

In this work we provide theoretical background for the analysis of second-order correlation functions in experiments performed at the soft x-ray free-electron lasers (XFELs). Typically, soft x-ray beamlines at XFELs are equipped by the variable line spacing (VLS) monochromators. We perform examination of the beam propagation through such VLS monochromator taking specially into account the interplay between the finite monochromator resolution and the exit slits width. We then provide general analysis of the second-order correlation intensities in spectral and spatial domains. Finally, we connect these functions with the statistical properties of the beam incoming to the monochromator unit in the limit of Gaussian Schell-model pulses.

Intensity Evolution of Cosine-Gaussian-Correlated Schell-Model Pulse Scattered by a Medium

According to first-order Born approximation, the scattering of a partially coherent pulse with cosine-Gaussian correlation by a medium was studied. On the basis of analytic expression, the changes in intensity evolution of the scattered pulse are discussed. The influences of pulse and medium characteristics on the intensity of the scattered pulse were investigated. The intensities of a Gaussian Schell-model (GSM) pulse and a cosine-Gaussian-correlated Schell-model (CGSM) pulse, both scattered by the same medium, are compared, and their similarities and differences are examined in detail. The effective angular width of the scattered pulse could be modulated by the parameters of the pulse and medium. The obtained results could find potential applications in pulsed beam scattering.

Anisotropic turbulence-induced statistical properties evolution of a radially polarized partially coherent pulsed beam on propagation

In this study, we introduce a new kind of partially coherent vector beam with Gaussian distribution in the spatial, temporal and correlation components named a radially polarized partially coherent Gaussian Schell-model pulsed (GSMP) beam as a natural extension of scalar Gaussian Schell-model pulsed beam. Analytical formulas for the two-frequency cross-spectral density matrix elements of this beam are derived based on the extended Huygens–Fresnel theory. Within the frame of extend anisotropic non-Kolmogorov spectrum, the effects of asymmetry anisotropic turbulence eddies on the statistical properties of a radially polarized partially coherent GSMP beam are investigated numerically. Our work improves the classical theory of stochastic electromagnetic beams on propagation and may be useful for applications involving free-space optical communications.

Temporal coherence and polarization modulation of pulse trains by resonance gratings.

We analyze the effects of subwavelength-period resonance gratings on temporally partially coherent optical plane-wave pulse trains. The interaction of the grating with pulses is simulated with the Fourier modal method and finite-difference time-domain method whose performances are compared. Both TE and TM linearly polarized Gaussian Schell-model pulse trains are examined, and partial temporal coherence is modeled with the identical elementary-pulse method. The polarization-dependent response of the grating is seen to lead to significant variations in the average intensity, polarization properties, and degree of temporal coherence of the reflected (and transmitted) pulse trains when the coherence time and polarization state of the incident field are altered. As an important example, we demonstrate that a fully polarized incident pulse train can become partially polarized in grating reflection. The results find use in tailoring of random electromagnetic pulse trains.

Spatial shaping of spectrally partially coherent pulsed beams.

A general formulation is presented for spatial shaping of single-spatial-mode broadband pulsed beams with partial spectral and temporal coherence properties. The model is based on the second-order coherence theory of non-stationary fields, and examples are presented on Gaussian to flat-top transformations. Spatiotemporal intensity distributions are evaluated in the target plane of the shaping element for idealized Gaussian Schell-model pulse trains and for realistic supercontinuum pulses.

Partially coherent Gaussian—Schell model pulse beam propagation in slant atmospheric turbulence

Based on the extended Huygens—Fresnel principle, a two-frequency, two-point cross-spectral density function of partially coherent Gaussian—Schell model pulse (GSMP) beam propagation in slant atmospheric turbulence is derived. Using the Markov approximation method and on the assumption that (ω1 − ω2)/(ω1 + ω2) ≤ 1, the theory obtained is valid for turbulence of any strength and can be applied to narrow-band signals. The expressions for average beam intensity, the beam size, and the two-frequency complex degree of coherence of a GSMP beam are obtained. The numerical results are presented, and the effects of the frequency, initial pulse width, initial beam radius, zenith angle, and outer scales on the complex degree of coherence are discussed. This study provides a better understanding of the second-order statistics of a GSMP beam propagating through atmospheric turbulence in the space-frequency domain.

Polarization changes in temporal imaging with pulses of random light

We consider polarization changes of randomly fluctuating electromagnetic pulsed light in temporal imaging. The polarization properties of pulses formed by the time lens are formulated in terms of the Stokes parameters. For Gaussian Schell-model pulses we show that the degree and state of polarization of the time-imaged pulse can be tailored in versatile ways, depending on the temporal polarization and coherence of the input pulse and the system parameters. In particular, weakly polarized central region of the pulse may become fully polarized without energy absorption. The results have potential applications in optical communication, micromachining, and light-matter interactions.

Ultrashort pulse coherence properties in coherent linear amplifiers

We examine coherence properties of small-area, intrinsically stationary statistical pulses propagating in amplifying media in the vicinity of an optical resonance. Any such medium acts as a coherent linear amplifier, amplifying and reshaping the pulse. We show that an initially nearly incoherent Gaussian Schell-model pulse becomes almost fully coherent and its state of coherence becomes nearly uniform across the temporal profile as the pulse propagates into the amplifying medium.

Degree of phase-space separability of statistical pulses

We introduce the concept of phase-space separability degree of statistical pulses and show how it can be determined using a bi-orthogonal decomposition of the pulse Wigner distribution. We present explicit analytical results for the case of chirped gaussian Schell-model pulses. We also demonstrate that chirping of the pulsed source serves as a powerful tool to control coherence and phase-space separability of statistical pulses.

Complex Gaussian representation of statistical pulses

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.

Second-order statistics of Gaussian Schell-model pulsed beams propagating through atmospheric turbulence

Novel analytical expressions for the cross-spectral density function of a Gaussian Schell-model pulsed (GSMP) beam propagating through atmospheric turbulence are derived. Based on the cross-spectral density function, the average spectral density and the spectral degree of coherence of a GSMP beam in atmospheric turbulence are in turn examined. The dependence of the spectral degree of coherence on the turbulence strength measured by the atmospheric spatial coherence length is calculated numerically and analyzed in depth. The results obtained are useful for applications involving spatially and spectrally partially coherent pulsed beams propagating through atmospheric turbulence.

Influence of Turbulent Atmosphere on Polarization Properties of Stochastic Electromagnetic Pulsed Beams

Using the coherence theory of non-stationary fields and the characterization of stochastic electromagnetic pulsed beams, the analytical expression for the spectral degree of polarization of stochastic electromagnetic Gaussian Schell-model pulsed (GSMP) beams in turbulent atmosphere is derived and is used to study the polarization properties of stochastic electromagnetic GSMP beams propagating through turbulent atmosphere. The results of numerical calculation are given to illustrate the dependence of spectral degree of polarization on the pulse frequency, refraction index structure constant and spatial correlation length. It is shown that, compared with free-space case, in turbulent atmosphere propagation there are two positions at which the on-axis spectral degree of polarization P is equal to zero. The position change depends on the pulse frequency, refraction index structure constant and spatial correlation length.

Spectral Properties of Spatially and Spectrally Partially Coherent Pulsed Beams in Fused-Silica Glass Medium

Using the coherence theory of non-stationary fields and the method of Fourier transform, the spectral properties of spatially and spectrally partially coherent Gaussian Schell-model pulsed (GSMP) beams in fused-silica glass medium are studied and analyzed numerically. It is shown that the spectral shift takes place, which depends on the position of the field point, spatial correlation length, temporal coherence length and dispersive property of medium, as GSMP beams propagate in fused-silica glass medium. The on-axis spectrum is blue-shifted, and the relative spectral shift increases with increasing propagation distance, and decreases as the spatial correlation length and temporal coherence length increases, and then approaches an asymptotic value. The dispersive property of medium plays an important role in the spectral properties of spatially and spectrally partially coherent beams.

Influence of Polarization on the Spectral Changes of Stochastic Electromagnetic Pulsed Beams

An analytical expression for the spectrum of stochastic spatially and temporally partially coherent electromagnetic Gaussian Schell-model pulsed (GSMP) beams is derived, and used to study the spectral changes of electromagnetic GSMP beams in free space. The influence of polarization on the on-axis relative spectral shift is emphasized. It is shown that the on-axis relative spectral shift increases with increasing the degree of polarization of source P0 for the case of δxx≠δyy, i.e. the spatial coherence length δxx of x component of the electric field at the source is not equal to that of y component. For δxx=δyy or δxx→∞ and δyy→∞, the on-axis relative spectral shift is independent of P0.

Generalized Stokes parameters of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams

The analytical expressions for the generalized (two-point) Stokes parameters of stochastic electromagnetic Gaussian Schell-model pulsed (GSMP) beams propagating in free space are obtained. The changes in the spectral Stokes parameters in free space propagation are studied. The dependence of on-axis and transverse spectral Stokes parameters of stochastic electromagnetic GSMP beams on the pulse parameters including pulse duration and temporal coherence length is stressed and illustrated numerically. The results are interpreted physically.

Distinguishing between deterministic and stochastic pulse broadening

Two mechanisms can cause similar broadening of pulses in a pulse train: variable temporal/spectral phase in a train of identical pulses (a deterministic mechanism) and partial correlations between different frequency components of the pulses (a stochastic mechanism). We discuss methods to distinguish between these two fundamentally different mechanisms. We show that their roles can be separated, at least for an important class of fields known as Gaussian Schell-model pulses, using time-resolved intensity measurements of pulses passing through Michelson's interferometer.

Effect of turbulence on the spectral switches of diffracted spatially and spectrally partially coherent pulsed beams in atmospheric turbulence

Taking the spectrally partially coherent Gaussian Schell-model pulsed (GSMP) beam as a typical example of spatially and spectrally partially coherent pulsed beams, an analytical expression for the spectrum of diffracted spectrally partially coherent GSMP beams propagating through atmospheric turbulence is derived by using the method of the complex Gaussian function expansion, and used to study the spectral switches of spectrally partially coherent GSMP beams in atmospheric turbulence. Numerical calculation results are given to illustrate the dependence of spectral switches on the refraction index structure constant and temporal coherent length. The results are interpreted physically.

Characterization of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams

The unified theory of coherence and polarization proposed by Wolf is extended from stochastic stationary electromagnetic beams to stochastic spatially and spectrally partially coherent electromagnetic pulsed beams. Taking the stochastic electromagnetic Gaussian Schell-model pulsed (GSMP) beam as a typical example of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams, the expressions for the spectral density, spectral degree of polarization and spectral degree of coherence of stochastic electromagnetic GSMP beams propagating in free space are derived. Some special cases are analyzed. The illustrative examples are given and the results are interpreted physically.

Spectral shifts and spectral switches of spatially and spectrally partially coherent pulsed beams in Young’s interference experiment

Taking the Gaussian Schell-model pulsed (GSMP) beam as a typical example of spatially and spectrally partially coherent pulsed beams, an analytical expression for the far-field spectrum of diffracted GSMP beams in Young’s interference experiment is derived, and used to study the spectral shifts and spectral switches of GSMP beams in the far field. Numerical calculation results are given to illustrate the dependence of spectral shifts and spectral switches on the obscuration ratio ε, temporal coherent length T c, spatial correlation parameter β and diffraction angle α. It is shown that the critical angle α c of the first- and second-order spectral switches moves away from the z axis with increasing T c, but α c of the third-order spectral switch moves towards the z axis with increasing T c. The spectral transition height Δ decreases and spectral minimum S min increases as T c increases. α c decreases, Δ increases and S min decreases as β increases. The potential application of spectral switches of spatially and spectrally partially coherent pulsed beams in information encoding and transmission is proposed.