Wave optics simulation of partially coherent beams

In military applications that use adaptive optics, an extended beacon instead of a point source beacon is created at the target due to atmospheric turbulence and other factors. These beacons, which have a finite spatial extent and exhibit varying degrees of coherence, are typically modeled in existing literature as a Gaussian Schell Model (GSM) due to its analytical tractability. Earlier, we used a full wave computational technique to evaluate the scattered field from a rough impedance surface in vacuum. The results showed some deviations from GSM behavior. The present work uses a simulation approach based on Physical Optics (PO) approximation to study the scattering behavior in presence of atmospheric turbulence. A fully coherent Gaussian beam is propagated through atmospheric phase screens to the rough surface target plane. The PO current is computed on the rough surface and the scattered field right above the surface is determined. The scattered light is propagated through a second set of atmospheric phase screens and thus the double passage through the atmosphere is realized. The rough surface is simulated using statistical parameters derived from profilometer measurements of standard targets. Through multiple realizations of the atmosphere and the rough surface, the statistics of the scattered field is determined. The simulations are done with different strengths of turbulence and different roughness scales of the target. The results are compared with a GSM. An effects model where the rough surface is modeled as a phase screen has also been implemented in order to verify the nature of the speckle returns.

Analytic expressions for the mutual coherence function (MCF) and the scintillation index of a partially coherent lowest order Gaussian beam wave propagating through the atmosphere (based on Kolmogorov spectrum model) are developed for the pupil plane of a receiving system. Partial coherence of the beam is modeled as a thin (complex) phase screen with Gaussian spectrum (Rytov theory and ABCD ray matrices are applied). The relation between the second- and fourth-order statistics for a beam with any degree of coherence in the atmosphere is introduced with the help of ''effective'' beam parameters, deduced from the free-space MCF. In particular, the scintillation (in weak and strong atmospheric conditions), based on these parameters, is stud- ied as a function of the diffuser's strength and that of the atmosphere. The model is applied for the calculation of the SNR and bit error rates (OOK modulation) of the communication link with diffuser at the trans- mitter and slow detection system. The improvement of bit error rates is observed in weak and strong atmospheric turbulence. In the weak re- gime, the optimal diffuser can be found. © 2004 Society of Photo-Optical Instru-

Free space optical (FSO) wireless communication has emerged as a viable alternative to the existing fiber optics and radio frequency (RF) communications due to its ability to operate in unlicensed spectrum, offering huge data handling capacities and being cost effective with easy deployment. The underlying communication mechanism in the FSO link is based upon the laser beam propagation model. The propagating free space optical beam undergoes signal degradation due to refraction and diffraction caused by atmospheric turbulence measured by refractive index structure parameter (C n 2). In this work, a novel, robust analytical model for propagating Gaussian-beam through atmospheric turbulence is presented, by solving the space-fractional paraxial wave equation. We report analytical expressions for the intensity and long-term beam spreading of a Gaussian beam in terms of space-fractional parameter D, for the range 2 < D ≤ 3. This range of parameter D, defines the effective number of euclidean space corresponding to atmospheric turbulence levels faced by the propagating Gaussian beam in the FSO link. The results of the proposed fractional model and the existing models agreed well, therefore the D-dimensional parameter can be used to effectively express the value of refractive index structure parameter (C n 2). The classical values of C n 2 ranges form 10−13 to 10−16 for strong to weak fluctuations respectively. However, in fractional-dimension scale, these fluctuations can be express as D = 2.668 (strong fluctuations) to D = 2.999 (weak fluctuations). The ideal case of free space beam propagation can be expressed as D = 3, with no turbulence. Moreover, we have studied the fractional-dimension model performance for varying wavelengths. Further, based upon a practical example, we proposed a self-sustainable FSO link architecture to efficiently minimize the effect of weak and strong fluctuations on the propagating optical beam, based upon the D-dimension fractional parameter, hence ensuring reliability of FSO link.

Free Space Optical (FSO) communication is a low cost and license free high bandwidth access technique, is a primary research area from last few years. Atmospheric turbulence plays a vital role in degrading the link performance. This paper presents the model study on the effects of atmospheric turbulence in FSO links. The study is based on the most popular gamma-gamma model distribution. The theoretical model is simulated by varying the height of link and the results are plotted in Mathworks® MATLAB®. The research demonstrates that the effects of turbulence depend primarily on wind speed and height of established FSO link. After varying the height of link, the effects of atmospheric turbulence on link performance can be clearly seen. The result also plotted for the attenuation of signal with varying visibility range conditions.

A multi-phase screen transmission model is usually applied to the simulation of an optical propagation process in atmospheric turbulence. The phase of an optical wave will be modulated by the phase screens, which function as atmospheric turbulence. This paper first analyzes the relationship between fractal Brownian motion and atmospheric turbulence as well as the relationship between a fractal Brownian surface and random phase screen. Then a phase screen generation algorithm based on fractal theory is proposed, which combines the random midpoint displacement principle with the successive random additions technique. Simulation results such as the phase structure function, power spectrum, and scintillation index conform more closely to the theoretical values compared with the traditional spectral inversion algorithm and Zernike polynomial method. Furthermore, it has better performance in both low- and high-frequency parts without increasing the algorithm complexity.

The channel characteristics of modulating retro-reflector (MRR) free-space optical (FSO) link are studied by using wave-optics (WO) simulation method. The optical wave launched from the transceiver is reflected back in the same direction to the transceiver by the use of cube-corner reflector (CCR). This propagation process is divided into three parts: forward propagation through atmospheric turbulence, reflection of CCR, and backward propagation through the turbulence. For WO simulation under turbulence conditions, the split-step beam propagation method is implemented, and the influence of atmospheric turbulence along the propagation path is described by a set of random thin phase screens. The reflection effect of CCR is taken into account by using ray-tracing approach to calculate the intensity and phase of the optical field output from CCR. Integrating the reflection effect into WO simulations, we study the statistics of the intensity fluctuations in the forward, backward and double-pass links, and the correlation of fluctuations in the forward and backward links. The histograms of the normalized intensity for three links could be approximated by Gamma-Gamma (GG) distributions except for relatively large receiver apertures. There exists a relatively large correlation between the forward and backward links.

A general analysis is presented for the scintillation index of a Gaussian beam wave propagating through a turbulent medium confined to a portion of the propagation path between input and output planes, the limiting case of which defines a thin random phase screen. For a plane wave incident on a phase screen located midway between input and output planes, the phase screen scintillation index agrees with that of a plane wave propagating through extended turbulence when the phase variance and spectrum for refractive index of the screen and extended medium are the same. However, for a finite Gaussian beam at the input plane, our analysis reveals that the distance from input plane to the phase screen must be many times greater than the distance from the screen to output plane to simulate a plane wave propagating through an extended medium.

Stimulated parametric down-conversion is a nonlinear optical process that can be used for phase conjugation and frequency conversion of an optical field. A precise description of the outgoing stimulated field has been developed for the case where the input pump and seed fields are coherent. However, partially coherent beams can have interesting and important characteristics that are absent in coherent beams. One example is the twist phase, a novel optical phase that can appear in partially coherent Gaussian beams and gives rise to a nonzero orbital angular momentum. Here, we consider stimulated down-conversion for partially coherent input fields. As a case study, we use twisted Gaussian Schell-Model beams as the seed and pump beams in stimulated parametric down-conversion. It is shown both theoretically and experimentally that the stimulated idler beam can be written as a twisted Gaussian Schell-Model beam, where the beam parameters are determined entirely by the seed and pump. When the pump beam is coherent, the twist phase of the idler is the conjugate of that of the seed. These results could be useful for the correction of wavefront distortion such as in atmospheric turbulence in optical communication channels, and synthesis of partially coherent beams.

Numerical modeling of optical wave propagation in atmospheric turbulence is traditionally performed with using the so-called “split”-operator method, when the influence of the propagation medium’s refractive index inhomogeneities is accounted for only within a system of infinitely narrow layers (phase screens) where phase is distorted. Commonly, under certain assumptions, such phase screens are considered as mutually statistically uncorrelated. However, in several important applications including laser target tracking, remote sensing, and atmospheric imaging, accurate optical field propagation modeling assumes upper limitations on interscreen spacing. The latter situation can be observed, for instance, in the presence of large-scale turbulent inhomogeneities or in deep turbulence conditions, where interscreen distances become comparable with turbulence outer scale and, hence, corresponding phase screens cannot be statistically uncorrelated. In this paper, we discuss correlated phase screens. The statistical characteristics of screens are calculated based on a representation of turbulent fluctuations of three-dimensional (3D) refractive index random field as a set of sequentially correlated 3D layers displaced in the wave propagation direction. The statistical characteristics of refractive index fluctuations are described in terms of the von Karman power spectrum density. In the representation of these 3D layers by corresponding phase screens, the geometrical optics approximation is used.

This paper presents some examples of behavioral model hierarchies for optronic and photonic devices. The methods use d to over come the limitations of VHDL-AMS in modeling propagation phenomena are described. This work is part of an ongoing development of mixed-domain simulation tools for the design of optical links in a standard EDA framework.

Atmospheric turbulence, characterized by irregular motions across various scales, poses significant challenges for accurate description using conventional methods due to its inherent complexity. This paper evaluates the reliability of detecting atmospheric turbulence using Mie-scattering lidar. We simulate non-Kolmogorov turbulence phase screens through both fractal and power spectrum methods, considering different internal and external scales. The impact of varying parameters on simulation accuracy is analyzed. By comparing the obtained phase structure function curves with theoretical curves and conducting error analysis for different methods, we verify the simulation speed and accuracy of the fractal method. A Mie-scattering lidar system is designed for detecting atmospheric turbulence, and the Gaussian laser beam is numerically simulated using the fractal method. Results indicate that the phase screen generated by this method possesses adequate high- and low-frequency components, offering faster simulation speeds and higher precision. The simulated scintillation index aligns with theoretical trends. Moreover, by employing Mie-scattering lidar for the actual detection of non-Kolmogorov turbulence profiles, the feasibility of these simulations has been validated, providing new insights into the multiscale structure and spatial distribution of atmospheric turbulence. Significance Statement Atmospheric turbulence presents significant challenges for various research areas, including space optical communication, laser propagation, and lidar technology. This paper investigates the reliability of detecting atmospheric turbulence using Mie-scattering lidar, employing non-Kolmogorov turbulent phase screens simulated through the fractal method. By analyzing the structure of turbulence and the motion of microscopic particles, this study offers a more robust theoretical foundation for atmospheric turbulence detection, ultimately contributing to more accurate predictions of weather and climate changes.

Free-space optical (FSO) links offer an attractive alternative to the radio frequency channel for the purpose of transmitting data at very high rates. A major impairment in FSO links is the turbulence-induced scintillations of an optical wave. Spatial diversity, which involves the deployment of multiple laser transmitters/receivers, can be used over FSO links to reduce the turbulence-induced scintillations. In this paper, the channel of a multiple-transmitter-multiple-receiver FSO link considering the spatial correlation between the constituent sub-channels was mathematically modeled and then the joint distribution function of the channel gain coefficients was derived. Base on the joint distribution function, the model for the outage probability of a FSO link with spatial diversity was established. With Monte Carlo method, simulations for the outage probability were performed. The results show that spatial correlations have a significant influence on the outage probability, and the diversity-induced performance improvement reduces to zero as the spatial correlation coefficient increases to 1.

The propagation performance of high-power partially coherent fibre laser beams in a real environment is investigated and the theoretical model of a high-power fibre laser propagating in a real environment is established. The influence of a collimating system and thermal blooming is considered together with atmospheric turbulence and mechanical jitter. The laser energy concentration of partially coherent beams in the far field is calculated and analysed based on the theoretical model. It is shown that the propagation performance of partially coherent beams depends on the collimating system, atmospheric turbulence, mechanical jitter and thermal blooming. The propagation performance of partially coherent beams and fully coherent beams is studied and the results show that partially coherent beams are less sensitive to the influence of thermal blooming, which results in that the energy degeneration for partially coherent beams is only 50% of that for fully coherent beams. Both partially coherent beams and fully coherent beams become less sensitive to thermal blooming when the average structural constant of the refraction index fluctuations increases to 1.7 × 10−14m−2/3. The investigation presents a reference for applications of a high-power fibre laser system.

In this paper, the characteristics of Gaussian beam propagation through turbulent plasma sheath are studied. According to the generalized Huygens-Fresnel principle, the random phase screen is generated by power spectrum inversion method based on the fast Fourier transform. The random phase screen is used to simulate turbulence effect. The thickness of the plasma sheath is of about centimeter order of magnitude. Compared with the single fast Fourier transform algorithm, the double fast Fourier transform algorithm is not prone to under-sampling and can obtain good image results, even if the diffraction distance is 1 mm. Therefore, double fast Fourier transform algorithm is used for investigating the beam propagation between two phase screens. The turbulence effect of the plasma sheath surrounding a hypersonic vehicle is simulated by the multi-random phase screens. When the flight altitude is 45 km and the flight speed is 18 Mach, the intensity of refractive index fluctuation variance ranges from &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}${10}^{ - 11} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20182169_M2.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20182169_M2.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; to &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$ {10}^{ - 14} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20182169_M3.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20182169_M3.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; indicated by analyzing the plasma flow field around the hypersonic vehicle. The characteristics of the Gaussian beam propagation through the turbulent plasma are numerically simulated. The results show that the refractive index fluctuation, wavelength and transmission distance are important factors affecting the Gaussian beam quality. The larger the refractive index variance, the more severe the spot dispersion and the more obvious the light intensity fluctuation. As wavelength is longer, the ability of the Gaussian beam to resist turbulence becomes stronger and the dispersion of the light spot and the intensity fluctuation are smaller. The beam distortion and the spot dispersion become more severe as the transmission distance is longer.

By using numerical simulation, the propagation of pseudo-partially coherent Gaussian-Schell model beam in atmospheric turbulence is simulated. The properties of intensity fluctuation of different receiving aperture and aperture averaging factors are statistically analyzed. And the influence of relative changing frequency of the modulating phase which models the partial coherence of beam source on scintillation index is also discussed. The simulation results of pseudo-partially coherent beam are compared with those of the well-developed partially coherent beam and fully coherent Gaussian beam. It is found that the reduction of coherence degree may cause scintillation index to decrease. However, the aperture averaging effect is weakened at the same time. At the same receiving aperture diameter, the aperture averaging factor of pseudo-partially coherent beam is greater than that of the fully coherent beam. The increase of relative changing frequency of modulating phase may cause a reduction of scintillation index to some degree. And with the increase of relative changing frequency, the scintillation index of pseudo-partially coherent beam tends to be coincident with that of the partially coherent beam.