Random Phase Screen Research Articles

Determining the fractional topological charge shifting in perfect vortices from laser speckle

We demonstrate analytically, numerically, and experimentally that the fractional topological charge shifting in perfect vortices having a ring-shaped distribution is precisely determined by the correlation coefficient of speckle distributions obtained by the scattering of these perfect vortices through a random phase screen. The scattering of elliptic perfect optical vortices is also analyzed and discussed.

Analysis of propagation characteristics of Gaussian beams in turbulent plasma sheaths

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 <inline-formula><tex-math id="M2">\begin{document}${10}^{ - 11} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20182169_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20182169_M2.png"/></alternatives></inline-formula> to <inline-formula><tex-math id="M3">\begin{document}$ {10}^{ - 14} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20182169_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20182169_M3.png"/></alternatives></inline-formula> 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.

Pointing and tracking errors due to low-frequency deformation in inter-satellite laser communication

ABSTRACTA Gaussian random-phase screen (GRPS) model is proposed to represent the low-frequency wave-front deformation in inter-satellite laser-communication links. The model is used to investigate mutual-alignment errors comprising pointing and tracking errors caused by the low-frequency deformation. Theoretical analysis and numerical simulation show that the GRPS root-mean-square (RMS) value, pointing error, and tracking error increase with the amplitude factor and the scale length in the model. The expectation of RMS increases in the form of a linear function with and increases in the form of a cubic function with . The expectations of the pointing and tracking errors increase with increases in the expected values for and . For a specific pointing error or tracking error, the 99.5% confidence interval of the RMS of the low-frequency wave-front deformation is provided. From this confidence interval, the lower limit of the processing precision of optical antennas corresponding to certain mutual-alignment errors can be predicted. These conclusions are expected to be instrumental in designing inter-satellite laser-communication systems.

Modeling optical memory effects with phase screens.

During the last decade, optical memory effects have been explored extensively for various applications. In this letter we propose phase screen models to facilitate the analysis and the simulation of wave propagation through optical media that exhibits memory effects. We show that the classical optical memory effect, which implies tilt wave correlations of the input and the scattered fields, can be readily modeled by a single random phase screen. For the recently discovered generalized optical memory effect, which implies the existence of shift wave correlations in addition to the tilt correlation, we propose an appropriate generalized random phase screen model.

Mean irradiance profile of a Gaussian beam under random jitter.

The mean irradiance profile has been widely applied in performance analysis and atmospheric channel research for free space optical communication; however, the modeling method and a closed-form expression of the mean irradiance profile under random jitter have rarely been discussed. To the best of our knowledge, this work presents a modeling method and a closed-form expression for a mean irradiance profile under random jitter through the ensemble average principle for the first time. We find that, with an increase in random jitter variance, the mean irradiance profile varied from an approximately Gaussian profile to a flat-topped profile to a hollow profile. These findings were verified using multilayer random phase screen simulations. The model of the mean irradiance profile under random jitter developed in this study will improve the accuracy of performance analysis and atmospheric channel research.

Designer vector beams maintaining a robust intensity profile on propagation through turbulence

We report experiments on propagation of scalar and vector optical beams through random phase screens mimicking turbulence and show that the intensity profile of the beam containing a C-point polarization singularity shows maximally robust behavior. This observation is explained in terms of the polarization and orbital angular momentum (OAM) diversity in the beam. The $l = 0$ and $l = 1$ OAM states whose vector combination leads to the C-point singularity are seen to produce complementary speckle intensity patterns with significant negative correlation on propagation through a random phase screen. This unique property of C-point singularity makes it superior to other inhomogeneous polarization states as demonstrated in our experiments. The results provide an important generic guideline for designing beams that can maintain optimally robust beam intensity profile on passing through random phase fluctuations and are expected to have a number of applications.

Random phase screen influence of the inhomogeneous tissue layer on the generation of acoustic vortices**Project supported by the National Natural Science Foundation of China (Grant Nos. 61575095, 11374155, and 11674173).

The influence of the inhomogeneous tissue layer on the generation of acoustic vortices (AV) is studied theoretically and experimentally based on the phase screen model. By considering the time-shift of a random phase screen, the formula of acoustic pressure for the AV beam generated by a circular array of eight planar piston sources is derived. With the actual correlation length of the abdominal wall, numerical simulations before and after the insertion of the inhomogeneous tissue layer are conducted, and also demonstrated by experimental measurements. It is proved that, when the thickness variation of the phase screen is less than one wavelength, no significant influence on the generation of AVs can be produced. The variations of vortex nodes and antinodes in terms of the location, shape, and size of AVs are not obvious. Although the circular pressure distribution might be deformed by the phase interference with a larger thickness variation, AVs can still be generated around the center axis with perfect phase spirals in a reduced effective radius. The favorable results provide the feasibility of AV generation inside the human body and suggest the application potential of AVs in object manipulation for biomedical engineering.

The Propagation Properties of a Longitudinal Orbital Angular Momentum Multiplexing System in Atmospheric Turbulence

A novel multichannel free-space optical (FSO) communication system based on orbital angular momentum (OAM) carried by frozen waves with different longitudinal patterns is studied in this paper. The longitudinal OAM multiplexing (LOAMM) system is simulated under atmospheric turbulence, which is based on the split-step Fourier transform method and includes multiple random phase screens. The influences of system parameters on the average OAM mode probability densities are analyzed and discussed, such as propagation distance, strength of turbulence, sizes of finite aperture function, OAM mode numbers, and source parameters. It is found that in the limited apertures, the detection probability spectrum of the LOAMM system is inversely proportional to OAM mode numbers, strength of turbulence, and propagation distance. The bit-error rate and aggregate capacities are compared between the traditional OAM-based space-division-multiplexing (OAM-SDM) system with Bessel beams and our proposed LOAMM system. Our work should contribute to proving that the LOAMM system has a number of advantages over the OAM-SDM system in FSO communication.

Evalution Bandwidth of Optical Signal via Statistical Moments of Random Phase Screen

The majority of the works are dedicated to the specific problem, for instance, scattering from the rough surface although, the general theoretical bases of the statistical and spectral characteristics of the scattered light for the light of non-Gaussian statistics have not been studied so far. The signals with such statistics are produced when the characteristic scales of the refraction factor is in comparison with the size of illuminated region. In the present paper, we discuss the method of signal processing for analyzing first and second order statistical moments of electromagnetic radiation.

Robust laser beam engineering using polarization and angular momentum diversity.

We describe a laser beam engineered to carry l = 0 and l = 1 orbital angular momentum (OAM) states in orthogonal polarizations. It is observed that on collinear transmission through a random phase screen, the far field diffraction intensity patterns for the individual polarization states are complementary with significant negative correlation. As a result the combined intensity profile for the beam remains robust against time varying phase fluctuations. In our simulation and experiment the SNR for the central lobe of the combined far-field diffraction pattern defined as mean divided by the standard deviation of intensity values shows significant improvement over that for individual polarizations. The concept of polarization and OAM diversity as demonstrated here can be considered valuable for robust laser beam engineering without the requirement of any active real-time correction methods.

Modulation transfer function of the imaging probe using an 8.8 mm-long and 125 µm-thick graded- index short multimode fiber

We measured the modulation transfer function (MTF) of a short multimode fiber (SMMF) probe and proposed the optical model including the thin random phase screen (TRPS) to explain degradations of imaging characteristics. SMMF is a graded index multimode fiber for optical communication. That length is 8.8mm and the diameter of core is 50µm. With the wavelength of 780nm, for spatial frequencies from128lp/mm to 228lp/mm MTFs were measured at 0.179–0.062 in reflection images and these contrasts were 19% to contrasts without TRPS. With parameters of σϕ of 1.5rad and W of 2–3.5µm calculated results almost correspond to measured ones. Dependences of contrasts on wavelength were also measured. With the spatial frequency of 200lp/mm, at the wavelength of 0.8µm the contrast decreased to 17% due to TRPS and at that of 0.5µm the contrast decreased to 6%. Measured dependences of contrasts on wavelength with the spatial frequency of 228 lp/mm approximately correspond to calculation results with 200lp/mm. These basic characteristics are useful to design the imaging optics by means of SMMF.

Random sources for cusped beams.

We introduce two novel classes of partially coherent sources whose degrees of coherence are described by the rectangular Lorentz-correlated Schell-model (LSM) and rectangular fractional multi-Gaussian-correlated Schell-model (FMGSM) functions. Based on the generalized Collins formula, analytical expressions are derived for the spectral density distributions of these beams propagating through a stigmatic ABCD optical system. It is shown that beams belonging to both classes form the spectral density apex that is much higher and sharper than that generated by the Gaussian Schell-model (GSM) beam with a comparable coherence state. We experimentally generate these beams by using a nematic, transmissive spatial light modulator (SLM) that serves as a random phase screen controlled by a computer. The experimental data is consistent with theoretical predictions. Moreover, it is illustrated that the FMGSM beam generated in our experiments has a better focusing capacity than the GSM beam with the same coherence state. The applications that can potentially benefit from the use of novel beams range from material surface processing, to communications and sensing through random media.

Scintillation behaviour of vortex beams in strong turbulence region

We study the scintillation behaviour of vectorial vortex beams in strong turbulence region. For this purpose, a list of vortex source beams is prepared. Then their scintillation performances are analysed one by one using the random phase screen approach. The results indicate that there will always be scintillation reductions with increasing values of topological charge, although its effect will diminish as we go towards higher values of the topological charge. The increases in the other specific beam parameters seem to have opposite effect. For the vectorial Hermite Gaussian beam, the use of higher orders will also aid scintillation reductions. It is foreseen that the outcome of this study will be useful for long haul optical communication links.

Imaging characteristics of an 8.8 mm long and 125 μm thick graded-index short multimode fiber probe.

We demonstrated the feasibility of an ultrathin imaging probe with a 50-μm core diameter, a 125 μm total diameter, and an 8.8 mm length, which is a typical graded-index multimode fiber for optical communications. We used an ABCD matrix to analyze the imaging conditions and magnification, which corresponded closely to the measured results. The lateral resolution was calculated at 1.2 μm with a wavelength of 730 nm, which reflects the image test pattern where a period of 4.38 μm was measured with a wavelength of 730 nm. In the numerical aperture of the objective lens, we experimentally evaluated the tradeoff between the magnification and the coupling efficiency. At four wavelengths of 540 nm, 632 nm, 730 nm, and 852 nm, the contrast and signal intensity versus the wavelength were investigated to show that the contrast at 632 and 730 nm is relatively high. By using a thin random phase screen model, we explained that as the wavelength decreases the greater the decrease in the optical transfer function at higher spatial frequencies. Using a 635 nm LED light source, we imaged the surfaces of chicken tendons in contact and the surface roughness was visible.

Propagation properties of cylindrical sinc Gaussian beam

We investigate the propagation properties of cylindrical sinc Gaussian beam in turbulent atmosphere. Since an analytic solution is hardly derivable, the study is carried out with the aid of random phase screens. Evolutions of the beam intensity profile, beam size and kurtosis parameter are analysed. It is found that on the source plane, cylindrical sinc Gaussian beam has a dark hollow appearance, where the side lobes also start to emerge with increase in width parameter and Gaussian source size. During propagation, beams with small width and Gaussian source size exhibit off-axis behaviour, losing the dark hollow shape, accumulating the intensity asymmetrically on one side, whereas those with large width and Gaussian source size retain dark hollow appearance even at long propagation distances. It is seen that the beams with large widths expand more in beam size than the ones with small widths. The structure constant values chosen do not seem to alter this situation. The kurtosis parameters of the beams having small widths are seen to be larger than the ones with the small widths. Again the choice of the structure constant does not change this trend.

Correction of amplitude distortions for truncated Bessel beam and SER estimation for 4ASK

We apply amplitude corrections to a truncated Bessel beam that has propagated through turbulent atmosphere modelled by random phase screens. These corrections are realized via transmitting an unmodulated beam in parallel to the one carrying the 4 amplitude shift keying (ASK) modulated message signal. On the receiver side, the amplitude corrections are obtained by dividing the intensity of the unmodulated beam by its free space equivalence. The corrections are then used to restore the amplitude distortions of the beam carrying the 4ASK modulated message signal and in the determination of decision boundaries for the received 4ASK symbols. The success of the system is visually inspected by comparing the received intensity profiles before and after the application of corrections. Furthermore, simulation analysis of symbol error rate (SER) is made, where the proposed set-up is found to be quite insensitive to wavelength difference between the unmodulated and modulated beams. On the other hand, the difference in the structure constant values of these two beams seems to have profound effect on system performance.

Simulation of Propagation and Transformation of THz Bessel Beams with Orbital Angular Momentum

Recently, terahertz Bessel beams with angular orbital momentum (“vortex beams”) with topological charges l = ±1 and l = ±2 were generated for the first time using radiation of the Novosibirsk free electron laser (NovoFEL) and silicon binary phase axicons (Knyazev et al., Phys. Rev. Letters, vol. 115, Art. 163901, 2015). Such beams are prospective for application in wireless communication and remote sensing. In present paper, numerical modelling of generation and transformation of vortex beams based on the scalar diffraction theory has been performed. It was shown that the Bessel beams with the diameters of the first ring of 1.7 and 3.2mm for topological charges ±1 and ±2, respectively, propagate at a distance up to 160mm without dispersion. Calculation showed that the propagation distance can be increased by reducing of the radiation wavelength or using a telescopic system. In the first case, the propagation distance grows up inversely proportional to the wavelength, whereas, in the latter case the propagation distance increases as a square of a ratio of the telescope lenses foci. Modelling of the passing of the vortex Bessel beams through a random phase screen and amplitude obstacles showed the self-healing ability of the beams. Even if an obstacle with a diameter of 10 mm blocks several central rings of Bessel beam, it reconstructs itself after passing a length of about 100 mm. Results of the simulations are in a good agreement with the experimental data, when the latter exist.

Complex degree of coherence and power moments of cylindrical sinc Gaussian beam

Complex degree of coherence and power moment aspects of cylindrical sinc Gaussian beam are investigated. To do this, we have used the random phase screen approach. It is seen that on the source plane, cylindrical sinc Gaussian beam has zero on-axis intensity and the sidelobes resemble the sinc or the Gaussian profile depending on the relative magnitudes of width parameter and the source size. Upon propagation in turbulent atmosphere, the initially flat complex degree of coherence becomes curved as the beam propagates, it then partially follows the intensity profile, and eventually turns into a delta function. Power moments are evaluated up to the fifth degree and over two different aperture sizes. In the aperture size of pointlike scintillations, the behaviors of power moments are similar to those of intensity moments. In aperture averaging conditions however, the differences between the variations of moments with respect to the propagation distance and degree of the moments become much less.

Comparative statistical analysis of phase profiles of a pseudo random phase plate with Kolmogorov phase screens

Experimentally retrieved phase profiles of a pseudo random phase plate (PRPP), obtained using coherent laser beam of 633nm wavelength in the Mach–Zehnder interferometric set up with an additional 4f imaging system, are statistically compared with numerically generated Kolmogorov random phase screens. The numerically generated phase screens are obtained using atmospheric structure constants ranging from very weak to very strong turbulence conditions. Our detailed quantitative analysis shows that the unwrapped phase profiles retrieved from the PRPP represent a different class of phase screens which donot match exactly with Kolmogorov phase screens.

High performance optical encryption based on computational ghost imaging with QR code and compressive sensing technique

In this paper, we propose a high performance optical encryption (OE) scheme based on computational ghost imaging (GI) with QR code and compressive sensing (CS) technique, named QR-CGI-OE scheme. N random phase screens, generated by Alice, is a secret key and be shared with its authorized user, Bob. The information is first encoded by Alice with QR code, and the QR-coded image is then encrypted with the aid of computational ghost imaging optical system. Here, measurement results from the GI optical system's bucket detector are the encrypted information and be transmitted to Bob. With the key, Bob decrypts the encrypted information to obtain the QR-coded image with GI and CS techniques, and further recovers the information by QR decoding. The experimental and numerical simulated results show that the authorized users can recover completely the original image, whereas the eavesdroppers can not acquire any information about the image even the eavesdropping ratio (ER) is up to 60% at the given measurement times. For the proposed scheme, the number of bits sent from Alice to Bob are reduced considerably and the robustness is enhanced significantly. Meantime, the measurement times in GI system is reduced and the quality of the reconstructed QR-coded image is improved.