Generalized Huygens-Fresnel Principle Research Articles

Spin–momentum properties in the gradient-index fiber

The vector characteristics of the kinetic momentum, spin angular momentum (SAM), and light field of a radially polarized vortex beam (RPVB) in the radial gradient-index (GRIN) fiber are analyzed using a unified methodology based on the generalized Huygens-Fresnel principle and the spin-momentum relationship. The kinetic momentum, SAM, transverse-type spin (t-SAM), longitudinal-type spin (l-SAM) and light field contain parallel and perpendicular components to the optical axis in the GRIN fiber. Moreover, the optical spin skyrmion from the SAM, t-SAM, and l-SAM can be observed at the semi-focal plane and the focal plane of the GRIN fiber. To the best of our knowledge, this is the first confirmation of spin skyrmions in the GRIN fiber. The analysis of spin-momentum properties of an RPVB in the GRIN fiber combined with the generalized Huygens-Fresnel principle and the spin-momentum relationship can be applied in describing the vector properties of transmission in atmospheric and optical systems.

Spin–Momentum Properties in the Gradient-index Fiber

The vector characteristics of the kinetic momentum, spin angular momentum (SAM), and light field of a radially polarized vortex beam (RPVB) in the radial gradient-index (GRIN) fiber are analyzed using a unified methodology based on the generalized Huygens-Fresnel principle and the spin-momentum relationship. The kinetic momentum, SAM, transverse-type spin (t-SAM), longitudinal-type spin (l-SAM) and light field contain parallel and perpendicular components to the optical axis in the GRIN fiber. Moreover, the optical spin skyrmion from the SAM, t-SAM, and l-SAM can be observed at the semi-focal plane and the focal plane of the GRIN fiber. To the best of our knowledge, this is the first confirmation of spin skyrmions in the GRIN fiber. The analysis of spin-momentum properties of an RPVB in the GRIN fiber combined with the generalized Huygens-Fresnel principle and the spin-momentum relationship can be applied in describing the vector properties of transmission in atmospheric and optical systems.

Twisted splitting and propagation factor of superimposed twisted Hermite-Gaussian Schell-model beams in turbulent atmosphere

We believe this to be a new superposition twisted Hermite-Gaussian Schell-model (STHGSM) beam hat is proposed. Analytic formulas for the intensity distribution and propagation factor of the STHGSM beam in non-Kolmogorov turbulence are derived by utilizing the generalized Huygens-Fresnel principle (HFP) and the Wigner function. The evolution characteristics of STHGSM beams propagating are numerically calculated and analyzed. Our findings indicate that the light intensity of the STHGSM beam gradually undergoes splitting and rotation around the axis during propagation through non-Kolmogorov turbulence, eventually evolving into a diagonal lobe shape at a certain distance of transmission. The anti-turbulence capability of the beam strengthens with higher beam order or twist factor values.

Echo scattering characteristics: Vortex beams reflected by rough surface in ocean turbulence

Optical field echo scattering characteristic is one of the essential technologies for the future integration of underwater laser communication and detection. Vortex beam (e.g. Laguerre-Gaussian (LG) beam) with a helical wavefront structure is better suited to reduce the effects of ocean turbulence. A double-path transmission model of LG beam scattering through rough surface in ocean turbulence is innovatively established. We developed a closed analytical expression for the echo speckle intensity of LG beams reflected by a rough surface with a Gaussian distribution in ocean turbulence based on the generalized Huygens-Fresnel principle. The autocorrelation function of intensity and complex degree of coherence (DOC) of echo speckle field were numerically simulated and analyzed. From the results we found a rule that when coherence length of rough surfaces (ρh) is greater than the coherence length (ρ0) of spherical waves propagating across ocean turbulence, the impact of a rough surface on DOC is much less than that of ocean turbulence. This conclusion provides the theoretical basis that the echo wave field cannot be obtained in target detection under ocean turbulence.

Propagation of noninteger cylindrical vector vortex beams in a gradient-index fiber

The characteristics of two noninteger cylindrical vector vortex beams (NCVVBs) propagating through a radial gradient-index (GRIN) fiber are analyzed on the basis of the generalized Huygens-Fresnel principle. The NCVVBs exhibit periodic and stable transmission characteristics in the radial GRIN fiber. Polarization changes, the presence of spin angular momentum (SAM), and changes in the orbital angular momentum (OAM) of the NCVVBs are observed at the focal plane of the radial GRIN fiber. Spin-orbit interactions of NCVVBs are verified in the radial GRIN fiber for the first time, to the best of our knowledge.

Beam Properties of a Partially Coherent Beam Propagating Horizontally in Atmospheric Turbulence

This study explored the impact of atmospheric turbulence on partially coherent light propagation. Atmospheric turbulence causes random modulation of the intensity and phase of light, resulting in a speckle pattern in the far field. This study focused on partially coherent Gaussian Schell model beams and derived an analytical expression of the cross-spectral density function for their transmission through atmospheric turbulence, based on the generalized Huygens–Fresnel principle and the Tatarski spectrum model. Numerical simulations were used to investigate the effects of the source parameters and turbulence strength on the intensity distribution, beam width, and coherence length of partially coherent light in horizontal atmospheric transmission. The results demonstrate that diffraction-induced broadening primarily affects the intensity distribution of light in free-space transmission. Short transmission distances in atmospheric turbulence have comparable characteristics to those in a vacuum; however, as the turbulence intensity and transmission distance increase, the beam broadening effect amplifies, and the coherence length is reduced. The findings are relevant to the design of acquisition, pointing, and tracking systems for wireless laser communication systems and offer insights into the optimization of optical systems for atmospheric conditions.

Spin-orbit interactions of a circularly polarized vortex beam in paraxial propagation.

Spin-orbit interactions (SOIs) of circularly polarized beam and circularly polarized vortex beam during paraxial propagation in a radial gradient-index (GRIN) fiber are analyzed using the generalized Huygens-Fresnel principle and the GRIN fiber's ABCD matrix. SAM is only associated with polarized light helicity and OAM is only associated with topological charge m. SAM and OAM do not crosstalk or convert between each other; SOIs did not occur at the GRIN fiber's focal plane. SOIs of partially coherent circularly polarized beam and partially coherent circularly polarized vortex beam in the GRIN fiber are also studied and show the same characteristics as the perfectly polarized beam.

A study of effects of a turbulent jet engine exhaust on partially coherent Laguerre-Gaussian Schell model vortex beam

In this study, based on the generalized Huygens-Fresnel principle, the evolution properties, such as spectral density, degree of coherence, and beam width of the propagation of partially coherent Laguerre-Gaussian Schell model vortex beam (PCLGSMvB) in jet engine exhaust are studied. Our results show that the spectral density of the corresponding beam can change their form shape during its propagation as the source coherence varies. When the source coherence width is high, the profile of PCLGSMvB changes from initially dark hollow into two spot beams at short propagation distances. If the source coherent width is very small, the shape of PCLGSMvB is converted to a Gaussian shape and keeps its form upon propagation. Also, we found that the spreading of PCLGSMvB is related with their initial parameters, and it will be spread faster with smaller source coherence width, larger mode order n, and longer wavelength. Furthermore, the beam width of the PCLGSMvB increasing as the structural constant increases and it means that the beam can resist to stronger fluctuation of turbulence. Outputs of this study has potential application on deriving the requirements of optical systems on aircrafts like laser range finder, laser designator, optical communication systems and directed infrared countermeasure (DIRCM).

Propagation of Gaussian vortex beams in electromagnetically induced transparency media.

Electromagnetically induced transparency (EIT) is an important phenomenon in quantum optics, and has a wide range of applications in the fields of quantum information processing and quantum precision metrology. Recently, with the rapid progress of the generation and detection of structured light, the EIT with structured light has attracted enormous interests and offers new and novel functionalities and applications. Here, we theoretically study the propagation and evolution of Gaussian vortex beams, a typical type of structured light, in an EIT medium with Λ-type three-level atoms. Based on the generalized Huygens-Fresnel principle, we derive the analytical expressions of fully and partially coherent Gaussian vortex beams propagating in the EIT medium, and study the evolution of the intensity and phase distributions of the beams and their dependencies on parameters such topological charge, coherence length, Rabi frequency, etc. It is shown that both the fully and partially coherent Gaussian vortex beams undergo focusing and diverging periodically during propagation. The phase singularity of the fully coherent beam keeps unchanged, while the phase singularity of the partially coherent beam experiences splitting and recombination periodically. In addition, new phase singularities with opposite topological charge are generated in the latter case. Our results not only advance the study of the interaction between structured light and coherent media, but also pave the avenue for manipulating structured light via EIT.

Spreading evolution of a linear phase-locked hollow beam array in atmospheric turbulence.

Based on the generalized Huygens-Fresnel principle, propagation characteristics of a linear phase-locked hollow beam (PLHB) array propagating through atmospheric turbulence are investigated. Analytical expressions of the average intensity and mean-squared beam width of the PLHB array are derived. It is shown that propagation properties of a PLHB array are related to the initial beam parameters (i.e., number of beamlets, size of beam waist, range of wavelength) of the PLHB array and the strength of turbulence. These findings may provide potential applications in free-space optical communications, lidar, remote sensing, and related fields.

Spin-orbit periodic conversion in a gradient-index fiber.

The characteristics of the cylindrical vector beam (CVB) and the cylindrical vector vortex beam (CVVB) in a radial gradient-index (GRIN) fiber are analyzed on the basis of the generalized Huygens-Fresnel principle. The CVB and CVVB exhibit periodic and stable transmission characteristics in the radial GRIN fiber. In the beam with a vortex phase (CVVB), the polarization changes and the spin angular momentum (SAM) is detected at the focal plane of the radial GRIN fiber. A spin-orbit periodic conversion is observed in the radial GRIN fibers. Finally, the SAM expression of partially coherent light is deduced and verified via a simulation.

Simulation of spatial coherence of laser echo light field from random rough surface in turbulent atmosphere

According to the generalized Huygens-Fresnel principle, we derive the analytical formula for the complex degree of coherence of the echo light field under the von Karman atmospheric turbulence spectrum condition. Based on split-step beam propagation method of the turbulent phase screen and the target surface model, the fold pass propagation simulation of the laser in the turbulent atmosphere is realized. The dynamic speckle characteristics on the image plane are consistent with the experimental phenomenon. Firstly, the simulation results of the complex degree of coherence and phase structure function of the mirrored reflection echo light field are compared with the theoretical values, which verifies the correctness of the algorithm. Based on this, the complex degree of coherence of the echo light field reflected by the optical rough surface is calculated and analyzed. The results show that on a double-path turbulent flow path of 1.1 km, in other words, it transmits 2.2 km in unfolded mode, the spatial coherence of the echo light field is very sensitive to the root mean square value of height. When the root-mean-square value of height is close to the wavelength, the coherence is seriously degraded. When the correlation length of the target surface is much larger than the atmospheric coherence length, the coherence length of the echo light field is relatively close to the set spatial coherence length. When the correlation length of the target surface is close to the atmospheric coherence length, the influence of the rough surface of the target on the beam coherence cannot be ignored. When the correlation length of the target surface is much smaller than the atmospheric coherence length, the target surface characteristics have a dominant influence on the echo coherence, the spatial coherence of the light field is seriously degraded, and the echo is close to incoherent light. Considering the smooth target reflection surface, the greater the strength of turbulence, the faster the complex coherence decreases with space. The atmospheric coherence diameter <inline-formula><tex-math id="M1">\begin{document}${r_0}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20212420_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20212420_M1.png"/></alternatives></inline-formula> can be calculated further according to the complex degree of coherence. For the Pearson correlation coefficient the simulation value and theoretical value are both 0.998, which indicates that the atmospheric coherence diameter calculated by the complex degree of coherence has a high correlation with the theoretical value. This research provides a theoretical basis for the coherent detection scheme of echoes from rough surfaces in the turbulent atmosphere. The simulation algorithm extracts the target surface features by analyzing the variation of the complex coherence of laser echo signals in the turbulent atmosphere with the spatial distance, and also provides a method of using the known target surface to obtain path turbulence information.

Propagation of partially coherent vortex beams in gain media

In this paper, the propagation of partially coherent vortex beams in gain media was investigated based on the generalized Huygens-Fresnel principle. Our research focused on the influences of topological charge (m) and coherence length (σ0) on light intensity distribution, phase and spectral degree of coherence during the propagation. The results show that partially coherent vortex beams can maintain their initial dark hollow intensity distributions for a longer distance with larger m and σ0 as the gain and diffraction effects appear simultaneously. The decay of the maximum value of light intensity caused by diffraction is more obvious with a smaller σ0. On the other hand, the larger σ0 is, the more obvious the gain effect on the maximum value of light intensity is. We also observe that the coherence vortex with topological charge equals to m will split into m coherence vortices with topological charges are 1, and the coherence vortices with negative topological charge will generate at the same time. Some phenomena also appear with a larger coherence length, for example, a larger distance between coherence vortices with negative topological charge, a bigger splitting of the coherence vortices, and a slower damping of spectral degree of coherence, et al. This study can be used in the research and application of vortex beams in the materials field.

Influence of gain or absorption media on transmission of partially coherent vortex beams.

The results show that the larger the real part of the wave number is, the farther the transmission of PCVBs with hollow distribution will be. The expression of partially coherent vortex beams passing through a gain/absorption medium is derived in this paper based on the generalized Huygens-Fresnel principle. The influences of the refractive index (related to the real part of the wave number) and the gain/absorption characteristics (related to the imaginary part of the wave number) on the transmission of partially coherence vortex beams are investigated. The results show that the larger the real part of the wave number is, the farther the transmission of PCVBs with hollow distribution will be. In gain media, the light power keeps increasing; on the other hand, in absorption media, the light power keeps decreasing. The diffraction effect of the media on the intensity distribution also is mentioned. We discover that, during the transmission, the evolutions of the spectral degree of coherence relate to the real and imaginary parts of the wave number, and the coherence vortices can split and generate. We believe the results of this study are important to the fields of singular optics and optical communications.

Propagation and evolution of rectangular vortex beam array through atmospheric turbulence

Based on the generalized Huygens–Fresnel principle and Rytov approximation, the intensity expression of arbitrary-order rectangular vortex beam array propagating through atmospheric turbulence is derived, and the evolution process is studied in this paper. Vortex beam array will merge into a single vortex beam in atmospheric turbulence, and then degenerate into a Gaussian-like beam. However, vortex beam array with a smaller topological charge will degenerate in a shorter distance. Strong turbulence will lead to a more uniform light field distribution. In weak turbulence, there are lots of spot lattices just like the case in free space. Besides, the studies in this paper found that the outer scale has little influence on the evolution of vortex beam array. The results in this paper can provide a theoretical reference for further applications of vortex beam array in atmospheric turbulence.

Evolution and Beam spreading of Arbitrary order vortex beam propagating in atmospheric turbulence

Based on the Generalized Huygens–Fresnel principle and Rytov approximation, the intensity expressions of arbitrary-order vortex beam and vortex beam array propagation through atmospheric turbulence are derived, which are given in series. The results can provide foundation for further research on atmospheric propagation characteristics of vortex beam. The light intensity evolution and beam spreading are studied through auxiliary numerical simulation, it can be observed that radial vortex beam array will evolve into a single vortex beam, and eventually evolve into a Gaussian beam. Moreover, the influences of beam/turbulence parameters variation to mean square beam widths of single beam and beam array are investigated, the results show that the beam width is closely related to turbulence intensity and topological charge. Vortex beam array is less susceptible to turbulence than single vortex beam. With beam array and its beamlet evolving, they will end up with equal beam width.

Generalized Rayleigh-Sommerfeld Diffraction Theory for Metasurface-Modulating Paraxial and Non-Paraxial Near-Field Pattern Estimation

In this paper, different diffraction theories for estimating the diffraction field patterns modulated by metasurfaces are firstly revisited. Further reformulation of these theories is performed to better reveal their inherent mechanisms and differences. To compute the metasurface-modulating paraxial and/or non-paraxial diffraction field patterns within the near-field region, including the evanescent area, a universal pattern-propagation Eigenfactor is introduced to generalize Rayleigh-Sommerfeld diffraction theory. To investigate its applicability and accuracy, a representative monofocal metasurface with an ultrahigh numerical aperture of 0.96, together with two coplanar and non-coplanar multifocal holographic metasurfaces, are constructed as illustrative examples. Their near-field patterns are calculated by the generalized Rayleigh-Sommerfeld (GRS) diffraction integral and compared with those extracted by the finite-different time-domain full wave analysis, generalized Huygens-Fresnel principle, and Huygens's Principle. It is demonstrated that within the near-field region including the non-paraxial and evanescent area, the GRS diffraction integral provides the best and satisfactory agreement with the full wave simulation, and thus offers a more accurate and efficient tool for quantitative analysis and iterative optimization.

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.

Propagation properties of partially coherent Lommel beams in non-Kolmogorov turbulence

Based on generalized Huygens–Fresnel principle, the analytical expressions of the partially coherent Lommel beams propagating in turbulent atmosphere are derived. The propagation properties of vortex mode intensity (including mode probability density and crosstalk probability density) of partially coherent Lommel beam in non-Kolmogorov turbulence are investigated in this paper. The research results show that coherence width of partially coherent Lommel beam plays a key role to determine the mode intensity in the process of propagation. The poor coherence of source beams leads to serious dispersion of spiral spectrum distribution. It is worth noting that crosstalk probability density increases to its peak and gradually decreases due to the enhancement of other-order crosstalk. Furthermore, long wavelength and small asymmetry parameter are helpful to mitigate the influence of atmospheric turbulence and restrain the mode crosstalk on the orbital angular momentum mode transmission.

Beam quality evolution of vortex beam with phase distortion

Based on the generalized Huygens Fresnel principle, the propagation equation of fundamental Gaussian vortex beam with phase distortion is derived. To quantitatively analyze the influence of random phase distortion on the quality of vortex beam, the variance of light intensity relative deviation is proposed as the evaluation parameter. The influences of some key factors on the quality of a vortex beam are emphatically discussed. The results show that with the increasing of distortion strength the beam quality becomes worse. On the contrary, with the increasing of the topological charge, the beam quality improves gradually.