Optical Wave Propagation Research Articles

Determination of the Paratellurite Stiffness Constants Temperature Coefficients by the Acousto-Optic Method

Acousto-optic (AO) phase matching condition is determined not only by the optical and acoustic waves propagation direction and parameters, but also by the physical characteristics of the AO interaction medium. Wherein, these characteristics, mainly the acoustic wave velocity, are temperature dependent. The change of ultrasound velocity relies on the medium stiffness constants cij variation with temperature. However, even for the most popular AO material – tellurium dioxide, the values of the stiffness constants temperature coefficients, given in various papers, vary significantly. The experimentally observed AO phase matching frequency temperature shift values do not coincide with those evaluated with literature data. In order to eliminate the observed discrepancy between theory and experiment, the AO phase matching frequency temperature dependencies for several AO cells based on TeO2 crystals with cut angles varying from 1.8° to 19° from the [110] axis in the (1‾10) plane were analyzed. The ultrasound velocity variation temperature coefficients were evaluated and the c11-c12 and c44 temperature coefficients that define the slow acoustic mode velocity in the selected plane were determined.

Spatial Property of Optical Wave Propagation through Anisotropic Atmospheric Turbulence

For the free‐space optical (FSO) communication system, the spatial coherence of a laser beam is influenced obviously as it propagates through the atmosphere. This loss of spatial coherence limits the degree to which the laser beam is collimated or focused, resulting in a significant decrease in the power level of optical communication and radar systems. In this work, the analytic expressions of wave structure function for plane and spherical wave propagation through anisotropic non‐Kolmogorov turbulence in a horizontal path are derived. Moreover, the new expressions for spatial coherence radius are obtained considering different scales of atmospheric turbulence. Using the newly obtained expressions for the spatial coherent radius, the effects of the inner scales and the outer scales of the turbulence, the power law exponent, and the anisotropic factor are analyzed. The analytical simulation results show that the wave structure functions are greatly influenced by the power law exponent α, the anisotropic factor ζ, the turbulence strength , and the turbulence scales. Moreover, the spatial coherence radiuses are also significantly affected by the anisotropic factor ζ and the turbulence strength , while they are gently influenced by the power law exponent α and the inner scales of the optical waves.

Wave optical simulation of retinal images in laser safety evaluations.

Lasers with wavelengths in the visible and near infrared region, pose a potential hazard to vision as the radiation can be focused on the retina. The laser safety standard IEC 60825-1:2014 provides limits and evaluation methods to perform a classification for such systems. An important parameter is the retinal spot size which is described by the angular subtense of the apparent source. In laser safety evaluations, the radiation is often described as a Gaussian beam and the image on the retina is calculated using the wave optical propagation through a thin lens. For coherent radiation, this method can be insufficient as the diffraction effects of the pupil aperture influence the retinal image. In this publication, we analyze these effects and propose a general analytical calculation method for the angular subtense. The proposed formula is validated for collimated and divergent Gaussian beams.

Neural holography with camera-in-the-loop training

Holographic displays promise unprecedented capabilities for direct-view displays as well as virtual and augmented reality applications. However, one of the biggest challenges for computer-generated holography (CGH) is the fundamental tradeoff between algorithm runtime and achieved image quality, which has prevented high-quality holographic image synthesis at fast speeds. Moreover, the image quality achieved by most holographic displays is low, due to the mismatch between the optical wave propagation of the display and its simulated model. Here, we develop an algorithmic CGH framework that achieves unprecedented image fidelity and real-time framerates. Our framework comprises several parts, including a novel camera-in-the-loop optimization strategy that allows us to either optimize a hologram directly or train an interpretable model of the optical wave propagation and a neural network architecture that represents the first CGH algorithm capable of generating full-color high-quality holographic images at 1080p resolution in real time.

On multi-geometric structures optical waves propagation in self-phase modulation medium: Sasa–Satsuma equation

The Raman effect leads to that the medium undergoes a self-frequency shift which is due to self-phase modulation SPM. It is included in the Sasa–Satsuma equation SSE. A variety of works, on this equation, occupied a remarkable area of research in the literature. Here, we are concerned with investigating optical waves propagation OWP in a SPM medium by studying SSE. Exact solutions of the SSE are obtained by using the unified method (UM). The solutions obtained show the propagation of optical waves with different geometric structures. Novel chirped, conoidal, M-shaped and mixed M-shaped and periodic solitons are visualized. The principle thought in this work is to construct solutions to the waves that arise from soliton-periodic waves collisions, by introducing a new transformation.

Analysis of numerical diffraction calculation methods: from the perspective of phase space optics and the sampling theorem.

Diffraction calculations are widely used in applications that require numerical simulation of optical wave propagation. Different numerical diffraction calculation methods have their own transform and sampling properties. In this study, we provide a unified analysis where five popular fast diffraction calculation methods are analyzed from the perspective of phase space optics and the sampling theorem: single fast Fourier transform-based Fresnel transform, Fresnel transfer function approach, Fresnel impulse response approach, angular spectrum method, and Rayleigh-Sommerfeld convolution. The evolutions of an input signal's space-bandwidth product (SBP) during wave propagation are illustrated with the help of a phase space diagram (PSD) and an ABCD matrix. It is demonstrated that all of the above methods cannot make full use of the SBP of the input signal after diffraction; and some transform properties have been ignored. Each method has its own restrictions and applicable range. The reason why different methods have different applicable ranges is explained with physical models. After comprehensively studying and comparing the effect on the SBP and sampling properties of these methods, suggestions are given for choosing the proper method for different applications and overcoming the restrictions of corresponding methods. The PSD and ABCD matrix are used to illustrate the properties of these methods intuitively. Numerical results are presented to verify the analysis, and potential ways to develop new diffraction calculation methods are also discussed.

Probability density of irradiance for optical waves propagating underwater in the presence of air bubbles

SummaryThe use of wireless optical waves could prove valuable to numerous underwater applications compared to radio frequency and acoustic waves. However, optical signals are susceptible to attenuations and scintillation (fading) due to the turbulent nature of underwater environments. Therefore, it is imperative to determine the wave intensity distribution. General approach to this problem is to apply existing atmospheric propagation models or to device a statistical distribution based on experimental data. Recent studies show that the well‐known probability density functions poorly describe EM optical wave propagation underwater in the presence of air bubbles, and thus, mixture distributions were proposed. This, however, ignores the physical aspects of the phenomena, and as such may limit the model region of validity. In this paper, a novel intensity distribution model is derived based on the Rytov theory of propagation through weak turbulence. Furthermore, the distribution is validated by experimental data over a large range of turbulence levels.

Peculiarities of adaptive phase correction of optical wave distortions under conditions of ‘strong’ intensity fluctuations

The reason for the loss of efficiency of adaptive phase correction in the propagation of optical waves in a turbulent atmosphere under conditions of ‘strong’ intensity fluctuations is experimentally explained for the first time. Based on the data from experiments conducted on both horizontal and vertical atmospheric paths, we have found that intensity fluctuations begin to significantly affect phase measurements when the coherence radius of the optical wave becomes less than the radius of the first Fresnel zone. Under these conditions, the main meter of adaptive optics systems, i. e. the Hartmann sensor, no longer provides correct measurements of the phase distribution in the presence of deep amplitude modulation. Based on the study of the behaviour of the mode components of the phase fluctuations reconstructed from the results of measurements in various operating regimes, we have found that, first of all, the amplitudes of the lowest modes of phase fluctuation expansion (tilts, defocusing, and astigmatism) are distorted, which, as the analysis shows, is very different from the regime of weak fluctuations.

Coherent fluctuations in time-domain diffuse optics

Near infrared light pulses, multiply scattered by random media, carry useful information regarding the sample key constituents and their microstructures. Usually, the photon diffusion equation is used to interpret the data, which neglects any interference effect in the detected light fields. However, in several experimental techniques, such as diffuse correlation spectroscopy or laser speckle flowmetry, the effect of light coherence is exploited to retrieve the information on the sample dynamical properties. Here, using an actively mode-locked Ti:Sapphire laser, we report the observation of temporal fluctuations in the diffused light pulse, which cannot be described by the diffusion theory. We demonstrate the sensitivity of these fluctuations on the sample dynamical properties and on the number of detected coherence areas (i.e., speckles). In addition, after interpreting the effect as a time-resolved speckle pattern, we propose a simple statistical method for its quantification. The proposed approach may enable the simultaneous monitoring of the static (absorption and scattering coefficients) and dynamical (Brownian diffusion coefficient) properties of the sample, and also provide physical insight on the propagation of optical waves in random media.

Broadband frequency translation through time refraction in an epsilon-near-zero material

Space-time duality in paraxial optical wave propagation implies the existence of intriguing effects when light interacts with a material exhibiting two refractive indexes separated by a boundary in time. The direct consequence of such time-refraction effect is a change in the frequency of light while leaving the wavevector unchanged. Here, we experimentally show that the effect of time refraction is significantly enhanced in an epsilon-near-zero (ENZ) medium as a consequence of the optically induced unity-order refractive index change in a sub-picosecond time scale. Specifically, we demonstrate broadband and controllable shift (up to 14.9 THz) in the frequency of a light beam using a time-varying subwavelength-thick indium tin oxide (ITO) film in its ENZ spectral range. Our findings hint at the possibility of designing (3 + 1)D metamaterials by incorporating time-varying bulk ENZ materials, and they present a unique playground to investigate various novel effects in the time domain.

Outer-Scale Effect of a Gaussian-Beam Wave Propagated Through Non-Kolmogorov Turbulent Atmosphere on the Beam Wander

To date, it is a common knowledge that there exists two kinds of turbulence in Earth’s aerosphere, the Kolmogorov turbulence and the non-Kolmogorov turbulence, which has been confirmed by both increasing experimental evidences and some results of theoretical investigations. Therefore, it is necessary to further develop theory of optical wave propagation through the atmospheric turbulence, namely, to study the propagation of laser beams in the non-Kolmogorov turbulence before analyzing the joint influence of the Kolmogorov turbulence and the non-Kolmogorov turbulence on satellite laser communication. Also it is well known that the beam wander results in the performance degradation of satellite laser communication systems and exert an influence on the achievement and stability of its links. In this paper, considering a non-Kolmogorov generalized exponential power spectrum of refractive-index fluctuations, we derive the variances of beam wander for a Gaussian-beam wave in weak turbulence for a horizonal path. This spectrum includes the inner and outer scales with a generalized power law; thus, we also analyze the effect of spectral power law and outer scale variations on the beam wander. It is important to note that the expression for the beam wander variance obtained is concise closed form and independent on the optical wavelength.

Application of Gaussian pulsed beam decomposition in modeling optical systems with diffraction grating.

A diffraction grating is one of the most commonly used components in ultrafast optical systems such as pulse stretchers and compressors. Hence, modeling the temporal dispersion and spatiotemporal distortions associated with the angular dispersion of a diffraction grating is very crucial for wave optical modeling of such systems. In this paper, the Gaussian pulsed beam decomposition (GPBD) method is extended to handle the propagation of ultrashort pulses, with arbitrary spatial and spectral profiles, through complex ultrashort pulse shaping systems containing diffraction gratings. Although the diffraction efficiencies are not rigorously computed, the GPBD method enables modeling of the large angular dispersion of idealized diffraction gratings without running into an impractically large number of spectral samples as in the case of Fourier-transform-based methods. The application of the extended method is demonstrated by performing the wave optical propagation of an ultrashort pulse through a single diffraction grating and then through a Treacy compressor system. By combining the Treacy compressor with the Martinez grating pair stretcher with internal lenses, the pulse shaping through a complete chirped pulse amplification (CPA) setup is modeled. Finally, the effects of using real dispersive lenses in the Martinez stretcher on the output pulse of the CPA setup are presented. For analysis of the output pulses, methods of computing the spatiotemporal and spatio-spectral amplitudes of the output pulse from the phase correct superposition of individual Gaussian pulsed beams are presented.

Precision analysis of turbulence phase screens and their influence on the simulation of Gaussian beam propagation in turbulent atmosphere.

The slip-step method is widely used in simulating optical wave propagation in turbulent atmosphere, which treats propagation and phase perturbations caused by turbulence separately and in discrete steps along the propagation axis. The phase perturbations are represented by a series of phase screens, and hence, the precision of the phase screen concerns the accuracy of the simulation. In this paper, we first discuss the precision and computational performance of phase screens generated by the subharmonic complemented discrete Fourier transformation (DFT) (DFT-SH) method, three kinds of randomized spectral sampling techniques (sparse spectrum (SS) technique, sparse spectrum technique with uniform wave vectors (SU), randomized DFT technique), and optimization-based (OB) method; then, the simulations are implemented with the phase screens generated by these methods. Some statistical quantities of the received optical field are calculated, such as beam wander variance, long-term beam radius, short-term beam radius, and on-axis scintillation index. The statistical results show that the undersampling of phase screen in the low-frequency region causes underestimation of the values of beam wander variance, long-term beam radius, and focused beam on-axis scintillation index because these quantities are sensitive to the large-scale inhomogeneities. However, the undersampling does not affect the predicted values of the short-term beam radius and collimated beam on-axis scintillation index because these quantities are insensitive to the large-scale inhomogeneities.

Valley-Hall Topological Plasmons in a Graphene Nanohole Plasmonic Crystal Waveguide

We demonstrate that unidirectional and backscattering immune propagation of terahertz optical waves can be achieved in a topological valley-Hall waveguide made of graphene nanohole plasmonic crystals. In order to gain deeper physical insights into these phenomena, the band diagram of graphene nanohole plamsonic crystals has been investigated and optimized. We found that a graphene plasmonic crystal with nanohole arrays belonging to the $C_{6v}$ symmetry group possesses gapless Dirac cones, which can be gapped out by introducing extra nanoholes such that the symmetry point group of the system is reduced from $C_{6v}$ to $C_{3v}$. Taking advantage of this feature, we design a mirror symmetric domain-wall interface by placing together two optimized graphene plasmonic crystals so as to construct valley-polarized topological interface modes inside the opened bandgap. Our computational analysis shows that the valley-Hall topological domain-wall interface modes can be achieved at an extremely deep subwavelength scale, and do not rely on the application of external static magnetic fields. This work may pave a new way to develop highly-integrated and robust terahertz plasmonic waveguides at deep-subwavelength scale.

Designing an ultra-fast all-optical full-adder based on nonlinear photonic crystal cavities

In this paper, a two-dimensional structure based on photonic crystal for adding three input bits is proposed. The dielectric rods used in this work are made of chalcogenide with a dielectric constant of 9.61. The lattice constant of the structure is 510 nm and the radius of the fundamental rods is 0.206 times the lattice constant. Three waveguides transmit the optical wave from input ports to the main waveguide. Based on the optical intensity in the main waveguide, two nonlinear cavities drop the waves toward the SUM and CARRY output ports. For using the optical Kerr effect, a rod made of the doped glass with a nonlinear coefficient of 10–14 m2/W is placed in each cavity. The radii of these rods are 1.12 and 1.06 times the radius of the fundamental rods. To calculate the band diagram and optical wave propagation throughout the proposed structure, the plane wave expansion and the finite difference time domain methods have been used. The maximum rise time of this structure is 400 fs that is less than one for the previous works. Furthermore, the area of the structure is around 115 µm2 which is proper to the optical circuits. Also, the obtained difference between margins of logic 0 and 1 is equal to 82%. According to the obtained results, one can be optimistic about the designed structure to be considered in optical processing applications.

Scintillation index and BER performance for optical wave propagation in anisotropic underwater turbulence under the effect of eddy diffusivity ratio.

Underwater optical communication has been a promising technology but is severely affected by underwater turbulence due to the resulting fluctuations in the index of refraction. In this paper, a revised spatial power spectrum model is obtained that considers the refraction index to be a function of the eddy diffusivity ratio, assuming the underwater turbulence is anisotropic. The scintillation indices for both plane and spherical waves that propagate in underwater turbulence are derived based on this model. Thereafter, the performance of an optical communication system, i.e., the outage probability and bit error rate, with the associated aperture averaging effect is considered. The simulation results demonstrate that temperature-induced and salinity-induced turbulence have distinct influences on the scintillation index and consequently result in different system performances. In addition, the variation in the eddy diffusivity ratio in some intervals induces more complicated results for underwater optical communication. Moreover, the effect of the receiver aperture diameter on the aperture averaging factor is presented in anisotropic underwater turbulence. Such an effect is more obvious in the plane wave case than in the spherical wave case. These results can find potential application in the engineering design of optical communication systems in an underwater environment.

Generation of homogeneous 3D Gaussian noise with spherically symmetric covariance.

In this paper, an approach for 3D noise generation is presented. The proposed algorithm might be a useful tool for the generation of correlated phase screens. These phase screens can be used for the simulation and modeling of optical wave propagation through atmospheric turbulence. Arbitrary user-defined covariance functions between voxel pairs can be achieved. Correlated 3D noise is formed by superposition of multiple uncorrelated 3D Gaussian noise patterns. These uncorrelated input noise patterns are of different dimensions. They are upsampled to the same target dimensions by linear interpolation. Each input pattern then contributes to total covariance on different spatial scales. The covariances between different voxels are expressed analytically by propagation of error. For a subset of randomly chosen voxels in the entire voxel space, relative deviations between the analytical and user-defined covariances are calculated. A sum of squares of these relative deviations is then minimized by machine learning methods. The optimized parameters are the weighting factors of individual uncorrelated 3D noise patterns. Corresponding covariance functions are numerically evaluated for two current atmospheric turbulence spectra. The first one is the generalized modified atmospheric spectrum. The second one is the generalized modified von Karman spectrum. Based on these covariance functions, optimal superpositions are calculated. Finally, statistical properties of these patterns are validated by ensemble sample covariance analysis.

Fiber-coupling efficiency of a Gaussian-beam in anisotropic non-Kolmogorov turbulence in the presence of random angular jitter

Increasing experimental evidence and theoretical results verify that the non-Kolmogorov property and anisotropy are both exhibited in the atmospheric turbulence. In the actual laser communication link, random angular jitter and bias error are important components that affect the laser communication performance. Therefore, in this study, we develop the fiber-coupling efficiency for a Gaussian-beam propagating horizontally through weak-to-strong anisotropic non-Kolmogorov turbulence in the presence of random angular jitter and bias error. The effects of anisotropic factors, power law, random angular jitter, and bias error, on the fiber-coupling efficiency are then evaluated. This study will be beneficial for the optimization of free-space optical communication systems and will enhance the understanding of optical wave propagation in anisotropic non-Kolmogorov link.

Picosecond-resolution phase-sensitive imaging of transparent objects in a single shot.

With the growing interest in the optical imaging of ultrafast phenomena in transparent objects, from shock wave to neuronal action potentials, high contrast imaging at high frame rates has become desirable. While phase sensitivity provides the contrast, the frame rates and sequence depths are highly limited by the detectors. Here, we present phase-sensitive compressed ultrafast photography (pCUP) for single-shot real-time ultrafast imaging of transparent objects by combining the contrast of dark-field imaging with the speed and the sequence depth of CUP. By imaging the optical Kerr effect and shock wave propagation, we demonstrate that pCUP can image light-speed phase signals in a single shot with up to 350 frames captured at up to 1 trillion frames per second. We expect pCUP to be broadly used for a vast range of fundamental and applied sciences.

Modulation theory and resonant regimes for dispersive shock waves in nematic liquid crystals

A full analysis of all regimes for optical dispersive shock wave (DSW) propagation in nematic liquid crystals is undertaken. These dispersive shock waves are generated from step initial conditions for the optical field and are resonant in that linear diffractive waves are in resonance with the DSW, resulting in a resonant linear wavetrain propagating ahead of it. It is found that there are six regimes, which are distinct and require different solution methods. In previous studies, the same solution method was used for all regimes, which does not yield solutions in full agreement with numerical solutions. Indeed, the standard DSW structure disappears for sufficiently large initial jumps. Asymptotic theory, approximate methods or Whitham modulation theory are used to find solutions for these resonant dispersive shock waves in a given regime. The solutions are found to be in excellent agreement with numerical solutions of the nematic equations in all regimes. It is found that for small initial jumps, the resonant wavetrain is unstable, but that it stabilises above a critical jump height. It is additionally found that the DSW is unstable, except for small jump heights for which there is no resonance and large jump heights for which there is no standard DSW structure.