Geometrical Optics Approximation Research Articles

Simulation of optical propagation based on wave optics for phase retrieval in shadowgraph of ultrasonic field

A shadowgraph method has been proposed for fast and noninterference measurement of ultrasonic pressure field. However, special care has been needed in choosing an appropriate optical propagation length to obtain a satisfactory signal-to-noise ratio of the measurement while avoiding error from a geometrical optics approximation. In this study, we propose a new numerical method replacing the geometrical optics approximation to retrieve the optical phase for the measurement. Optical intensity distribution obtained from the numerical simulation of optical propagation based on the Huygens–Fresnel principle agreed well with the measurement at a relatively large optical propagation length at which the geometrical optics approximation failed. Optical phase retrieval from the simulated optical intensity distribution by the proposed method was then tested. The range of optical propagation for successful phase retrieval was extended a few times by the proposed method compared with the geometrical optics approximation.

Spherical aberration of an optical system and its influence on depth of focus.

This paper analyzes the influence of spherical aberration on the depth of focus of symmetrical optical systems for imaging of axial points. A calculation of a beam's caustics is discussed using ray equations in the image plane and considering longitudinal spherical aberration as well. Concurrently, the influence of aberration coefficients on extremes of such a curve is presented. Afterwards, conditions for aberration coefficients are derived if the Strehl definition should be the same in two symmetrically placed planes with respect to the paraxial image plane. Such conditions for optical systems with large aberrations are derived with the use of geometric-optical approximation where the gyration diameter of the beam in given planes of the optical system is evaluated. Therefore, one can calculate aberration coefficients in such a way that the optical system generates a beam of rays that has the gyration radius in a given interval smaller than the defined limit value. Moreover, one can calculate the maximal depth of focus of the optical system respecting the aforementioned conditions.

Features of HF Radio Wave Attenuation in the Midlatitude Ionosphere Near the Skip Zone Boundary

We briefly describe the history of studying the decameter radio wave attenuation by different methods in the midlatitude ionosphere. A new method of estimating the attenuation of HF radio waves in the ionospheric F region near the skip zone boundary is presented. This method is based on an analysis of the time structure of the interference field generated by highly stable monochromatic X-mode radio waves at the observation point. The main parameter is the effective electron collision frequency νeff, which allows for all energy losses in the form of equivalent heat loss. The frequency νeff is estimated by matching the assumed (model) and the experimentally observed structures. Model calculations are performed using the geometrical-optics approximation. The spatial attenuation caused by the influence of the medium-scale traveling ionospheric disturbances is taken into account. Spherical shape of the ionosphere and the Earth’s magnetic field are roughly allowed for. The results of recording of the level of signals from the RWM (Moscow) station at a frequency of 9.996 MHz at point Rostov are used.

Benchmarking grey particle approximations against nongrey particle radiation in circulating fluidized bed combustors

ABSTRACTInvestigation of the effect of grey/nongrey particle property models on radiative heat fluxes and source terms is performed in the dilute zone of the lignite-fired 150 kW Middle East Technical University circulating fluidized bed combustor test rig. Predictive accuracy and computational economy of several grey particle models, geometric optics approximation (GOA) with average particle reflectivity (GOA2), GOA with Fresnel solution for particle reflectivity (GOA3), and Planck mean particle properties from spectral Mie solution are tested by benchmarking their predictions against spectrally banded solution of radiative transfer equation (RTE). Comparisons reveal that all grey models lead to accurate and CPU efficient radiative heat flux predictions. On the other hand, only GOA3 and Planck mean properties are in favorable agreement with the benchmark solution for both incident fluxes and source terms. These findings indicate that grey particle approximation with GOA3 is a more practical choice in solution of RTE as it eliminates the need for spectral calculations.

Theoretical investigation on optical Kerr effect in femtosecond laser trapping of dielectric microspheres

Stable trapping of individual dielectric nanoparticles under high-repetition-rate ultrafast pulsed excitation has been demonstrated and theoretically explained based on repetitive instantaneous trapping as well as optical nonlinearity assisted trapping. Here we estimate the force exerted on a micron-sized spherical dielectric particle including optical Kerr effect. Using geometric optics approximation, we show how inclusion of optical Kerr effect results in significant change of the force curves along axial direction under femtosecond pulsed excitation compared with continuous-wave excitation. The results show excellent agreement with previous experimental findings. Most importantly, similar to the optical trapping of nanoparticles under ultrafast pulsed excitation, we show that the efficiency of trapping of micron-sized particles is also governed by the barrier height (and not the absolute depth) of the axial trapping potential.

Influence of geomagnetic storms of September 26–30, 2011, on the ionosphere and HF radiowave propagation. II. radiowave propagation

A study of HF wave propagation in the three-dimensional inhomogeneous ionosphere has been carried out in an approximation of geometrical optics. The three-dimensional medium of radio wave propagation is considered to be inhomogeneous, absorbing, and anisotropic due to the influence of the geomagnetic field. The parameters of the medium are described by the results of calculations on the basis of the Global Self-Consistent Model of the Thermosphere, Ionosphere, and Protonosphere (GSM TIP). The propagation of radio waves in the equatorial, middle-, and high-latitude ionosphere was studied. Comparisons of the ray trajectories, integral attenuation, deviations of the projection of radio wave trajectories onto the Earth’s surface from the great-circle arc, and the behavior of the angle between the wave phase and wave energy directions, as well as the angle between the direction of propagation and the external magnetic field obtained for quiet and disturbed conditions, have been performed. We consider a geomagnetic storm that occurred in 2011, with the main storm phase occurring on September 26, and the day after geomagnetic disturbances, September 29, as disturbed conditions in the ionosphere.

Superluminality phenomenon at a femtosecond laser pulse propagation in a medium containing nanorods

We show a possibility for soliton formation and superluminality phenomenon at a femtosecond pulse propagation in a medium with noble nanorods. These effects take place if a positive phase grating is induced by laser radiation. We take into account the dependence of two- or one-photon absorption [single-photon absorption (SPA)] on the nanorod aspect ratio and time-dependent nanorod aspect ratio changing due to nanorods reshaping (or melting) because of laser energy absorption. We demonstrate that a fast light propagation mode occurs for various detuning between wave packet carrier frequency and nanorod resonance frequency, which is a key parameter for practical observation of fast or slow light in a physical experiment. We also developed analytical approaches for explanation of laser pulse propagation peculiarities in a medium with nanorods. In particular, in the framework of nonlinear geometric optics approximation, we derived the laws for the pulse intensity and instantaneous frequency evolution if a phase grating is induced by laser radiation in a medium with SPA. We also developed an approximate analytical soliton and derived the chirped soliton amplitude, duration and homogeneous shift evolution, carrier frequency changing, and pulse chirp evolution. The results of analytical consideration are confirmed by computer simulation results.

From parabolic-trough to metasurface-concentrator: assessing focusing in the wave-optics limit

Metasurfaces are promising tools toward novel designs for flat optics applications. As such, their quality and tolerance to fabrication imperfections need to be evaluated with specific tools. However, most such tools rely on the geometrical optics approximation and are not straightforwardly applicable to metasurfaces. In this Letter, we introduce and evaluate for metasurfaces parameters such as intercept factor and slope error usually defined for solar concentrators in the realm of ray-optics. After proposing definitions valid in physical optics, we put forward an approach to calculate them. As examples, we design three different concentrators based on three specific unit cells and assess them numerically. The concept allows for comparison of the efficiency of the metasurfaces and their sensitivities to fabrication imperfections and will be critical for practical systems implementation.

Computation of total hemispherical emissivity from directional spectral models

Kirchoff’s law and experimentally obtained data and/or theory (such as from Drude’s model) for optical constants have been used in a modified geometric optics approximation (GOA) to obtain directional spectral emissivity. Then this spectral emissivity is used to obtain the total hemispherical emissivity by integration over direction and spectral range as weighted by the Planck distribution. The computations account for surface dependencies on temperature, composition, and roughness. The computed results for both the spectral directional and the total hemispherical emissivity are compared with the available data for platinum, stainless steel 304, and tungsten surfaces.

Analytical calculations of optical trapping forces for drag calibration: Effects of mismatch between beam focus and particle center

We present analytical calculations of optical forces for drag calibrations via the geometrical optics approximation (GOA) for the case in which a single laser beam is strongly focused on a polystyrene microsphere dispersed in an aqueous phase. When the beam focus is mismatched with the particle center owing to the presence of vertical forces, such as gravity, buoyancy, and the radiation force caused by the laser beam, the trapped particle would be displaced in a radial direction when the lateral drag force is applied. Based on the analytical calculations of optical trapping forces and the force balance upon dragging, we found that the critical laser power at which the beam focus matches the particle center exhibits a power-law relationship with the particle radius a according to the empirical expression log(Pcrit (mW)) = 2.899 log(2a (µm)) - 2.316. We also found an empirical expression for the mechanical equilibrium position of the vertical displacement Δzeq0(Δy=0) as functions of the laser power P and the particle radius, \(\Delta z_{eq}^0 = \frac{{\left[ {{F_{gb}}\left( {pN} \right) - 0.068P\left( {mW} \right)} \right]\left[ {2.7a\left( {\mu m} \right) - 0.252} \right]}}{{P\left( {mW} \right)}}\), where Fgb is the sum of the gravitational and buoyant forces.

On the applicability of asymptotic formulas of retrieving “optical” turbulence parameters from pulse lidar sounding data: II–results of numerical simulation

The applicability of formulas derived in the first part of this work has been studied in a numerical experiment. The geometrical optics approximation is shown to be applicable only on short paths whose length is less than the corresponding diffraction lengths by a factor of hundreds. The restrictions are caused by oscillations of the kernel of the initial integral equation. They lead to strong oscillations of the third derivative of the measured data. The formulas based on the asymptotic formula of the kernel for a point receiver are slightly sensitive to oscillations of the measured data. Applying the formulas for a point receiver in the case of receivers with a finite radius smoothes the retrieved distributions and shifts them with respect to the given ones. A technique of taking these factors into account in the process of retrieving has been proposed. Together with smoothing of the retrieved distributions, applying the point receiver approximation leads to partial loss of the information about the turbulence spectrum in the retrieved data. This allows one to simplify the retrieval procedure by reducing it to calculating usual derivatives of the second order.

Influence of January 2009 stratospheric warming on HF radio wave propagation in the low-latitude ionosphere

We have considered the influence of the January 23–27, 2009 sudden stratospheric warming (SSW) event on HF radio wave propagation in the equatorial ionosphere. This event took place during extremely low solar and geomagnetic activity. We use the simulation results obtained with the Global Self-consistent Model of the Thermosphere, Ionosphere and Protonosphere (GSM TIP) for simulating environmental changes during the SSW event. We both qualitatively and quantitatively reproduced total electron content disturbances obtained from global ground network receiver observations of GPS navigation satellite signals, by setting an additional electric potential and TIME-GCM model output at a height of 80 km. In order to study the influence of this SSW event on HF radio wave propagation and attenuation, we used the numerical model of radio wave propagation based on geometrical optics approximation. It is shown that the sudden stratospheric warming leads to radio signal attenuation and deterioration of radio communication in the daytime equatorial ionosphere.

Hybrid asymptotic method for analyzing caustics of optical elements in the axially symmetric case

In this work we propose a new approach to calculating the distribution of light fields in the framework of geometrical optics. A new integral operator for computing the intensity distribution in the geometrical optics approximation is suggested. Using the proposed method, we derive the intensity distributions of previously studied wavefronts. Singular points of these distributions are found and the intensity distributions near the caustics are calculated. The developed method is used to calculate the formation of caustics by harmonic diffractive optical elements in the axially symmetric case.

Statistical Characteristics of New Type Internal Wave in the Ionospheric F Region

Second order statistical moments of new internal MHD wave in the ionospheric F region are investigated analytically by geometrical optics approximation. Degree of a curvature of a constant phase surface and the variance of an instant frequency measuring by experiment has been obtained for arbitrary correlation function of electron density fluctuations. Energy exchange between the internal wave and turbulent plasma flow is considered calculating the mean energy flux density in the first and second approximations. Numerical calculations are carrying out for both anisotropic Gaussian correlation function and power law-spectrum characterizing elongated plasma irregularities using experimental data of satellites and incoherent scatter radar observations.

Asymptotic methods of solving problems of diffraction by non-periodic structures

An asymptotic method for calculating the complex amplitude of a light field in the case of diffraction by non-periodic band gap structures. The novelty of the approach consists in the expansion of the solution of the integral equation into a basis that describes the propagation of light through a DOE within the geometrical optics approximation and changes into a basis of plane waves used in the calculation of diffraction gratings. We present the results of focusing into a point by a gradient-index diffractive optical element with a band-gap structure. Simulation results confirm the efficiency of the proposed method.

Modeling and simulations on the propagation characteristics of electromagnetic waves in sub-atmospheric pressure plasma slab

Sub-atmospheric pressure plasma slabs exhibit the feature of relatively high plasma number density and high collisional frequency between electrons and neutral gases, as well as similar thickness to the electromagnetic (EM) wavelength in communication bands. The propagation characteristics of EM waves in sub-atmospheric pressure plasma slabs are attracting much attention of the researchers due to their applications in the plasma antenna, the blackout effect during reentry, wave energy injection in the plasma, etc. In this paper, a numerical model with a one-dimensional assumption has been established and therefore, it is used for the investigations of the propagation characteristics of the EM waves in plasma slabs. In this model, the EM waves propagating in both sub-wavelength plasma slabs and plasmas with thicker slabs can be studied simultaneously, which is superior to the model with geometrical optics approximation. The influence of EM wave frequencies and collisional frequencies on the amplitude of the transmitted EM waves is discussed in typical plasma profiles. The results will be significant for deep understanding of the propagation behaviors of the EM waves in sub-atmospheric pressure nonuniform plasma slabs, as well as the applications of the interactions between EM waves and the sub-atmospheric pressure plasmas.

Modeling the illuminance distribution in the detection plane of a spaceborne Offner hyperspectrometer

The modeling of the illuminance distribution in the detection plane of an optical scheme composed of an objective and an Offner spectrometer is conducted. We calculate the illuminance distribution in the detection plane of the hyperspectrometer in the geometric optics approximation. The calculations use models of the atmospheric brightness, earth's surface irradiance, and the spectral transmission of the atmosphere.

From geometric optics to plants: the eikonal equation for buckling.

Optimal buckling of a tissue, e.g. a plant leaf, growing by means of exponential division of its peripheral cells, is considered in the framework of a conformal approach. It is shown that the boundary profile of a tissue is described by the 2D eikonal equation, which provides the geometric optic approximation for the wavefront propagating in a medium with an inhomogeneous refraction coefficient. A variety of optimal surfaces embedded in 3D is controlled by spatial dependence of the refraction coefficient which, in turn, is dictated by the local growth protocol.

Влияние внезапного стратосферного потепления в январе 2009 г. на распространение коротких радиоволн в экваториальной ионосфере

For the first time, we consider the effect of the January 23–27, 2009 sudden stratospheric warming (SSW) event on HF radio wave propagation in the equatorial ionosphere. This event took place during extremely low solar and geomagnetic activity. We use the simulation results obtained with the Global Self-consistent Model of the Thermosphere, Ionosphere and Protonosphere (GSM TIP) for simulating environmental changes during the SSW event. We both qualitatively and quantitatively reproduce total electron content disturbances obtained from global ground network receiver observations of GPS navigation satellite signals, by setting an additional electric potential and TIME-GCM model output at a height of 80 km. In order to study the influence of this SSW event on HF radio wave propagation and attenuation, we use the numerical model of radio wave propagation based on geometrical optics approximation. It is shown that a sudden stratospheric warming leads to radio signal attenuation in the day-time equatorial ionosphere.

Dynamics of zonal flows: failure of wave-kinetic theory, and new geometrical optics approximations

The self-organisation of turbulence into regular zonal flows can be fruitfully investigated with quasi-linear methods and statistical descriptions. A wave-kinetic equation that assumes asymptotically large-scale zonal flows leads to ultraviolet divergence. From an exact description of quasi-linear dynamics emerges two better geometrical optics approximations. These involve not only the mean flow shear but also the second and third derivative of the mean flow. One approximation takes the form of a new wave-kinetic equation, but is only valid when the zonal flow is quasi-static and wave action is conserved.