Quasi-optical Approximation Research Articles

Field structures in nonlinear large-aperture cavity schemes with lens elements

An equation for the slowly varying envelope of a field in a large-aperture interferometer or a laser with intracavity lens elements is obtained using the quasi-optical approach and mean-field approximation. The case of a negative diffraction length of the cavity is analyzed. Ways for determining the transverse dimensions of dissipative spatial optical solitons in nonlinear interferometers and lasers are discussed.

Calculation of Radiation from a Helically Cut Waveguide for a Gyrotron Mode Converter in the Quasi-Optical Approximation

We present results of calculations of the radiation from a helically cut waveguide launcher, a so-called Vlasov launcher, which is commonly used either internal or external to a gyrotron for purposes of mode conversion. A gyrotron internal mode converter consists of such a launcher that radiates the waveguide mode as a nearly Gaussian beam in free space followed by a set of mirrors to focus and direct the radiation. The radiation from the launcher is first calculated using a geometric optics representation of the waveguide mode. Then the radiation is calculated in the quasi-optical limit, including diffraction. These analytic results are compared to a rigorous calculation using the computer code SURF3D, which uses an electric field integral equation (EFIE) approach. Good agreement is obtained between the quasi-optical theory and the SURF3D calculation. The present results provide new insights into the accuracy of the quasi-optical theory and may be useful for the design and improvement of Vlasov-type mode converters.

Formation, propagation, and focusing of acoustic beams in oceanic waveguides. The quasi-optics approximation

Using the WKB approximation and assuming that the spatial spectrum of modes excited by a vertical array is sufficiently narrow, a quasi-optical theory is developed to describe the fundamental regularities manifesting themselves in the formation, propagation, and focusing of multimode acoustic beams in oceanic waveguides. Functional dependences on the parameters of both the transmitting array and the oceanic waveguide are obtained for horizontal distances at which ordinary beams form refraction focusing zones. Conditions ensuring the formation of a beam with the minimum wave front divergence are formulated for the distribution of the source excitation factor over the array aperture.

Effect of dissipation on the propagation of wave beams in inhomogeneous anisotropic and gyrotropic media

For wave beams propagating in inhomogeneous anisotropic absorbing media with spatial dispersion, a quasi-optical approximation is developed that makes it possible to account for the combined influence of the refraction, diffraction, and dissipation effects. It is shown that, in the aberration-free approximation, the problem of calculating the beam structure is reduced to that of solving a set of ordinary differential equations for the parameters of the kernel of an integral transformation and calculating the convolution with the spatial Fourier spectrum of the initial field distribution. In particular, the case of a Gaussian beam is analyzed. The applicability limits of the aberration-free solution, which are especially relevant to the ECR absorption regime, are discussed. The effect of aberrations associated with the Hermitian and anti-Hermitian parts of the dielectric tensor of the medium is considered. It is found that the beam deviates toward the region of weaker absorption and that, during the deviation, the beam may become wider or narrower, depending on the type of the inhomogeneity. It is demonstrated that, when absorption is taken into account correctly, the width of the power deposition region during plasma heating in controlled fusion devices can turn out to be substantially larger than that given by the existing estimates.

Nonstationary 2D models of the electron-wave interaction

A 2D nonstationary model of induced emission of ribbon-shaped electron beams and clusters in free space is developed in the quasi-optical approximation. On the basis of this model, the problem of enhancement of a short electromagnetic pulse propagating along a quasi-stationary ribbon electron flow, the theory of a BWT-type oscillator with radiation channeling by an electron beam, and the process of collective acceleration of a short electron cluster in the field of an intense cocurrent wave are considered.

Application of corpuscular and wave Monte-Carlo methods in optics of dispersive media

Two ways of simulating statistically the propagation of laser radiation in dispersive media by the Monte-Carlo method are compared. The first approach can be called corpuscular because it is based on the calculation of random photon trajectories, while the second one can be referred to as the wave approach because it is based on the calculation of characteristics of random wave fields. It is shown that, although these approaches are based on different physical concepts of radiation scattering by particles, they yield almost equivalent results for the intensity of a restricted beam in a dispersive medium. However, there exist some differences. The corpuscular Monte-Carlo method does not reproduce the diffraction divergence of the beam, which can be taken into account by introducing the diffraction factor. The wave method does not consider backscattering, which corresponds to the quasi-optical approximation.

On a Gaussian beam in an amplifying medium

The model of a Gaussian beam in an amplifying medium is analyzed within the framework of the paraxial (quasi-optical) approximation. Upon violation of the obtained restrictions, the model leads to a physically inconsistent conclusion about an infinitely high radiation power after a passage of an ordinary Gaussian beam through a layer of the amplifying medium. The importance of a limitation on the transverse dimensions of the amplifying medium or of the introduction of intracavity angular selection is demonstrated. The fundamental mode in the form of a Gaussian beam appears in the model with a quadratic dependence of the gain on the transverse coordinates.

Diffractive Multifocal Focusing of Gaussian Beams

The problem of diffraction of a spherical wave with Gaussian amplitude distribution on two infinitesimally thin and ideally reflecting screens with apertures on an optical axis is solved within the quasi-optical approximation. It is shown that when a Gaussian beam illuminates a bicomponent diffraction system with small Fresnel numbers in a near zone of the second screen, the effect of diffractive multifocal focusing of radiation is observed. In this case, the diffraction picture from the second screen in the focal planes represents the circular nonlocal bands of the Fresnel zones with a bright narrow peak at the center, whose intensity can exceed by six times the value of the incident wave intensity. The energy efficiency of diffractive focusing of Gaussian beams by the bicomponent diffraction system can be as high as 70%. The proposed diffractive method allows the focusing of the wide-aperture beams without using classical refraction elements such as lenses and prisms, and it is applicable to both low-intensive and high-power radiation.

Diffractive Focusing of a Gaussian Beam

The problem of diffraction of a spherical wave with Gaussian amplitude distribution on two infinitesimally thin and ideally reflecting screens with apertures on an optical axis is solved within the framework of the quasi-optical approximation. It is shown theoretically and experimentally that when a Gaussian beam illuminates such a type of bicomponent diffraction system with small Fresnel numbers in a near zone of the second screen, the effect of diffractive multifocal focusing of radiation is observed. In this case, the diffraction picture from the second screen in the focal planes represents the circular nonlocal bands of the Fresnel zones with a bright narrow peak at the center, whose intensity can exceed by six times the value of the incident wave intensity. The energy efficiency of diffractive focusing of Gaussian beams by the bicomponent diffraction system can be as high as 70%. The diffractive method proposed allows the focusing of wide-aperture beams without using classical refraction elements such as lenses and prisms, and it is applicable to both low-intensity and high-power radiation.

Wave packets in smoothly inhomogeneous dispersive media

In the quasi-optical aberration-free approximation, a parabolic equation for the envelope of an electromagnetic wave packet propagating along a geometric optical ray in a smoothly inhomogeneous isotropic medium with time dispersion is obtained. The corresponding Green’s function is found whose parameters are determined by integrating a system of ordinary differential equations. The effects of the combined influence of the refraction, diffraction, and dispersion on the evolution of the packet are analyzed; in particular, the effects that cause precession of the envelope waves about the binormal to the propagation trajectory are considered.

Polarized radiative transfer in plasmas with sheared magnetic field

The propagation of electromagnetic waves through a (homogeneous) plasma (slab) in a sheared magnetic field is dealt with by adopting a frame of reference which follows the local direction of the magnetic field. The choice of such a local reference frame is particularly appropriate in order to obtain both the dispersion relation and the polarization of the two eigenmodes relevant to the radiative transfer at an arbitrary angle with respect to the magnetic field, and, in particular, so that no linear mode coupling occurs in the limit of uniform shear. The dispersion relation thus obtained is discussed in detail and the conditions for which the true eigenmodes of a sheared plasma can be identified with the extraordinary and ordinary mode in the absence of shear are assessed. Effects due to the non-uniformity of the magnetic shear are also considered in a quasi-optical approximation and the consequent imaginary part of the refractive index is discussed in the context of the transport equation for the electromagnetic energy density.

The effect of focusing on the parametric interaction of Gaussian sound beams

Using the method of quasi-optical approximation we study the parametric interaction of Gaussian sound beams with wave fronts having different radii of curvature on the boundary. We give a numerical and analytic analysis of the behavior of the amplitudes of a wave at the difference frequency in the cases when: 1) the focal length of one of the primary waves varies and the other is fixed (large or small in comparison with the length of the diffraction zone); 2) the focal lengths of both primary high-frequency waves are equal in absolute value.

Characteristics of modes in a crossed-flute optical cavity

A numerical analysis is made of azimuthally uniform modes in a crossed-flute cavity with central apertures in the mirrors. The complex frequencies and the mode field distributions are calculated by the Galerkin method in the quasi-optical approximation. The characteristics both of the principal mode with an annular field distribution and of the nearest higher-order modes are considered as a function of the cavity parameters. It is shown that modes with low radiation losses may exist in the presence of relatively large aperture at the mirror centres.

On permittivity measurement by a resonance method

In a quasioptical approximation we develop a theory of an open cavity with a dielectric plate placed normally to the cavity axis. We find conditions under which some natural frequencies of the cavity are practically independent of the plate position in the cavity. From experimental measurements of one of these frequencies and with variation of the length of the cavity with and without the plate, with the same oscillation- mode structure, we determine the refractive index and plate thickness. Coincidence between the obtained (“design”) thickness and mechanically measured one is a correctness criterion for the results obtained.

Mirror conversion of gaussian beams with simple astigmatism

The surface of an inclined mirror, which converts Gaussian beams with simple astigmatism hase been found within the quasi-optical approximation. The beam reflected from the found mirror was examined. Power losses of the reflected beam, when the beam is incident on a selective system, which transmits a Gaussian beam of one polarization only have been found.

The barrel shaped resonator for the photon storage ring

The eigenmodes of a barrel shaped resonator are analyzed to optimize the optical cavity of the photon storage ring. The results are obtained by the Galerkin technique and the quasi-optics approximation. It is shown that there are two types of eigenmodes in the system: the quasi-E and quasi-H modes. The dependences of the mode losses and the field distribution on the resonator geometry and wall impedances are examined. The effects of intermodal coupling are considered.

Selection of a phase-conjugate wave in an oscillator based on a four-wave interaction with feedback in an extended nonlinear medium

A quasi-optical approximation without allowance for beam spreading over its envelope is used to show that selection of a conjugate wave occurs in a volume hologram whose dimensions are greater than the longitudinal correlation length of the fields forming the hologram. The condition under which the signal power exceeds the noise power is found. Phase conjugation of a speckle field with a divergence of 2×10-2 by a four-wave interaction with feedback was achieved experimentally for neodymium-activated glass and the efficiency was 5%. The input energy threshold was 100 mJ and the maximum energy in the phase-conjugate wave was 10 mJ.

Stimulated Rayleigh-line-wing scattering in nematic liquid crystals

The effect of self-focusing on backward stimulated Rayleigh-line-wing scattering is analyzed in the quasioptical approximation. The longitudinal length scale over which the stimulated scattering develops and also the gain depend on the parameter α = 1 – P/Pcr, where P is the pump power, and Pcr is the critical power for self-focusing. The correlation function and the gain for the scattered radiation are calculated for stimulated scattering in the isotropic phase of nematic liquid crystals. The behavior of these properties near the phase transition to the mesophase is discussed.

Mathematical Simulation of Pressure Pulse Propagation in Biological Tissues

The propagation of pressure pulses of arbitrary time form in inhomogeneous attenuating media with characteristics similar to real biological tissues is considered. A mathematical model using the quasi-optical approximation is developed to solve the wave equation. Such a model proves to be convenient for computer realization. A spectral analysis of known experimental data on frequency dependent backscatter is realized to separate coherent and incoherent components of backscatter from tissues and determine their parameters. The characteristics of the scattering are utilized for digital simulations of ultrasound propagation from an interrogated tissue volume. The results presented describe the expected space distribution of the pressure amplitude and phase near the transducer focus in the presence of an aberrating layer with parameters characteristic of abdominal imaging.

Mathematical Simulation of Pressure Pulse Propagation in Biological Tissues

The propagation of pressure pulses of arbitrary time form in inhomogeneous attenuating media with characteristics similar to real biological tissues is considered. A mathematical model using the quasi-optical approximation is developed to solve the wave equation. Such a model proves to be convenient for computer realization. A spectral analysis of known experimental data on frequency dependent backscatter is realized to separate coherent and incoherent components of backscatter from tissues and determine their parameters. The characteristics of the scattering are utilized for digital simulations of ultrasound propagation from an interrogated tissue volume. The results presented describe the expected space distribution of the pressure amplitude and phase near the transducer focus in the presence of an aberrating layer with parameters characteristic of abdominal imaging.