Optical Wavenumber Research Articles

Angle-of-Arrival Fluctuations and Adaptive Optics Correction in Non-Kolmogorov Turbulent Atmosphere

In this study, angle-of-arrival (AOA) fluctuations of plane and spherical waves propagating through a non-Kolmogorov turbulent atmosphere are examined. Moreover, the effects of adaptive optics compensation are investigated. Here, the terms non-Kolmogorov turbulence spectrum and generalized power-law are used in the sense that the refractive index spectrum is allowed to differ from the classical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa ^{-11/3}$ </tex-math></inline-formula> power law. The AOA variance observed with a circular aperture and various adaptive-optics correction methods is analyzed for plane and spherical waves propagating through non-Kolmogorov turbulence. Results are obtained depending on the power-law exponent, the aperture size, the optical wavenumber, and various combinations of adaptive optics correction methods.

Soliton interactions of a (2+1)-dimensional nonlinear Schrödinger equation in a nonlinear photonic quasicrystal or Kerr medium

Under investigation are the soliton interactions for a (2[Formula: see text]+[Formula: see text]1)-dimensional nonlinear Schrödinger equation, which can describe the dynamics of a nonlinear photonic quasi-crystal or vortex Airy beam in a Kerr medium. With the symbolic computation and Hirota method, analytic bright N-soliton and dark two-soliton solutions are derived. Graphic description of the soliton properties and interactions in a nonlinear photonic quasicrystal or Kerr medium is done. Through the analysis on bright and dark one solitons, effects of the optical wavenumber/linear opposite wavenumber and nonlinear coefficient on the soliton amplitude and width are studied: when the absolute value of the optical wavenumber or linear opposite wavenumber increases, bright soliton amplitude and dark soliton width become smaller; nonlinear coefficient has the same influence on the bright soliton as that of the optical wavenumber or linear opposite wavenumber, but does not affect the dark soliton amplitude or width. Overtaking/periodic interactions between the bright two solitons and overtaking interactions between the dark two solitons are illustrated. Overtaking interactions show that the bright soliton with a larger amplitude moves faster and overtakes the smaller, while the dark soliton with a smaller amplitude moves faster and overtakes the larger. When the absolute value of the optical wavenumber or linear opposite wavenumber increases, the periodic-interaction period becomes longer. All the above interactions are elastic. Through the interactions, soliton amplitudes and shapes keep invariant except for some phase shifts.

Optical propagation through non-overturning, undulating temperature sheets in the atmosphere.

It is a standard assumption in the theory of optical propagation through the turbulent atmosphere that the refractive-index fluctuations n1(x) are statistically isotropic. It is well known, however, that n1(x) in the free atmosphere and in the nocturnal boundary layer is often strongly anisotropic, even at very small scales. Here we present and discuss a model atmosphere characterized by randomly undulating, non-turbulent and non-overturning, quasi-horizontal refractive-index interfaces, or "sheets." We assume n1(x)=v[z-h(x,y)], where v(z) is a random function that has a 1D spectrum V(κz), and where h(x,y) is a vertical displacement that varies randomly as a function of the horizontal coordinates x and y. We derive a closed-form expression for the 3D spectrum Φ(κ) and show that the horizontal 1D spectra have the same power law as V(κz) if the structure function of h(x,y) is quadratic. Moreover, we evaluate the scintillation index σI2 for a plane wave propagating horizontally through the undulating sheets, and we compare σI2 predicted for undulating sheets with Tatarskii's classical predictions of σI2 for fully developed, isotropic turbulence. For Phillips-type sheets, where V(κz)∝κz-2, in the diffraction limit we find σI2∝k (where k=2π/λ is the optical wavenumber), which is only slightly different from Tatarskii's famous k7/6 law for propagation through fully developed, Obukhov-Corrsin-type, isotropic turbulence where Φ(κ)∝κ-11/3. Our model predicts that σI2 is inversely proportional to the sheet tilt angle standard deviation 〈θx2〉, regardless of whether or not diffraction plays a role and regardless of the value of the power-law exponent of V(κz).

Optical binding and the influence of beam structure

An optically induced interparticle potential, applicable to particles of any shape, is derived in a formulation that accommodates the effects of beam structure. The theory allows the consideration of optical binding interactions in beams of spatially varying irradiance and polarization. Results of specific calculations are exhibited for spherical particles in linearly, circularly, and radially polarized Laguerre-Gaussian beams, leading to the identification of several possible optically induced particle arrangements. The patterning of these optically induced structures is shown to have an identical dependence on the optical wavenumber and spot size at the beam waist.

Comparison of scintillation methods for measuring the inner scale of turbulence

One method of inner scale measurement uses the irradiance variance of a diverging monochromatic wave (the irradiance being obtained through a small aperture at the receiver position) and the irradiance variance of a large-aperture C(2)(n) scintillometer. The ratio of these two variances depends on the inner scale of turbulence l(0) but not on the refractive-index structure parameter C(2)(n). Another method uses the bichromatic correlation of irradiances from waves having two different wavelengths, transmitted through a common small aperture (the irradiance being obtained through a small aperture at the receiver position) and the two corresponding monochromatic irradiance variances. The ratio of the bichromatic correlation to the geometric mean of the two monochromatic variances depends on l(0) but not on C(2)(n). A third method is to obtain the ratio of the two monochromatic variances without using the bichromatic correlation. These methods are compared graphically using calculations based on an accurate atmospheric refractive-index spectrum. A scaling analysis is performed to determine the minimum number of parameters needed to describe the methods. It is suggested that systematic errors, rather than signal-to-noise limitations, determine the accuracy with which inner scale is measured. The effects of refractive-index dispersion between the two wavelengths must be taken into account. The results indicate that the bichromatic method has advantages when l(0) less, similar0.6 radicalL/k, whereas the method using small and large apertures has the advantage when l(0) greater, similar0.6 radicalL/k were L is the propagation path length and k is the optical wave number.

Scaling and renormalization in transmittance of thin metal films near the percolation threshold

Recent transmittance measurements of thin metal films near the percolation threshold Pc [Y. Yagil and G. Deutscher, Thin Solid Films 152, 456 (1987)] are interpreted by scaling arguments reflecting the special structure of the film near Pc. Based on the claim that the relevant length scale over which the optical properties are measured is the optical wave number 1/k=λ/2π, we present an argument showing how the optical transmittance scales with this quantity. Our interpretation, based on real-space renormalization, yields a power law wavelength dependence near the percolation threshold, with a coefficient that vanishes at Pc.

Optical beam propagation for a partially coherent source in the turbulent atmosphere

The extended Huygens-Fresnel principle is used to formulate general expressions of the mutual intensity function for a finite optical source with partial spatial coherence propagating in the weakly turbulent atmosphere. Formulations are developed for both the focused and collimated Gaussian beam. Generalized criterion for the effective far-field range is defined in terms of the source aperture, optical wave number, source coherence, and characteristic length associated with the atmospheric turbulence. Beam spread and lateral coherence length in the near and far field are investigated for a combination of parameter variations and the physical implications discussed. Finally, analytic results are calculated and plotted to illustrate the functional behavior of relevant physical parameters.

Physical model for strong optical-amplitude fluctuations in a turbulent medium

Tatarskii’s geometrical-optics model of scintillation has been generalized to include both diffraction and the loss of spatial coherence of the wave as it propagates through the turbulent medium. An estimate is obtained of the amplitude fluctuations that agrees with the results of perturbation theory for σϒ2⪡1 and saturates to a constant value of the order unity for σT2⪢1 ( σT2 is the amplitude variance calculated on the basis of perturbation theory). In addition, we have calculated the amplitude correlation function. For σT2⪡1, the amplitude correlation function agrees with the results of perturbation theory and for the Kolmogorov spectrum is characterized by a correlation length of the order (L/k)1/2, where L is the propagation distance and k is the optical wave number. Conversely, for σT2⪢1 the amplitude correlation length decreases with increasing propagation distance and is shown to be equal to the lateral coherence length of the wave ρ0(L). In this regime, a residual correlation tail is obtained in agreement with recent experiments.