Wave Propagation in a One‐Dimensional Random Medium

Bassanini, Piero

doi:10.1002/rds196724429

Cited by 4 publications

(5 citation statements)

References 10 publications

(8 reference statements)

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“…Unfortunately this method cannot be generalized to other equations such as the electromagnetic wave equation (3). Finally, it must be stressed that no rigorous mathematical treatment (existence, unity) of (21) has been given up to now. This is mainly because one is not able to solve linear partial differential equations with nonconstant coefficient in the large.…”

Section: Random Equationsmentioning

confidence: 99%

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Theoretical Aspects of Wave Propagation in Random Media Based on Quanty and Statistical Field Theory

Blaunstein¹

2004

PIER

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Abstract-In this work, we summarize the existing theoretical methods based on statistical and quanty theory and give some non-standard mathematical approaches based on such theories to explain the principal scalar and vector electrodynamic problems for future applications to acoustic, radio and optical wave propagation in homogeneous, isotropic, anisotropic and inhomogeneous media. We show of how the statistical description of wave equations can be evaluated based on quantum field theory with presentation of Feynman's diagrams by a limited-to-zero finite set of expanded Green functions according to perturbation theory for single, double, triple, etc, scattering phenomenon. It is shown that at very short wavelengths, the Green's function is damped over a few wavelengths if the refractive index fluctuations in the medium are strong; at long wavelengths the effective phase velocity of electromagnetic waves may be increased. It is shown, that the coupling between different wave modes and the energy transfer between different wave modes, may be important, even for week random fluctuations of parameters of the medium, but it takes a very long time.

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Section: Random Equationsmentioning

confidence: 99%

“…It is then possible to get an exact solution of (21) through functional integration, which gives all the moments of the wave functions in terns of mean value and covariance of n 2 (r) (see Section 7). Unfortunately this method cannot be generalized to other equations such as the electromagnetic wave equation (3).…”

Section: Random Equationsmentioning

confidence: 99%

Theoretical Aspects of Wave Propagation in Random Media Based on Quanty and Statistical Field Theory

Blaunstein¹

2004

PIER

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“…ator BiW) are defined by and ex P ress the Physical operators in terms of them." Here, the new operators have the same algebraic relab{8/8j e (t 1 ))G(t h t 2 ) = [ dtAa(h,t)G(t,t 2 ), tions as those for ^h e ol f operators, and hence their j as U is of q, p, and j), we find that q= U~1qU=q-im(2v)~' 1 p+mv~2j, p = p +i v -ij y jss j 9 (3.28)…”

Section: G a Fi(t H T2) = -I(t[}//a(ti)\f/^(t2)l}mentioning

confidence: 91%

“…On the other hand, the solution of the Fokker-Planck equation (2.6) for the Hamiltonian (3.31) may be expressed by (Q2^2 f \qi^i) in terms of the new operators in the same way as for the original operators. Here, using where q4=q4 } ft4 = fa' y q4 = q4 9 and tfei / =^i / . The two stationary states 10) and (01 were originally defined by (2.40) and (2.18b) with respect to the medium and, using (3.28), the equations for these states are found to be expressed exactly by for vanishing external sources r)-^ = k~ j e =0* Hence, these stationary states are found to be the eigenvectors of the new operators, and the evaluation of expectation values of physical quantities may become easier in view of (2.47).…”

Section: Dq/dt^lqfi^-vq-i^lqa^-i^lq^ Dp/dt=vp-itf[_pa-]i-i^lprflmentioning

confidence: 98%

Application of the Methods of Quantum Mechanics in the Statistical Theory of Waves in a Fluctuating Medium

Furutsu¹

1968

Phys. Rev.

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The basic equations for the statistical system of waves in a randomly fluctuating medium are presented in the same form as in quantum mechanics, assuming a Markov process for the temporal change of the medium. A simple model is chosen for the Fokker-Planck equation of the medium which gives rise to a fluctuation of the Gaussian process, and several results are given to illustrate how the methods used in quantum mechanics or quantum field theory can be applied almost without change. Thus, the physical variables are represented by linear operators, and their equations of motion are determined by an equation similar to the Heisenberg equation of motion. The system has two stationary states (corresponding to the vacuum states (0| and |0) in quantum field theory), and the rather standard methods in field theory can be used for the evaluation of the Green's functions. When the temporal changes of the medium are sufficiently large compared with those of the waves, an adiabatic approximation is possible, and the isomorphic transformation (corresponding to the unitary transformation) is employed to lead to the result that the statistical system of the waves for this model is in perfect correspondence with the waves of bosons which interact with each other only through a two-body potential.

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“…The propagation of radio, acoustic, and optical waves through random media was a subject matter of investigation due to the practical interest, particularly in terrestrial, atmospheric, and ionospheric (e.g., plasma) media [1][2][3][4][5][6][7][8][9][10][11][12]. Also, it was of interest in connection with work in optical communications, imaging, and targeting systems to understand the effects of turbulence on the propagation of beams [13][14][15][16][17], in order to minimize the beams distortion as little as possible by the presence of the fluidic media.…”

Section: Introductionmentioning

confidence: 99%

Spectral Intensity Variation by the Correlation Function of Refractive Index Fluctuations of the Liquid Medium

Singh

2013

International Journal of Optics

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It is proposed that a macroscopic theory of propagation and scattering of light through random media can be functional for the dye liquid flowing media in the microscopic levels too, with modest approximations. Maxwell’s equation for a random refractive index medium is approximated and solved for the electric field. An analytical expression for the spectral intensity of the field scattered by the refractive index fluctuations inside a medium has been derived which was valid within the first Born approximation. Far field spectral intensity variation of the radiation propagating through the liquid medium is a consequence of variation in correlation function of the refractive index inhomogeneities. The strength of radiation scattered in a particular direction depends on the spatial correlation function of the refractive index fluctuations of the medium. An attempt is made to explain some of the experimentally observed spectral intensity variations, particularly dye emission propagation through liquid flowing medium, in the presence of thermal and flow field.

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Wave Propagation in a One‐Dimensional Random Medium

Cited by 4 publications

References 10 publications

Theoretical Aspects of Wave Propagation in Random Media Based on Quanty and Statistical Field Theory

Theoretical Aspects of Wave Propagation in Random Media Based on Quanty and Statistical Field Theory

Application of the Methods of Quantum Mechanics in the Statistical Theory of Waves in a Fluctuating Medium

Spectral Intensity Variation by the Correlation Function of Refractive Index Fluctuations of the Liquid Medium

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