The reference wave solution for a two-frequency wave propagating in a random medium

Bronshtein, Alexander; Mazar, Reuven

doi:10.1088/0959-7174/12/3/301

Cited by 10 publications

(5 citation statements)

References 11 publications

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“…Exact and Asymptotic Solutions for Narrow-Band Geometrical Optics. Neither (27) nor the resulting equation for Γ 12 is exactly solvable and various approximations have been proposed (see [3], [12], [15], [18], [19], [21], [23]). However, the geometrical optics limit…”

Section: Time Reversal Of Parabolic Waves and Two-frequency Wigner Di...mentioning

confidence: 99%

Time reversal of parabolic waves and two-frequency Wigner distribution

Fannjiang¹,

Sølna²

2006

Discrete &Amp; Continuous Dynamical Systems - B

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We consider propagation and time reversal of wave pulses in a random environment. The focus of our analysis is the development of an expression for the two frequency mutual coherence function for the harmonic wave field. This quantity plays a crucial role in the analysis of many wave propagation phenomena and we illustrate by explicitly considering time reversal in the context of time pulses with a high carrier frequency. In a time-reversal experiment the wave received by an active transducer or antenna (receiver-emitter) array, is recorded in a finite time window and then re-emitted into the medium time reversed, that is, the tails of the recorded signals are sent first. The re-emitted wave pulse will focus approximately on the original source location. We use explicit expressions for the mutual coherence functions and their asymptotic approximations in the regime of long or short propagation distance and a high carrier frequency to analyze the refocusing of the wave pulse in the time reversal experiment. A novel aspect of our analysis is that we are able to characterize precisely the decoherence length in temporal frequency. This allows us to analyze for instance the time reversal experiment when the mirror has a finite aperture in time.

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Section: Time Reversal Of Parabolic Waves and Two-frequency Wigner Di...mentioning

confidence: 99%

Time reversal of parabolic waves and two-frequency Wigner distribution

Fannjiang¹,

Sølna²

2006

Discrete &Amp; Continuous Dynamical Systems - B

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“…(22), expanding the refractive index function, and applying the averaging procedure as in the section (3), we arrive to the expression for the two-frequency mutual coherence function obtained by the reference-wave method [5].…”

Section: Two-frequency Mutual Coherence Functionmentioning

confidence: 99%

“…For computations of the statistical field measures it is desirable to possess a field solution that accounts for the information accumulated by the propagating field along an isolated ray path. Such solutions have been derived for the homogeneous background case [3,4] using a recently developed reference wave method (RWM) for solving parabolic type wave equations [5]. The methodology is based on defining a paired field measure as a product of an unknown field propagating in a disturbed medium and the complex conjugate component propagating in a medium without random fluctuations.…”

Section: Introductionmentioning

confidence: 99%

Reference-wave solutions for the high-frequency fields in random media

Mazar

Bronshtein

2004

SPIE Proceedings

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Ray theory plays an important role in determining the propagation properties of high-frequency fields and their statistical measures in complicated random environments. For computations of the statistical measures it is desirable therefore to possess a solution for the high-frequency field propagating along an isolated ray trajectory. In this work a reference wave is applied to obtain an analytic solution of the parabolic wave equation describing propagation along the ray trajectory of the deterministic background medium. The methodology is based on defining a paired field measure as a product of an unknown field propagating in a disturbed medium and the complex conjugate component propagating in a medium without random fluctuations. Once a solution of the equation for the paired field measure is obtained, the solution of the unknown field can be determined in an explicit form by extracting from the paired solution the solution of the deterministic component.

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“…Among recent results, the method developed in the papers by Bitjukov et al [2002Bitjukov et al [ , 2003 to asymptotically solve the two-frequency two-position Markov's parabolic equation, based on the quasi-classic approximation with complex trajectories, seems to be the most general. It produces automatically other known solutions to this equation [Sreenivasiah et al, 1976;Knepp, 1983a;Oz and Heyman, 1996, 1997a, 1997b, 1997cBronshtein and Mazar, 2002]. However, even the exhaustive knowledge of the two-frequency two-position coherence functions (both, the first and second) is not sufficient to comprehensively characterize the transionospheric fluctuating channel of propagation.…”

Section: Introductionmentioning

confidence: 99%

Propagation model for transionospheric fluctuating paths of propagation: Simulator of the transionospheric channel

2005

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[1] A new model for scintillation on transionospheric links, based on a hybrid method and valid for strong scintillations, has been developed and used to construct a software transionospheric channel simulator. The method is a combination of the complex phase method and the random screen technique. The parameters of the random screen are determined as the result of a rigorous solution to the problem of propagation inside the ionosphere using the extended Rytov approximation (the complex phase method). The random two-dimensional spatial spectrum at the screen is then transferred down to the Earth's surface employing the rigorous relationships of the random screen theory. Thus the complex phase method can adequately introduce a random screen below the ionosphere for L-band frequencies. The technique is capable of producing statistical characteristics and simulating time realizations of the field for a wide range of input parameters. Preliminary results are presented for both weak and strong scintillations.

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The reference wave solution for a two-frequency wave propagating in a random medium

Cited by 10 publications

References 11 publications

Time reversal of parabolic waves and two-frequency Wigner distribution

Time reversal of parabolic waves and two-frequency Wigner distribution

Reference-wave solutions for the high-frequency fields in random media

Propagation model for transionospheric fluctuating paths of propagation: Simulator of the transionospheric channel

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