Generalized definition of group velocity of signal in dispersive medium and its application to very short pulses in waveguides

1967 ◽  
Vol 17 (3) ◽  
pp. 203-215 ◽  
Author(s):  
J. L. Klapka
Keyword(s):  
Group Velocity ◽  
Dispersive Medium ◽  
Short Pulses ◽  
Definition Of ◽  
Very Short Pulses

On the Group Front and Group Velocity in a Dispersive Medium Upon Refraction From a Nondispersive Medium

2004 ◽  
Vol 126 (2) ◽  
pp. 244-249 ◽  
Author(s):  
Z. M. Zhang ◽  
Keunhan Park
Keyword(s):  
Wave Packet ◽  
Phase Velocity ◽  
Wave Front ◽  
Group Velocity ◽  
Dispersive Medium ◽  
Front Velocity ◽  
Nondispersive Medium ◽  
Definition Of ◽  
Positive Index ◽  
Special Case

Conventional definitions of velocities associated with the propagation of modulated waves cannot clearly describe the behavior of the wave packet in a multidimensional dispersive medium. The conventional definition of the phase velocity, which is perpendicular to the wave front, is a special case of the generalized phase velocity defined in this work, since there exist an infinite number of solutions to the equation describing the wave-front movement. Similarly, the generalized group-front velocity is defined for the movement of a wave packet in an arbitrary direction. The group-front velocity is the smallest speed at which the group-front travels in the direction normal to the group front. The group velocity, which is the velocity of energy flow in a nondissipative medium, also satisfies the group-front equation. Because the group-front velocity and the group velocity are not always the same, the direction in which the wave packet travels is not necessarily normal to the group front. In this work, two examples are used to demonstrate this behavior by considering the refraction of a wave packet from vacuum to either a positive-index material (PIM) or a negative-index material (NIM).

ON THE THEORY OF THE DOPPLER EFFECT IN A MOVING MEDIUM

1998 ◽  
Vol 13 (01) ◽  
pp. 1-6 ◽  
Author(s):  
BRUNO BERTOTTI
Keyword(s):  
Solar Wind ◽  
Doppler Effect ◽  
Dispersive Medium ◽  
Time Derivative ◽  
Optical Path ◽  
Moving Medium ◽  
Perturbation Theorem ◽  
Hamiltonian Theory ◽  
The Doppler Effect ◽  
Definition Of

The increase in the accuracy of Doppler measurements in space requires a rigorous definition of the observed quantity when the propagation occurs in a moving, and possibly dispersive medium, like the solar wind. This is usually done in two divergent ways: in the phase viewpoint it is the time derivative of the correction to the optical path; in the ray viewpoint the signal is obtained form the deflection produced in the ray. They can be reconciled by using the time derivative of the optical path in the Lagrangian sense, i.e. differentiating from ray to ray. To rigorously derive this result an understanding, through relativistic Hamiltonian theory, of the delicate interplay between rays and phase is required; a general perturbation theorem which generalizes the concept of the Doppler effect as a Lagrangian derivative is proved. Relativistic retardation corrections O(v) are obtained, well within the expected sensitivity of Doppler experiments near solar conjunction.

scholarly journals Another Note on Rossby Wave Energy Flux

2020 ◽  
Vol 50 (2) ◽  
pp. 531-534
Author(s):  
Theodore S. Durland ◽  
J. Thomas Farrar
Keyword(s):  
Group Velocity ◽  
Energy Flux ◽  
Rossby Wave ◽  
Wave Energy ◽  
Energy Equation ◽  
Divergent Part ◽  
Pressure Work ◽  
Wave Energy Flux ◽  
The Difference ◽  
Definition Of

AbstractLonguet-Higgins in 1964 first pointed out that the Rossby wave energy flux as defined by the pressure work is not the same as that defined by the group velocity. The two definitions provide answers that differ by a nondivergent vector. Longuet-Higgins suggested that the problem arose from ambiguity in the definition of energy flux, which only impacts the energy equation through its divergence. Numerous authors have addressed this issue from various perspectives, and we offer one more approach that we feel is more succinct than previous ones, both mathematically and conceptually. We follow the work described by Cai and Huang in 2013 in concluding that there is no need to invoke the ambiguity offered by Longuet-Higgins. By working directly from the shallow-water equations (as opposed to the more involved quasigeostrophic treatment of Cai and Huang), we provide a concise derivation of the nondivergent pressure work and demonstrate that the two energy flux definitions are equivalent when only the divergent part of the pressure work is considered. The difference vector comes from the nondivergent part of the geostrophic pressure work, and the familiar westward component of the Rossby wave group velocity comes from the divergent part of the geostrophic pressure work. In a broadband wave field, the expression for energy flux in terms of a single group velocity is no longer meaningful, but the expression for energy flux in terms of the divergent pressure work is still valid.

XXIX.—On Group-Velocity and on the Propagation of Waves in a Dispersive Medium

1909 ◽  
Vol 29 ◽  
pp. 445-470 ◽  
Author(s):  
George Green
Keyword(s):  
Group Velocity ◽  
Dispersive Medium ◽  
Light Waves ◽  
Propagation Of Waves

§ 1. The theory of group-velocity has been developed by Stokes, Osborne Reynolds, Lord Rayleigh, and later by Professor Lamb. The application of the theory to light-waves was made by Gouy and Lord Rayleigh, and its importance in this connection was emphasised by Professor Schuster in his paper “On Interference Phenomena,” Phil. Mag., vol. xxxvii., 1894.

XI.—On Waves in a Dispersive Medium resulting from a Limited Initial Disturbance

1910 ◽  
Vol 30 ◽  
pp. 242-253 ◽  
Author(s):  
George Green
Keyword(s):  
Stationary Phase ◽  
Group Velocity ◽  
Dispersive Medium ◽  
Initial Disturbance ◽  
Wave System ◽  
Satisfactory Explanation ◽  
Modus Operandi ◽  
Propagation Of Waves

§ 1. In a former paper “On Group-Velocity and on the Propagation of Waves in a Dispersive Medium” (Proc. R.S.E., xxix. pp. 445–470, 1909), it was shown that group-velocity, or the principle of “stationary phase,” provides us with a satisfactory explanation of the modus operandi of dispersion; and the principle was applied to obtain an expression for the effect of a single impulse confined to the neighbourhood of a point of the medium. The present paper is intended to fulfil a promise given in § 29 of that paper, to show that by means of this principle we can arrive at the general features of the wave-system in a dispersive medium resulting from any limited initial disturbance.

scholarly journals LOCALIZATION OF MACROMOLECULES IN ESCHERICHIA COLI

1961 ◽  
Vol 9 (3) ◽  
pp. 539-553 ◽  
Author(s):  
Lucien G. Caro
Keyword(s):  
Escherichia Coli ◽  
Poisson Distribution ◽  
Cross Sections ◽  
Morphological Changes ◽  
Nuclear Region ◽  
High Concentration ◽  
Short Pulses ◽  
Thin Sections ◽  
Change Concerns ◽  
Very Short Pulses

If thin sections of Escherichia coli, labeled uniformly with tritium, are radioautographed calculations, based on the distribution of section sizes show that the number of H3 decays per section should be very close to a Poisson distribution. We might, therefore, expect that the distribution of radioautographic grain counts among random cross-sections should follow a Poisson distribution. It can then be inferred that a deviation from a Poisson indicates a high concentration of label in a preferred region. This region can then be identified by analysis of serial section and comparison with electron micrographs. Sections of cells labeled with leucine-H3 gave a Poisson distribution of grain counts, and it was concluded that proteins were distributed fairly uniformly throughout the cell. The situation was not changed if labeled cells were placed in chloramphenicol or if very short pulses of label were used. When Escherichia coli is grown in presence of chloramphenicol a major morphological change concerns the nuclear region: it becomes more regular in outline, nearly spherical, and occupies a smaller proportion of the cell length. The previously described association between DNA labeled with thymidine-H3 and the nuclear region was confirmed by showing that the distribution of the label in the cell followed exactly the morphological changes of the nuclear region. It was also shown that the concentration of DNA in the nuclear region was at least 45 times higher than that of the cytoplasm. Several morphological features of cells grown in chloramphenicol and examined in the electron microscope are discussed.

The response of 741 op amps to very short pulses

1980 ◽  
Vol 15 (5) ◽  
pp. 908-910 ◽  
Author(s):  
V.G. Ruediger ◽  
B.J. Hosticka
Keyword(s):  
Short Pulses ◽  
Op Amps ◽  
Very Short Pulses

Measurement of group-velocity walk-off of short pulses in nonlinear crystals: a novel method

1995 ◽  
Vol 20 (4) ◽  
pp. 392 ◽  
Author(s):  
X. D. Cao ◽  
L. Zheng ◽  
D. D. Meyerhofer
Keyword(s):  
Group Velocity ◽  
Short Pulses ◽  
Nonlinear Crystals ◽  
Novel Method
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