What is the relation between phase velocity and group velocity in a dispersive medium?
Vg is the group velocity. Vp is the phase velocity. k is the angular wavenumber.
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Group Velocity and Phase Velocity relation for Dispersive wave non-dispersive wave.
| Type of wave | Condition | Formula |
|---|---|---|
| Dispersive wave | d V p d k ≠ 0 | V p ≠ V g |
| Non-dispersive wave | d V p d k = 0 | V p = V g |
What is the group velocity and phase velocity?
Phase and group velocity are related through Rayleigh’s formula, If the derivative term is zero, group velocity equals phase velocity. In this case, there is no dispersion. Dispersion is when the distinct phase velocities of the components of the envelope cause the wave packet to “spread out” over time.
What is phase velocity and group velocity in optical fiber?
The phase velocity of light is the velocity with which phase fronts propagate in a medium. It is related to the wavenumber k and the (angular) optical frequency ω: In vacuum, the phase velocity is c = 299 792 458 m/s, independent of the optical frequency, and equals the group velocity.
In which medium phase velocity and group velocity are equal?
Dispersion. When these two monochrome waves are propagating in vacuum, they have the same phase velocity c (the speed of light in vacuum), and the superposed wave’s phase velocity equals its group velocity(both are c).
What is the relation between VG and VP?
Solution: The product of the phase and the group velocities is given by the square of the speed of the light. Thus Vp x Vg = c2 is the relation.
Why group velocity is less than phase velocity in dispersive medium?
Hence, the group velocity is less than the phase velocity
Dispersion is when the distinct phase velocities of the components of the envelope cause the wave packet to “Spread out” over time.
What is group velocity formula?
In a given medium, the frequency is some function ω(k) of the wave number, so in general, the phase velocity vp= ω/k and the group velocity vg = dω/dk depend on the frequency and on the medium. The ratio between the speed of light c and the phase velocity vp is known as the refractive index, n = c/vp = ck/ω.
Which is greater group velocity or phase velocity?
For most substances, therefore, the group velocity is smaller than the phase velocity.
What is group velocity in optical fiber?
The group velocity is the velocity with which the envelope of a pulse propagates in a medium, assuming a not too short pulse with narrow bandwidth (so that higher-order chromatic dispersion is not relevant) and the absence of nonlinear effects (i.e., low enough optical intensities).
Is the group velocity faster or slower than phase velocity?
But since in the anomalous region the group velocity is faster than the phase velocity, it is no longer equal to the speed of information transfer.
What is phase velocity formula?
Phase velocity defines the speed at which waves oscillating at a particular frequency propagate. Like the wavelength, the phase velocity depends on the real component of the wavenumber ( ) and is given by: v p h = ω α = ( μ ϵ 2 [ ( 1 + σ 2 ϵ 2 ω 2 ) 1 / 2 + 1 ] ) − 1 / 2.
What is meant by group velocity?
The group velocity of a wave is the velocity with which the overall envelope shape of the wave’s amplitudes—known as the modulation or envelope of the wave—propagates through space.
Can the group velocity be zero?
Zero-group-velocity (ZGV) waves have the peculiarity of being stationary, and thus locally confining energy. Although they are particularly useful in evaluation applications, they have not yet been tracked in two dimensions.
How phase velocity and group velocity are same When light travels in a medium?
Product of phase velocity and group velocity is equal to square of speed of light. ➢ Vg=Vp for a non-dispersive medium ( in a non-dispersive medium all the waves travel with phase velocity).
Can group velocity be greater than phase velocity?
For most substances, therefore, the group velocity is smaller than the phase velocity. In such cases, it is mathematically possible that the group velocity may be larger than the phase velocity.
Why is phase velocity faster than light?
So if you interfere two plane waves propagating in opposite directions, but off by a fraction of a degree from being exactly opposite, the interference pattern will produce humps that propagate faster than the speed of light.
What do you mean by phase velocity?
The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity.
What is the formula of group velocity?
u=dωdk|k=k0 (group velocity). The derivative of ω(k) with respect to k is first computed and then evaluated at k=k0 the central wavenumber of the wave packet of interest. The relationship between the angular frequency and the wavenumber for a wave, ω=ω(k) depends on the type of wave being considered.
Can group velocity be higher than phase velocity?
Which one is greater phase velocity and group velocity?
What is the another name of phase velocity?
The ratio between the speed of light c and the phase velocity vp is known as the refractive index, n = c/vp = ck/ω. except one cannot create a group with only a finite number of wave frequencies/wave vectors.