How do you calculate group velocity dispersion?
The group velocity dispersion is the group delay dispersion per unit length. The basic units are s2/m. For example, the group velocity dispersion of fused silica is +35 fs2/mm at 800 nm and −26 fs2/mm at 1500 nm. Somewhere between these wavelengths (at about 1.3 μm), there is the zero-dispersion wavelength.
How do you calculate group delay dispersion?
Group delay dispersion (GDD) considers the length of the medium and can be found by multiplying the GVD by the length. GVD is highly wavelength dependent and has typical units of fs2/mm. For example, the GVD of fused silica is +57 fs2/mm at 589.3nm and −26 fs2/mm at 1500nm.
How is dispersion relation calculated?
Plugging either (1) or (2) into the equation yields an algebraic relationship of the form ω = ω(k) or σ = σ(k), called the dispersion relation. It characterizes the dynamics of spatially oscillating modes of the form exp(ikx).
What is group velocity in optical fibers?
Definition: the velocity with which the envelope of a weak narrow-band optical pulse propagates in a medium. More general term: velocity of light.
What is group velocity formula?
The group velocity vg is defined by the equation: where ω is the wave’s angular frequency (usually expressed in radians per second), and k is the angular wavenumber (usually expressed in radians per meter). The phase velocity is: vp = ω/k.
What is phase velocity group velocity?
Waves can be in the group and such groups are called wave packets, so the velocity with a wave packet travels is called group velocity. The velocity with which the phase of a wave travels is called phase velocity. The relation between group velocity and phase velocity are proportionate.
What is PS nm km dispersion?
Chromatic dispersion is measured in ps/nm/km, meaning that for every km of fiber traveled through, a pulse with a 1 nm spread of wavelengths will disperse by 1 ps for a dispersion of 1 ps/nm/km. You will see that it is possible to have negative chromatic dispersion in which the longer wavelengths travel faster.
How do you find velocity from group velocity?
The phase velocity is: vp = ω/k. The function ω(k), which gives ω as a function of k, is known as the dispersion relation. If ω is directly proportional to k, then the group velocity is exactly equal to the phase velocity.
How do I calculate phase velocity?
For this reason, phase velocity is defined as v p = ω / k . This relation is generalized to three dimensions in Eq. (59). Given the phase velocity, the phase refractive index np is the factor describing how much slower the phase is propagating than the speed of light c0.
What is phase and group velocity?
What is group velocity expression?
The group velocity is velocity of the envelope. For two waves group velocity is defined by vgroup = Δω / Δk where Δω = ω1 – ω2 and Δk = k1 – k2. This expression for group velocity is the slope of a frequency versus wavenumber graph.